v2C4rSbqxtqD2nV7Oiz5i4NFGtp8TyRu

Answer Key
Cumulative Review
1. 2.
8
3. 4.
3
0 3.2 6
2
2 1 0 1 2 3 4 5 6
5. 6.
4.5
6 4 2 0 2 4 6
7. Commutative property of addition
8. Associative property of addition
9. Identity property of addition
10. Inverse property of addition
11. Distributive property
12. Inverse property of multiplication 13. 17
14. 15. 35 16. 17. 18.
19. 20. 10 21. 22.
23. $15.75 24. 2520 feet per minute 25. 64
26. 27. 28. 25 29. 25 30.
31. 32. 33. 29 34. 35. 17
36. 2485 37. 38.
39. 40. 41.
42. 43. 2 44. 10 45.
46. 47. 2 48. 1 49. 8 50. 5 51. 2
52. 2 53. 54. 55. 9 56.
57.
61.
58.
d1
59. 60.
62. y > 6
63. y ≥ 4
2A
d2 d C
h V
r
lw
I
Pt
16
5
6
3
4
3
23
2
6
2b 2
7
2 6x
13n 27 7a 8b 14a 16b
7b
3 2x2 2x2 8
64 64
25
1 8
62
10x
1
6 liters
956
feet
18
11
9 8 30
3
64. x < 2
65. x < 8
5 4 3 2 1 0 1
66. x < 3
67. x ≥ 6.5
0
4
1
5
2
2
5 5
3
8 6 4 2 0 2 4 6
6
3
4
3
7
4
9
8 9
5
5
6
5
0
4.3
8
1
5
0 3.7 7
4
2 0 2 4 6 8
3.2
4 3 2 1
7 6 5 4 3 2 1
5
0
6
1
4
2 8
5
7
0 1 2 3 4
10
11
7.5 7 6.5 6 5.5
2
8
3
9
4
5
68. x > 1
69. 1 < x < 2
2 1 0 1 2
70. 0.4 < x < 0.4 71. 1 ≤ x ≤ 2
3
72. 9 or 73. or 2 74. 14 or 2
2 3
75. 1 or 8 76. 36 or 18 77. 1 or
80. or x ≤ 16 81. x < 2 or x > 6
16
7
x ≥ 12
7
3 2 1
0.4 0.4
1 0 1
78. 9 < x < 7 79. x > 2 or x < 4
9 7
10 5 0 5 10
82. x ≥ 6 or x ≤ 18 83.
18 6
20 10 0 10
0
1
12
7
2
3
6 4 2 0 2 4 6 8
0 ≤ x ≤ 5
2
1 0 1 2 3
84. $9.45 85. 64% 86. 16 87. $24
7
2 1 0 1 2
2 1 0 1 2
6 4 2 0 2 4
5
2
19
3

Review and Assess
CHAPTER
1 Cumulative Review
NAME _________________________________________________________ DATE ____________
For use after Chapter 1
Use a number line to order the real numbers. (1.1)
1. 2. 3. 0, 6,
4. 5. 6. 2, 4
5, 4.5, 9, 5, 8, 3.2
4
3.7, 3
5
4, 0, 7
3
4.3, 0, 2, 3.2
5
5, 8, 5, 8
2
3
Tell what property the statement illustrates. (1.1)
7. 3 2 2 3
8. 3 4 5 3 4 5 9. 6 0 6
10. 5 5 0
11. 42 5 42 45 12.
Select and perform an operation to answer the question. (1.1)
13. What is the sum of 25 and 14. What is the sum of and
15. What is the difference of 26 and 16. What is the difference of and 6?
17. What is the product of 4 and 18. What is the product of and 6?
19. What is the quotient of 6 and 20. What is the quotient of and 1
5 2?
1
8?
5 6?
9?
3
2?
5
3?
Perform the given operation. Give the answer with the appropriate
unit of measure. (1.1)
21. feet 22.
23. 4.5 yards 24.
$3.50
5
1 yard
1
4 3 feet
1
2
Evaluate the power. (1.2)
25. 26. 4 27.
28. 29. 30.
3
43 5 2
Evaluate the expression for the given value of x. (1.2)
31. when 32. when 33. x when x 5
2 x 9 x 8
4xx 3 x 2
4
34. when 35. when 36. 4x when x 5
4 2x x 2
3x
2 x x 4
5x 1
3 2
Simplify the expression. (1.2)
37. 38. 39.
40. 41. 42. 4b2 b 32b2 3x 42n 3 5n 3
3a 2b 4a 6b
4a b 52a 3b 5b
b
3 2x2 3x3 4x2 4x2 3x 2x2 7x
Solve the equation. (1.3)
43. 44. 45.
46. 47. 48.
49. 50.
1
5x 51. 6x 3 42x 5 45
2
3 2
5x 1
2x 3 7
5x 30 20
2a 8 4a 12
3b 11 5 4b
2.3a 1.8 2.8
32a 7 5a 22
1
2m 4 2m 16
3
Solve for y; find the value of y when x 3. (1.4)
52. 2x y 8
53. 5x 2y 8
54. 5x 6y 10
55. 56. 57. 2 3
4x 2y 6 0
x 4y 6
3x 4y 6
118 Algebra 2
Chapter 1 Resource Book
5 2
23 1
2 liters 15 1
3 liters
42 feet 60 seconds
1 second 1 minute
6 1
6 1
4 3
5 2
Copyright © McDougal Littell Inc.
All rights reserved.

CHAPTER
1
CONTINUED
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ____________
Cumulative Review
For use after Chapter 1
Solve the formula for the indicated variable. (1.4)
58. Simple interest 59. Volume of a prism
Solve for r: I Prt
Solve for h: V lwh
60. Circumference of a circle 61. Area of a rhombus
Solve for d: Solve for A 1
C d
d1: 2d1d2 Solve the inequality. Graph its solution. (1.6)
62. 4y 24
63. 5y 6 26
64.
65. 2x 4 8
66. x 6 5x 12
67.
Solve the compound inequality. Graph its solution. (1.6)
68. 2x 5 7 or 3x 9 12 2x 69. 6 6x 12
70. 0.5 5x 1.5 3.5
71. 0.7 2x 1.3 5.3
Solve the absolute value equation. (1.7)
72. 73. 74.
75. 7 2x 9
76. x 3 9
77. 8 3x 11
1
2x 6 12
4n 7 1
2x 3 4
Solve the inequality. Graph its solution. (1.7)
78. 79. 80.
81. 82. 2 83.
84. Driving Time You drive to school Monday, Wednesday, and Friday. The
school is 34 miles from your home on an interstate highway. The rest of
your driving is in town. In a typical week, you drive 300 miles. Gasoline
costs $1.28 per gallon, and your car’s fuel efficiency is 23 miles per gallon
on the highway and 13 miles per gallon in town. How much do you spend
on gasoline when you drive in town? (1.5)
1
x 1 8
3x 3 9
4 2x 8
3x 4
85. Consumer Debt Last year 1.4 million Americans sought help from credit
counseling agencies. Five hundred four thousand of these people, with total
debts of $2.3 billion, got into formal debt management or “workout”
programs. What percent chose not to go into a formal program? (1.5)
86. Travel Services A local travel service advertised a round trip to Toronto
by motorcoach to see a popular stage show for $205. The same trip was
available to attend a concert for $195. The travel service sold 14 tickets to
the stage show. How many tickets to the concert were sold if the total sales
were $5990? (1.5)
87. Buying Slacks A local store is advertising slacks for $31.99, which is 20%
off the original price. You purchase 3 pairs of slacks. How much did you
save from the original price? (1.5)
1 3
2x 8 5x 14
4.6 2x 8.4
7x 2 14
4x 5 5
Algebra 2 119
Chapter 1 Resource Book
Review and Assess

Answer Key
Practice A
1.
2.
3.
4.
5.
6.
1 0 1 2 3 4 5
1 0 1 2 3 4 5
4 5 6 7 8 9 10
3 2 1 0 1 2 3
3 2 1 0 1 2 3
10
9 8 7 6 5 4
1 < 1
2
7. 8. 9.
10. 11. 12.
13. Associative property of addition
14. Inverse property of addition
15. Commutative property of multiplication
16. Commutative property of addition
17. Inverse property of multiplication
18. Identity property of addition
19. Distributive property
20. Associative property of multiplication
21. Identity property of multiplication
22. 10 23. 3 24. 5 25. 26. 20
27. 28. 3 29. 30. in.
31. 15 oz 32. 500 m/sec 33. $80 34. 52 in.
35. 3 touchdowns
7
2
8
3
3 < 5 8 > 11
4 > 2 6 < 0 4 < 2.7
7
72
6 4

LESSON
1.1
Copyright © McDougal Littell Inc.
All rights reserved.
Practice A
For use with pages 3–10
Plot the numbers on a number line.
1. 0 and 4 2. 1 and 3 3. 5 and 8
4. 3 and 2 5. 2 and 1
6. 5 and 9
Use the graph to decide which number is greater and use the
symbol < or > to show the relationship.
7. 3, 5
8. 8, 11
1, 1
2
9. 10.
1
2
2 1 0 1 2
11. 6, 0
12. 4, 2.7
7 6 5 4 3 2 1 0 1
Identify the property shown.
NAME _________________________________________________________ DATE ___________
4 3 2 1 0 1 2 3 4 5 6 7
13 12 11 10 9 8 7
0 1 2 3 4 5 6
5 4 3 2 1 0 1 2 3
13. 14. 15.
16. 17. 6 18. 5 0 5
19. 34 2 3 4 3 2 20. 4 3 5 4 3 5 21. 41 4
1
3 5 5 3 5 5 9 9 0
37 73
6 11 11 6
6 1
Select and perform an operation to answer the question.
22. What is the sum of 4 and 6? 23. What is the sum of 2 and 5?
24. What is the difference of 8 and 3? 25. What is the difference of 2 and 5?
26. What is the product of 5 and 4? 27. What is the product of 9 and 8?
28. What is the quotient of 21 and 7? 29. What is the quotient of 12 and 2?
Give the answer with the appropriate unit of measure.
30. 6 inches inches 31. ounces ounces
32. 33. 10 miles $8
4
30 kilometers 1000 meters 1 minute
1 minute 1 kilometer60 seconds
1 mile
3
11 8
1
3 2
1
4
34. Filing Cabinet A cabinet has 4 drawers.
Each drawer is 13 inches tall. How tall is the
cabinet?
4, 2
2.7
35. Touchdown A football team scored 18 of
their 27 points from touchdowns. If a touchdown
is worth 6 points, how many touchdowns
did the team score?
Algebra 2 13
Chapter 1 Resource Book
Lesson 1.1

Answer Key
Practice B
1. ; 7 > 10
11
2. ;
3. ;
4. ;
5. ; 0.8 > 0.9
6. ; 3 < 2.5
1 0 1 2 3
7. ;
3 2 1 0 1
8. ; 3.2 > 4.1
5
8
3
10
2 1 0 1 2
4.1 3.2
4
9 8 7 6
25
14
2
5
14 12 10 8 6 4 2
0.9 0.8
2
7
5
3
2
5
3 2.5
2
9. ;
3
4
10
3
0 1 2 3 4 5
3 2 1 0 1
8
3
< 7
5
10. 11.
12. 13.
14.
15. 6, 5,
16. Identity property of multiplication
17. Commutative property of addition
18. Inverse property of addition
19. Associative property of multiplication
20. Associative property of addition
21. Identity property of addition
22. 5 23. 20 24. 4 25. 3 26. 24
27. 27 28. 4 29. 18 30. 52 in.
31. 3 touchdowns 32. 3 pieces
33. 2 or 2 under par
1
7 13
2 , 3 , 4
5
10, 2.9,
2, 3, 1, 2, 3
15
1
3, 7, 5 , 2.1
2 , 8
1
4,
3 7
3 , 0, 4 , 2
3 1
2 , 2 , 1, 2
17
4
7
4
2 1 0 1 2
1
0
3
4
10
3
< 7
4
25
2
< 17
4
< 14
5
2 < 2
5

Lesson 1.1
LESSON
1.1
Practice B
For use with pages 3–10
Plot the numbers on a number line. Decide which number is greater
and use the symbol < or > to show the relationship.
1. 2. 3.
4. 5. 6.
7. 8. 9. 8
3, 7
2, 3.2, 4.1
5
2
0.8, 0.9
3, 2.5
5
25
7, 10
4
2 , 14 5
Write the numbers in increasing order.
10. 11. 12.
13. 14. 2, 3, 15.
5
8, 2, 3, 1
15
1
2, 32
, 4, 1, 2
7 3
2 , 4 , 13
, 0
2 , 2.9, 10
Identify the property shown.
16. 61 6
17. 3 1 2 1 3 2 18. 7 2 2 7 0
19. a b c a b c 20. a b c a b c 21. a 0 a
Select and perform an operation to answer the question.
22. What is the sum of and 3? 23. What is the sum of and
24. What is the difference of 4 and 8? 25. What is the difference of and
26. What is the product of and 27. What is the product of and
28. What is the quotient of and 9? 29. What is the quotient of and 2
8
12 8?
5 2?
4 6?
9 3?
36
12 3?
30. Filing Cabinet A cabinet has 4 drawers. Each drawer is 13 inches tall.
How tall is the cabinet?
31. Touchdown A football team scored 18 of their 27 points from touchdowns.
If a touchdown is worth 6 points, how many touchdowns did the team score?
32. Eating Pizza Eight friends buy 4 pizzas. Each pizza is cut into 6 pieces.
Each person eats the same number of pieces. How many pieces does each
person eat?
33. Playing Golf The following table shows how many strokes over or under
par Susan shot when she played nine holes of golf on Saturday. How far
over or under par was her final score?
14 Algebra 2
Chapter 1 Resource Book
NAME _________________________________________________________ DATE ___________
3
4, 7
Hole 1 2 3 4 5 6 7 8 9
Score 2 1 0 2 1 1 1 0 2
10
3 , 17
4
1
5
, 2.1, 7, 3
7
3, 5, 6, 13
4 , 1
2
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice C
1. ; 5 > 1
0 1
2 3
2. ; 1.3 > 2.1
3 2 1
4
5
3. ;
2 1
4. ; 3 < 7
2
2
3
0 1 2
4
3
5. ;
2 1
3 7
6. ; 7 < 2.8
0 1 2
0 1 2
7
4
2.1 1.3
0 1 2 3
3
3
5
0
2.8
4
4
6
4
5
4
3
< 2
3
> 2
7. 8.
9.
10. Commutative Property of Addition
11. Commutative Property of Multiplication
12. Associative Property of Addition
13. Distributive Property
14. Commutative Property of Multiplication
15. Identity Property of Addition 16.
17. 4 18. $45
revolutions
19. 120
minute
20. 70 miles per hour 21. 30.4 points per game
22. 158.4 feet per hour 23. Yes
1
12 in.
68 7
1.5,
2.9. 8, 3, 2
8 lb
3
4, 0, 1
5
2
9, 1
8, 4
3, 2

LESSON
1.1
Copyright © McDougal Littell Inc.
All rights reserved.
Practice C
For use with pages 3–10
Graph the numbers on a number line. Then decide which number is
greater and use the symbol < or > to show the relationship.
1. 2. 3.
4. 5. 6. 7, 2.8
4
3, 7
, 2
4
5, 1
1.3, 2.1
5 , 23
Write the numbers in increasing order.
7. 8. 0, 1.5, 9. 3, 8, 2.9, 2
3
4
, 2, 1,
2
1
,
3
8
NAME _________________________________________________________ DATE ___________
9
Identify the property shown.
10. a b c a c b
11. a b c b c a
12. a b 3 a b 3
13. bc a b c b a
14. ca b a bc
15. a b 0 a b
Perform the given operation. Give the answer with the appropriate
unit of measure.
16. 17.
18.
$3
15 ounce1
ounce
19.
5634
pounds 121 8 pounds
20. Cheetah’s Speed A cheetah can run 2 miles in 4 hour. What is the speed
of a cheetah in miles per hour?
21. Basketball During the 1995–96 season, Michael Jordan scored 2491 points
in 82 games. Find his average number of points scored per game. Give your
answer to 3 significant digits.
22. Snail’s Speed A snail can travel about 0.03 miles per hour. Convert this
speed into feet per hour. Note that there are 5280 feet in 1 mile. Give your
answer to 4 significant digits.
23. First Down A football team must move 10 yards from its original position
to gain a first down. In three plays a team ran for 6 yards, lost 8 yards due to
a quaterback sack, and passed for 12 yards. Did the team make a first down?
3
17 1
4
5
1
6 1
3 inches 21 4 inches
2 revolutions 60 seconds
second minute
Algebra 2 15
Chapter 1 Resource Book
Lesson 1.1

Answer Key
Practice A
1. 2. 3. 4. 5. 6.
7. 36 8. 81 9. 64 10. 11. 15
12. 42 13. 10 14. 12 15. 16. 5 17. 1
18. 24 19. 81 20. 32 21. 8 22. 8
23. 24. 25. 13 26. 27. 18
28. 15 29. 7 30. 28 31. 7 32. 9 33. 12
34. 35. 36. 1 37. 38.
39. 25 40. 41. 42.
43. 1
x
7
1
3 3
1
6 11
4
7
3
2 2 2yx y; 30
2x4x 1; 75
4 93 75 3x2 56 23

LESSON
1.2
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ____________
Practice A
For use with pages 11–17
Write the expression using exponents.
1. 2 2 2
2. 5 5 5 5 5 5
3. 3x 3x
4. 7 to the fifth power 5. 9 to the third power 6. x to the fourth power
Evaluate the expression.
7. 8. 9.
10. 11. 12.
13. 14. 15.
16. 17. 18.
19. 20. 2 21. 14 7 5 1
5
34 3 23 2
3 2 5
11 8 2
4 3 6 5
4 3 2
16 16 4
9 3 2 1
4 4 2 1
3 2 4 6
6
34 62 Evaluate the expression for the given value of x.
22. x 5 when x 3
23. 2x 3 when x 0
24. 4 x when x 7
25. 3x 1 when x 4
26. 2 3x when x 1
27. 4 7x when x 2
28. when 29. when 30. x when x 4
2 x2 x x 5
3x 0.5x 1 x 3 3x
31. when 32. 11 when x 4
33. 6x 3 when x 5
1
x x 2
2x
2 3
Evaluate the expression for the given values of x and y.
34. when and 35. x when x 2 and y 3
2 2x 3y x 3 y 4
5y
36. when and 37. 4x y when x 1 and y 2
3
x 5y x 4 y 1
38. when and 39. x when x 4 and y 3
2 y2 4 x 5 y 3
x
40. when and 41. 2y when x 2 and y 1
3 2x y x 3 y 2
5x
3
Write an expression for the area of the figure. Then evaluate the
expression for the given value(s) of the variable(s).
42. x 2 and y 3
43. x 6
x y
y
2y
x
4x 1
Algebra 2 27
Chapter 1 Resource Book
Lesson 1.2

Answer Key
Practice B
1. 2. 3. 4.
5. 6. 7. 81 8.
9. 32 10. 5 11. 8 12. 13. 15
14. 32 15. 16. 15 17. 7 18. 28
19. 20. 9 21. 12 22. 2 23. 2
24. 2 25. 4 26. 2yx y; 30
27.
1
2x4x 1; 75 28. 8.95x 29.95; $65.75
29. 6.95x 24.995 x; $70.83
30. $270; $415
5
8 64
24
3
2
n
4b2 2a2 2y3 x 7
3
94 a5

Lesson 1.2
LESSON
1.2
28 Algebra 2
Chapter 1 Resource Book
NAME _________________________________________________________ DATE ___________
Practice B
For use with pages 11–17
Write the expression using exponents.
1. a a a a a
2. 9999
3. xxx
4. 2y 2y 2y 7
5. 4b 4b 2a 2a
6. 8 to the nth power
Evaluate the expression.
7. 8. 9.
10. 11. 12.
13. 14. 15. 5 23 2 3 1 9 6
2
5 23 1 3 2
3 4
2
2
3 2 1 4
14 7 5 1
5
26 34 Evaluate the expression for the given value of x.
16. when 17. when 18. x when x 4
2 x2 x x 5
3x 0.5x 1 x 3 3x
19. when 20. when 21. 6 x when x 2
3 2x 1 x x 5 25x 3 8 x 3
x
Evaluate the expression for the given values of x and y.
22. when and 23. 2y when x 2 and y 1
3 2x y x 3 y 2
5x
3
y 2
24. when and 25. when x 1 and y 4
3
3x y
x 3 y 1
2x 1
2x y
Write an expression for the area of the figure. Then evaluate the
expression for the given value(s) of the variable(s).
26. x 2 and y 3
27. x 6
x y
2y
28. Photography Studio A photography studio advertises a session with a
sitting fee of $8.95 per person. The standard package of pictures costs
$29.95. Write an expression that gives the total cost of a session plus the
purchase of one standard package. Evaluate the expression if a family of
four purchases this package.
29. Books You want to buy either a paperback or hard covered book as a
gift for 5 friends. Paperbacks cost $6.95 each and hard covered books
cost $24.99 each. Write an expression for the total amount you must
spend. Evaluate the expression if 3 of your friends get a paperback.
30. Weekly Earnings For 1980 through 1990, the average weekly
earnings (in dollars) for workers in the United States can be modeled
by E 14.5t 270, where t is the number of years since 1980.
Approximate the average weekly earnings in 1980 and 1990.
x
4x 1
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice C
1. 2. 3. 4.
5. 6. 7. 112 8. 9. 16
10. 1 11. 12. 81 13. 66 14.
15. 43 16. 2 17. 18.
19. 20. 21. 2x
22. 10x 2 23. 13.99 0.10x 0.08y; $20.99
24. 21.82 0.06x; $22.72.
3 3x2 9x
x 5y x y
2
2
64
5
7
4x 20 12x
1
x y 2
3
68 3x3 x2 34 45 x3y2

LESSON
1.2
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ____________
Practice C
For use with pages 11–17
Write the expression using exponents.
1. x x xy y
2. 44444 3. 3 3 3 3
4. 3x3x3x x x 5. 6 to the 8th power 6. the sum of x and y to
the third power
Evaluate the expression.
7. 8. 9.
10. 11. 12. 4 20 42 25 3 55 41 32 8 6 3 1 5 1
2
4 31 52 3 1 2 3 5
Evaluate the expression for the given values of x and y.
5x y
13. 7x 3y when x 6 and y 2
14. when x 2 and y 5
2xy 1
3
4 x
y
15. when and 16. when x and
1
x y
2
2 3
y
x y
1
3x 2y x 4
2
Simplify the expression.
17. 18.
19. 20.
21. x 22. 0.52x 8 32 3x
3 2x2 1 x2 6x
4x y 3x y
4x y 3y x
x 1
2 x 32x x2 10x 3 25 3x
23. Phone Bill A phone company charges a basic rate of $13.99 per month.
In addition the user is charged $0.10 per minute for all long distance calls
made during the week and $0.08 per minute for all long distance calls
made during the weekend. Write an expression that gives the total monthly
bill. Evaluate the expression if you talk long distance for 30 minutes
during the week and 50 minutes during the weekend.
24. Engraving A gift shop advertises that they will engrave any gift purchased
in their store at a rate of $0.06 per letter and the first three letters
are free. A desk plate sells for $22. Write an expression for the total cost
of buying the desk plate and having it engraved. Evaluate the expression if
you wish to engrave a name that has 15 letters.
y 3
2
Algebra 2 29
Chapter 1 Resource Book
Lesson 1.2

Answer Key
Practice A
1. 2. 9 3. 4. 24 5. 3 6. 8
7. 4 8. 9. 18 10. 11.
12. 13. 5 14. 15. 16. 17.
18. 19. 20. 21. 22. 3 23. 4
24.
25. Six should be subtracted,
not added, from the right side
of the equation.
26. Twelve should be added,
not subtracted, to the right side
of the equation.
27. The right side of the equation
should be divided, not multiplied
by 5.
28. One should be subtracted,
not added, from the right side
of the equation.
29. The right side of the
equation should be divided,
not multiplied, by 3.
30. The distributive property
leads to on the left side
of the equation.
31. should be subtracted,
not added, from the left side
of the equation.
32. The right side of the
equation should be multiplied,
not divided, by 2 in the last step.
33. The distributive property
leads to on the left side
of the equation.
x
34. 9 in. 9 in. 35. 13 in. sides 36. $22
7
3x
6
7
3x
3
22x 1 5
2
3
x 12
3
22x 1 5
2
1
1
12
2
5
5
x 6 17
x 11
x 12 2
x 14
5x 10
x 2
2x 1 7
2x 6
x 3
3x 2 7
3x 9
x 3
2x 3 8
2x 6
2x 6 8
2x 2
x 1
2x
3x 3 2x 1
x 4
1
2x 4 2
2x 6
7
1
2
5
6
3
1
1
3
4
10
3
8
1
3
1
3
6
3
37. 3 tickets

Lesson 1.3
LESSON
1.3
42 Algebra 2
Chapter 1 Resource Book
NAME _________________________________________________________ DATE ___________
Practice A
For use with pages 19–24
Solve the equation. Check your solution.
1. 2. 3.
4. 5. 6.
7. 8. 9.
10. 11. 12.
13. 14. 15.
16. 17. 18.
19. 20. 21. 7x
22. 5x 2 13
23. 9 3x 3
24. x 4 2x 9
14
4x 5
1
x 3
2
3 3
x 3
x
1 5
x 3 6
1
4 12
1
3 9x
4 12x
3 x 8
3x 12
6x 20
3
2 8
4
x 3 0
x 7 2
5 x 4
18 x 6
5 x 2
3 x 11
6x 24
5x 15
1
3x 6
x 8 3
Describe the error. Then write the correct steps.
25. x 6 17
26. x 12 2
27.
x 23
x 10
28. 2x 1 7
29. 3x 2 7
30.
2x 8
3x 9
x 4
x 27
31. 32. 33.
x x 3
4
5
1
3x 3 2x 1
x 4 2
2
5x 4
2x 6
34. Perimeter The perimeter of a square is
36 inches. Find its dimensions.
36. Sales Tax The state sales tax in Pennsylvania
is 0.06 (or 6%). If your total bill at the
music store included $1.32 in tax, how much
did the merchandise cost?
1
5x 10
x 50
x 5
2x 3 8
2x 3 8
2x 5
2
3
2
2x 1 5
3x 1 5
3x 4
x 4
3
35. Perimeter An equilateral triangle has sides
of equal length. Find the dimensions of an
equilateral triangle with a perimeter of
39 inches.
37. Movie Tickets A ticket to the movies costs
$7. You have $21. How many tickets can
you buy?
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice B
1. 20 2. 2 3. 3 4. 2 5. 4 6. 7.
8. 9. 10. 11. 12.
13. 14. 15. 16. 17. 0
18. 19.
29
3 20. 1 21.
7
6
22. 2x 3 11 ft; 3x 5 16 ft;
15 x 8 ft
23. 15 2x 9 ft; x 7 10 ft
24. $22 25. 3 tickets 26. 7.5 hours
27. 2.75 hours 28. 4.2 hours 29. 3 children
27
1
4
14
3
5
5
2 3 20 24
1
7 13
4
7
4
3
2

LESSON
1.3
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice B
For use with pages 19–24
Solve the equation. Check your solution.
1. x 8 12
2. 2x 3 7
3. 5x 2 13
4. 6 x 4
5. 9 3x 3
6. 8x 3 5
7. 3x 5 9
8. x 4 2x 9
9. 3x 1 x 4
10. 4 5x x 8
11.
1
x 6 4
2 12.
2
x 1 x 7
3
13. x 1 23x 1
14. 3x 2 54 x
15. 27 x 61 2x
16. 3x 4 38 2x
17.
1
4x 10 5 3x
2 18.
1
x 1 1x
8
3 3
19.
3
x 5 7
20.
1
3
x 2 3 21. 52x 2 4 2x
2
Find the dimensions of the figure.
22. The perimeter of the figure is 35 feet. 23. The perimeter of the figure is 38 feet.
3x 5
15 x
2x 3
24. Sales Tax The state sales tax in Pennsylvania
is 0.06 (or 6%). If your total bill at the
music store included $1.32 in tax, how much
did the merchandise cost?
26. Weekly Pay You have a summer job that
pays $5.60 an hour. You get $8.40 an hour for
overtime (anything over 40 hours). How
many hours of overtime must you work to
earn $287?
28. Travel Time You want to visit your aunt
who lives 255 miles away. The interstate is 10
miles from your house and once you get off
the interstate, you must travel 14 miles more
to get to your aunt’s house. If you drive 55
miles per hour on the interstate, how many
hours will you travel on the interstate?
4
4 x
15 2x
x 7
25. Movie Tickets A ticket to the movies costs
$7. You have $21. How many tickets can
you buy?
27. Plumbing Bill The bill from your plumber
was $134. The cost for labor was $32 per
hour. The cost for materials was $46. How
many hours did the plumber work?
29. Babysitting Rate You charge $2 plus $.50
per child for every hour you babysit. You earn
$3.50 an hour when you watch the Crandell
children. How many children are in this
family?
Algebra 2 43
Chapter 1 Resource Book
Lesson 1.3

Answer Key
Practice C
1. 3 2. 1 3. 4. 5. 0 6.
7. 8. 9. 10. 11.
12. No solution 13. 14. 15.
16. No solution 17. Identity 18. Identity
19. No solution 20.
21.
22. 8 23. 50 ft
1
3
5 10 8 and 4 11 8
in. 132
13
4
1
1
3 0.8
39
2 and 2 4
2
2 21
7
9
5
14
3
5
3
3 in.
1
8

Lesson 1.3
LESSON
1.3
Practice C
For use with pages 19–24
44 Algebra 2
Chapter 1 Resource Book
NAME _________________________________________________________ DATE ___________
Solve the equation. Check your solution.
1. 2.
3. 4.
5. 6.
7. 8.
9. 10.
11. 12.
13.
2
33x 14. 5x 23 x 4 x
15. 1.54x 2 20.5x 3.5
6
5 1
1
5 3.6x 3.1 35.2 1.2x
55x 1
5
18 6x
3x 7 10
4x 1 x 8
3x 2 2x 4
43 x 6 2x 3
2x 1 4 32x 1
31 x 3 x 8
2x 1 3x 7 2
62x 1 3 62 x 1
3
42x 8 5 x
2x 10 4x 3
Determine whether the following equations have no solution or are
identities.
16. 17.
18. 6x 2 4x 32x 1 22x 19. 52x 3 24 3x 4x
1
3x 2 35 x
5x 2 22x 1 x
2
Find the dimensions of the figures.
20. The two rectangles shown have the same
area.
3
2x 3
22. Photo Frame You want to mat and frame
a 5 7 photograph. The perimeter of the
outside of the mat is 44 inches. The mat is
twice as wide at the top and bottom as it is at
the sides. Find the dimensions of the mat.
2
x 8
21. The two triangles shown have the same
perimeter.
x
23. Garden Fencing Your garden has an area
of 136 square feet. You want to put a fence
around the entire garden. How much fencing
do you need?
8
x 5 2x 1
x 1
x 3 x 3
3x 2
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice A
1. 2 2. 3. 4. 4 5. 6.
7. 8. 2 9. 10.
11. 12. y 1
13. y 6x 12; 0 14.
3x 4
y ; 1
x
1
y
y 2x 12; 18
2x; 4
1
3
2
12
2
13
2
3
2 2x; 7
15. 16.
17. 18.
19. 20. 21. 22. t I
r
Pr
I
r
Pt
d
t
t
d
y
r
8
y
10
3x 3 ; 22 3
3
y
2x 2; 4
2
8 2x
y ; 2
3x
x 1; 3
3
23. 24. w 25.
A
s
l
2
3 h
P
26. s 27.
3
28. 29.
30. l A
2A
h
b1 b2 ; 3 ft
w
C 5
F 32
9
b A
h
s P
; 11 cm
4
1
3

Lesson 1.4
LESSON
1.4
56 Algebra 2
Chapter 1 Resource Book
NAME _________________________________________________________ DATE ___________
Practice A
For use with pages 26–32
Find the value of y for the given value of x by first substituting the
value of x into the equation and solving for y.
1. 2x 3y 12; x 3
2. 4x 5 3 2y; x 1 3. xy x 3; x 3
4. 4x 3xy 16; x 2 5. 2y 5x 1; x 5
6. x 3y 1 2; x 0
7. 3x 7y 8; x 2
8. x 12 xy; x 4
9. 5x 2y 8; x 1
Find the value of y for the given value of x by first solving for y and
then substituting the value of x into the equation.
10. 11. 12.
13. 2x 14. xy 3x 4; x 2 15. 2x 3xy 8; x 2
16. 6x 9y 9; x 3 17. 3x 7 2y 3; x 4 18. 8x 3y 10; x 4
1
3x 2y 1; x 5
y 2x 12; x 3
1
2x y 1; x 6
3y 4 0; x 2
Solve the formula for the indicated variable.
19. Distance 20. Distance
Solve for t: d rt
Solve for r: d rt
21. Simple Interest 22. Simple Interest
Solve for r: I Prt
Solve for t: I Prt
23. Height of an Equilateral Triangle 24. Area of a Rectangle
Solve for s: h
Solve for w: A lw
3
2 s
25. Area of a Parallelogram 26. Perimeter of an Equilateral Triangle
Solve for b: A bh
Solve for s: P 3s
27. Celsius to Fahrenheit 28. Area of a Trapezoid
Solve for C: Solve for h: A h
2 b1 b F 2
9
C 32
5
Solve the formula for the indicated variable. Then evaluate the
rewritten formula for the given value(s). (Include units of measure
in the answer.)
29. Perimeter of a Square: P 4s 30. Area of a Rectangle:
Solve for s.
Solve for l.
Find s when P 44 cm.
Find l when A 24 ft and w 8 ft.
2
A lw
s
s s
s
w
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice B
1. 2. 2 3. 4. 8 5. 4
6. 1 7.
8. 9.
10. 11. y 21
y
5x 2
y ; 7
x
21
x ; 21
16 2 8
y
10
3x 3 ; 22 3
3
y
2x 2; 4
2
2
13
2
3x 1; 3
27 117
12. y x ; 99 13.
10 2
3V
14. 15. h 16.
r2 s P
3
17. 18.
19. 20. 21. s P
V
h
r
; 11 cm
4 2
r S
b2
2h
2A
h b h 1
2A
b1 b2 22. 23.
24. 8 m 25. 64 m2 201.1 m2 r3 3V
A
l ; 3 ft
w
; 4 m
4
s 2
3 h
C 5
F 32
9

LESSON
1.4
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice B
For use with pages 26–32
Find the value of y for the given value of x by first substituting the
value of x into the equation and solving for y.
1. 3x 7y 8; x 2
2. x 12 xy; x 4
3. 5x 2y 8; x 1
4.
4 3
x y 4; x 10
5.
2 1
x y 6; x 6
6. 2x 3y 1; x 1
5
2
Find the value of y for the given value of x by first solving for y and
then substituting the value of x into the equation.
7. 6x 9y 9; x 3
8. 3x 7 2y 3; x 4 9. 8x 3y 10; x 4
10. 2 xy 5x; x 1 11.
3 4
x y 6; x 8 12.
2
x y 13; x 15
Solve the formula for the indicated variable.
13. Height of an Equilateral Triangle 14. Perimeter of an Equilateral Triangle
Solve for s: h Solve for s: P 3s
3
2 s
15. Volume of a Right Circular Cone 16. Celsius to Fahrenheit
Solve for h: Solve for C: F 9
C 32
5 V r 2h 3
17. Area of a Trapezoid 18. Area of a Trapezoid
Solve for h: Solve for : A h
2 b1 b A b2 2
h
2 b1 b2 19. Lateral Surface Area of a 20. Volume of a Right Circular Cylinder
Right Circular Cylinder
Solve for r: S 2rh
Solve for h: V r2h Solve the formula for the indicated variable. Then evaluate the
rewritten formula for the given value(s). (Include units of measure
in the answer.)
21. Perimeter of a Square: 22. Area of a Rectangle:
Solve for s. Solve for l.
Find s when Find l when A 24 ft and w 8 ft.
2
P 4s
A lw
P 44 cm.
Hot Air Balloons In 1794, the French Army sent soldiers up in hot air balloons
to observe enemy troop movements. One such balloon, the L’Entrepenant, had a
volume of cubic meters.
23. Solve the formula for the volume of a sphere for r Then use
3 3
4
V .
256
this formula to calculate the radius of the L’Entrepenant balloon.
24. What was the diameter of the L’Entrepenant balloon?
25. Use the formula for surface area of a sphere S 4r to approximate the
surface area of the L’Entrepenant balloon.
2 3
4
2
7
3 r3
3
5
9
Algebra 2 57
Chapter 1 Resource Book
Lesson 1.4

Answer Key
Practice C
1. 0 2. 3. 4. 1 5. 6.
7. 8. y 10
4x 5
y ;
3x
5
x ; 5
3 3 1
25
2
1
19
3
3x 8 14
9. y 10. y ;
2x 1 5
5 1
;
x 3 2
4x 7
11. y ; 3 12. y
3x 1
13. 14.
15. 16. 3; T represents the total
amount earned, x represents the number of regular
washes, y represents the number of washes and
waxes. 17. 35 customers 18. V r
19.
3V 2r3
h 20. 12 6 18 ft
2h 2
3r3 R
T 7x 15y
S
b1 r
s 2A
h b2 3r 2
2x 7
; 1
4 3x 5
13
3

Lesson 1.4
LESSON
1.4
Practice C
For use with pages 26–32
58 Algebra 2
Chapter 1 Resource Book
NAME _________________________________________________________ DATE ___________
Find the value of y for the given x by first substituting the value of
x into the equation and solving for y.
1. xy 3x 6; x 2
2. 5x 2y 13 x; x 3
3. yx 3 2x 1; x 4
4. y2x 1 5; x 3
5. 6x y3 x 7; x 2
6. yx 2 7x 3 1; x 1
Find the value of y for the given x by first solving for y and then
substituting the value of x into the equation.
7. 4x 3xy 5; x 1
8.
9. yx 3 5; x 7
10. y2x 1 3x 8; x 2
11. y3x 1 4x 2 1; x 2
12. y4 3x 2x 1 9; x 3
Solve the formula for the indicated variable.
13. Area of a Trapezoid 14. Lateral Surface Area of a Frustrum of
Solve for A a Right Circular Cone
Solve for R: S sR r
h
2 b1 b b1 :
2
Fundraising The high school girls softball team is holding a car wash to raise
money for new uniforms. At the car wash they offer a regular wash for $7 and a
wash and wax for $15.
15. Write an equation that represents the total amount of money they earned.
16. How many variables are in the equation? What do they represent?
17. The softball team earned $365. If they washed and waxed 8 cars, how
many customers only wanted a wash?
Silo The silo pictured at the right is a cylinder with half of a sphere on top. The
silo can hold cubic feet of grain. The radius of the sphere is 6 feet.
576
18. Given that the volume of a cylinder is and the volume of a
sphere is V write a formula for the volume of the silo.
19. Solve the formula you found in Exercise 18 for h.
4
3 r3 V r
,
2h 20. Find the height of the silo.
2
3
x 1
5
1
y ; x 2
3
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice A
1. Total Cost
Price per case
Number of cases
2. 3. About 20.03 4. 20 cases
5. Distance traveled miles
Rate of travel
Time traveled hours
6. 168 7. 48 8. 48 miles per hour
9. Total cost $80.96
Cost for first 8 books $1
Cost of a book $19.99
Number of books x
10. 80.96 1 19.99x 11. 4 12. 4 books
13. Yard size 27,500 square feet
Coverage for one bag 5000 square feet
Number of bags x
14. 27,500 5000x 15. 5.5 16. 6 bags
7
2r 3 1
$120
$5.99
x
120 5.99x
168
r
2

Lesson 1.5
LESSON
1.5
68 Algebra 2
Chapter 1 Resource Book
NAME _________________________________________________________ DATE ___________
Practice A
For use with pages 33–40
Party Supplies In Exercises 1–4, use the following information. You
have $120 to purchase juice for a party. Each case of 24 bottles costs $5.99.
Assuming there is no sales tax, how many cases can you purchase? Use the
following verbal model.
Total cost
1. Assign labels to the parts of the verbal model.
2. Use the labels to translate the verbal model into an algebraic model.
3. Solve the algebraic model.
4. Answer the question.
Vacation Trip In Exercises 5–8, use the following information. On a
trip to the Grand Canyon, you drove 168 miles in 3 hours. What was your
average speed? Use the following verbal model.
1
2
Distance
5. Assign labels to the parts of the verbal model.
6. Use the labels to translate the verbal model into an algebraic model.
7. Solve the algebraic model.
8. Answer the question.
Book Club In Exercises 9–12, use the following information. A book
club promises to send 8 books for $1, if you join the club. After you receive the
8 books, you may select more books at a rate of $19.99 per book. If you spend
a total of $80.96, how many extra books did you purchase? Use the following
verbal model.
Total cost
Price per case
Rate
Time
Cost for first 8 books
9. Assign labels to the parts of the verbal model.
Number of cases
10. Use the labels to translate the verbal model into an algebraic model.
11. Solve the algebraic model.
12. Answer the question.
Lawn Fertilizer In Exercises 13–16, use the following information. A
bag of lawn fertilizer claims that it will cover 5000 square feet of grass. If your
yard is 27,500 square feet, how many bags of fertilizer will you need? Use the
following verbal model.
Yard size Coverage for one bag Number of bags
13. Assign labels to the parts of the verbal model.
14. Use the labels to translate the verbal model into an algebraic model.
15. Solve the algebraic model.
16. Answer the question.
Cost of a book
Number of books
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice B
1. Distance traveled 100
miles
Rate of travel 763 miles per hour
Time traveled t
2. 100 763t 3. About 0.131
4. About 0.131 hour or about 7.86 minutes
5.
6. Total cost $450
Price per square yard x
Number of square yards 30 square yards
7. 450 30x 8. 15 9. $15 per square yard
10.
Your
speed
11. Distance traveled 300 miles
Your speed r
Your time 3 hours
Friend’s speed 52 miles per hour
Friend’s time 3 hours
12. 300 3r 156 13. 48
14. 48 miles per hour
15.
Total
time
Total cost
Distance
traveled
Your
time
Time
per trial
Price per
square yard
Friend’s
speed
Number
of trials
Friend’s
time
16. Total time 1 hours or 90 minutes
Time per trial 5 minutes
Number of trials x
Time to write report 30 minutes
17. 90 5x 30 18. 12 19. 12 trials
1
2
Number of
square yards
Time to
write report

LESSON
1.5
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice B
For use with pages 33–40
Land Speed Record In Exercises 1–4, use the following information.
The land speed record was broken in 1997 by a British car called the Thrust SSC.
The Thrust SSC traveled at a rate of 763 miles per hour. This was accomplished by
using a jet engine. How long would it take the Thrust SSC to travel 100 miles?
Use the following verbal model.
Distance
Rate
Time
1. Assign labels to the parts of the verbal model.
2. Use the labels to translate the verbal model into an algebraic model.
3. Solve the algebraic model.
4. Answer the question.
New Carpeting In Exercises 5–9, use the following information. You
just added a family room to your home. You have budgeted $450 for carpeting. If
you need 30 square yards of carpeting, how much can you spend per square yard?
5. Write a verbal model.
6. Assign labels to the parts of the verbal model.
7. Use the labels to translate the verbal model into an algebraic model.
8. Solve the algebraic model.
9. Answer the question.
Sharing the Driving In Exercises 10–14, use the following information.
You and a friend share the driving on a 300 mile trip. Your friend drives for
3 hours at an average speed of 52 miles per hour. How fast must you drive for the
remainder of the trip if you want to reach your hotel in 3 more hours?
10. Write a verbal model.
11. Assign labels to the parts of the verbal model.
12. Use the labels to translate the verbal model into an algebraic model.
13. Solve the algebraic model.
14. Answer the question.
Time Management In Exercises 15–19, use the following information.
You need to do an experiment at home for your science class and write a lab report
on your findings. The experiment involves trials that take 5 minutes each to perform.
You want to watch a basketball game that starts in 1 hours. If it takes about 30 minutes
to write the lab report, how many trials can you perform before the game starts?
15. Write a verbal model.
16. Assign labels to the parts of the verbal model.
17. Use the labels to translate the verbal model into an algebraic model.
18. Solve the algebraic model.
19. Answer the question.
1
2
Algebra 2 69
Chapter 1 Resource Book
Lesson 1.5

Answer Key
Practice C
1. Distance
Rate Time
2. Distance 2198 miles
Rate 2 miles per hour
Time t hours
3. 2198 2t 4. 1099 5. 1099 hours
6. 9.141 meters per second 7. $138,000
8. 0.5 hour 9. $175.92 10. $250 11. 3.1 ft

Lesson 1.5
LESSON
1.5
Practice C
For use with pages 33–40
70 Algebra 2
Chapter 1 Resource Book
NAME _________________________________________________________ DATE ___________
Wagon Trains In Exercises 1–5, use the following information. In the
1800s settlers traveled across the country in wagon trains. A wagon train consisted
of a group of families who traveled together. Each family had its own wagon and
oxen or mules to pull the wagons. The wagons followed each other in a long line
called a wagon train. Wagon trains traveled at a rate of approximately 2 miles per
hour. The distance between Buffalo, New York and Los Angeles, California is
2198 miles. How long would it have taken for the wagon trains to travel from
Buffalo to Los Angeles?
1. Write a verbal model.
2. Assign labels to the parts of the verbal model.
3. Use labels to translate the verbal model into an algebraic model.
4. Solve the algebraic model.
5. Answer the question
6. 100-Meter Dash In 1996 Gail Devers won the 100-meter dash in the
Olympic Games. Her time was 10.94 seconds. What was her speed in
meters per second? Round your answer to 4 significant digits.
7. Commission A salesman’s salary is $18,500 per year. In addition, the
salesman earns 5% commission on the year’s sales. Last year the salesman
earned $25,400. How much was sold that year?
8. Visiting Friends Your friend’s family moved to a town 300 miles from
where you live. You and your friend decide to meet halfway between the
two towns to visit. Your friend averages 50 miles per hour on his trip. You
average 60 miles per hour on your trip. If you and your friend leave at the
same time, how much earlier do you arrive at the same meeting place?
9. Wallpaper Project You want to wallpaper a room that will require
320 square feet of wallpaper. The wallpaper you selected costs $21.99 per
roll. Each roll will cover 40 square feet. How much will your project cost?
10. Soccer Trophies After winning the league title, a soccer team receives a
team trophy as well as individual trophies. The table gives the cost of
trophies at a local store.
Trophy Team 1 2 3 4 5
Total cost $40 $50 $60 $70 $80 $90
Determine the total cost of giving trophies to a team with 21 members.
11. Area Rug A circular rug covers about 30 square feet. Use the guess,
check, and revise method to approximate the radius of the rug to the
nearest tenth of a foot.
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice A
1. E 2. C 3. B 4. F 5. A 6. D 7. no
8. yes 9. yes 10. yes 11. no 12. yes
13. x < 2
14. x ≥ 7 15. x ≥ 3
16. x > 3 17. x ≤ 10 18. x > 3
19. x > 4 20. x < 9 21. x ≥ 21
22. 8 < x < 3 23. 3 < x < 2
24. 4 ≤ x ≤ 11 25. x < 6 or x > 2
26. x < 3 or x > 10 27. x ≤ 4 or x ≥ 1
28. x > 4
29. x ≥ 1
0 1 2 3 4 5 6
30. x ≤ 5
31. x < 6
0 1 2 3 4 5 6
x ≤ 2
3
32. 33.
3 2 1
0
2
3
1 2 3
3 2 1
0 1 2 3 4 5 6
x < 3
6 5 4 3 2 1
34. 221,463 ≤ x ≤ 252,710
35. 80 ≤ x ≤ 98 36. 0.4 ≤ x ≤ 8
0 1 2 3
0

LESSON
1.6
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice A
For use with pages 41–47
Match the inequality with its graph.
1. x ≤ 0
2. 2 < x < 3
3. x < 2 or x > 3
4. x > 2
5. x < 3
6. x ≥ 0
A. B. C.
3 2 1 0 1 2 3 4
3 2 1 0 1 2 3 4
3 2 1 0 1 2 3 4
D. E. F.
3 2 1 0 1 2 3 4
3 2 1 0 1 2 3 4
3 2 1 0 1 2 3 4
Decide whether the given number is a solution of the inequality.
7. 3x 2 < 5; 1
8. 5x 9 > 4; 4
9. 2x 3 ≤ 3; 4
10. 5 3x ≥ 7; 4
11. 6x 2 < 14; 2
12. 2 ≤ x 2 ≤ 5; 3
Solve the inequality.
13. 14. 15.
16. 17. 18.
19. 20. 21.
22. 3 < x 5 < 2
23. 4 < 2x < 6
24. 0 ≤ x 4 ≤ 7
25. x 1 < 5 or x 1 > 3 26. x 2 < 1 or x 2 > 8 27. 7x ≤ 28 or 7x ≥ 7
1
x 3 < 1
x 5 ≥ 2
4 ≤ 7 x
2x > 6
1
2x ≤ 5
3x > 9
3x < 12
2x > 18
3x ≤ 7
Solve the inequality. Then graph the solution.
28. 29. 30.
31. 32. 7 33. 1 2x > x 10
3
2x 3 > 11
3 2x ≤ 5
3 x ≥ 2
1
x 3 < 5
x ≥ 6
3
34. Moon’s Orbit As the moon orbits Earth, the closest it ever gets to Earth is
221,463 miles. The farthest away it ever gets is 252,710 miles. Write an
inequality that represents the various distances of the moon from Earth.
35. January Temperatures The highest January temperature in the United
States was 98 F in Laredo, Texas in 1954. The lowest January temperature
in the United States was 80 F in Prospect Creek, Alaska in 1971. Write
an inequality that represents the various temperatures in the United States
during January.
36. Bird Eggs The largest egg laid by any bird is that of the ostrich. An
ostrich egg can reach 8 inches in length. The smallest egg is that of the vervain
hummingbird. Its eggs are approximately 0.4 inch in length. Write an
inequality that represents the various lengths of bird eggs.
2
Algebra 2 83
Chapter 1 Resource Book
Lesson 1.6

Answer Key
Practice B
1. 2.
1
0 1 2 3 4 5
3. 4.
4 3 2 1
5. 6.
7. 8. 9.
10. 11. 12. 13.
14. 15. 16.
17. 18.
19. 20.
21. or 22. or
23. 24.
25. 26. x ≤ 1
x >
x ≤ 0 x ≤ 3
3
2 < x < 4 4 < x < 6
x ≤ 6 x ≥ 16 x < 2 x > 4
8 ≤ x ≤ 12 x < 7
x > 9
3
5
x < 6 x < 7 x > 2
x < 2 x ≥ 1 x ≤ 6 x ≤ 1
x ≥ 2 x < 2
9
7 8 9 10 11 12 13
27. x < 1
28.
4 3 2 1
0 1 2
0 1 2 3 4 5 6
0 1 2
29. x < 3
30. x ≤ 1
6 5 4 3 2 1
1855 ≤ x ≤ 7123
0
4 3 2 1
4 5 6 7 8 9 10
5 4 3 2
5 4 3 2
x ≤ 2
3
3 2 1
4 3 2 1
0 1 2 3
0 1 2
31.
32. x 444 ≥ 540; x ≥ 96
33. d ≤ 652; d ≤ 130 34. 80 ≤ x ≤ 98
35. 0.4 ≤ x ≤ 8
1
1
2
3
0 1 2
1
3
0 1
0 1

Lesson 1.6
LESSON
1.6
84 Algebra 2
Chapter 1 Resource Book
NAME _________________________________________________________ DATE ___________
Practice B
For use with pages 41–47
Graph the solution of the inequality.
1. x < 4
2. x > 3
3. x ≤ 1
4. x ≥ 7
5. 3 < x < 5
6. x ≤ 4 or x ≥ 1
Solve the inequality.
7. 8. 9.
10. 11. 12.
13. 14. 15.
16. 17. 18.
19. 20. 21.
22. 23. 3 ≤ 24. 2x 3 < 8
1
x 8 < 14
11x > 77
2x 1 > 5
3x 2 < 8
5x 8 ≥ 3
1
2x 4 ≤ 7
x 5 ≥ 6
4 2x ≤ 0
3x 5 > 1
7 9x < 12
5x 1 ≥ 1
3x 1 ≤ 2x 2
2 < 2x 5 < 3
4 < 2 x < 6
x 4 ≤ 2 or x 4 ≥ 12
x 1 < 3 or x 1 > 3
2x 1 ≤ 5
Solve the inequality. Then graph the solution.
25. 26. 27.
28. 7 29. 1 2x > x 10
30. 24 x ≥ 6
3
2
3x 5 > 1
6 3x ≤ 5
3 x > 2
2x ≥ 6
31. Extreme Points The northernmost point of the United States is Point
Barrow, Alaska. It lies on the latitude line. The southernmost point
of the United States is Ka Lae, Hawaii. It lies on the latitude line.
Write an inequality that represents the various latitudes of locations in
the United States.
32. Exam Grades The grades for a course are based on 5 exams and 1 final.
All six of the tests are worth 100 points. In order to receive an A in the
course, you must earn at least 540 points. Your grades on the 5 exams
are as follows: 87, 95, 92, 81, and 89. Write an inequality that represents
the various grades you can earn on the final and still get an A. Solve
the inequality.
33. Speed Limit The speed limit on a certain stretch of highway is 65 miles
per hour. Write an inequality that represents the distances you can travel if
you obey the speed limit for 2 hours. Solve the inequality.
34. January Temperatures The highest January temperature in the United
States was 98 F in Laredo, Texas in 1954. The lowest January temperature
in the United States was 80 F in Prospect Creek, Alaska in 1971. Write
an inequality that represents the various temperatures in the United States
during January.
35. Bird Eggs The largest egg laid by any bird is that of the ostrich. An
ostrich egg can reach 8 inches in length. The smallest egg is that of the
vervain hummingbird. Its eggs are approximately 0.4 inch in length. Write
an inequality that represents the various lengths of bird eggs.
7123
1855
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice C
1. 2. 3.
4. 5. 6.
7. 8. 9.
10. 11.
12. 13.
14. 15. x ≤ 16. No solution
17. No solution 18. All real numbers
19. 57.9 < d < 5900
20. Calm
0 ≤ S < 1
Light Air 1 ≤ S ≤ 3
Light Breeze 4 ≤ S ≤ 7
Gentle Breeze 8 ≤ S ≤ 12
Moderate Breeze 13 ≤ S ≤ 18
Fresh Breeze 19 ≤ S ≤ 24
Strong Breeze 25 ≤ S ≤ 31
Near Gale 32 ≤ S ≤ 38
Gale
39 ≤ S ≤ 46
Strong Gale 47 ≤ S ≤ 54
Storm
55 ≤ S ≤ 63
Violent Storm 64 ≤ S ≤ 72
Hurricane S > 72
21. 1.50 0.50x ≤ 4.25; x ≤ 5.5
You can play 5 games.
3
x <
x ≥ 6
2
2
x ≤ x ≤ 3 3 < x < 1
0.84 < x < 1.76 2 ≤ x ≤ 2.8
10 < x < 16.5
8
3 or x > 3
13
x >
8
17
x ≥ 12 ≤ x ≤ 18
x < 2 or x > 2
2
1
x < 1
2
x > 1
8

LESSON
1.6
Solve the inequality.
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice C
For use with pages 41–47
1. 2. 3. 5 ≤
4. 1 2x < 3 or 3 x > 5 5. 3x 5 > x 2
6. 4 3x < 5x 1
7. 2x 1 ≤ 62 x 3 8. 7 3x ≥ 2x 4
9. 4 < 3x 2 1 < 2
10. 2.2 < 5x 2 < 6.8
11. 3.2 ≤ 2.5x 1.8 ≤ 5.2 12. 2.5 < 0.2x 0.5 < 3.8
13.
3
3
x 1 < 0 or x 1 > 5
2 2
14.
2
x 8 ≤ 3x 2
3
15.
5 1 3
x ≥
4 6 2
1
4 2x > x 1
5x 7 ≤ 7x 6
x 1 ≤ 8
2
Decide which inequalities have no solution and which inequalities
are true for all real numbers.
16. 2x 7 < 2x 3
17. 3x 2 4x > x 2x 8
18. 54 x ≤ 4x 20 x
19. Distance from the Sun Mercury is the closest planet to the sun.
Mercury is 57.9 million kilometers from the sun. Pluto is the farthest
planet from the sun. Pluto is 5900 million kilometers from the sun. Write
an inequality that represents the various distances from a planet to the sun.
20. Beaufort Scale The Beaufort Scale is a system for describing the speed
of wind. The table below shows the 13 descriptions of the Beaufort Scale.
Write an inequality for each of the descriptions.
Description Speed, S Description Speed, S
Calm under 1 mph Strong Breeze 25–31 mph
Light Air 1–3 mph Near Gale 32–38 mph
Light Breeze 4–7 mph Gale 39–46 mph
Gentle Breeze 8–12 mph Strong Gale 47–54 mph
Moderate Breeze 13–18 mph Storm 55–63 mph
Fresh Breeze 19–24 mph Violent Storm 64–72 mph
Hurricane over 72 mph
21. Video Arcade You have $4.25 to spend at a video arcade. Some games
cost $0.75 to play and other games cost $0.50 to play. You decide to play
2 games that cost $0.75. Write and solve an inequality to find the possible
number of $0.50 video games you can play.
Algebra 2 85
Chapter 1 Resource Book
Lesson 1.6

Answer Key
Practice A
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13. 14. 15.
16. 17. 18. 19.
20. 21. 22.
23.
24.
25. or
26. or
27. or
28. 29.
30. or
31. or
32.
33. 34.
35. or 36.
37. 38.
39. 40. or
41. or 42. x <
43. x ≤ 27 44. x 58 ≤ 15
or x > 5
7
3 ≤ x ≤
1 < x < 9 x ≤ 11 x ≥ 5
x < 2 x > 3
3
5
8 < x < 8
x < 6 x > 6 3 ≤ x ≤ 3
4 < x < 6
3
5
3 ≤ 9 < 2 8x < 9
3.5 2.1x ≤ 1.5 3.5 2.1x ≥ 1.5
3
4x 1 ≥ 2
3
4x 1 ≤ 2
3.3 < 2.3x 1.7 < 3.3
2 1 5
4 ≤ 3 4x ≤ 4
1
1, 3 < x 7 < 3
10 ≤ 2x 4 ≤ 10
7 < 5 3x < 7
x 4 < 5 x 4 > 5
5x 1 ≤ 4 5x 1 ≥ 4
2 x < 9 2 x > 9
3x 5 ≤ 3
1
3, 7
13
2, 10, 4 6, 10
3
10
x
2.3 5.7x 11.4, 2.3 5.7x 11.4
9, 9 25, 25 4, 4
8, 2
3
1
1
2 9, x 2 9
x 2 7, x 2 7
2x 1 5, 2x 1 5
5x 11 6, 5x 11 6
1
1
2t 3 1, 2t 3 1
5 t 3, 5 t 3
1 4t 9, 1 4t 9
5x 4 6, 5x 4 6
3x 4 8, 3x 4 8
2x 3 7, 2x 3 7
3x 7 5, 3x 7 5

Lesson 1.7
LESSON
1.7
98 Algebra 2
Chapter 1 Resource Book
NAME _________________________________________________________ DATE ___________
Practice A
For use with pages 50–56
Rewrite the absolute value equation as two linear equations.
1. x 2 7
2. 2x 1 5
3.
4. t 3 1
5. 5 t 3
6.
1 2
7. 5x 4 6
8. 3x 4 8
9.
10. 3x 7 5
11. 9
12. 2.3 5.7x 11.4
Solve the equation.
13. x 9
14. x 25
15.
16.
19.
x 3 5
t 4 1
17.
20.
3x 2 8
11 3t 2
18.
21.
1 2
Rewrite the absolute value inequality as a compound inequality.
22. 23. 24.
25.
28.
31.
x 1 ≥ 2
26.
29.
32.
2 8x < 9
2.3x 1.7 < 3.3
27.
30.
33.
3.5 2.1x ≥ 1.5
1
x 7 < 3
2x 4 ≤ 10
5 3x < 7
x 4 > 5
3x 5 ≤ 3
5x 1 ≥ 4
2 x > 9
3 4
x
1
2x 6 14
7t 3 4
Solve the inequality.
34. x < 8
35. x > 6
36. x ≤ 3
37. x 5 < 1
38. 3x 2 ≤ 7
39. 4 x < 5
40. x 8 ≥ 3
41. 2x 1 > 5
42. 11 3x > 4
43. Touring a Ship The diagram below shows
the water line of a large ship. The ship
extends 27 feet above the water and 27 feet
below the water. Suppose you toured the
entire ship. Write an absolute value inequality
that represents all the distances you could
have been from the water line.
27 ft
0 ft
27 ft
2
5x 11 6
1 4t 9
2x 3 7
t 4
2
3
1
4
5 x ≤ 4
44. Water Temperature Most fish can adjust to
a change in the water temperature of up to
15 F if the change is not sudden. Suppose a
lake trout is living comfortably in water that
is 58 F. Write an absolute value inequality
that represents the range of temperatures at
which the lake trout can survive.
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice B
1. yes 2. yes 3. no 4. no 5. no 6. yes
7. 8. 9. 10.
11. 12. 13. 14.
15. 16. 17.
18. 19. or
20. or 21. or
22. 23. or
24. 25. x ≤ 27
26. x 58 ≤ 15 27. x 12.25 ≤ 8.75
28. x 35 ≤ 5
1
x < x > 5
4 ≤ x ≤ 16 x ≤ 24 x ≥ 36
2 < x < 1
7
3 ≤ x ≤
1 < x < 9 x ≤ 11 x ≥ 5
x < 2 x > 3
3
5
4 < x < 6
3
2
1, 0, 7 12, 15
5, 2
1
3, 7
13
8, 2
3 10, 4 6, 10
3
2, 10

LESSON
1.7
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice B
For use with pages 50–56
Decide whether the number is a solution of the equation.
1. 2. 3.
4. 5. 6. 1
5x 4 6; 2
3x 4 8; 4
2x 3 7; 2
5 3x 8; 1
2x 2 4; 1
4x 4; 28
Solve the equation.
7.
10.
x 3 5
t 4 1
8.
11.
3x 2 8
11 3t 2
9.
12.
1 2
13. 2x 7 7
14. 9
15. 4 5x 6
Solve the inequality.
16. 17. 18.
19.
22.
20.
23.
21.
24. 4x 1 < 3
1
x 5 < 1
3x 2 ≤ 7
4 x < 5
x 8 ≥ 3
2x 3 ≤ 5
2x 1 > 5
3x ≥ 10
11 3x > 4
1
1
1
2
2
25. Touring a Ship The diagram below shows
the water line of a large ship. The ship
extends 27 feet above the water and 27 feet
below the water. Suppose you toured the
entire ship. Write an absolute value inequality
that represents all the distances you could
have been from the water line.
27 ft
0 ft
27 ft
27. Hours of Daylight According to the Old
Farmer’s Almanac, the hours of daylight in
Fairbanks, Alaska, range from approximately
3 hours in mid-December to approximately
21 hours in mid-June. Write an absolute value
inequality that represents the hours of daylight
in Fairbanks.
1
2
3x
3
2x 6 14
7t 3 4
26. Water Temperature Most fish can adjust to
a change in the water temperature of up to
15 F if the change is not sudden. Suppose a
lake trout is living comfortably in water that is
58 F. Write an absolute value inequality that
represents the range of temperatures at which
the lake trout can survive.
28. Elephant Longevity On average an elephant
will live from 30 to 40 years. Write an
absolute value inequality that represents the
typical ages of an elephant.
Algebra 2 99
Chapter 1 Resource Book
Lesson 1.7

Answer Key
Practice C
1. 2. 3. 4.
5. 6. 7.
8. 9.
10. 11. 12.
13. 14.
15.
16. No solution 17.
18. All reals 19. x
20. No solution 21. All reals
22. D x ≤ 0.001; 12.999 ≤ x ≤ 13.001;
8.999 ≤ x ≤ 9.001; 5.999 ≤ x ≤ 6.001
23. x 2978.95 ≤ 2921.05 24. x 10 ≤ 3
2
x ≤
5
34
x <
38
5 or x ≥ 5
15
11 13
3 , 3
2, 10
4 28
5 , 5 a, a
b a, b a b a, b a
b b
,
a a
ab, ab 2a, 0
x < 1 or x > 7 1 ≤ x ≤ 2
2 or x > 32
11
2,
5
8 , 8
18
1, 2
5

Lesson 1.7
LESSON
1.7
Solve the equation.
Practice C
For use with pages 50–56
100 Algebra 2
Chapter 1 Resource Book
NAME _________________________________________________________ DATE ___________
1. 6x 3 9
2. 4 5x 14
3.
4. 3x 4 1
5. 24 x 12
6.
Solve for x. Assume that a and b are positive numbers.
7. x a
8. x a b
9. x a b
10. ax b
11. b
12. |x a a
Solve the inequality. If there is no solution, write no solution.
13. 14. 15.
16. 17. 6 18.
19. 2 5x ≤ 0
20. x 7 < 0
21.
5
4 x > 3
8x 12 ≤ 4
5x 2 < 4
x
1
≥
6 3
22. Machine Shop Three circles have to be cut into a piece of metal.
The specifications state that each of the diameters must be within
0.001 centimeter of the given measurements. Let D represent the given
measurement and let x represent the actual diameter of the circle. Write an
absolute value inequality that describes the acceptable diameters of
the circle. If the circles are to be 13 centimeters, 9 centimeters, and
6 centimeters, describe the acceptable diameters of each circle.
23. Distance to the Sun The distance to the sun from the nine planets
ranges from 57.9 million kilometers to 5900 million kilometers. Write an
absolute value inequality that describes the possible distances from a
planet to the sun.
24. Distance Your house is 10 miles away from your school. Your friend’s
house is 3 miles from your school. Write an absolute value inequality that
describes the possible distances from your house to your friend’s house.
x a
3
2x
2
4
4
5
2 3 x > 2
3
1
1
4
3
4
x 3
5
x > 1
2x 3 ≥ 0
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Test A
1. y 2.
1
The relation is The relation is not
a function. a function.
3. 0 4. 0 5. 3
6. y
7.
y
8. y 9. y 2x 1 10. y x 1
11. y x 1 12. y 2x 3
13. y
14.
y
1
2x 15. y
16.
17. y
18.
(0, 1)
1
19. 2s 4a 2800
1
1
1
2
1
1
1
1
x
x
x
x
x
1
y
1
1
1
1
1
y
1
1
x
x
x
x

CHAPTER
2
NAME _________________________________________________________ DATE
Chapter Test A
For use after Chapter 2
____________
Graph the relation. Then tell whether the relation is a
function.
1.
2.
x 0 1 2 1 2
y 1 2 3 0 1
x 3 4 5 3 0 1
y 3 4 5 6 0 1
Evaluate the function for the given value of x.
3. when 4. f x x when x 3
5. f x x 2 when x 5
2 f x x 3 x 3
3x
Graph the equation.
6. x 1
7.
Write an equation of the line that has the given properties.
1
8. slope: 2 9. slope: 2, 10. points: 2, 1,
y-intercept:
0 point: 1, 3
3, 2
,
11. Write an equation of the line that passes through 4, 3 and is
parallel to the line y x 1.
12. Write an equation of the line that passes through and is
perpendicular to the line y 1
2, 1
2x 1.
Copyright © McDougal Littell Inc.
All rights reserved.
1
y
1
x
1
y
1
1
y
1
y 2
3x 2
1
y
1
x
x
x
Answers
1. Use grid at left.
2. Use grid at left.
3.
4.
5.
6. Use grid at left.
7. Use grid at left.
8.
9.
10.
11.
12.
Algebra 2 119
Chapter 2 Resource Book
Review and Assess

Review and Assess
CHAPTER
2
CONTINUED
NAME _________________________________________________________ DATE ____________
Chapter Test A
For use after Chapter 2
Graph the inequality in a coordinate plane.
13. y ≥ 2
14. y ≥ 2x 1
1
Graph the function.
15.
0, if x > 0
f x 2, if x ≤ 0
16.
1
17. f x x 1
18.
1
y
y
y
19. Ticket Prices Student tickets for a football game cost $2 each.
Adult tickets cost $4 each. Ticket sales at last week’s game totaled
$2800. Write a model that shows the different numbers of students
and adults who could have attended the game.
120 Algebra 2
Chapter 2 Resource Book
1
1
1
x
x
x
f x 1
2x 4
1
y
1
1
1
y
x 2,
f x x 2,
y
1
1
x
if x ≥ 0
if x < 0
x
x
13. Use grid at left.
14. Use grid at left.
15. Use grid at left.
16. Use grid at left.
17. Use grid at left.
18. Use grid at left.
19.
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Test B
1. y
2.
The relation is The relation is
a function. not a function.
3. 17 4. 3 5. 7
6. y 7.
8. y
9.
4
1
10. 11. 12.
13. 14. y
15. y
16.
y
1
y y x 5 y x 1
y x 5
2x 2
1
2x 2
2
17. y
18.
1
19. y
20.
1
1
4
1
1
1
2
21. n ≥ 300 22. (a) (b) 20 feet
x
1 x
x
x
x
x
3
4
1
y
1
1
2
1
y
y
1
1
1
y
1
x
1
2
y
(0, 3)
x
x
x
1 x
x

CHAPTER
2
NAME _________________________________________________________ DATE
Chapter Test B
For use after Chapter 2
____________
Graph the relation. Then tell whether the relation is a
function.
1. x 3 1 0 2 3 2.
x 3 3
4 0 3 2
y 2 0 1 2 3
y 3 2 1 1 4 2
Evaluate the function for the given value of x.
3. f x 25 2x when x 4 4. f x x 5 when x 2
5. f x x when x 1
2 5x 1
Graph the equation.
6. y 7. y 2
1
x 3
2
8. 4x y 8
9. x 2
y
4
Write an equation of the line that has the given properties.
1
2 ,
10. slope: 11. slope: 1 12. points:
y-intercept: 2 point: 2, 3 3, 4, 1, 0
Copyright © McDougal Littell Inc.
All rights reserved.
1
y
1
4
1
y
x
1 x
x
1
1
y
y
1
1
1
y
1
x
x
x
Answers
1. Use grid at left.
2. Use grid at left.
3.
4.
5.
6. Use grid at left.
7. Use grid at left.
8. Use grid at left.
9. Use grid at left.
10.
11.
12.
Algebra 2 121
Chapter 2 Resource Book
Review and Assess

Review and Assess
CHAPTER
CHAPTER
2
CONTINUED
Chapter Test B
For use after Chapter 2
13. Write an equation of the line that passes through 1, 6 and is
13.
parallel to the line x y 4.
14. Write an equation of the line that passes through 2, 3 and is
perpendicular to the line y 2x 1.
14.
Graph the inequality in a coordinate plane.
15. y ≥ 1
16. y > 2x 1
2
1
y
y
Graph the function.
19. 20.
f x 1, if x > 0
1, if x < 0
1
21. Profit The sophomore class needs to raise money. They sell boxes
of holiday cards at a profit of $2 per box. How many boxes must
they sell to make a profit of at least $600? Express your answer as
an inequality.
22. Roofs A roof rises 3 units for every 4 units of horizontal run.
(a) What is the slope of the roof?
(b) If the roof is 15 feet high, how long is it?
122 Algebra 2
Chapter 2 Resource Book
1
y
2
17. x 2y ≤ 0
18. x ≥ 2
1
x
x
x
2
f x 4x 3
y
4
y
4
1
2
y
x
1 x
x
15. Use grid at left.
16. Use grid at left.
17. Use grid at left.
18. Use grid at left.
19. Use grid at left.
20. Use grid at left.
21.
22. (a)
(b)
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Test C
1. 2.
The relation is The relation is
a function. a function.
3. 5 4. 1
5. 7
6. 7.
8. 9. y
10. y x 5 11. y x 12. y 2x 8
13. 14.
1
3
y 4x 2
2x 5
15. 16.
17. 18.
19. 8w 10x 3100; 150

CHAPTER
2
NAME _________________________________________________________ DATE
Chapter Test C
For use after Chapter 2
____________
Graph the relation. Then tell whether the relation is a
function.
1. x 1 2 3 4 5 2.
y 2 2 2 2 2
1
y
Evaluate the function for the given value of x.
3. when 4. f x x when x 1
2 f x x 5
x 1
x
5. f x 2x when x 0
2 4 1
Graph the equation.
6. y 0
7.
Write an equation of the line that has the given properties.
8. slope: 9. slope: 10. points: 0, 5,
y-intercept:
2 point: 4, 3 5, 0
1
2 ,
3
4 ,
11. Write an equation of the line that passes through 5, 5 and is
parallel to the line 2x 2y 3.
12. Write an equation of the line that passes through and is
perpendicular to the line y 1
2, 4
2x 3.
Copyright © McDougal Littell Inc.
All rights reserved.
1
1
y
1
x
x
x 3
2 1 0 1
y 3 3 3 3 3
y 2
3x 1
1
y
1
1
y
1
x
x
Answers
1. Use grid at left.
2. Use grid at left.
3.
4.
5.
6. Use grid at left.
7. Use grid at left.
8.
9.
10.
11.
12.
Algebra 2 123
Chapter 2 Resource Book
Review and Assess

Review and Assess
CHAPTER
2
CONTINUED
NAME _________________________________________________________ DATE ____________
Chapter Test C
For use after Chapter 2
Graph the inequality in a coordinate plane.
13. x ≥ 3
14. x > 2y 1
Graph the function.
15. f x 16.
x, if 2 < x < 2
2x, if x < 2
3x, if x > 2
2
17. f x 18.
1
2x 2
1
y
y
1 x
19. Car Wash A local car wash charges $8 per wash and $10 per
wash and wax. At the end of a certain day, the total sales were
$3100. Write a model that shows the different numbers of the
two types of car washes. Then find the number of wash and
waxes there were if 200 were washes only.
124 Algebra 2
Chapter 2 Resource Book
2
1
y
1 x
x
1
f x
x 1 ,
x 1 ,
y
f x 1
2
x 2,
3
4x 3,
1
1
1
y
y
1
1
if
if
x
x
if
if
x ≥ 0
x < 0
x
x > 0
x < 0
13. Use grid at left.
14. Use grid at left.
15. Use grid at left.
16. Use grid at left.
17. Use grid at left.
18. Use grid at left.
19.
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Cumulative Review
1. inverse property of addition
2. associative property of addition
3. distributive property
4. 7 5. 31 6. 32 7. 6 8. 6 9. 7
10. 71 11. 49 12. 13. 14.
15. 2 16. 6 17. 9 18. b1 2A b2 19.
r C
20. x < 2 or x > 1 21. 3 < x < 5
4 2 0 2
22. 4 ≤ x ≤ 2 23. x < 1 or x > 4
6 4 2 0 2 4
16
3
24. or 25. 28 or 4 26. 10 or 3
27. or 28.
29. 2 < x < 30. 2
31. 10 32. 4
33. 1 34. 7 35. 16 36. The relation is a
function. 37. The relation is a function.
38. The relation is not a function. 39. parallel
16
x > 4 x < 8
5
≤ x ≤ 2
40. perpendicular
41. 42.
43. 44.
1
1
1
2
8
3
y
1
y
x
x
7
2
9
2
2
0
2
3
1
1
y
y
1
3
1
1
2
1
4
4
3
5
6
4 5
x
x
45. 46.
1
1
2
Sample answer:
y
61. 62.
8 3
7x 7
63. 64.
1
y
y
y
2
1
1
1
y
x
47. 48.
49. 50. 51.
52. 53.
54. 55.
56. y 57. y x; 5
58. y 4x; 20
59. 60.
1
y
y 2x; 10 y 8x; 40
4x; 54
7
y y 1 x 4
y x 5
35
3x; 3
8
y
32
5x 5
3
y 2x 6
7
4x 4
x
1 x
x
1
y
1
1
1
1
y
y
1
1
y
1
x
x
x
x

Answer Key
65. y
66. 1
67. 24 68. 5 69. 3 70. 2
71. 19
72.
0, 7; up; same width
74.
2, 1; down; narrower
76. 77.
0, 2;
2
1
y
y
1
2
1
1
y
1
1
x
x
x
x
up; wider 0, 4; up; same width
1
y
1
x

Review and Assess
CHAPTER
2 Cumulative Review
NAME _________________________________________________________ DATE ____________
For use after Chapters 1–2
Tell what property the statement illustrates. (1.1)
1. 4 4 0
2. 2 5 7 2 5 7 3. 32 4 32 34
Select and perform an operation to answer the question. (1.1)
4. What is the sum of 13 and 6?
5. What is the difference of 23 and 8?
6. What is the product of 4 and 7. What is the quotient of 4 and
8?
Evaluate the expression for the given value of x. (1.2)
8. when 9. x when x 3
2 x 8 x 2
2
10. when 11. 3x when x 2
4 3x x 5
x 1
2 x 1
Solve the equation. (1.3)
12. 13. 14.
15. 16. 17.
1
7
3x 4 9x 2x 1 8
2a 1 4a 8
6x 4 10x
4.5a 1.7 7.3
32a 8 8a 12
Solve the formula for the indicated variable. (1.4)
18. Area of trapezoid 19. Circumference of circle
Solve for A Solve for r. C 2r
1
b1 . 2b1 b2 Solve the compound inequality. Graph its solution. (1.6)
20. 3x 7 > 10 or 2x > 4
21. 15 < 5x < 25
22. 0.3 ≤ 0.2x 0.5 ≤ 0.9
23. 3x 1 < 11 or 5x 2 < 7
Solve the absolute value equation or inequality. (1.7)
24. 25. 26. 7 2x 13
27. x 2 > 6
28. 6x 4 † 8
29. 3 5x < 13
1
3x 4 12
2x 6 8
Evaluate the function when (2.1)
30. 31. 32.
33. 34. 35. jx x3 2x2 hx 2x2 rx x
gx 3x 5
1
2
x 2.
f x x
gx 5x
Use the vertical line test to determine whether the relation is a
function. (2.1)
36. y
37. y
38.
(2, 6)
(5, 4)
2 x
(5, 1)
130 Algebra 2
Chapter 2 Resource Book
2
(6, 5)
(2, 4)
1
1
x
1
y
2
3 ?
1
Copyright © McDougal Littell Inc.
All rights reserved.
x

CHAPTER
2
CONTINUED
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ____________
Cumulative Review
For use after Chapters 1–2
Tell whether the lines are parallel, perpendicular, or neither. (2.2)
39. Line 1: through 1, 8 and 7, 9
40. Line 1: through 3, 4 and 5, 8
Line 2: through 2, 5 and 10, 6
Line 2: through 1, 2 and 3, 6
Graph the equations. (2.3)
41. 42. 43.
44. 45. y 46. 5x 10y 20
2
y 3x 2y 4
x 5
2
y 3x 4
3x 5
Write the equation of the line that passes through the given
points. (2.4)
47. 4, 2 and 7, 8
48. 5, 2 and 3, 4
49. 4, 0 and 1, 8
50. 2, 1 and 3, 1
51. 4, 5 and 4, 9
52. 0, 5 and 5, 0
The variables x and y vary directly. Write an equation that relates
the variables. Then find y when x 5. (2.4)
53. 54. 55. x
56. x 8, y 2
57. x 6, y 6
58. x 0.2, y 0.8
1
x 3, y 7
x 2, y 4
2 , y 4
Draw a scatter plot of the data. Then approximate the best-fitting
line for the data. (2.5)
59.
x 3 3 0 1 1 2 4
y 7 3 1 1 5 1 5
Graph the inequality in a coordinate plane. (2.6)
60. 5x 2y > 10
61. 4x < 20
62. 8y > 10
63.
1
y > x 3
64. 0.25x 1 > 2
65.
3
Evaluate the function for the given value of x. (2.7)
f(x) 3x, if x > 5 {
x 2, if x ≤ 5
66. f3 67. f8 68. f3 69. f5 70. f0 71.
3
3x < 1
2 y
Graph the function. Then identify the vertex, tell whether the
graph opens up or down, and tell whether the graph is wider,
narrower, or the same width as the graph of (2.8)
72. 73. 74.
75.
1
76. y 2x 2
77. y x 4
y y x 8
y 2x 2 1
3
x 2
y y x .
x 7
f 19
3
Algebra 2 131
Chapter 2 Resource Book
Review and Assess

Answer Key
Practice A
1. domain: 1, 0, 2; range: 3, 6, 16
2. domain: 3, 4, 9; range: 9, 0
3. domain: 1, 2; range: 12, 6, 24
4. y
5.
The relation is a The relation is not
function. a function.
6. y The relation is a function.
7. The relation is a function. 8. The relation is
not a function. 9. The relation is a function.
10.
11.
1
1
1
12. y
13.
1
1
x 2 1 0 1 2
y 1 1 3 5 7
x 2
1 0 1 2
y 5
9
4
7
3
1
2
x
x
x
2
2
y
1
2
y
2
1
1
y
y
2
1
x
x
x
x
14. y
15.
16. y
17.
18. y
19.
20.
21.
Scores
286
285
284
283
282
281
280
279
278
277
276
275
274
0
0
1
1
2
1
y
1
1
2
1
x
x
x
x
U. S. Open Champion Scores
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
Year
1
y
1
1
y
y
1
1
1
x
x
x

LESSON
2.1
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice A
For use with pages 67–74
Identify the domain and range.
1. Input Output
2. Input Output
3.
2
1
0
Graph the relation. Then tell whether the relation is a function.
4. x 0 1 2 3 4
5. x 3 3 4 5 9 6. x 2 1 0 1 2
y 3 5 3 1 0
y 0 1 2 3 11 y 1 2 3 4 5
Use the vertical line test to determine whether the relation is a function.
7. y
8. y
9.
1
3
6
16
1
x
Complete the table of values for the given function. Then graph the
function.
10. y 2x 3
11.
y 1
2x 4
Graph the function.
12. 13. 14.
15. 16. 17.
18. 19. 20. y 1
y x 2
y x 3
y 3x 4
y 6x 2
y 4x 3
y 3x 5
y 8x
y 2
2x 5
21. U.S. Open Champions The table shows the golf scores of the U.S. Open
Champions from 1986 to 1996. Use a coordinate plane to graph these results.
3
9
4
9
0
1
1
x
Input Output
x 2 1 0 1 2
x 2 1 0 1 2
y
y
Year 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996
Score 279 285 281 283 278 277 275 277 279 274 276
1
2
12
24
6
Algebra 2 13
Chapter 2 Resource Book
1
y
1
x
Lesson 2.1

Answer Key
Practice B
1. y
2.
1
The relation is a The relation is not a
function. function.
3. The relation is a function. 4. The relation is
not a function. 5. The relation is a function.
6. y
7.
1
8. y
9.
1
10. y
11.
1
12. y
13.
1
14. y
15. linear; 4
16. not linear; 2
1
1
1
1
1
1
1
x
x
x
x
x
x
y
1
17. linear; 2
18. not linear; 14
19. not linear;
20. linear; 5
21. 54; S3 represents the surface area of a cube
with sides of length 3. 22. 6, 7, 9, 10
23. 6, 7, 9, 10 24. yes
2
2
2
1
1
y
y
y
y
2
1
1
1
1
2
x
x
x
x
x

Lesson 2.1
LESSON
2.1
Practice B
For use with pages 67–74
14 Algebra 2
Chapter 2 Resource Book
NAME _________________________________________________________ DATE ___________
Graph the relation. Then tell whether the relation is a function.
1. x 2 1 0 1 2
2. x 2 1 0 1 2 2
y 0 5 6 0 3
y 4 1 3 2 1 8
Use the vertical line test to determine whether the relation is a function.
3. y
4. y
5.
3
1
Graph the function.
1
6. 7. 8.
9. 10. 11.
12. 13. 14. y 1
y y 3x 5
y 2x 3
y 2
3x 1
1
y 5x 1
y 3x 7
y 2x
y x 2
2x 3
Decide whether the function is linear. Then find the indicated value of
15. 16. 17.
18. 19. 20. fx 3
3
fx ; f4
x 2
x 1; f8
4 fx fx x fx 4 3x; f2
3x 1 ; f5
3 fx.
fx x 7; f3
x 2; f1
21. Geometry The surface area of a cube with side length x is given by the
function Sx 6x Find S3. Explain what S3 represents.
2 .
Statistics In Exercises 22–24, use the following information.
The table below shows the number of games won and lost by the teams in the
Eastern Division of the NFL’s National Football Conference for the 1996 season.
Team Won, x Lost, y
Dallas Cowboys 10 6
Philadelphia Eagles 10 6
Washington Redskins 9 7
Arizona Cardinals 7 9
New York Giants 6 10
22. What is the domain of the relation?
23. What is the range of the relation?
x
24. Is the number of wins a function of the number of losses?
x
3
1
y
1
Copyright © McDougal Littell Inc.
All rights reserved.
x

Answer Key
Practice C
1. The relation is not a function. 2. The
relation is a function. 3. The relation is not a
function. 4. First quadrant 5. Second quadrant
6. Third quadrant 7. Fourth quadrant
8. y 9.
y
10. y 11.
12. y
13.
14. linear; 16 15. not linear; 1
16. not linear; 0 17. not linear; 49
18. not linear; 6 19. not linear; 2
20. Domain 8.3, 8.4, 8.6, 8.7, 8.9
Range 1530,
2000, 2990, 5000, 10,700, 20,000,
28,000, 100,000, 200,000
21.
Deaths (thousands)
1
y
200
150
100
50
1
1
1
1
1
5
0
0 8.3 8.5 8.7 8.9 x
Magnitude
x
x
x
22. No. For each input there is not exactly one output.
For example 200,000, 28,000, and 5000
are all outputs for the input 8.3.
1
1
y
1
1
1
y
1
x
x
x

LESSON
2.1
Tell whether the relation is a function.
3
2
5
4
1
5
5
6
State the quadrant in which each point lies. Assume that a and b
are positive numbers.
4. a, b
5. a, b
6. (a, b
7. a, b
Graph the function.
8. 9. 10.
11. 12. 13. y 3
5 x
3
y 4
4 x
y 3x 5
y 3
y 4 7x
1
y x 2
2
Decide whether the function is linear. Then find the indicated value
of
14. 15. 16.
17. 18. 19. f x 2x f 1
3 x 7
f x
3x
f 2
4,
,
f 4
f x x 32 f 3 f x x x, f 5
,
f x x2 f x.
f x 7x 2, f 2
3x 1,
Earthquakes In Exercises 20–22, use the table below which shows
10 of the worst earthquakes of the 20th century.
20. Identify the domain and range of the relation.
21. Graph the relation.
22. Is the number of deaths a function of the magnitude of an earthquake? Explain.
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice C
For use with pages 67–74
1. Input Output
2. x 1 2 4 7 0
3.
y 0 0 0 0 0
Location (Year) Magnitude, x Deaths, y
Chile (1960) 8.3 5000
India (1950) 8.7 1530
Japan (1946) 8.4 2000
Chile (1939) 8.3 28,000
India (1934) 8.4 10,700
Japan (1933) 8.9 2990
China (1927) 8.3 200,000
Japan (1923) 8.3 200,000
China (1920) 8.6 100,000
Chile (1906) 8.6 20,000
1
y
Algebra 2 15
Chapter 2 Resource Book
1
x
Lesson 2.1

Answer Key
Practice A
1. 2 2. 0 3. 1
4. 2 5. 3 6. 8
1
2
1
3
7. 8. 9. 10. rises
11. is horizontal 12. falls 13. rises 14. falls
15. is vertical 16. neither 17. neither
18. perpendicular 19. parallel
20. perpendicular 21. neither
22. 12.5 quarts per hour 23. Yes, 3
200
4
3
< 1
64

LESSON
2.2
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ____________
Practice A
For use with pages 75–81
Estimate the slope of the line.
1. y
2. y
3.
1
1
x
Find the slope of the line passing through the given points.
4. 2, 3, 5, 9
5. 1, 4, 3, 2
6. 2, 7, 3, 1
7. 5, 1, 7, 5
8. 11, 0, 4, 5
9. 3, 4, 0, 0
Decide whether the line with the given slope rises, falls, is horizontal,
or is vertical.
10. 11. 12.
13. 14. m 15. m is undefined.
4
m
5
2
m 2
m 0
m 7
3
Tell whether the lines with the given slopes are parallel, perpendicular,
or neither.
16. Line 1: 17. Line 1: 18. Line 1:
Line 2: Line 2: Line 2:
19. Line 1: 20. Line 1: 21. Line 1:
Line 2: Line 2: Line 2: m 2
m
m 4
m 3
3
2
m
3
1
m
m 4
3
8
m
3
1
m
m 2
5
3
m 2
m 5
8
22. Picking Strawberries One afternoon your family goes out to pick
strawberries. At 1:00 P.M., your family has picked 3 quarts. Your family
finishes picking at 3:00 P.M. and has 28 quarts of strawberries. At what
rate was your family picking?
23. Ramp The specifications of a ramp that leads onto a loading dock state
that the slope of the ramp must be no steeper than If the ramp begins
200 feet from the base of the loading dock and the dock is 3 feet tall, does
the ramp’s slope meet the specification?
200 ft
3 ft
1
1
1
64 .
x
Algebra 2 27
Chapter 2 Resource Book
1
y
1
x
Lesson 2.2

Answer Key
Practice B
1. 2. 3. 4. 5. 6.
7. Line 1: Line 2: Line 2 is
steeper than Line 1.
8. Line 1: Line 2: Line 2 is
steeper than Line 1.
9. Line 1: Line 2:
steeper than Line 1.
Line 2 is
10. Line 1: Line 2:
steeper than Line 2.
Line 1 is
11. rises 12. is horizontal
13. falls 14. m is undefined; is
vertical 15. m falls
zontal 17. perpendicular
16. m 0; is hori-
18. perpendicular 19. neither
20. perpendicular 21.
1
12
22. 0.85 ticket per minute
5
3 ;
m 1
m
m 1;
m 0;
4;
1
8 ;
1
m 3 ;
m m 1;
1
3
2 1
3
2
m 1; m 4;
m 2; m 3;
2;
1
2
1 3

Lesson 2.2
LESSON
2.2
NAME _________________________________________________________ DATE ____________
Practice B
For use with pages 75–81
Find the slope of the line passing through the given points.
1. 4, 5, 2, 9
2. 1, 4, 5, 0
3. 3, 5, 6, 2
4. 2, 7, 4, 4
5. 0, 8, 3, 5
6.
Tell which line is steeper.
7. Line 1: through 2, 1 and 3, 6
8. Line 1: through 3, 1 and 5, 5
Line 2: through 4, 5 and 2, 3
Line 2: through 2, 2 and 1, 11
9. Line 1: through 0, 3 and 2, 4
10. Line 1: through 10, 2 and 5, 3
Line 2: through 8, 6 and 4, 6
Line 2: through 4, 1 and 12, 0
Find the slope of the line passing through the given points. Then
tell whether the line rises, falls, is horizontal, or is vertical.
11. 4, 2 and 3, 3
12. 9, 2 and 3, 2 13. 3, 5 and 5, 3
14. 7, 5 and 7, 8
15. 10, 5 and 4, 15
16. 0, 4 and 3, 4
Tell whether the lines are parallel, perpendicular, or neither.
17. Line 1: through 3, 2 and 1, 5
18. Line 1: through 3, 1 and 4, 8
Line 2: through 1, 6 and 2, 8
Line 2: through 5, 3 and 4, 2
19. Line 1: through 2, 1 and 5, 3
20. Line 1: through 0, 6 and 5, 0
Line 2: through 0, 3 and 3, 5
Line 2: through 4, 4 and 2, 1
21. Mountainside The halfway point of a tunnel through a mountain is
3
2 miles from either end of the tunnel. The mountain is 660 feet
high. Find the slope of the side of the mountain.
3
mi
2
1
mi
8
22. Prom Tickets You volunteered to take a shift selling prom tickets during
your morning study hall. When your shift began at 11:00 A.M., 50 tickets
had been sold. At 11:40 A.M., when your shift ended, 84 tickets had been
sold. At what rate did you sell prom tickets?
28 Algebra 2
Chapter 2 Resource Book
1
8 mile
1 3
,
2
4 , 3 9
,
2 4
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice C
1. 2. 3. 4. 5. 5 6.
7. rises 8. is vertical 9. falls 10. Line 2
11. Line 1 12. Line 2 13. Line 1
14. They are equal. 15. They are negative
reciprocals of each other. 16. vertical lines
17. horizontal lines 18.
1000 55
21 ; 17 19.
964 180
755 ; 151
20. y
This is true for an
equilateral triangle
m 3 m 3 of any size.
1
4
17
2
5
3
2 11
m 0
x
16
17

LESSON
2.2
Find the slope of the line passing through the given points.
1. 6, 3, 4, 1
2. 5, 3, 7, 6
3.
4. 5. 6. 5, 2, 12, 14
3
5 , 3 , 6 1
1, 3, 2
, 0 5
3 ,
3
Decide whether the line passing through the given points rises, falls, is horizontal, or is
vertical.
7. 9, 11, 5, 5
8. 1, 6, 1, 7
9. 7, 0, 1, 12
Determine which line is steeper.
10. Line 1: through 3, 7 and 6, 2
11. Line 1: through 1, 1 and 0, 2
Line 2: through 2, 4 and 3, 8
Line 2: through 1, 4 and 2, 2
12. Line 1: through 5, 2 and 1, 3
13. Line 1: through 6, 2 and 1, 1
Line 2: through 3, 4 and 2, 5
Line 2: through 4, 3 and 1, 3
14. Parallel Lines If two nonvertical lines are parallel, what do you know about their slopes?
15. Perpendicular Lines
slopes?
If two nonvertical lines are perpendicular, what do you know about their
16. Vertical Lines All vertical lines are parallel to what type of line?
17. Vertical Lines All vertical lines are perpendicular to what type of line?
18. Washington Monument The Washington Monument is 555 feet tall. The monument is composed of
a 500-foot pillar topped by a 55-foot pyramid. The base of the pillar is 55 feet wide. The base of the
pyramid is 34 feet wide. Approximate the slope of the sides of the pillar and the slope of the pyramid.
19. Pyramids of Egypt The sides of the base of the largest pyramid, Khufu, has length 755 feet. The
height of Khufu was originally 482 feet, but now is approximately 450 Feet. Find the slope of a side
of the pyramid at its original size and at its present size.
20. Equilateral Triangles An equilateral triangle has the same side lengths and angle measures. Draw
an equilateral triangle on a coordinate plane such that one of the vertices is the origin. Approximate
the slopes of the sides of your triangle. What are the slopes of the sides of any equilateral triangle in
this position?
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ____________
Practice C
For use with pages 75–81
1 3
,
5
5 , 3
4
, 1
4
Algebra 2 29
Chapter 2 Resource Book
Lesson 2.2

Answer Key
Practice A
1. y
2.
3. y
4.
1
5. y
6.
7. y
8.
1
y
9. 10. m 3; b 1
11. 12.
13. 14.
15. m
16. y
17.
y
1
m
5 ; b 3
5
m 4; b 7 m 6; b 4
m 8; b 2
3 ; b 1
1
1
1
1
1
1
1
(0, 2)
1
1
1
(4, 0)
x
x
x
x
x
x
y
1
1
1
1
1
y
y
y
(3, 0)
1
1
1
1
(0, 1)
1
x
x
x
x
x
18. y
19.
(2, 0)
20. y
21.
1
22. y
23.
1
24. y
25.
1
26. y
27.
1
28. F 29. 3 30. 100
31. y
10
1
1
1
1
10
1
( )
1
, 0
2
1
(0, 3)
x
(0, 4)
x
x
x
x
C
50
50
1
y
(0, 2)
1
1
1
1
1
1
y
y
y
y
(2, 0)
3
( 0,
2 )
1
1
1
(5, 0)
x
x
x
x
x
x

LESSON
2.3
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ____________
Practice A
For use with pages 82–89
Draw the line with the given slope and y-intercept.
1. m 2, b 3
2. m 3, b 1
3. m 1, b 4
4. m 2, b 1
5. m 0, b 6
6.
4
7. m 2,
b 3
8. m , b 4
9.
3 5
Find the slope and y-intercept of the line.
10. 11. 12.
13. 14. 15. y 1
y 3x 1
y 4x 7
y 6x 4
y 8x 2
5
y x 1
3
x 3
5
Draw the line with the given intercepts.
16. x-intercept: 4 17. x-intercept: 3
18. x-intercept: 2
y-intercept: 2
y-intercept: 1 y-intercept: 4
19. x-intercept: 5 20. x-intercept: 21. x-intercept: 2
y-intercept: 2
y-intercept: y-intercept: 3
1
2
3
2
Graph the equation.
22. y 2x 1
23. y 6x 4
24. y 3x 1
25. y x 1
26. y 3x
27. y 2x
28. Temperature The formula which converts degrees Celsius to degrees
Fahrenheit is given by F Graph the equation.
9
C 32.
Simple Interest In Exercises 29–31, use the following information.
If you deposit $100 into an account that pays 3% simple interest, the amount of
money in your account after t years is modeled by y 3t 100.
29. What is the slope of the line?
30. What is the y-intercept of the line?
31. Graph the line.
5
m 1
, b 2
3
m 3
, b 0
2
Algebra 2 41
Chapter 2 Resource Book
Lesson 2.3

Answer Key
Practice B
1. 2.
3. 4.
5. 6. m
1
7. x-intercept: y-intercept: 1
2
m 3; b 2
3
7; b 5
m
7
1
m
1
2 ; b 4
1
m 8; b 7 m 10; b 0
3
4 ; b 2
8. x-intercept: 6; y-intercept: 6
9. x-intercept: 3; y-intercept: 2
10. x-intercept: 12; y-intercept: 3
11. x-intercept: y-intercept: 4
12. x-intercept: 7; y-intercept: 3
13. x-intercept: 2; y-intercept: 4
14. x-intercept: 4; y-intercept: 3
15. x-intercept: y-intercept: 4
16. x-intercept: 4; y-intercept:
17. x-intercept: 4; y-intercept:
18. x-intercept: 2; y-intercept: 3
19. y
20.
3
21. y
22.
1
23. y 24.
25. y
26.
1
1
1
1
6
12
5 ;
8
5 ;
1
3 ;
1
x
x
1 x
x
8
5
4
3
1
y
1
1
y
y
1
1
1
1
y
1
x
x
x
x
27. y 28. 29. 2
1
1 x
30. y 31. 0.10d 0.25q 50
32. 0.03x 0.04y 250
2
7x 2
2
7

Lesson 2.3
LESSON
2.3
Practice B
For use with pages 82–89
42 Algebra 2
Chapter 2 Resource Book
NAME _________________________________________________________ DATE ___________
Find the slope and y-intercept of the line.
1. y 8x 7
2. y 10x
3. x 4y 6 0
4. 2x 4y 1 0
5. 3x 7y 5 0
6. 2x 3y 6 0
Find the intercepts of the line.
7. y 3x 1
8. y x 6
9.
10. 11. 12. y
13. 2x y 4 0
14. 3x 4y 12 0 15. 5x 2y 8 0
16. x 3y 4
17. 2x 5y 8
18. 6x y 3
7
y 1x
3
4
5
y x 4
3
x 3
2
Graph the equation.
19. y 4x 3
20. y 3x 2
21. x 6y 3 0
22. 7x 2y 6 0
23. 4x 8y 20 0 24. 6x 9y 18
25. 2x y 2
26. 8x 2y 6
27. 3x 5y 15 0
Teeter-Totter In Exercises 28–30, use the following information.
The center post on a teeter-totter is 2 feet high. When one end of the teetertotter
rests on the ground, that end is 7 feet from the center post.
28. Find the slope of the teeter-totter.
29. Assume the base of the center post is at (0, 0) with the ground along the
x-axis. Find the y-intercept of the teeter-totter.
30. Write an equation of the line that follows the path of the teeter-totter.
31. Saving Change Each time you get dimes or quarters for change, you
throw them into a jar. You are hoping to save $50. Write a model that
shows the different numbers of dimes and quarters that you could accumulate
to reach your goal.
32. Commission Sales A salesperson receives a 3% commission on furniture
sold at a sale price and a 4% commission on furniture sold at the regular
price. The salesperson wants to earn a $250 commission. Write a
model that shows the different amounts of sale-priced and regular-priced
furniture that can be sold to reach this goal.
y 2
x 2
3
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice C
1. 2.
3. 4.
5. 6.
7. 8.
9. 10.
11. 12. m
13. x-intercept: 4 14. x-intercept: 4
y-intercept: 3 y-intercept: 8
1
m
5
2 ; b 2
3
m
1
7 ; b 7
2
m
7
5 ; b 5
8
m
3 ; b 0
3
m
7 8
m 5 ; b 5
2 ; b 2
4
m m 2; b 3
m 0; b 6
1
3 ; b 3
2
m 3; b
3 ; b 4
1
m 4; b 2
2
15. x-intercept: 3 16. x-intercept: 0
5
y-intercept: y-intercept: 0
17. x-intercept: 4 18. x-intercept: 13
y-intercept: 3 y-intercept: none
19. x-intercept: none 20. x-intercept: 1
3
y-intercept: y-intercept:
21. x-intercept:
y-intercept:
22. y 23.
1
24. y 25.
1
26. y 27.
1
28. y 29. y
1
1
1
1
1
5
2
3
1
4
1
4
2
x
x
x
x
1
y
1
1
1
1
1
y
y
1
1
1
4
x
x
x
x
30.
31.
Sweatshirts
y
200
100
0
0
Sample answers:
210, 102
300, 60
390, 18
32. a. 300,000; The V-intercept represents the
initial value of the equipment.
100,001
1
y
1
x
100 200 300 400 x
T-shirts
7x 15y 3000
b. 2
The slope represents the
decrease in value per year.
50,000.5;

LESSON
2.3
Find the slope and the y-intercept of the line.
1. 2. 3. y
4. y 3 2x
5. y 6
6. 4x 3y 1 0
7. 7x 5y 8 0
8. 3x 2y 4 0
9. 8x 3y 0
10. 2x 5y 7 0 11. 3x 7y 1 0
12. x 2y 5 0
2
y 4x 2
1
y 3x
2
x 4
3
Find the intercepts of the line.
13. 3x 4y 12 0
14. 2x y 8 0
15. 3x 2y 5 0
16. 5x 2y 0
17. 4x y 3
18. x 13 0
19. 4y 3 0
20. 2x 3y 3x y 1 21. x 5y 3 3x y 4
Graph the equation.
1
22. y 3x 5
23. y 2x 24.
2
25. x 26. 2x 3y 6 0
27. 3x 4y 10
4
3
1
28. x 2y 8 0
29. x 2y 3 0
30.
2
31. Fund Raiser The marching band holds a fund raiser each year in which
they sell t-shirts and sweatshirts with the school’s name and mascot on it.
The t-shirts sell for $7 and the sweatshirts sell for $15. The band needs
to raise $3000. Write a model that shows the number of t-shirts and
sweatshirts that must be sold. Then graph the model and determine three
combinations of t-shirts and sweatshirts that satisfy the model.
32. Linear Depreciation A business purchases a piece of equipment for
$300,000. The value, V, of the machine after t years is represented by the
model 2V 100,001t 600,000.
a. Find the V-intercept of the model. What does the V-intercept represent?
b. Find the slope of the model. What does the slope represent?
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ____________
Practice C
For use with pages 82–89
y 3
x 1
4
4x 3
y 1 0
2
Algebra 2 43
Chapter 2 Resource Book
Lesson 2.3

Answer Key
Practice A
1. 2.
3. 4.
5. 6. 7.
8. 9.
10. 11. 12.
13. 14.
15. 16.
17. 18.
19. 20.
21. 22.
23. 24.
25. 26.
27. y
28. The data do not show direct variation.
29. The data do show direct variation, and the
direct variation equation is y x.
30. y 0.06x
1
y
y 3x 15 y 2x 3
1
3x 3
1
2x 17
y y 5x 11
y 2x 22
2
3
y 3x 2
y 4x 5
y 6x 1 y x 9
y 2x y 7 y 5x 3
y 3x 2 y 2x 4
y 4x 11 y 6 y x 5
y x 3 y 2x 1
y x 10 y 2x 1
y 8x 17 y 4x 8
y x 1 y 3x 20
4x 3

LESSON
2.4
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ____________
Practice A
For use with pages 91–98
Write an equation of the line that has the given slope and
y-intercept.
1. m 3, b 2
2. m 4, b 5
3. m 6, b 1
4. m 1, b 9
5. m 2, b 0
6. m 0, b 7
Write an equation of the line that passes through the given point
and has the given slope.
7. 0, 3, m 5
8. 0, 2, m 3
9. 1, 2, m 2
10. 3, 1, m 4
11. 2, 6, m 0
12. 4, 1, m 1
13. 5, 2, m 1
14. 3, 7, m 2
15. 8, 2, m 1
Write an equation of the line that passes through the given points.
16. 1, 1, 5, 9
17. 2, 1, 3, 7
18. 1, 4, 2, 16
19. 3, 2, 1, 0
20. 5, 5, 8, 4
21. 0, 3, 4, 0
22. 2, 1, 1, 6
23. 7, 8, 2, 18
24. 9, 4, 1, 8
Write an equation of the line.
25. 26. 27.
1
y
1
x
Tell whether the data show direct variation. If so, write an equation
relating x and y.
28. x 1 2 3 4 5
29.
y 2 3 4 5 6
30. Sales Tax The amount of sales tax in Pennsylvania varies directly with
the price of merchandise. Use the given tax table to write an equation
relating the price x and the amount of sales tax y.
Price, x (dollars) 10 20 30 40 50
Tax, y (dollars) 0.60 1.20 1.80 2.40 3
y
1
1
x
x 2
1 0 1 2
y 2 1 0 1 2
Algebra 2 55
Chapter 2 Resource Book
2
y
2
x
Lesson 2.4

Answer Key
Practice B
1. 2.
3. 4. 5.
6. 7. 8.
9. 10.
11. 12.
13. 14.
15. 16. 17.
18. 19.
20. 21.
22. 23.
24. 25.
26. 27.
28. y 29. Yes, you are traveling about
88.5 km/hr. 30. y 0.2t 14.7
31. 16.7 pounds
103
y
64 x
27
y y 0.25x; 2.5
y 14x;
52
10x; 27
5
y
y 3x; 30 y 5x; 50
2x; 25
3
y 2x 19
3
7x 5
y y x 4
y 2x 1 y 3x 19
7
1
y 2x
1
2x 1
y y 2x 1
2
3
y 4x
5
4x 2
8
y y 8x
y 5 y 2x 5 y 5x 23
y x 12 y 3x 7
y 8x 8
3
1
y 4x 4
y 6x 3
4
y 3x 6
2x 4

Lesson 2.4
LESSON
2.4
Practice B
For use with pages 91–98
56 Algebra 2
Chapter 2 Resource Book
NAME _________________________________________________________ DATE ___________
Write an equation of the line that has the given slope and y-intercept.
1. m 4, b 4
2. m 6, b 3
3.
4. m 5. m 8, b 0
6. m 0, b 5
1
, b 4
2
Write an equation of the line that passes through the given point
and has the given slope.
7. 8. 9.
10. 11. 12. 2
, 0 , m 4
3 1
2, 1, m 2
4, 3, m 5
7, 5, m 1
1, 10, m 3
, 4 , m 8
2
Write an equation of the line that passes through the given points.
13. 2, 1, 2, 4
14. 1, 3, 1, 1
15. 3, 1, 3, 2
16. 4, 2, 6, 3
17. 1, 5, 4, 0
18. 3, 7, 2, 3
19. 6, 1, 5, 4
20. 3, 2, 4, 1
21. 10, 4, 6, 10
The variables x and y vary directly. Write an equation that relates
the variables. Then find y when x 10.
22. x 2, y 6
23. x 1, y 5
24. x 4, y 10
25. x 1, y 0.25
26. x 8, y 2
27.
Measuring Speed In Exercises 28 and 29, use the following information.
The speed of an automobile in miles per hour varies directly with its speed in
kilometers per hour. A speed of 64 miles per hour is equivalent to a speed of
103 kilometers per hour.
28. Write a linear model that relates speed in miles per hour to speed in
kilometers per hour.
29. You are driving through Canada and see a speed limit sign that says the
speed limit is 80 kilometers per hour. You are traveling 55 miles per
hour. Are you speeding?
Fish and Shellfish Consumption In Exercises 30 and 31, use the
following information.
For 1992 through 1994, the per capita consumption of fish and shellfish in the
U.S. increased at a rate that was approximately linear. In 1992, the per capita
consumption was 14.7 pounds, and in 1994 it was 15.1 pounds.
30. Write a linear model for the per capita consumption of fish and shellfish
in the U.S. Let t represent the number of years since 1992.
31. What would you expect the per capita consumption of fish and shellfish
to be in 2002?
m 4
, b 6
3
x 1 9
, y
3 10
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice C
1.
4.
6.
2.
5.
3.
7. 8.
9. 10.
11. 12. 13.
14. 15. 16.
17. y 18. y 9
19. y 0.49t 31.4
20. Yes. The model gives 41.2%, and the actual
number was 41.1%. 21. No. The model gives
46.1%, and the actual number was 47%.
22. y 1420t 15,500
23. y 1420t 2,810,300 24. $29,700; yes.
3
y
9
4x 2
1
y
x 7 y 2 y 2x 5
y x y x 2
11
2x 2
3
y
y 2x 3
11
2x 2
1
y
11
4x 4
1
y
y 8 y x
7
2x 2
8 34
11x 11
y x 1
1
y 9x 19
16
7x 7

LESSON
2.4
Write an equation of the line that passes through the given points.
1. 2, 1, 3, 8
2. 5, 3, 2, 2
3. 1, 6, 1, 2
4. 7, 2, 4, 6
5. 3, 8, 1, 8
6. 6, 6, 2, 2
Write an equation of the line that passes through the given point
and is perpendicular to the given line.
7. 1, 3, y 2x 1
8. 3, 2, y 4x 3 9.
10. 3, 1, y 11. 7, 3, y 8
12. 5, 2, x 2
2
x 4
3
Write an equation of the line that passes through the given point
and is parallel to the given line.
13. 14. 15.
16. 17. 10, 12, y 18. 4, 9, y 14
3
2, 1, y 2x 5
1, 1, y x 3
3, 5, y 12 x
1
3, 4, y x 8
2
x 1
4
Labor Force In Exercises 19–21, use the following information.
From 1840 to 1850, the rate at which the percent of the labor force in nonfarming
occupations increased was approximately linear. In 1840, 31.4% of the labor
force held nonfarming jobs. In 1850, 36.3% of the labor force held nonfarming
jobs.
19. Write a linear model for the percentage of the labor force in nonfarming
occupations. Let t 0 represent 1840.
20. In 1860, the percent of the labor force in nonfarming occupations was
41.1%. Is the model for the percentage of nonfarming occupations from
1840 to 1850 still an appropriate model?
21. In 1870, the percent of the labor force in nonfarming occupations was
47.0%. Is the model for the percentage of nonfarming occupations from
1840 to 1850 still an appropriate model?
College Tuition In Exercises 22–24, use the following information.
The rate of increase in tuition at a college from 1990 to 1995 was approximately
linear. In 1990, the tuition was $15,500 and in 1995 it was $22,600.
22. Write a linear model for the tuition from 1990 to 1995. Let t 0
represent 1990.
23. Write a linear model for the tuition from 1990 to 1995. Use the actual
years as the coordinates for time.
24. Although the models in Exercises 22 and 23 are different, use both
models to approximate the tuition in 2000. Do both models yield the
same result?
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ____________
Practice C
For use with pages 91–98
1, 1, y 1
x 7
2
Algebra 2 57
Chapter 2 Resource Book
Lesson 2.4

Answer Key
Practice A
1. positive correlation 2. negative correlation
3. relatively no correlation
4. y
5.
negative correlation relatively no
correlation
6. y
positive correlation
7. Answers may vary. Sample:
8. Answers may vary. Sample:
9.
1
1
1
1
Computers
per 1000 people
380
360
340
320
300
280
x
Computers per Capita
260
240
0
0 1 2 3 4 5 6
Years since 1990
positive correlation
x
1
y
1
y 1
y
3
4x 2
3 7
4x 2
x

LESSON
2.5
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ____________
Tell whether x and y have a positive correlation, a negative
correlation, or relatively no correlation.
1. y
2. y
3.
Draw a scatter plot of the data. Then tell whether the data have a positive
correlation, a negative correlation, or relatively no correlation.
4.
5.
6.
Approximate the best fitting line for the data.
7. y
8.
4
3
2
1
1
1
Practice A
For use with pages 100–106
x 1 2 3 4 5 6 7 8
y 6 6 5 5 6 5 4 3
x 1 2 3 4 5 6 7 8
y 4 5 1 6 6 3 1 6
x 1 2 3 4 5 6 7 8
y 2 2 4 6 8 8 10 10
1 2 3 4 x
x
1 2 3 4 x
9. Computers Per Capita The table shows the number of computers per 1000
people in the U.S. from 1991 through 1995. Draw a scatter plot of the data
and describe the correlation shown.
Year 1991 1992 1993 1994 1995
Computers per
1000 people
245.4 266.9 296.6 329.2 364.7
1
1
4
3
2
1
y
x
Algebra 2 69
Chapter 2 Resource Book
1
y
1
x
Lesson 2.5

Answer Key
Practice B
1. y 2.
positive correlation relatively no
correlation
3. y
negative correlation
4. Answers may vary. Sample:
5. Answers may vary. Sample:
6. Answers may vary.
Sample: y 1
y x
y
7
3x 3
1
y
4
2 11
5x 4
7. Answers may vary.
Sample: y 1
y
15
4x 4
8.
Pounds
b
4
3
2
1
1
1
1
1
1
1
1
1
Broccoli Consumption
0 0 1 2 3 4 5 6 7 8 9 t
Years since 1980
answer: b 0.3t 1.5
10. Sample answer: 8.1 pounds
x
x
x
x
1
y
1
x
9. Sample

Lesson 2.5
LESSON
2.5
70 Algebra 2
Chapter 2 Resource Book
NAME _________________________________________________________ DATE ___________
Draw a scatter plot of the data. Then tell whether the data have a
positive correlation, a negative correlation, or relatively no correlation.
1.
2.
3.
Approximate the best-fitting line for the data.
4. y
5.
4
Draw a scatter plot of the data. Then approximate the best-fitting
line for the data.
6.
7.
3
2
1
Practice B
For use with pages 100–106
x 3 2.5 2 1.75 1.5 1 0.5 0 0.5 0.75 1 1.5
y 0.25 0.5 1 1.5 1.25 2 2.5 2.5 3 3.25 3.5 3.75
x 0 0.5 1 1.25 1.5 2 2.5 3 3.25 3.5 4 4.25
y 2.75 3 2.5 2 1.75 1 1.25 1.5 2.5 3 3.25 3
x 2 1 0.5 0 0.25 1 1.5 2.5 2.75 3.5 4 4.5
y 1 1.25 0.5 0 1 1.25 2 2.25 2 3 3.25 3.5
1 2 3 4 x
x 2 1.5 1 0.5 0 0.5 1 1.5 2
y 3 2.5 3 2.4 2.2 2 2.1 1.8 1.5
x 5 4 3 2 1 0 1 2 3
y 3 2.5 2.8 3.2 3 4 4.2 4.3 4.5
Broccoli Consumption In Exercises 8–10, use the following information.
The table shows the per capita consumption of broccoli, b (in pounds), for the
years 1980 through 1989.
8. Draw a scatter plot for the data. Let t represent the number of years
since 1980.
9. Approximate the best-fitting line for the data.
10. If this pattern were to continue, what would the per capita consumption of
broccoli be in 2002?
4
3
2
1
y
1 2 3 4 x
Year, t 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989
Pounds, b 1.6 1.8 2.2 2.3 2.7 2.9 3.5 3.6 4.2 4.5
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice C
1. 2.
3. Answers may vary. 4. Answers may vary.
Sample: y Sample: y x 2.5
3
y 7.6x 4.5
y 1.2x 3.5
31
x
5. Answers may vary. 6.
Sample: 3.3x 0.87
7. Answers may vary. 8. Answers may vary.
Sample: Sample:
y 16.05t 319.44 approximately 640
9. y
55
50
10. Answers may vary.
Sample:
y 0.43x 45
Home runs
2
y
y
2
0
0 2 4 6 8 10 12 t
2 x
Years since 1980
45
40
2
0
0
5
x
5
1 2 3 4 5 6
Years since 1990
t
African-American officials
2
y
500
400
300
y
2
x

LESSON
2.5
Approximate the best-fitting line for the data.
1. y
2.
Draw a scatter plot of the data. Then approximate the best-fitting
line for the data.
3.
4.
5.
African-American Elected Officials In Exercises 6–8, use the following information.
The table shows the number of African-American elected officials in U.S. and
state legislatures for the years 1984 to 1993.
6. Draw a scatter plot for the data. Let t 4 represent 1984.
7. Approximate the best-fitting line for the data.
8. If this pattern continues, how many African-American officials will be in
the U.S. and state legislatures in 2000?
Home Run Champions In Exercises 9 and 10, use the following information.
The table shows the number of home runs hit by the American League Home
Run Champion from 1990 to 1996.
9. Draw a scatter plot for the data. Let t 0 represent 1990.
10. Approximate the best-fitting line for the data.
Copyright © McDougal Littell Inc.
All rights reserved.
5
NAME _________________________________________________________ DATE ____________
Practice C
For use with pages 100–106
1
x
x 3 2 1 0 1 2 3
y 8 7.2 6.4 6 5.5 5 4.8
x 0 1 2 3 4 5 6
y 4 3.5 3.8 4.6 6 7.8 10
x 0 0.5 1 1.5 2 2.5 3
y 0.6 3.2 4.4 5.8 7 8.2 12
Year 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993
Officials 396 407 420 440 436 448 447 484 510 571
Year 1990 1991 1992 1993 1994 1995 1996
Home Runs 51 44 43 46 40 50 52
1
y
1
x
Algebra 2 71
Chapter 2 Resource Book
Lesson 2.5

Answer Key
Practice A
1. yes; no 2. no; yes 3. no; yes
4. yes; yes 5. yes; no 6. yes; no
7. y
8.
9. y
10.
1
1
1
11. y
12.
3
13. y
14.
1
1
1
x
x
3 x
x
y
3
y
2
15. D 16. F 17. C 18. E 19. B 20. A
21. 2x 3y ≥ 34 22. no 23. Answers may
vary. Sample: 13 2-point and 3 3-point or 17
2-point and 0 3-point.
1
y
2
1
2
3 x
y
2 x
x
x

Lesson 2.6
LESSON
2.6
Practice A
For use with pages 108–113
82 Algebra 2
Chapter 2 Resource Book
NAME _________________________________________________________ DATE ___________
Check whether the given ordered pairs are solutions of the inequality.
1. x y < 5; 1, 2, 7, 2
2. x > 3; 0, 4, 5, 1
3. y ≤ 1; 1, 3, 2, 1
4. y x ≥ 1; 5, 6, 3, 1
5. x < 2y 5; 4, 0, 4, 5
6. y ≥ x 7; 2, 4, 8, 3
Graph the inequality in a coordinate plane.
7. x > 3
8. x < 1
9. x ≥ 5
10. x ≤ 7
11. y > 1
12. y < 6
13. y ≤ 2
14. y ≥ 4
Match the inequality with its graph.
15. 3x y > 1
16. 2x y ≤ 3
17. 4x y < 1
18. 2x y ≤ 0
19. 5x > 2
20. 3y < 6
A. B. C.
1
D. y
E. y
F.
1
y
1
1
x
x
Basketball Stats In Exercises 21–23, use the following information.
In order for this year’s star basketball player to break the school record for
most points (excluding free throws), he must score at least 34 points. The
points may be scored by two-point shots and three-point shots.
21. Write an inequality that represents the number of two- and three-point
shots he needs to break the record.
22. In the first game he scored 13 two-point shots and 2 three-point shots.
Did he break the record?
23. Give two possible combinations of two- and three-point shots that will
give him the record.
y
1
1
1
1
x
x
1
y
1
y
1
1
Copyright © McDougal Littell Inc.
All rights reserved.
x
x

Answer Key
Practice B
1. no; yes 2. no; yes 3. no; yes
4. yes; no 5. yes; no 6. no; yes
7. y
8.
3
9. y
10.
1
1
11. y
12.
1
13. y
14.
1
15. y
16.
1
17. y
18. y
1
3
1
1
1
1
x
x
x
x
x
x
1
1
1
2
1
y
y
y
1
1
2
1
y
1
1 x
y
x
x
1 x
x
x
19. y
20.
21.
24. Yes, a 2-pound roast takes at most 10 hours to
defrost, so it will be completely defrosted
before 12 hours passed.
25. 3x 5y ≤ 800 26. 50, 150
Number of T-shirts
300
200
100
Time (hours)
0
0
t
7
6
5
4
3
2
1
1
1
Defrosting Meat
0
0 1 2 3 4 5 6 7 p
Fundraiser
Weight (pounds)
100 200 300
Number of caps
y
1
1
x
x
22. t ≤ 5p 23. 2, 12
27. No, 50, 150 is not a
solution of
3x 5y ≤ 800.
1
y
1
x

LESSON
2.6
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ____________
Practice B
For use with pages 108–113
Check whether the given ordered pairs are solutions of the inequality.
1. 2x 3y ≤ 2; 0, 1, 3, 2
2. x 2y > 4; 2, 1, 3, 6
3. 5x y ≥ 3; 3, 6, 2, 5
4. 3x 10y < 8; 6, 3, 4, 2
5. 4y 2x < 5; 2, 0, 3, 1
6. 2y x ≥ 3; 1, 2, 1, 1
Graph the inequality in a coordinate plane.
7. 8. x < 9. 2x > 6
1
x ≥ 1
2
10. y < 4
11. y ≥ 5
12.
13. 14. y ≥ 15. 4x y ≤ 2
16. x 2y > 4
17. 5x 5y > 1
18. 3x y ≤ 7
19. 2x 4y > 8
20. 6x 3y ≥ 1
21. 12x 4y < 8
1
y < 2x 1
x 5
2
Defrosting Meat In Exercises 22–24, use the following information.
According to one cookbook, you should always defrost meat in the original
wrappings on a refrigerator shelf. You should allow 5 hours for each pound, less
for thinner cuts.
22. Write and graph an inequality that represents the time t (in hours) and the
number of pounds p of meat being defrosted. Use t on the vertical axis
and p on the horizontal axis.
23. What are the coordinates of a 2-pound roast that has been defrosting for
12 hours?
24. Is it possible that the roast in Exercise 23 is completely defrosted? Explain
your answer.
Fundraiser In Exercises 25–27, use the following information.
An environmentalist group is planning a fundraiser. The group wants to purchase
caps and T-shirts with their logo on them and sell them at a profit. They
can buy caps for $3 each and T-shirts for $5 each. They have $800 to spend.
25. Write and graph an inequality that represents the numbers of caps x and
T-shirts y that the group can buy.
26. Suppose the group purchased 50 caps and 150 T-shirts. What point on
the coordinate plane represents this purchase?
27. Is the point in Exercise 26 a solution of the inequality?
1
y ≥ 2
3
Algebra 2 83
Chapter 2 Resource Book
Lesson 2.6

Answer Key
Practice C
1. y
2.
2
2
3. y 4.
1
5. y
6.
1
7. y
8.
1
9. y 10.
1
11. y 12. y
2
1
1
1
1
2
x
x
x
x
x
x
y
1
1
1
y
y
1
1
1
1
1
1
y
y
1
1
1
x
x
x
x
x
x
13. y 14.
17. 18. No.
19.
True/false
Stewarts
50
40
30
20
10
3T 3.50S ≥ 47.50
S
18
15
12
0
0
9
6
3
0
0
y
1
15. y 16. 4x 2y ≤ 92
1
(0, 46)
1
1
(23, 0)
x
10 20 30 40 50
Multiple choice
3 6 9 12 15 18 T
Thompsons
x
x
20. Sample answers: 10 hours at Thompson’s and
10 hours at Stewart’s, 15 hours at Thompson’s and
5 hours at Stewart’s, 5 hours at Thompson’s and 10
hours at Stewart’s
21. 22. y ≥ 2 1
y < 3x 2
3
5x 2
1
y
1
x

Lesson 2.6
LESSON
2.6
Practice C
For use with pages 108–113
84 Algebra 2
Chapter 2 Resource Book
NAME _________________________________________________________ DATE ___________
Graph the inequality in a coordinate plane.
1. x 3 < 5
2. y 2 > 3
3. 3x 2y ≥ 0
4. 4x 7y > 0
5. 2x 3y ≤ 6
6. 4x 3y > 12
7. 3x 2y ≥ 9
8. 5x 3y < 10
9. 7x 4y ≤ 8
10. 6x 5y > 10
11. 4x 3y ≥ 2
12. 8x 9y ≤ 3
13. 2x 3y < 5
14. 4x 3y > 1
15. 3x 5y ≤ 8
Test Scores In Exercises 16–18, use the following information.
A history exam included multiple choice questions that were worth 4 points
each and true/false questions that were worth 2 points each. The highest
score earned by a person in your class was 92.
16. Write an inequality that represents the number of multiple choice
questions and true/false questions that could have been answered correctly
by any member of your class.
17. Graph the inequality.
18. Is it possible that someone answered 20 multiple choice questions and 7
true/false questions correctly?
Babysitting Wages In Exercises 19 and 20, use the following
information.
You earn $3 per hour when you babysit the Thompson children. You earn $3.50
per hour when you babysit the Stewart children. You would like to buy a $47.50
ticket for a concert that is coming to town in 5 weeks.
19. Write and graph an inequality that represents the number of hours you
need to babysit for the Thompson’s and Stewart’s to earn enough money
to buy your concert ticket.
20. Give three possible combinations of babysitting hours that satisfy the
inequality.
Visual Thinking Write the inequality represented by the graph.
21. y
22. y
1
1
x
1
1
x
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice A
1. 2 2. 3 3. 3 4. 2 5. 13 6. 5 7. 4
8. 8 9. 6
10. 5 11. 5 12. 9
13. E 14. B 15. D 16. F 17. C 18. A
19.
fx 0,
5,
12,
18,
y
18
16
14
12
10
8
6
4
2
0 ≤ x ≤ 5
5 < x ≤ 12
12 < x ≤ 18
x > 18
2 4 6 8 10 12 14 16 18 x

Lesson 2.7
LESSON
2.7
Practice A
For use with pages 114–120
96 Algebra 2
Chapter 2 Resource Book
NAME _________________________________________________________ DATE ___________
Evaluate the function for the given value of x.
1. 2. 3. 4. f 1
3, if x ≤ 0
fx 2, if x > 0
x 5, if x ≤ 3
gx 2x 1, if x > 3
f2
f4
f0
5. g7
6. g0
7. g1
8. g3
9. h4
10. h2
11. h1
12. h6
Match the piecewise function with its graph.
13.
x 4, if x ≤ 1
fx 3x, if x > 1
14.
x 4, if x ≤ 0
fx 2x 4, if x > 0
15.
16.
2x 3, if x ≥ 0
fx x 4, if x < 0
17.
3x 1, if x ≥ 1
fx 5, if x < 1
18.
A. y
B. y
C.
4
D. y
E. y
F.
2
2
4
x
x
19. Amusement Park Rates The admission rates at an amusement park are as
follows.
Children 5 years old and under: free
Children over 5 years and up to (and including) 12 years: $5.00
Children over 12 years and up to (and including) 18 years: $12.00
Adults: $18.00
Write a piecewise function that gives the admission price for a given age.
Graph the function.
2
2
2
2
x
x
hx 1
2x 4, if x ≤ 2
3 2x, if x > 2
3x 2, if x ≤ 1
fx x 2, if x > 1
3x 1, if x ≤ 1
fx 5, if x > 1
2
2
y
y
2
2
2
Copyright © McDougal Littell Inc.
All rights reserved.
x
x

Answer Key
Practice B
1. 7 2. 1 3. 2 4. 16 5. 2
6. 7 7. 14 8. 7 9. 21 10. 9
24.
2x 2,
fx 1,
x 3,
if x < 1
if x 1
if x > 1
11. 5 12.
5
3
25. C
26. x > 0; C > 0
13. y
14.
y
15. y
16.
17. y
18.
21.
22.
1
1
1
2
1
1
y
1
2
2x 2,
fx x 3,
2x 2,
23. fx x 3,
1
y
1
x
x
x
x
x
19.
20.
if x ≤ 1
if x > 1
if x < 1
if x ≥ 1
1
1
1
1
y
y
2
1
1
y
2
x
x
x
x
75
45
15
2 6 10
27. C 0.05x,
0.08x,
x
if 0 < x ≤ 100,000
if x > 100,000

LESSON
2.7
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ____________
Practice B
For use with pages 114–120
Evaluate the function for the given value of x.
3x 7, if x ≤ 2
fx 6 2x, if x > 2
1. f0
2. f2
3. f4
4.
5. g5
6. g4
7. g3
8.
9. h9
10. h3
11. h6
12.
Graph the function.
13.
3, if x ≤ 4
fx 1, if x > 4
14.
x 3, if x ≤ 0
fx 2x, if x > 0
15.
2x 3, if x ≥ 1
x, if x > 5
16. fx 17. fx 2 18.
3x 1, if x < 1
x, if x ≤ 5
x 1, if x < 0
2x, if x ≥ 1
19. fx x 1, if 0 ≤ x ≤ 2 20. fx 3x, if 2 < x < 1 21.
x 1, if x > 2
x, if x ≤ 2
Write equations for the piecewise function whose graph is shown.
22. y
23. y
24.
1
1
x
3x 5, if x < 5
gx x 3, if x ≥ 5
Tour Bus In Exercises 25 and 26, use the following information.
A company provides bus tours of historical cities. The given function describes
the rate for small groups and the discounted rate for larger groups, where x is the
number of people in your group.
8.95x, if 0 < x ≤ 10
C 7.50x, if x > 10
25. Graph the function.
26. Identify the domain and range of the function.
27. Commission Rate You are employed by a company in which commission
rates are based on how much you sell. If you sell up to $100,000 of merchandise
in a month, you earn 5% of sales as a commission. If you sell
over $100,000, you earn 8% commission on your sales. Write a piecewise
function that gives the amount you earn in commission in a given month
for x dollars in sales.
5
1
1
x
hx 2
3x 1, if x > 3
2x 3, if x ≤ 3
x 4, if x < 2
fx 3 x, if x ≥ 2
fx 1
x, if x > 0
2
2x 3, if x ≤ 0
2, if x ≤ 3
fx 1, if 3 < x < 3
3, if x ≥ 3
1
y
Algebra 2 97
Chapter 2 Resource Book
1
f3
g10
h1
x
Lesson 2.7

Answer Key
Practice C
1. 7 2. 2 3. 6 4. 6 5. 3 6. 1 7. 3
8. 7 9. 8 10. 14 11. 2 12. 7
13. y 14.
y
15. y 16.
17. y 18.
19. y 20.
21.
35
22. f x 33.80
0.20x
if
if
0 ≤ x ≤ 6
x > 6
23. 24. $36.60
Price
y
40
38
36
34
32
1
1
2
3
1
1
2
1
y
1
1
0
0 2 4 6 8 10 12 14x
Letters
x
x
x
x
x
1
y
1
y
1
1
1
y
1
1
1
x
x
x
x
25.
26.
f x
f x x,
x,
x 5,
27. f x x 1,
if x ≥ 0
if x < 0
if x < 3
if x ≥ 3

Lesson 2.7
LESSON
2.7
Practice C
For use with pages 114–120
98 Algebra 2
Chapter 2 Resource Book
NAME _________________________________________________________ DATE ___________
Evaluate the function for the given value of x.
1
3x 5, if x <
fx 2 gx x
2x 1, if x ≥ 1
2
1. f3
2. 3. 4.
5. g3.2
6. g1.8
7. g2.4
8.
9. h1.8
10. h3.1
11. h0.4
12.
f 1
Graph the function.
13.
1
x 3, if x < 2
fx 2x 1, if x ≥
14.
2x, if x < 2
fx x2, if 2 ≤ x ≤ 2
2x, if x > 2
15.
1
2
2
16. f x x 1
17. f x 3x 2
18.
19. f x 2x 3
20. f x 23x 1 4 21.
Engraving In Exercises 22–24, use the following information.
A gift shop sells pewter mugs for $35. They are currently running an engraving
promotion. The first six letters are engraved free. Each additional letter costs $0.20.
22. Write a piecewise model that gives the price of the mug with x engraved
letters.
23. Graph the function.
24. What is the price of a mug with the name Jamie Lynn Krane engraved?
25. Commission Sales A company pays its employees a combination of
salary and commission. An employee with sales less than $100,000 earns a
$15,000 salary plus 3% commission. An employee with sales of $100,000
to $200,000 earns an $18,000 salary plus 4% commission. An employee
who earns more than $200,000 in sales earns a $20,000 salary plus 5%
commission. Write a piecewise model that gives the pay of an employee
with x in annual sales.
26. Absolute value Write the function
f x as a piecewise function.
x
1
y
1
x
3
f 1
hx 3x 2 1
x 1, if x < 1
fx 3x 1, if x > 1
f x 4x
2
f 5
g6.9
h3.1
f x 2x 1 3
27. Absolute value Write the function
f x x 3 2 as a piecewise function.
1
y
1 x
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice A
1. E 2. B 3. C 4. F 5. D 6. A
7. down 8. up 9. up 10. up 11. down
12. down 13. 0, 3
14. 1, 2
15. 3, 5 16. 7, 2 17. 1, 9
18. 3, 0 19. same 20. narrower
21. wider
25.
22. narrower 23. wider 24. wider
Swimsuits sold
600
500
400
300
200
Swimwear
(6, 540)
100
(0, 0)
0
0 2 4 6
(12, 0)
8 10 12
Month
26. $540; month number six

Lesson 2.8
LESSON
2.8
Practice A
For use with pages 122–128
110 Algebra 2
Chapter 2 Resource Book
NAME _________________________________________________________ DATE ___________
Match the function with its graph.
1. 2. 3.
4. 5. 6. fx
A. y
B. y
C.
y
1
4x fx x 4
fx x 4
fx x 4
fx x 4
fx 4x
1
D. y
E. y
F.
3
1
3 x
Tell whether the graph of the function opens up or down.
7. y 3 8. y 3x 1
9.
10. y 4x 1 3
11. y 2x 1 7
12.
x
Identify the vertex of the graph of the given function.
13. 14. 15.
16. 17. y 2x 1 9
18.
y x 7 2
y y 2x 3
x 1 2
Tell whether the graph of the function is wider, narrower, or the
same width as the graph of y x .
19. y x 8
20. y 2x 1
21.
22. y 3x 1 7
23. y 2 x 6 3
24.
Swimwear In Exercises 25 and 26, use the following information.
A sporting goods store sells swimming suits year round. The number of suits
sold can be modeled by the function S 90t 6 540, where t is the
time in months and S is the sales in dollars.
25. Graph the function for 0 ≤ t ≤ 12.
x
26. What is the maximum sales in one month? In what month is the
maximum reached?
1
1
3
1
x
1 x
y
1
y x 1 10
y x 2 4
y x 3 5
y 5x 3
y 1
2x 3 2
1
1
1
y 9
10x 13
Copyright © McDougal Littell Inc.
All rights reserved.
x
x

Answer Key
Practice B
1. up 2. down 3. up 4. 13, 6
5. 4, 7 6. 2, 11 7. wider
8. narrower 9. narrower
10. y
11. y
12. y 13.
14. y
15.
16. y
17.
1
1
1
1
1
18. y 19.
20. y
21. y
1
1
1
2
1
x
1 x
x
x
2 x
x
1
1
1
y
1
1
1
1
y
y
1
1
1
y
x
x
x
x
x
x
22. 23.
24. y 25. 0, 22
26. The home is 22 feet high.
27.
1
y 2x 3 1
y x 2 3
2x 2 1
Number of people served
120
100
80
60
40
20
People Served
0
0 2 4 6 8 10 12
Hours since noon
28. 6.5, 105; the restaurant serves the greatest
number of people, 105, at 6:30 P.M.

LESSON
2.8
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ____________
Practice B
For use with pages 122–128
Tell whether the graph of the function opens up or down.
1. 2. y 4x 1 6
3.
y x 3 5
Identify the vertex of the graph of the given function.
4. y 2x 13 6
5. y 3x 4 7
6.
Tell whether the graph is wider, narrower, or the same width as the
graph of y x .
7.
3
y
5x 3 7
8. y 8x 9 12
9.
Graph the function.
10. 11. 12.
13. 14. 15.
16. 17. 18.
19. 20. 21. y 1
y x 4
y x 4
y x 2 3
y x 1 3
y 2x 3
y x 5
y x 4 5
y 3x 1 2
y 2x 7 4
1
y
2x 2
2
y x
3 2 1
x
2 1 2
Write an equation of the graph shown.
22. 23. 24.
1
y
1
A-Frame Home In Exercises 25 and 26, use the following
information.
The roof line of an A-frame home follows the path given by
Each unit on the coordinate plane represents one foot.
25. Find the vertex of the graph.
x
26. What does the y-value of the vertex tell us about the home?
y 11
6 x 22.
Fine Dining In Exercises 27 and 28, use the following information.
An exclusive restaurant is open from 3:00 P.M. to 10:00 P.M. Each evening, the
number of people served S increases steadily and then decreases according to
the model S 30t 6.5 105 where t 0 represents 12:00 P.M.
27. Graph the function.
28. Find the vertex of the graph. Explain what each coordinate of the vertex represents.
1
y
1
x
y 2
x
3 2 9
y 1
x
5 2 11
y 5
2x 1 3
Algebra 2 111
Chapter 2 Resource Book
5
y
1
5
y
1 x
x
Lesson 2.8

Answer Key
Practice C
1. down 2. up 3. down 4.
5.
9. narrower
6. 7. wider 8. wider
10. y 11. y
2
3 , 6
3
2, 5
8 , 1
12. y 13.
14. y 15.
16. y 17.
1
18. y 19.
1
1
1
1
1
1
x
1 x
1 x
x
1 x
1
1
y
1
1
1
y
1
2
1
y 2 x
y
y
1
1
x
x
x
x
x
20. y 21.
22. y
23.
1
24. y 25.
26. y
27.
1
1
1
2
y 3 x
y 5x 4
y 2x 3
1
1
1
y 3x 3 2
50t 2 200,
28. f x 100t 5 350,
50t 9 400,
29. f x 1.2x 450
x
x
x
x
y 2x 3
y 4x 2
1
y
y 2x 4 1
y 4x 5 1
if
if
if
1
1
1
2
y
y
y
1 x
x
1 x
2 x
0 ≤ t < 3
3 ≤ t < 6
6 ≤ t ≤ 10

Lesson 2.8
LESSON
2.8
Practice C
For use with pages 122–128
112 Algebra 2
Chapter 2 Resource Book
NAME _________________________________________________________ DATE ___________
Tell whether the graph of the function opens up or down.
1. 2. y 3 3. y 4 2x 3
1
y 1 2x 1
2 4
3x
Identify the vertex of the graph of the given function.
4. 5. y 6.
1 3
y 3x 2 5
x 1
Tell whether the graph is wider, narrower, or the same width as the
graph of
7. 8. y 9.
5
y 3 1
6x 2
y x .
1 4
3x
Graph the function.
10. y 2x 1 4
11. y 3x 3 2
12.
13.
1
y
2x 3 1
14. y 1
3x 2 3
15.
3
2
16. y x 1
17. y 2.5x 1.32.4 18.
3
y 6 4 5
2 3 x
y 4 7
6x 3
y 4 5x 2
2
1
y x
y 1.8x 2.2 1.6
Graph the function by making a table and plotting points. Then write a
function of the form that has the same graph.
19. 20. 21.
22. 23. 24.
25. 26. 27. y 22x 10 1
y 3x 9 2
y y 2x 3
2x 8 1
y 4x 2
y y y 2x 6
5x 20
3x
y 2x y ax h k
28. Company’s Profit The profit for a company
from 1988 to 1998 is modeled by the graph.
The profit is measured in thousands of dollars
and t 0
corresponds to 1988. Write a
piecewise function that represents the profit.
Profit (thousands of dollars)
P
450
400
350
300
250
200
150
100
50
0
0
1 2 3 4 5 6 7 8 9 t
Years since 1988
8
2
3
29. Pyramids of Egypt The largest pyramid
included in the first wonder of the world is
Khufu. It stands 450 feet tall and its base is
755 feet long. Imagine that a coordinate
plane is placed over a side of the pyramid.
In the coordinate plane, each unit represents
one foot and the origin is at the center of the
pyramid’s base. Write an absolute value
function for the outline of the pyramid.
450 ft
755 ft
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Review and Assessment
Test A
1. y
2.
1 (3, 1)
3, 1
infinitely many solutions
3. y 4. 2, 0 5. 3, 9
no solution
6. 6, 0
7.
8. y
9.
10. minimum of 0 at 0, 0;
maximum of 4 at 4, 0
11. minimum of 16at
4, 1;
maximum of 14 at 2, 6
12. 13.
x
1
y x 4
z
4
1
(1, 0, 1)
14. 15.
4
x 1
2
y
x
x
x
1
y
1 x 0
x
y
1
1
y x 2
1
z
y
1
x
x 3
y 2
x
y 4
x
(3, 4, 2)
y
x
z
(6, 0, 0)
(0, 0, 6)
(0, 6, 0)
(2, 0, 0)
16. f x, y x y 9; 1 17.
18. 1, 2, 1 19. 5 20. 14
y
x
z
(0, 0, 4)
2, 3, 4
(0, 4, 0)
y

CHAPTER
3
NAME _________________________________________________________ DATE
Chapter Test A
For use after Chapter 3
____________
Graph the linear system and tell how many solutions it has.
If there is exactly one solution, estimate the solution and
check it algebraically.
1. x y 4
2. y 3x
3.
1
x y 2
y
Solve the system using any algebraic method.
4. x y 2
5. y 3x
6. 5x 2y 30
1
1
3x 2y 6
y ≤ 2
y
1
Find the minimum and maximum values of the objective
function subject to the given constraints.
10. Objective function:
Constraints:
y ≤
11. Objective function: C 5x 4y
Constraints: x ≤ 2
1
C x y
x ≥ 0
y ≥ 0
2x 2
x ≥ 4
y ≥ 1
y ≤ 6
Copyright © McDougal Littell Inc.
All rights reserved.
x
Graph the system of linear inequalities.
7. x > 3
8. y > x 4 9. x y ≤ 2
x
2y 6x
1
x y 12
x ≤ 1
1
y
y
1
1
x
x
1
y 1
2x 2
y 1
2x 2
x 2y 6
x ≥ 0
y ≥ 4
y
1
4
y
4
x
x
Answers
1. Use grid at left.
2. Use grid at left.
3. Use grid at left.
4.
5.
6.
7. Use grid at left.
8. Use grid at left.
9. Use grid at left.
10
11.
Algebra 2 93
Chapter 3 Resource Book
Review and Assess

Review and Assess
CHAPTER
3
CONTINUED
NAME _________________________________________________________ DATE ____________
Chapter Test A
For use after Chapter 3
Plot the ordered triple in a three-dimensional coordinate
system.
12. 1, 0, 1
13. 3, 4, 2
Sketch the graph of the equation. Label the points where
the graph crosses the x-, y-, and z-axes.
x
x
z
16. Write the linear equation x y z 9 as a function of x and y.
Then evaluate the function when x 3 and y 5.
Solve the system using any algebraic method.
17. 2x 3y 2z 3
18. x 2y 3z 8
2y 3z 6
z 4
z
19. Compact Discs At a music store, compact discs cost $14.95 each,
but are now on sale for $12.95 each. If you bought ten compact
discs in the past month, and spent a total of $139.50, how many
did you buy on sale?
20. Ages You are 4 years older than your brother. Two years ago, you
were 1.5 times as old as he was. What is your present age?
94 Algebra 2
Chapter 3 Resource Book
y
14. x y z 6
15. 2x y z 4
y
x
x
z
2x 3y z 3
2x y 2z 2
z
y
y
12. Use graph at left.
13. Use graph at left.
14. Use graph at left.
15. Use graph at left.
16.
17.
18.
19.
20.
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Test B
1. y
2.
1, 3
3. y
4.
5.
1
6.
infinitely many solutions
7. y
8.
9.
1
1
1
x 0
1
y
1
1
y 2 x
2
1
10. minimum of 0 at 0, 0;
maximum of 30 at 0, 6
11. minimum of 0 at 0, 0;
maximum of 17 at 3, 4
12. z 13.
(3, 4, 2)
y x 3
y 4 2x
x
(1, 3)
1
x
x
x
y 0
x
y
1, 2
1
y
1
x 3
x
1
1, 3
2, 1
1, 6
z
y
1
(1, 2)
y 2
x
x
y
(4, 1, 2)
14. z
15.
x
(10, 0, 0)
(0, 0, 5)
(0, 10, 0)
(1, 0, 0)
16. f x, y 2x 3y 6; 7
17. 1, 2, 3 18. (7, 6, 3)
19. daytime $6; evening $8 20. 360
y
x
z
(0, 0, 4)
(0, 2, 0)
y

CHAPTER
3
NAME _________________________________________________________ DATE
Chapter Test B
For use after Chapter 3
____________
Graph the linear system and tell how many solutions it has.
If there is exactly one solution, estimate the solution and
check it algebraically.
1. y 3x
2. y x 1
3. x 2y 2
y x 4
y x 3
3x 6y 6
Solve the system using any algebraic method.
4. x y 2
5. y 2x 5 6. 2x y 8
y 2x 5
y x 3
2x y 4
Graph the system of linear inequalities.
7. x 2y ≥ 4 8. y ≤ 2
9. x ≥ 0
x y ≤ 3
x > 3
y ≥ 0
2x y ≤ 4
1
y
1
1
y
1
x
1
y
1
Find the minimum and maximum values of the objective
function subject to the given constraints.
10. Objective Function: C 4x 5y
Constraints: x ≥ 0
y ≥ 0
x y ≤ 6
11. Objective Function: C 3x 2y
Constraints: x ≥ 0
y ≥ 0
x 3y ≤ 15
4x y ≤ 16
Copyright © McDougal Littell Inc.
All rights reserved.
x
1
y
1
x
x
1
y
1
1
y
1
x
x
Answers
1. Use grid at left.
2. Use grid at left.
3. Use grid at left.
4.
5.
6.
7. Use grid at left.
8. Use grid at left.
9. Use grid at left.
10.
11.
Algebra 2 95
Chapter 3 Resource Book
Review and Assess

Review and Assess
CHAPTER
3
CONTINUED
NAME NAME _________________________________________________________ DATE ____________
Chapter Test B
For use after Chapter 3
Plot the ordered triple in a three-dimensional coordinate
system.
12. 3, 4, 2
13. 4, 1, 2
Sketch the graph of the equation. Label the points where the
graph crosses the x-, y-, and z-axes.
x
16. Write the linear equation 2x 3y z 6 as a function of x and y.
Then evaluate the function when x 2 and y 3.
Solve the system using any algebraic method.
17. x 4y z 12
18. x y 2z 5
y 3z 7
z 3
z
x
19. Earning money You work at a grocery store. Your hourly wage is
greater after 6:00 P.M. than it is during the day. One week you work 20
daytime hours and 20 evening hours and earn $280. Another week you
work 30 day time hours and 12 evening hours and earn a total of
$276. What is your daytime rate? What is your evening rate?
20. Telethon During a recent telethon, people pledged $25 or $50.
Twice as many people pledged $25 as $50. Altogether, $18,000 was
pledged. How many people pledged $25?
96 Algebra 2
Chapter 3 Resource Book
z
y
14. x y 2z 10
15. 4x 2y z 4
y
x
z
x
x 2y z 8
2x 3y z 1
z
y
y
12. Use grid at left.
13. Use grid at left.
14. Use grid at left.
15. Use grid at left.
16.
17.
18.
19.
20.
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Test C
1. y
2.
no solution
3. y infinitely many solutions
4. 0, 5
5. infinitely many solutions 6. no solution
7. y
8.
y
9. x 2 y 10. minimum of 0 at
0, 0;
1
maximum of 12 at
3, 0
11. minimum of 46 at 3, 4; no maximum
12. 13.
x
1
z
1
2, 1
1
1
(2, 1)
1
1
x 0
1 x
y 2x 3
(2, 1, 4)
y 0
x
y
x
x
x
z
1
1
y x 1
y
2
3
y x 2
2
2
x
x
y
(3, 4, 4)
14. 15.
(4, 0, 0)
x
z
(0, 4, 0)
(0, 0, 4)
(0, 4, 0)
16. f x, y 2x 3y 12; 1
17. 2, 3, 4 18. 1, 2, 2
19. 30 postcard and 20 letter 20. 36
y
x
z
(0, 0, 4)
(4, 0, 0)
y

CHAPTER
3
NAME _________________________________________________________ DATE
Chapter Test C
For use after Chapter 3
____________
Graph the linear system and tell how many solutions it has.
If there is exactly one solution, estimate the solution and
check it algebraically.
1. 2x y 5 2. 2x 3y 6 3. 3x y 1
x y 3 3y 2x 3 2y 2 6x
1
y
1
Solve the system using any algebraic method.
4. 3x 2y 10 5. 2x 4y 6 6. 3x 5y 10 0
5x 3y 15
Graph the system of linear inequalities.
7. x ≤ 0
8. x y > 1 9. y ≤ 2x 3
y ≥ 0
1
y
Find the minimum and maximum values of the objective
function subject to the given constraints.
10. Objective function: C 4x y
Constraints: x ≥ 0
y ≥ 0
x y ≤ 3
11. Objective function: C 6x 7y
Constraints: x ≥ 0
y ≥ 0
x 3y ≥ 15
Copyright © McDougal Littell Inc.
All rights reserved.
1
x
x
4x 3y ≥ 24
1
x 2y 3
3x 2y > 4
1
y
y
1
1
x
x
1
y
9x 15y 30
x 2 ≤ 0
1
1
y
1
x
x
Answers
1. Use grid at left.
2. Use grid at left.
3. Use grid at left.
4.
5.
6.
7. Use grid at left.
8. Use grid at left.
9. Use grid at left.
10.
11.
Algebra 2 97
Chapter 3 Resource Book
Review and Assess

Review and Assess
CHAPTER
3
CONTINUED
NAME _________________________________________________________ DATE ____________
Chapter Test C
For use after Chapter 3
Plot the ordered triple in a three-dimensional coordinate
system.
12. 2, 1, 4
13. 3, 4, 4
x
Sketch the graph of the equation. Label the points where
the graph crosses the x-, y-, and z-axes.
16. Write the linear equation 2x 3y z 12 as a function of x and
y. Then evaluate the function when x 4 and y 1.
Solve the system using any algebraic method.
17. 3x 4y 6
18. 3x 2y 2z 3
5x 3z 22
x
3y 2z 1
z
z
19. Stamps Postcard stamps are 20¢ each, while letter stamps are 33¢
each. If you have 50 stamps worth $12.60, how many of each type
do you have?
20. Numbers The sum of the digits of a two-digit number is 9. If the
digits are reversed, the new number is 27 more than the original
number. Find the original number.
98 Algebra 2
Chapter 3 Resource Book
y
14. x y z 4
15. 3x 3y 3z 12
y
x
x
2x 3y 3z 2
3x 5y z 9
z
z
y
y
12. Use grid at left.
13. Use grid at left.
14. Use grid at left.
15. Use grid at left.
16.
17.
18.
19.
20.
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Cumulative Review
1. commutative property of multiplication
2. inverse property of multiplication
3. associative property of multiplication
4. 47 5. 6 6. 7. 10
8. 9.
10. 10x 11. 22x 32y
12. 3 13. 4 14. 2 15. 2 16. 4 17. 15
18.
8 x
x
19.
3x 6
2
20.
x 18
3
2 10x 13x 54
x 28
2 45
3x 16
21. 22. 23.
24. 25. x < 11
30 6x
5
x 8
x
x 12
x
n < 7
9
5 6 7 8 9
26. x ≥ 8
27.
6 7 8 9 10
28. x < 2 or x > 7 29.
1 2 3 4 5 6 7 8
30. yes 31. yes 32. no 33. Line 2
34. Line 2 35. Line 1 36. Line 2
37.
39.
41.
38.
40.
42.
43. 44.
45. 46. y
47. y 4x 20 48. y 3x 7
49. 50.
2
y
5
3x 3
2
m m 9, b 0
y 5x 7 y 4
7
3x 3
1
m
8 , b 2
3
m
m 0, b 10
2 , b 7
2
m 4, b 6
3 , b 5
1
y
1
x
11
9
3 2 1 0 1
x ≥ 1
1 0 1 2 3
3 < x < 7
4 2 0 2 4 6 8
y
1
1
x
51. 52.
53. 54.
55. 7, 1; down; 56. 3, 2; up;
same width same width
2
y
1
2
y
1
2
57. 0, 2; down; 58. 2, 0; up;
same width same width
1
y
y
1
2
x
x
x
x
1
1
y
y
1
1
1
y
1
1
y
x
1
x
x
x

Answer Key
59. 0, 2;
up; 60. 0, 4; down;
narrower wider
61. 62.
1
1
y
63. 64.
1
65. 66.
2
1
y
y
y
1
1
2
67.
infinitely many solutions of the form
x, 2, x 2
68. infinitely many solutions of the form
x, 2 x 5, x 5
69. infinitely many solutions of the form
3z 17, 4z 27, z
70. 34,509 sq ft 71. 3460 sq mi
x
x
x
x
1
1
1
y
2
y
y
1
2
1
y
x
x
x
1 x

Review and Assess
CHAPTER
3 Cumulative Review
NAME _________________________________________________________ DATE ____________
For use after Chapters 1–3
Tell what property the statement illustrates. (1.1)
1. 3 4 4 3
2. 1
3.
Select and perform an operation to answer the question. (1.1)
4. What is the sum of 55 and 8?
5. What is the difference of 2 and 8?
6. What is the product of 9 and 5?
7. What is the quotient of 15 and
Simplify the expression. (1.2)
8. 7x 9. 3x 8 52x 6
10. 11. 84x 2y 25x 8y
2 5x 9 3x2 2x 7
4x 2 x 7 32x 2 x
Solve the equation. Check your solution. (1.3)
12. 5x 7 22
13. 3a 5 7a 21
14. 2x 8 2x 12
15. 32x 8 4x 2 4 16.
9
2x 2 3x 4
17.
1 5 2 5
2x 3 3x 6
Solve the equation for y. (1.4)
18. x xy 8
19. 6x 4y 12
20. x 3y 18
21. 6x 5y 30 0
22. xy 8 x
23. x 12 xy
Solve the inequality. Then graph the solution. (1.6–1.7)
24. 3n 4 < 9
25. 4 4x > 53 x
26.
1
2x 8 ≥ 12
27. 3x 7 ≥ 10
28. 4x 2 < 6 or 3x 1 > 22 29. 5 < 2x 1 < 15
Use the vertical line test to determine whether the relation is a function. (2.1)
30. 31. 32.
(1, 6)
(3, 5)
2
(1, 1)
2
(3, 4)
Tell which line is steeper. (2.2)
33. Line 1: through 3, 5 and 0, 1 34. Line 1: through 4, 5 and 8, 5
Line 2: through 1, 10 and 6, 14
Line 2: through 6, 3 and 8, 4
35. Line 1: through 2, 3 and 3, 6
36. Line 1: through 0, 0 and 4, 2
Line 2: through 0, 7 and 2, 9
Line 2: through 3, 2 and 4, 4
104 Algebra 2
Chapter 3 Resource Book
y
(5, 5)
x
4 1
4
1
y
1
x
2 3 5 2 3 5
1
3
2?
y
1
Copyright © McDougal Littell Inc.
All rights reserved.
x

CHAPTER
3
CONTINUED
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ____________
Cumulative Review
For use after Chapters 1–3
Find the slope and y-intercept of the line. (2.3)
37. 38. y 39. y 10
40. 3x 2y 14
41. x 8y 16
42. 9x y 0
2
y 4x 6
3x 5
Write an equation of the line that passes through the given point
and has the given slope. (2.4)
43. 44. 45.
46. m 47. 5, 0, m 4
48. 2, 1, m 3
2
m
4, 1,
2
0, 7, m 5
6, 4, m 0
5, 1, 3
Graph the inequality in a coordinate plane. (2.6)
49. x ≤ 3
50. 2y > 10
51. y ≥ 3x 2
52. y < 4 2x
53. 3x 4y > 12
54.
2 1
3x 2y > 1
Graph the absolute value function. Then identify the vertex, tell
whether the graph opens up or down, and tell whether the graph
is wider, narrower, or the same width as the graph of (2.8)
55. 56. 57.
58. 59. f x 2x 2
60.
f x x 2
f x y x .
f x x 7 1
x 3 2
Graph the system of linear inequalities. (3.3)
61. y ≥ 5
62. x y ≥ 4
63. 5x 3y ≤ 6
x ≤ 2
64. y > x 5
65. x y ≥ 5
66. x > 6
y < 2x 1
Solve the system using either the linear combination method or
the substition method. (3.6)
67. x 2y z 2
68. x y z 0
69. x y z 10
2x 3y 2z 10
x 3y z 4
3
2x y ≤ 3
3x y ≤ 8
5x 3y z 10
x y z
70. Size of House In 1997, a house was reported to have sold for $98.8 million.
At $2,863 per square foot, it was the world’s most expensive house.
How big was the house to the nearest square foot? (1.1)
71. Surface Area Lake Superior, the largest of the Great Lakes, has a surface
area of 20,600 square miles. This is 3300 square miles larger than five
times the size of Lake Ontario, the smallest. What is the surface area of
Lake Ontario? (1.5)
f x 1
f x x 2
x 4
2x 4y > 8
x y ≥ 0
2
2x y 2z 7
6x 4y 2z 6
Algebra 2 105
Chapter 3 Resource Book
Review and Assess

Answer Key
Practice A
1. no solution 2. infinitely many solutions
3. one solution 4. 1, 5is
not a solution.
5. 2, 3is
not a solution.
6. 3, 4 is a solution.
7. 1, 3 is a solution.
8. 2, 1is
not a solution.
9. 0, 4is
a solution.
10. y
11.
no solution one solution
12. y
13.
infinitely many
solutions
no solution
14. y
15. y
infinitely many one solution
solutions
16. y
17.
1, 2
1
1
1
1
1
1
1
(1, 2)
x
x
x
x
4
y
1
5, 2
4
1
1
y
y
1
1
(5, 2)
x
x
x
x
18. y 19.
2, 6
20. 21.
1, 4
22. y
23.
infinitely many solutions
24. y
25.
1
1, 2
(2, 6)
1
1 y
1
1
1
1
(1, 2)
5
(1, 4)
x
x
x
x
3, 4
no solution
2, 0
y
1
y
1
1
x y 42
16x 12y 568
16, 26
1
2
(3, 4)
y
2
(2, 0)
x
x
x

Lesson 3.1
LESSON
3.1
14 Algebra 2
Chapter 3 Resource Book
NAME DATE
The graph of a system of two linear equations is shown. Tell
whether the linear system has infinitely many solutions, one
solution, or no solution.
1. y
2. y
3.
Check whether the ordered pair is a solution of the system.
7. 1, 3
8. 2, 1
9. 0, 4
x 2y 5
2x 5y 1
3x 4y 16
2x y 1
3x 2y 4
2x y 4
Graph the linear system and tell how many solutions it has.
10. 2x y 1
11. 4x y 3
12. 5x y 2
4x 2y 8
2x y 1
10x 2y 4
13. x 2y 6
14. 2x 3y 3
15. 3x y 2
3x 6y 2
6x 9y 9
5x 2y 2
Graph the linear system and estimate the solution. Then check the
solution algebraically.
16. x y 3
17. x y 7
18. y 3x
2x y 4
x y 3
x 2y 14
19. x 3
20. y 4
21. x y 4
x y 7
2x y 2
x y 5
22. x y 1
23. 2x y 4
24. 3x 2y 1
2x 2y 2
3x 6
x y 3
25. Amusement Park A group of 42 people go to an amusement park. The
admission fee for adults is $16. The admission fee for children is $12. The
group spent $568 to get into the park. How many adults and how many
children were in the group? Use the verbal model to write and solve a
system of linear equatoins.
Number
of adults
Price for
adults
1
4. 1, 5
5. 2, 3
6. 3, 4
3x y 2
3x 5y 2
4x 7y 16
4x 2y 5
2x 3y 13
6x y 14
Practice A
For use with pages 139–145
1
x
Number
of children
Number
of adults
Total in
the group
Price for
children
1
1
Number
of children
x
Total cost
of admission
1
y
1
Copyright © McDougal Littell Inc.
All rights reserved.
x

Answer Key
Practice B
1. 2, 1is
a solution.
2. 3, 5is
not a solution.
3. 1, 2is
not a solution.
4. B; one solution 5. C; no solution
6. A; infinitely many solutions.
7. y
8.
3, 0
1
9. y 10.
3, 1
11. y 12.
(2, 2)
2, 2
13. y
14.
1, 1
1
1
(1, 1)
15. y no solution
1
1
(3, 1)
1
1
(3, 0)
x
1
1
x
x
3 x
x
4, 2
2, 5
0, 4
infinitely many solutions
16. There were 340 $38 tickets sold and 200 $56
tickets sold.
1
1
y
y
1
1
5
1
(4, 2)
y
y
x
5 (2, 5)
(0, 4)
2
x
x
x
17.
19.
R 5600t
18.
Thousands of dollars
y
500
400
300
200
100
Cost and Revenue
Cost
C 3800t 110,000
Revenue
0
0 10 20 30 40 50 60 70 80 90 x
Time (months)
20. Somewhere between 61 and 62 months.

LESSON
3.1
Copyright © McDougal Littell Inc.
All rights reserved.
NAME DATE
A. y
B. y
C.
1
1
Practice B
For use with pages 139–145
Check whether the ordered pair is a solution of the system.
1. 2, 1
2. 3, 5
3. 1, 2
x 2y 4
3x 7y 34
4x 5y 6
3x y 5
5x 2y 5
7x y 5
Match the linear system with its graph. Tell how many solutions
the system has.
4. 2x y 9
5. 3x 2y 4
6. x 2y 6
3x y 1
6x 4y 10
2x 4y 12
x
Graph the linear system and estimate the solution. Then check the
solution algebraically.
7. x 2y 3
8. 2x 3y 2
9. 3x y 8
7x 3y 21
5x 2y 16
2x 5y 1
10. 3x 5y 19
11. 4x 3y 14
12. x 7y 28
5x 2y 20
2x 5y 14
9x 2y 8
Graph the linear system and tell how many solutions it has. If
there is exactly one solution, estimate the solution and check it
algebraically.
1
13. 3x 5y 2
14. 2x 2y 5
15. 7x 2y 1
4x 2y 2
x 4y 10
14x 4y 8
16. Ballet Performance A ballet company says that 540 tickets
have been sold for its upcoming performance of Swan Lake.
Tickets for the Orchestra Center and Front Balcony seats are
$56. Tickets for the Left and Right Orchestra and Balcony
seats are $38. The company has sold $24,120 in tickets. How
many $56 and $38 seats were sold?
Break-Even Analysis In Exercises 17–20, use the following information.
You purchase a skateboard shop for $110,000. You estimate that monthly costs
will be $3800. The monthly revenue is expected to be $5600.
17. Let R represent the revenue you bring in
during the first t months. Write a linear
model for R.
19. Graph the revenue and cost equations on the
same coordinate plane.
2
2
x
Orchestra
Left
1
Algebra 2 15
Chapter 3 Resource Book
y
1
Orchestra
Center
Front Balcony
Balcony
x
Orchestra
Right
18. Let C represent your costs, including the
purchase price, during the first t months.
Write a linear model for C.
20. How many months will it take until revenue
and costs are equal (the “break-even point”)?
Lesson 3.1

Answer Key
Practice C
1. is a solution. 2. is a solution
3. is not a solution.
4. y
5.
1, 3
6. y
7.
1, 1
8. y
9.
1 , 0 2
10. y 11.
1 1
, 2
12. y
13.
1 3
2 , 2
1, 1
1 3
2 ,
4
2
2
2
1
1
( , 1
2 )
1
(1, 3)
4
1
1
1
4
1
( , 1 3
2 2)
1
(1, 1)
( , 0)
1
2
1
x
x
x
x
x
1 3
3 ,
2, 5
3, 1
4
0, 3
(2, 5)
2
, 1
3
8 9
5 , 5
8
( , 2 1
3 2)
2
2
1
( 0, )
3
4
( , 8 9
5 5)
y
y
y
1
2
1
(3, 1)
y
1
1
y
x
1 x
x
x
x
14. y
15.
16. y
17.
infinitely many
solutions
5, 0
infinitely many
solutions
18. y
19. consistent and
dependent
1
20. inconsistent
1 x 21. consistent and
independent
no solution
In Exercises 22–24, sample answers are given.
22. 23.
24.
25. The lines look parallel, but one has a slope of
19
and the other has a slope of So, they are not
20
parallel and therefore intersect.
26.
P C 30,
Comparing Department
Store Sales
C 50
P
P 0.70C, , C 50
140
120
You must buy less
100
than $100.
80
.
x y 6
2x 2y 8
x y 4
2x 2y 8
x y 4
2x y 6
9
10
27.
1
1
11 5 , 2 5
1
1
( , 11
5
)
x 2
5
(5, 0)
x
Sale price (dollars)
60
40
4x 8y 100
x y 20
15 multiple-choice, 5 essay
1 y
P 0.70C
20
P C 30
0
0 20 40 60 80 100 120 140 C
Regular price (dollars)
1
1
y
1
x
x

Lesson 3.1
LESSON
3.1
16 Algebra 2
Chapter 3 Resource Book
NAME DATE
Practice C
For use with pages 139–145
Check whether the ordered pair is a solution of the system.
1, 1
2
1. 2. 3.
3x 4y 5
4x 6y 1
Graph the linear system and estimate the solution. Then check the
solution algebraically.
4. x 2y 7
5. 2x 3y 11
6. 4x 5y 9
3x y 6
3x 2y 16
2x 3y 1
7. 3x 5y 4
8. 4x 5y 2
9. 3x 4y 3
x 2y 1
8x y 4
x 8y 6
10. 4x 4y 3
11. 3x 2y 3
12. 4x 2y 1
2x 8y 1
6x 2y 3
3x 3y 3
Graph the linear system and tell how many solutions it has. If
there is exactly one solution, estimate the solution and check it
algebraically.
13. 4x 3y 1
14. 2x y 4
15. x y 6
3x 6y 6
x 2y 3
2x 2y 12
16. 3x 4y 15
17. 2x y 4
18. 8x 2y 10
2x 3y 10
4x 2y 8
4x y 5
Determine whether the following systems are consistent and
independent, consistent and dependent, or inconsistent.
19. 3x 7y 5
20. 3x y 3
21. 4x 3y 6
6x 14y 10
12x 4y 1
6x 8y 8
22. Write a system of equations that has no solution.
23. Write a system of equations that has infinitely many solutions.
24. Write a system of equations that has exactly one solution.
25. The graph of the system
9x 10y 3
19x 20y 34
is shown to the right. Explain why
there is a solution to this system.
1 3
3 ,
26. Bargain Hunting A local department store
is having a coupon sale in which you receive
$30 off any purchase over $50. A competing
store is offering 30% off all purchases over
$50. Write and graph two equations that
describe the prices at both stores. When does
the store offering the coupon sale have a
better deal than their competitor?
8
3x 8y 2
9x 16y 9
2
1 3
2 ,
2x 6y 8
5x y 4
27. Test Questions A history test is to have 20
questions. The teacher uses multiple choice
and essay questions. The multiple choice
questions are worth 4 points each. The essay
questions are worth 8 points each. The test has
a total of 100 points. Write a system of
equations to determine how many of each type
of question appears on the exam.
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice A
1. 2. 3. 4.
5.
8.
6.
9.
7.
10.
11. 12. 13.
14. 15. 16.
17. 18. 19. 20.
21. 22. 23.
24. 25. 2, 26. 4, 0
27. 3, 18 28. 70x 8y 226,
280x 70y 980; The boosters should rent
3 buses and 2 vans.
2
7
46
37 , 21
37
80
4
31 , 31 61
1, 4
2, 2 5, 4 3, 7 0, 0
1, 2
6
23 , 23
1
1, 3
0, 4 3, 2 2, 1
1
6, 2 2 , 3
97
5
11 , 11 23
7 , 6 7
17 2, 1
3, 0 1, 1 2, 5
7, 5 3, 4 , 9
7 7

Lesson 3.2
LESSON
3.2
28 Algebra 2
Chapter 3 Resource Book
NAME DATE
Solve the system using the substitution method.
7. 3x y 6
8. 4x 6y 8
9. x 7y 12
2x 4y 10
3x y 9
2x 8y 14
Solve the system using the linear combination method.
10. 4x 2y 2
11. 7x 3y 12
12. 6x 7y 4
5x 2y 11
7x 2y 8
x 7y 17
13. 6x 3y 15
14. x 2y 7
15. 2x y 2
6x 5y 7
x 2y 5
2x 5y 16
Solve the system using any algebraic method.
16. x 2y 7
17. x 3y 8
18. x y 9
3x 5y 17
4x 3y 2
x y 1
19. x y 4
20. 3x 4y 0
21. 2x y 0
x 2y 17
9x 4y 0
2x y 4
22. 2x 5y 4
23. 5x 7y 12
24. 3x 4y 6
3x 4y 9
3x 2y 8
4x 7y 1
25. 4x 7y 10
26. 2x 3y 8
27. 6x y 0
3x 7y 4
x 5y 4
15x 2y 9
28. Band Competition The band boosters are organizing a trip to a national
competition for the 226-member marching band. A bus will hold 70 students
and their instruments. A van will hold 8 students and their instruments.
A bus costs $280 to rent for the trip. A van costs $70 to rent for the
trip. The boosters have $980 to use for transportation. Use the verbal
model below to write a system of equations whose solution is how many
buses and vans should be rented. Solve the system.
Students
per bus
Price
per bus
Practice A
For use with pages 148–155
1. x 3y 5
2. 2x y 6
3. 3x 7y 10
2x 3y 1
3x 5y 9
x 4y 5
4. 5x 2y 20
5. x y 12
6. 4x y 8
6x y 7
2x 3y 1
x 3y 9
Number
of buses
Number
of buses
Students
per van
Price
per van
Number
of vans
Number
of vans
Students
on trip
Cost of
transportation
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice B
1.
5.
9.
12.
15.
2. 3. 4.
6. 7. 8.
10. 11.
13. 14.
16. no solution 17.
18. infinitely many solutions 19.
20. 21. 22. 1993
full size bags and 84 collapsible bags.
23. Forty
24. You
drove 3 hours and your friend drove 2 hours.
35
4, 2
8
2, 7 11 , 11
5
2, 4, 0
1
3, 18
3 , 2
2
1, 5
7
2
3, 7 2, 2
3 , 7 2
1
2, 4 , 1 2 5
5, 3
1
6, 9 , 2 2
1
2, 1
3, 2 2 , 4

LESSON
3.2
Copyright © McDougal Littell Inc.
All rights reserved.
NAME DATE
Solve the system using the substitution method.
Solve the system using the linear combination method.
7. 5x y 6
8. 2x 3y 4
9. 4x y 5
5x 3y 22
8x 3y 1
4x 3y 9
10. 2x 7y 10
11. 3x 4y 12
12. 5x 2y 15
3x 2y 10
6x 2y 11
7x 5y 18
Solve the system using any algebraic method.
13. 4x 7y 10
14. 2x 3y 8
15. 6x y 0
3x 7y 4
x 5y 4
15x 2y 9
16. 6x 3y 1
17. 3x 8y 1
18. 4x 16y 4
4x 2y 7
6x 2y 11
3x 12y 3
19. 2x 8y 8
20. 5x y 17
21. 3x 9y 3
3x 2y 16
3x 2y 8
x 8y 9
22. CDs and Cassettes For 1990 through 1998, the manufacturer’s
shipments for audio cassettes, A (in millions), and compact discs, C
(in millions), can be modeled by the equations
A 31.8t 322
C 42.8t 110
Audio cassette shipments
Compact disc shipments
where t is the number of years since 1990. In what year did the number of
compact discs shipped surpass the number of audio cassettes shipped?
23. Golf Bags A sporting goods store receives a shipment of 124 golf bags.
The shipment includes two types of bags, full-size and collapsible. The
full-size bags cost $38.50 each. The collapsible bags cost $22.50 each.
The bill for the shipment is $3430. How many of each type of golf bag
are in the shipment?
24. Vacation Trip You and a friend share the driving on a 280 mile trip.
Your average speed is 58 miles per hour. Your friend’s average speed is
53 miles per hour. You drive one hour longer than your friend. How many
hours did each of you drive? Use the following verbal model.
Your speed
Your time
Practice B
For use with pages 148–155
1. 2x 5y 9
2. 3x 4y 1
3. 6x 2y 11
3x y 7
x 2y 1
4x y 6
4. x 2y 1
5. 4x 3y 3
6. 10x 16y 17
5x 7y 4
2x y 3
x y 3
Your time
Friend’s time
Friend’s speed
1 hour
Friend’s time
Total distance
Algebra 2 29
Chapter 3 Resource Book
Lesson 3.2

Answer Key
Practice C
1. 2. 3.
4. 5. no solution 6. infinitely many
solutions 7. 8. 9.
10. infinitely many solutions 11.
12.
15.
13. 14.
16. 17. 3
10, 20 8, 5
1
5, 6 3, 4
5 , 1
4, 3
2, 5 1, 3
1, 5
3, 2 1, 4 2, 3
6, 2
2 , 1 3
2
2
3
18. 19. 20.
21.
23.
2.3, 0.4 22. 1876
7
3 , 5
6
, 2
14 3 , 0
24. Sample answer: U 20.51t 104.4;
N 24.96t 83.1 25. 4.8, 202.6In
1994 the
United Kingdom and Netherlands both had about
202 computers per 1000 people.
4

Lesson 3.2
LESSON
3.2
30 Algebra 2
Chapter 3 Resource Book
NAME DATE
Practice C
For use with pages 148–155
Solve the system using the substitution method.
1. 2x y 5
2. 4x 2y 2
3. x 3y 8
4x 3y 7
x 3y 13
2x 3y 7
4. 6x 2y 4
5. x 3y 18
6. 4x y 6
1
8x y 3
x 3y 12
x y 2
Solve the system using the linear combination method.
7. 2x 3y 12
8. 7x 2y 1
9. 3x 4y 6
3x 4y 1
8x 4y 8
2x 5y 19
10. 2x 5y 1
11. x 3y 9
12. 4x 6y 4
5
x 2
y 1
Solve the system using any algebraic method.
13. 0.25x 0.5y 12.5
14. 0.75x 0.3y 4.5
15. 0.2x 1.4y 9.4
0.3x 0.5y 13
0.125x 0.4y 1
0.5x 0.7y 1.7
16. 0.8x 2.1y 10.8
17. 5x 4y 4
18.
1.6x 0.7y 7.6
2
1
3x y 4
2x 2y 7
10
19. 6x 9y 1
20. 0.3x 0.2y 1.4
21. 4.2x 2.1y 10.5
2x 4y 5
0.12x 0.8y 0.56
1.4x 1.3y 2.7
22. Labor Force From 1840 to 1990 the percent of the labor force in
farming and non-farming occupations can be modeled by the following
equations where t is the number of years since 1840.
y 0.48t 67.2 farming occupations
y 0.48t 32.9 nonfarming occupations
In what year was the labor force split equally into farming and nonfarming
occupations? Round your answer to the nearest year.
Computers Per Capita Use the table below of the number of computers per
1000 people in the United Kingdom and Netherlands from 1991 through 1995.
Years since 1990, t 1 2 3 4 5
United Kingdom, U 125.7 144.8 164.8 187.4 216.5
Netherlands, N 109.7 131.1 156.9 184.3 214.8
23. Use a graphing calculator to make scatter plots for the data.
24. For each scatter plot, find an equation of the line of best fit.
25. Find the coordinates of the point of intersection. Describe what this point
represents.
1
2
4
3
3
6x 3y 2
5x y 5
6
3x 4y 8
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice A
1. 0, 1is
a solution. 2. 3, 2is
a solution.
3. 5, 2is
not a solution.
4. 0, 0is
not a solution.
5. 1, 1is
not a solution.
6. 1, 2is
not a solution.
7. Answers may vary. Sample: 0, 0
8. Answers may vary. Sample: 1, 2
9. Answers may vary. Sample: 1, 1
10. B 11. A 12. C
13. y 14.
15. y
16.
1
1
1
1
x
x
t 0
t 2
d 65t
17. No; To drive 200 miles at 65 miles per hour,
you would need to drive over 3 hours.
1
y
1
x

Lesson 3.3
LESSON
3.3
42 Algebra 2
Chapter 3 Resource Book
NAME DATE
Give an ordered pair that is a solution of the system.
7. 2x 3y < 5
8. x 3y > 3
9. 5x ≤ 2y
x < 12
y < 8
x < 0
y > 0
Match the system of linear inequalities with its graph.
10. y ≤ x
11. y ≥ x
12. y ≤ x
y ≥ 2
y ≥ 2
y ≤ 2
x ≤ 3
x ≤ 3
x ≤ 3
A. y
B. y
C.
2
1
Tell whether the ordered pair is a solution of the system.
4. 0, 0
5. 1, 1
6. 1, 2
x y ≥ 2
2x y < 1
2x y < 4
x ≥ 0
x y ≥ 2
x y < 1
x > 0
2
y
1
Practice A
For use with pages 156–162
Tell whether the ordered pair is a solution of the system.
1. 0, 1
2. 3, 2
3. 5, 2
x
x
Graph the system of linear inequalities.
13. x > 4
14. x ≥ 0
15. 2x y < 1
y < 2
y ≤ x 2
y ≥ 2
Distance Traveled In Exercises 16 and 17, use the following information.
You are taking a trip with your family. You are going to share driving time with
your dad. You are only allowed to drive for at most two hours at one time. The
speed limit on the highway on which you are traveling is 65 miles per hour.
16. Write a system of inequalities that describes the number of hours and
miles you might possibly drive.
17. Is it possible for you to have driven 200 miles?
2
y
2
2
2
x
x
1
y
2
1
y
2
Copyright © McDougal Littell Inc.
All rights reserved.
x
x

Answer Key
Practice B
1. B 2. C 3. A
4. y
5.
6. y
7.
1
8. y
9.
10. y
11.
1
1
1
1
1
12. y
13.
2
1
14. 15.
4 y
1
2
4
x
x
x
x
x
x
2
y
1
3
2
2
y
y
y
y
1
1
6
3
2
2
y
1
x
x
x
x
x
x
16. y
17.
18.
19. x y 44 20.
y 3
x 0
1
y
2
1
4
x
x
y 0
y x
1
y x 30
2
y 3x 105
y
2
2
x

LESSON
3.3
Copyright © McDougal Littell Inc.
All rights reserved.
NAME DATE
Match the system of linear inequalities with its graph.
2x 3y < 1
A. y
B. y
C.
1
1
Practice B
For use with pages 156–162
1. x y > 2
2. x y ≥ 2
3. x y > 2
Graph the system of linear inequalities.
x
2x 3y > 1
4. x > 2
5. y < 2
6. y ≥ 0
y ≤ 4
y > 3
x < 5
7. x y < 3
8. y ≤ 2x
9. 2x y ≤ 1
2x y > 5
x < 3
y > 3x
10. x 2y > 4
11. y ≤ 5
12. x ≥ 3
x 3y < 1
x > 3
x ≤ 4
y ≤ 2x 2
y < x 5
13. 14. 15.
y ≤
y ≤ 2x
x ≥ 2
x > 2
1
y >
y ≤ x 3
x y < 1
2x y < 4
y ≥ 3x 4
2x 3
1
2x 4
16. 2x y < 3
17. x 2y ≤ 10
18. 2x y > 1
x y > 6
2x y ≤ 8
x 2y < 4
y ≥ 0
2x 5y < 20
x 2y > 4
19. Field Trip Your class has rented buses for a field trip. Each bus seats
44 passengers. The rental company’s policy states that you must have at
least 3 adult chaperones on each bus. Let x represent the number of students
on each bus. Let y represent the number of adult chaperones on each
bus. Write a system of linear inequalities that shows the various numbers
of students and chaperones that could be on each bus. (Each bus may or
may not be full.)
20. Iceberg The diagram at the right shows the cross section of
an iceberg. Write a system of inequalities that represents the
portion of the iceberg that extends above the water.
1
1
x
(0, 0)
2x 3y > 1
10
y
1
Algebra 2 43
Chapter 3 Resource Book
y
1
(20, 20)
(30, 15)
(35, 0)
10
x
x
Water
level
Lesson 3.3

Answer Key
Practice C
1. y
2.
3. y
4.
5. y
6.
7. y
8.
9. y
10.
4
2
11. y
12.
2
1
1
1
2
8
1
1
1
2
x
x
x
x
x
x
13. x 4 14. y
x 2 y x
y 3
y 1
y 2
2
3x 3
1
y
4
1
1
y
3
y
y
2
1
1
y
y
1
1
4
4
x
x
x
x
x
x
15. y x 1
y x 1
y 2
16. C 900
C 1700
F 0
F 0.30C
No
17.
1 3
x y 80
5 10
1 3
5x 10y 90
x 0
x 200
y 0
y 200
Fat calories
Test score
F
510
470
430
390
350
310
270
0
0
y
350
250
150
50
0
0
900 1300 1700 2100C
Total calories
50 150 250 350 x
Quiz score

Lesson 3.3
LESSON
3.3
44 Algebra 2
Chapter 3 Resource Book
NAME DATE
Practice C
For use with pages 156–162
Graph the system of linear inequalities.
1. x 2y < 4
2. 2x 3y ≥ 6
3. 3x y < 0
3x y > 1
x 4y ≤ 8
3x 4y > 8
4. 2x y < 3
5. x y ≤ 2
6. 2x y < 1
x y < 0
3x y ≥ 4
x 3y < 6
x > 3
y ≥ 4
x > 0
7. x y > 3
8. 2x y ≥ 2
9. 3x 6y > 4
x 2y > 4
2x y ≤ 1
3x 4y > 4
x y < 4
x 3y ≥ 3
x y < 5
10. 2x y < 3
11. x y ≤ 1
12. x y < 2
x y > 1
x 2y ≥ 2
x y > 3
x ≥ 0
x y ≤ 4
2x 3y > 0
x < 2
x ≥ 1
2x 3y < 9
Write a system of linear inequalities for the shaded region.
13. y
14. y
15.
2
1
x
16. Toddler Nutrition Each day the average toddler needs to consume 900
to 1700 calories. At most 30% of a toddler’s total calories should come
from fat. Write and graph a system of linear inequalities describing the
number of fat calories F and total calories C for the diet of a toddler.
According to your model, is a toddler following a healthy diet
if he or she consumes 1200 calories a day and 372 of those calories are
from fat?
17. Weighted Averages To determine your grade in science class, your
teacher uses a weighted average. Your grade is a combination of quiz
and test scores. There are a total of 200 quiz points and 200 test points.
1
5
Your grade is calculated by adding of your quiz points to of your test
points. To receive a B your weighted total must be less than 90 and at
least 80. Write and graph a system of inequalities describing the possible
combination of quiz and test points that you can earn to receive a B.
1
1
x
3
10
2
y
1
Copyright © McDougal Littell Inc.
All rights reserved.
x

Answer Key
Practice A
1. minimum 6;
maximum 5
2. minimum 4; maximum 10
3. minimum 15; maximum 5
4. minimum 0; maximum 18
5. minimum 3; maximum 17
6. minimum 11; maximum 21
7. minimum 0; maximum 8
8. minimum 0; maximum 8
9. minimum 9; maximum 1
10. P 40x 55y 11.
12.
Granola bars (cases)
40
35
30
25
20
15
10
5
Production Hours
(0, 25)
(15, 20)
(31, 0)
0
0 5 10 15 20 25 30 35 40
Breakfast bars (cases)
2x 6y 150
5x 4y 155
x 0
y 0
13. Fifteen cases of breakfast bars and 20 cases of
granola bars should be made to maximize profit.

LESSON
3.4
NAME _________________________________________________________ DATE ___________
The feasible region determined by a system of constraints is given. Find the
minimum and maximum values of the objective function for the given feasible
region.
1. C x y
2. C x 2y
3. C 2x y
(0, 4)
1
(0, 0)
(0, 6)
2
(0, 0)
y
1
y
2
Practice A
For use with pages 163–169
(2, 7)
(5, 0)
x
4. C x 3y
5. C 3x 4y
6. C 3x 5y
(3, 5)
(3, 0)
x
(0, 5)
(1, 0)
Find the minimum and maximum values of the objective function
subject to the given constraints.
7. Objective function: 8. Objective function: 9. Objective function:
C 2x y
C x y
C x y
Constraints: Constraints: Constraints:
x ≥ 0
x ≥ 0
x ≤ 0
y ≥ 0
x ≤ 3
y ≤ 4
x y ≤ 4
y ≥ 0
y ≤ 5
x y ≥ 1
Breakfast Bars In Exercises 10–13, use the following information.
Your factory makes fruit filled breakfast bars and granola bars. For each case
of breakfast bars, you make $40 profit. For each case of granola bars, you
make $55 profit. The table below shows the number of machine hours and
labor hours needed to produce one case of each type of snack bar. It also
shows the maximum number of hours available.
2
(0, 2)
1
y
y
2
(1, 3)
1
(3, 3)
x
(5, 1)
(3, 2)
x
(4, 0)
Production Hours Breakfast bars Granola bars Maximum hours
Machine hours 2 6 150
Labor Hours 5 4 155
10. Write an equation that represents the profit
(objective function).
12. Sketch the graph of the constraints found in
Exercise 11 and label the vertices.
Copyright © McDougal Littell Inc.
All rights reserved.
(0, 3)
(3, 1)
2
(3, 3)
(1, 2)
(2, 1)
6
y
y
2
(6, 1)
(2, 3)
x
(6, 3)
6 x
(6, 0)
11. Write a system of inequalities that represents
the constraints.
13. How many cases of each product should you
make to maximize profit?
Algebra 2 57
Chapter 3 Resource Book
Lesson 3.4

Answer Key
Practice B
1. minimum 6;
maximum 5
2. minimum 0; maximum 24
3. minimum 4; maximum 26
4. minimum 6; maximum 9
5. minimum 6; maximum 26
6. minimum 2; maximum 20
7. minimum 9; maximum 20
8. minimum 8; no maximum
9. minimum 6; maximum 30
10. two batches of bread and 16 batches of muffins
11. zero long distance calls (0 minutes) and
24 local calls (240 minutes)

Lesson 3.4
LESSON
3.4
58 Algebra 2
Chapter 3 Resource Book
NAME _________________________________________________________ DATE ___________
The feasible region determined by a system of constraints is given. Find the minimum
and maximum values of the objective function for the given feasible region.
1. C x y
2. C 2x 4y
3. C x 5y
(0, 6)
2
(0, 0)
y
2
Practice B
For use with pages 163–169
(2, 7)
(5, 0)
x
1
(0, 0)
Find the minimum and maximum values of the objective function
subject to the given constraints.
4. Objective function: 5. Objective function: 6. Objective function:
C 3x y
C 2x 4y
C x 5y
Constraints: Constraints: Constraints:
x ≥ 0
x ≤ 3
3x 2y ≤ 8
y ≥ 0
x y ≥ 3
2x y ≥ 4
2x y ≤ 6
2x 3y ≥ 9
x 4y ≤ 2
7. Objective function: 8. Objective function: 9. Objective function:
C 4x 3y
C 2x 3y
C 5x 2y
Constraints: Constraints: Constraints:
x ≥ 0
x ≥ 0
x ≤ 4
x ≤ 5
y ≥ 1
2x y ≥ 3
y ≥ 0
4x y ≥ 6
x 3y ≤ 2
2x 5y ≥ 15
x 2y ≥ 5
x 2y ≤ 6
10. Bakery A bakery is making whole-wheat bread and apple bran muffins. For
each batch of bread they make $35 profit. For each batch of muffins they
make $10 profit. The bread takes 4 hours to prepare and 1 hour to bake. The
muffins take 0.5 hour to prepare and 0.5 hour to bake. The maximum
preparation time available is 16 hours. The maximum baking time available
is 10 hours. How many batches of bread and muffins should be made to
maximize profits?
11. Phone Bill On a typical long distance call you talk for 30 minutes. On a
typical local call you talk for 10 minutes. Your phone company offers a
special low rate of $.08 per minute for long distance calls and $.03 per
minute for local calls for customers who spend at least 240 minutes on the
phone per month. Your parents have set a limit of no more than 15 long
distance calls per month and 30 local calls per month. How many minutes
of long distance and local calls should you make to qualify for the special
rate plan and minimize your phone bill?
1
y
(0, 3)
(4, 4)
(6, 1)
x
(6, 0)
1
y
(0, 2)
1
(1, 1)
(6, 4)
(4, 1)
Copyright © McDougal Littell Inc.
All rights reserved.
x

Answer Key
Practice C
1. min. of 12at
(0,4); max. of 8 at (4,0)
2. min. of 4 at (1, 1); max. of at 3
3. min. of 0 at (0, 0); max. of 12 at 4, 0
4. min. of 6 at (0, 3); max. of 20 at (4, 0)
3
5. min. of 0 at (0, 0); max. of at 3,
6. min. of 6 at 0, 2; max. of 27 at (6, 5)
7. min. of 2 at (0, 2); max. of 8 at (4, 4)
8. min. of 3 at 3, 5; max. of 42 at (3, 8)
9. min. of 30 at (0, 6); max. of 16 at 1, 3
10. 7 paperbacks and 1 hard cover book
11. 0.625 servings of pork, 3.75 servings of
potatoes
32
15
2
8 8
3 ,
3
2

LESSON
3.4
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice C
For use with pages 163–169
Find the minimum and maximum values of the objective function subject to the
given constraints.
1. Objective function: 2. Objective function: 3. Objective function:
C 2x 3y
C x 3y
C 3x 2y
Constraints: Constraints: Constraints:
x ≥ 0
x 2y ≤ 8
x ≥ 0
y ≥ 0
x y ≥ 0
y ≥ 0
x y ≤ 4
y ≥ 1
x y ≤ 4
x y ≥ 3
4. Objective function: 5. Objective function: 6. Objective function:
C 5x 2y
C 2x y
C 2x 3y
Constraints: Constraints: Constraints:
x ≥ 0
x ≥ 0
x ≤ 6
y ≥ 0
x ≤ 3
y ≤ 5
3
2x y ≥ 0
2x y ≤ 8
2x 3y ≤ 6
x 3y ≤ 9
3x 2y ≤ 12
x 3y ≥ 6
7. Objective function: 8. Objective function: 9. Objective function:
C 3x y
C 6x 3y
C x 5y
Constraints: Constraints: Constraints:
y ≤ 4
x ≥ 3
x ≥ 3
x y ≥ 2
x y ≥ 0
y ≥ 3
2x y ≤ 4
2x y ≤ 11
y ≤ 6
x y ≤ 2
x y ≤ 11
x y ≤ 6
2x y ≥ 2
3x y ≤ 6
x y ≥ 3
10. Gift Basket You want to make a gift basket for your mother who is an
avid reader. You decide to include hard cover books and paperbacks in the
basket. You have $80 to spend on books. Each hard cover costs $24 and
each paperback costs $8. The basket will hold at most 3 hardcover books
or 7 paperbacks. Find the maximum number of books you can include in
the basket.
11. Nutrition You are planning to have roast pork and twice baked potatoes
for dinner. You want to consume at least 250 grams of carbohydrates, but
no more than 60 grams of fat per day. So far today you have consumed
170 grams of carbohydrates and 30 grams of fat. The table below shows
the number of grams of carbohydrates, fat, and protein in a serving of
roast pork and twice baked potatoes. How many servings of each can you
eat to fulfill your daily requirements for carbohydrates and fat while
maximizing the amount of protein you consume?
Pork Potatoes
carbohydrates 8 g 20 g
fat 6 g 7 g
protein 23 g 5 g
Algebra 2 59
Chapter 3 Resource Book
Lesson 3.4

Answer Key
Practice A
1. z
2.
3. z
4.
5. z
6.
7. (1, 2, 4) 8.
9.
x
(2, 0, 1)
x
x
x
x
z
z
(0, 1, 2)
(1, 1, 0)
(2, 3, 1)
y
y
y
y
y
x
x
x
z
z
z
(3, 2, 5)
x
(2, 2, 4)
z
(1, 3, 1)
y
y
(2, 5, 0)
y
y
10. x-intercept: 4 11. x-intercept: 3
y-intercept: 4 y-intercept: 6
z-intercept: 4 z-intercept: 2
12. x-intercept: 4 13. x-intercept: 10
y-intercept: 3 y-intercept: 4
z-intercept: 2 z-intercept: 20
14. x-intercept: 2 15. x-intercept:
y-intercept: 7 y-intercept: 9
z-intercept: z-intercept: 3
2
4
16. 13 17. 18 18. 0 19. 3 20. 17
21. 27 22. 1 23. 26 24. 2
25. fx, y 12 2x 3y
26. fx, y 1 3x 2y
27. fx, y x 3y 8
28. fx, y 5x 2y 4
29. fx, y 9 7x 8y
30. fx, y 6x y
31. A: 2, 0, 0 32. A: 0, 0, 2
B: 2, 4, 0 B: 0, 6, 2
C: 0, 4, 5 C: 0, 6, 0
D: 2, 0, 5 D: 4, 6, 0
3
33. z 18x 12y 50; Answers may vary.
Sample: x 1 0 1 2 1
y 0 1 1 1 2
z 68 62 80 98 92
3

Lesson 3.5
LESSON
3.5
Practice A
For use with pages 170–175
72 Algebra 2
Chapter 3 Resource Book
NAME _________________________________________________________ DATE ___________
Plot the ordered triple in a three-dimensional coordinate system.
1. 0, 1, 2
2. 1, 3, 1
3. 2, 0, 1
4. 2, 2, 4
5. 1, 1, 0
6. 2, 5, 0
7. 1, 2, 4
8. 3, 2, 5
9. 2, 3, 1
Find the x-intercept, y-intercept, and z-intercept of the graph of the
linear equation.
10. x y z 4
11. 2x y 3z 6
12. 3x 4y 6z 12
13. 2x 5y z 20
14. 7x 2y 21z 14
15. 12x y 3z 9
Evaluate the function for the given values.
16. fx, y 3x 2y, f1, 5 17. fx, y x 6y, f0, 3 18. fx, y 3x 2y, f2, 3
19. fx, y x y, f1, 4 20. fx, y 5x y, f3, 2 21. fx, y 7x 2y, f3, 3
22. fx, y 3x 4y, f1, 1 23. fx, y 4x 3y, f5, 2 24. fx, y 8x 3y, f2, 6
Write the linear equation as a function of x and y.
25. 2x 3y z 12
26. 3x 2y z 1
27. x 3y z 8
28. 5x 2y z 4
29. 7x 8y z 9
30. 6x y z 0
31. Geometry Write the coordinates of the
vertices A, B, C, and D of the rectangular
prism shown, given that one vertex is the
point 2, 4, 5.
x
D
A
z
B
C
(2, 4, 5)
y
32. Geometry Write the coordinates of the
vertices A, B, C, and D of the rectangular
prism shown, given that one vertex is the
point 4, 6, 2.
33. Music Club A music club requires an initial purchase of $50 worth of
merchandise. After this initial fee, compact discs may be purchased for $18
and audio cassettes may be purchased for $12. Write an equation for the
amount that you will spend as a function of the number of compact discs
and audio cassettes that you buy. Make a table to show the different cost for
several different numbers of compact discs and audio cassettes.
x
z
A
(4, 6, 2)
D
B
C y
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice B
1. z
2.
3. z
4.
5. z
6.
7. z
8.
9.
10.
x
(0, 3, 2)
x
(6, 0, 0)
x
x
(8, 0, 0)
x
z
(0, 0, 5)
x
z
(6, 0, 0)
(0, 0, 8)
(0, 0, 4)
(0, 0, 5)
(1, 3, 1)
y
y
y
(0, 8, 0)
y
(0, 12, 0)
y
(0, 15, 0)
y
x
x
(1, 3, 2)
x
x
z
z
z
(4, 0, 0)
(3, 5, 2)
z
(0, 0, 4)
y
(4, 1, 3)
y
y
(0, 2, 0)
y
11. z
12.
13. z
14.
15. z 16.
17.
18.
3
( , 0, 0
2 )
x
(0, 4, 0)
0, 0, 5
( 2)
x (1, 0, 0)
x
(0, 2, 0)
x
(0, 14, 0) (4, 0, 0)
z
6
( 0, 0,
5)
(0, 3, 0)
(0, 0, 3)
(3, 0, 0)
0, 0, 1
( 2)
x
y
(3, 0, 0)
z
y
(0, 5, 0)
y
19.
20.
21.
22.
23.
24.
25.
26.
27. fx, y
28. 30 29. 48
30. fx, y 35x 60y 200; $1500
31. fx, y 2x 3.5y 12; $25
1
fx, y 2
1 1 3
x y ; 4 5 2 4
3
fx, y 3
1 5
8x 4y; 2
2
fx, y
1
5x 5y; 0
3
fx, y 3 x
1
x y 6; 33
4 2 4
1
fx, y 5 4x y; 4
fx, y 3 3x 2y; 1
fx, y 5x 3y 7; 21
fx, y 3x y 2; 11
y; 2 2
y
y
14
( 0, 0,
3 )
x
z
(1, 0, 0)
x
z
(0, 0, 3)
(0, 1, 0)
x
(0, 0, 3)
z
3
( 0, , 0
2 )
( )
1
, 0, 0
6
y
(0, 0, 1)
(4, 0, 0)
(0, 6, 0)
y
y

LESSON
3.5
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice B
For use with pages 170–175
Plot the ordered triple in a three-dimensional coordinate system.
1. 1, 3, 1
2. 3, 5, 2
3. 0, 0, 5
4. 4, 1, 3
5. 0, 3, 2
6. 1, 3, 2
Sketch the graph of the equation. Label the points where the graph
crosses the x-, y-, and z-axes.
7. x y z 8
8. x 2y z 4
9. 2x y 3z 12
10. 5x 2y 6z 30 11. 2x y z 3
12. 3x 2y z 3
13. 5x y 2z 5
14. 6x y z 1
15. 4x 3y 24z 12
16. 3x 2y 4z 12 17. 2x 3y 5z 6
18. 7x 2y 6z 28
Write the linear equation as a function of x and y. Then evaluate the
function for the given values.
19. 4x y z 5, f1, 5 20. 3x 2y z 3, f0, 2 21. 5x 3y z 7, f2, 6
22. 3x y z 2, f2, 3 23. 2x y 2z 6, f4, 2 24. 3x 2y 4z 24, f1, 3
25. 2x y 5z 15, f6, 3 26. 3x 2y 8z 16, f0, 2 27. 5x 4y 20z 10, f1, 5
28. Geometry Use the given point 3, 5, 2
to
find the volume of the rectangular prism.
x
z
(3, 5, 2)
y
29. Geometry Use the given point 4, 2, 6 to
find the volume of the rectangular prism.
30. Yearbook Advertisements The yearbook club’s bank account has $200
remaining from last year’s advertising campaign. You are now trying to sell
advertisements to local businesses for this year’s yearbook. A quarter page
ad costs $35. A half page ad costs $60. Write an equation for the total
amount of money you may spend as a function of the number of quarter and
half page ads that you sell. Evaluate the model if you sell 20 quarter page
ads and 10 half page ads.
31. Baseball Game You and a group of your friends go to a professional
baseball game. Your ticket costs $12. Bottled water costs $2 and hotdogs
cost $3.50. Write an equation for the cost of going to the game as a function
of the number of bottled waters and hotdogs you purchase. Evaluate the
model if you buy 3 bottled waters and 2 hotdogs.
x
z
(4, 2, 6)
y
Algebra 2 73
Chapter 3 Resource Book
Lesson 3.5

Answer Key
Practice C
1. z
2.
3. z 4.
5. z
6.
7. z (0, 5, 0) 8.
9. z
10.
11. z
12.
13. 14.
x
z
x
x
3
( 4)
(2, 4, 1)
x
(4, 0, 0)
x
(0, 0, 1)
(0, 3, 0)
1
( 4)
2
0, 0, ( , 0, 0
3 )
x
(2, 1, 4)
y
3
, 0, 0
2
(0, 2, 0) y
3
0, 0, ( , 0, 0
2 )
x
(0, 0, 10)
( )
(0, 3, 0)
y
y
2
(1, , 3)
3
y
y
y
x
z
x
z
( , 2, )
5 1
2 3
x
(0, 7, 0)
(0, 1, 0)
1 3
( , 3,
2 2 )
2
0, , 0
1
( 3 )
( , 0, 0
2 )
y
x 0, 0, 2
z
( 5)
4
( 0, , 0
3 )
x
z
z
(0, 0, 2)
z
(1, 3, 2)
x
y
x
y
z
(0, 0, 1)
y
4
, 0, 0
5
( )
y
y
(2, 0, 0)
3
( 0, 0,
2)
1
( , 0, 0
2 )
y
15.
x
( )
z
( 0, ,0)
4
, 0, 0
3
5
4
(0, 0, 2)
y
16.
17.
18.
19.
20.
21. f x, y 7
In Exercises 22–24, sample answers are given.
3
f x, y 2 5x 3y;
7
2x 2y; 19
6
21
f x, y
2
3
f x, y
1 1 2
2 6x 3y; 3
3
f x, y
3 1
4 4x 2y; 0
1
f x, y 4 2x ; 6
1 1 1
4 2x 4y; 4
2
3y 22. 3x 2y 3z 6
23. 10x 15y 6z 30
24. 10x 5y 2z 5
25. f x, y 3x y;
7 points
26. f x, y 14.95 6.95x 24.95
10y 2 19.90 6.95x 10y; $73.80
27. 3x 2y z 38,387; 4129 3-point shots

Lesson 3.5
LESSON
3.5
Practice C
For use with pages 170–175
74 Algebra 2
Chapter 3 Resource Book
NAME _________________________________________________________ DATE ___________
Plot the ordered triple in a three-dimensional coordinate system.
1. 2. 3.
4. 5. , 3
6.
1
2, 1, 4
1, 3, 2
3
, 3,
2
2
1, 2
3
Sketch the graph of the equation. Label the points where the graph
crosses the x-, y-, and z-axes.
7. 5x 4y 2z 20
8. 7x 2y 14z 14
9. 2x y 3z 3
10. 4x 3y 5z 2
11. 3x y 8z 2
12. 5x 3y 2z 4
13. 2x y 4z 3
14. 6x 3y 2z 3 15. 3x 5y 2z 4
Write the linear equation as a function of x and y. Then evaluate
the function for the given values.
16. 17.
18. 19.
20. 21.
f 1, 2
f 3x 7y 2z 14, 3
1
6x 2y 3z 12, f 0, 3
2x y 4z 1, f 1, 2
3x 2y 4z 3, f 1, 0
x 2y 6z 9, f 3, 4
5x 3y z 2, 2 , 2
Write an equation of the plane having the given x-, y-, and
z-intercepts. Explain the method you used.
22. x-intercept: 2 23. x-intercept: 3
24. x-intercept:
y-intercept: 3 y-intercept: 2 y-intercept: 1
z-intercept: 2 z-intercept: 5 z-intercept:
25. Place-kicker In football a placekicker is responsible for kicking field
goals worth 3 points and extra points after touchdowns worth 1 point.
Write a model for the total number of points that a placekicker can score
in a game. In Super Bowl XXXII, Jason Elam kicked 4 extra points and
1 field goal for the Denver Broncos. Use the model to determine the total
number of points scored by Elam.
26. Photography Studio A photography studio charges a $14.95 sitting fee.
A sheet of pictures can consist of one 8 x 10, two 5 x 7’s, four 3 x 5’s, or
twenty-four wallets. The studio charges $6.95 for a sheet of pictures.
Holiday cards with your photo may be purchased. Twenty holiday cards
cost $24.95 plus $10 for each addition 10-card order. Write a model for
the total cost (not including tax) of buying pictures if you intend to
purchase at least 20 holiday cards. Evaluate the model if you buy
40 holiday cards and two sheets of pictures.
27. N.B.A. Lifetime Leader Kareem Abdul-Jabbar is the N.B.A. lifetime
leader in points scored with 38,387. Today, a player can score a threepoint
shot worth 3 points, a field goal worth 2 points, or a free throw
worth 1 point. Write a model for the types of points needed to match
Abdul-Jabbar’s record. How many three-point shots are needed in a career
to match the record if 12,000 field goals and 2000 free throws are scored?
1
2, 4, 1
5
2 , 2, 3
1
2
5
2
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice A
1. 1, 1, 1is
a solution. 2. 0, 3, 1is
a
solution. 3. 2, 1, 6is
not a solution.
4. 3, 2, 1 5. 4, 1, 3 6. 3, 5, 4
7. 9, 4, 2 8. 2, 2, 0 9. 1, 3, 2
10. 1, 1, 3 11. 2, 1, 4 12. 1, 0, 5
13. infinitely many solutions 14. no solutions
15. 2, 1, 3 16. x y z 22
3y 4z 54
x z
17. Six are under age 5, 10 are ages 5–16, and
6 are ages 16 and up.

Lesson 3.6
LESSON
3.6
84 Algebra 2
Chapter 3 Resource Book
NAME _________________________________________________________ DATE ___________
Solve the system using the substitution method.
4. x 2y 3z 4
5. x 3y 1
6. x 5y 7z 6
y z 3
y 2z 5
y 3z 7
z 1
z 3
z 4
7. x 2y z 1
8. 4x y 2z 6
9. x 2y z 3
y z 2
y 4z 2
x 2y 5
4z 8
2y 4
x 1
Solve the system using the linear combination method.
10. x y z 5
11. x 2y 3z 8
12. 2x y z 7
2x y z 4
2x y 3z 17
2x y 3z 17
3x y 2z 8
x 3y 3z 11
2x 3y 2z 12
13. x 2y 4z 2
14. 2x 3y z 4
15. x y z 6
x 2y 4z 2
4x 6y 2z 6
x y z 0
x 2y 4z 2
2x y z 2
x y z 4
Pool Admission In Exercises 16 and 17, use the following information.
A public swimming pool has the following rates: ages under 5 are free, ages
5–16 are $3, and ages 16 and up are $4. The pool also has a policy that every
child under age 5 must be accompanied by an adult. The families in your neighborhood
decide to go to the pool as part of a summer party. There are 22 people
in your group and an equal number of children under age 5 as people 16 years
old and older. The total admission cost was $54. Use the model below.
Number of people
under age 5
Rate for
under
age 5
Number of
people
under age 5
Number of
people
under age 5
Practice A
For use with pages 177–184
Decide whether the given ordered triple is a solution of
the system.
1. 1, 1, 1
2. 0, 3, 1
3. 2, 1, 6
x y z 3
x 2y z 7
x y z 3
2x y 4z 5
4x y 3z 0
2x y z 9
x 4y 2z 3
2x y 5z 2
4x y z 15
Number of
people ages
16 and over
Number of people
ages 5–16
Rate
for ages
5–16
16. Write a system of linear equations in three
variables to find the number of people in
each age category in your group.
Number of people
ages 16 and up
Number
of people
ages 5–16
Rate for
ages 16
and over
Total number
of people
Number of
people ages
16 and over
Total
cost
17. How many people in your group are in the
different age categories designated by the
pool?
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice B
1. 0, 0, 3is
a solution.
2. 1, 2, 5is
a solution.
3. 0, 0, 0is
not a solution.
4. 1, 3, 2 is a solution.
5. 5, 7, 1is
not a solution.
6. 4, 8, 9 is not a solution.
7. 2, 8, 1 8. 3, 5, 2 9. 1, 0, 2
10. 2, 3, 5 11. 1, 1, 2 12. 6, 5, 3
13. 3, 2, 5 14. 0, 2, 3
15. infinitely many solutions
16. 0.6x 0.5y 0.5z 1770
0.25x 0.35y 0.45z 1165
0.15x 0.15y 0.05z 365
There were 1200 pounds of pet food in the first
shipment, 800 pounds of pet food in the
second shipment, and 1300 pounds of pet food in
the third shipment.
17. 0.55x 0.65y 0.60z 3405
0.25x 0.10y 0.20z 1070
0.20x 0.25y 0.20z 1225
There are 2000 comedies, 1700 dramas, and
2000 action movies at the store.

LESSON
3.6
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice B
For use with pages 177–184
Decide whether the given ordered triple is a solution of the system.
1. 0, 0, 3
2. 1, 2, 5
3. 0, 0, 0
3x 4y z 3
2x y 5z 29
x y z 0
2x 7y 2z 6
6x 4y z 19
2x 3y z 0
10x 12y z 3
x y 2z 7
3x y 4z 1
4. 1, 3, 2
5. 5, 7, 1
6. 4, 8, 9
x 5y 6z 2
x y z 13
x 2y 3z 39
3x y 8z 16
2x 7y 5z 34
2x y 7z 63
4x 2y 7y 4
3x y 4z 25
3x y z 13
Use any algebraic method to solve the system.
7. x y 2z 4
8. x y z 6
9. x 2y z 3
x 3z 1
2y 3z 4
x 3y z 1
2y z 15
y 2z 1
x y 3z 5
10. x 2y z 3
11. 2x 3y 2z 1
12. x 2y 3z 7
x y 2z 9
x 4y z 7
4x 5y z 4
2x 3y z 0
3x y 3z 2
x y 2z 5
13. 8x 2y z 25
14. x 5y 2z 16
15. 3x 2y 8z 4
3x 3y 5z 10
x 7y 3z 23
6x 4y 16z 8
5x 6y 2z 17
3x 10y 5z 5
12x 8y 32z 16
16. Pet Store Supplies A pet store receives a shipment of pet foods at the
beginning of each month. Over a three month period, the store received
1770 pounds of dog food, 1165 pounds of cat food, and 365 pounds of bird
seed. Write and solve a system of equations to find the number of pounds of
pet food in each of the three shipments.
Pet food 1st shipment 2nd shipment 3rd shipment
Dog food 60% 50% 50%
Cat food 25% 35% 45%
Bird seed 15% 15% 5%
17. Movie Rental Store The table below shows the percent of comedies,
drama, and action videos available at a video store. Write and solve a system
of equations to find out how many comedies, dramas, and action movies are
at the store. Assume that the store has a collection of 3405 general videos to
be rented, 1070 children’s videos to be rented, and 1225 videos for sale.
Store section Comedy Drama Action
General rental 55% 65% 60%
Children’s rental 25% 10% 20%
Videos for sale 20% 25% 20%
Algebra 2 85
Chapter 3 Resource Book
Lesson 3.6

Answer Key
Practice C
1. 2. 3. no solution
4. 5.
6. All points of the form
7.
10.
8. 9.
11.
12. All points of the form
13. 7, 8, 14. 2, 1, 3, 2
15. a b c 3 16. 4a 2b c 12
17. a b c 3, a b c 3,
17
z, z 2, z
4 , 9 4
5 1
3 , 1
3 , 4
1 2
2 , 3 , 1
5
3 49
76 , 38 , 76
1 2
3 , 3 , 1 3
1
2 , 0, 2
4
1, 4, 2 1, 1, 1
34 7
13 z 13 , 13 1
5, 2, 6
2 , 1, 3 2
4a 2b c 12, a 2, b 3, c 2
18. y 2x 2 3x 2
14
z 13 , z

Lesson 3.6
LESSON
3.6
Practice C
For use with pages 177–184
86 Algebra 2
Chapter 3 Resource Book
NAME _________________________________________________________ DATE ___________
Solve the system using the linear combination method.
1. 2x 3y z 10
2. 2x y 4z 4
3. 5x 3y 2z 3
2x 3y 3z 22
3x 2y z 2
2x 4y z 7
4x 2y 3z 2
5x 2y 3z 0
x 11y 4z 3
Solve the system using the substitution method.
4. 3x y 2z 3
5. x 3y 5z 3
6. 2x 3y z 2
2x 3y 5z 4
4x 5y 2z 7
x 5y 3z 8
2x y z 4
3x 2y 4z 9
5x y z 12
Solve the system using any algebraic method.
7. 8. 9.
5x 2y 4z 11
2x 3y 6z
4x 2y 3z 8
2x 2y 9z 1
3x 4y 7z 4
2x 8y 5z 11
5x y 6z 3
4
7
2x 5y 4z 7
6x 3y 9z 7
2
10. 6x 6y 2z 5
11. 3x 3y 4z 3
12. x 2y z 4
12x 3y 4z 0
x 2y 8z 1
3x y 4z 2
4x 9y 2z 6
6x 9y 4z 12
6x 5y z 10
Solve the system of equations.
13. w x y z 1
14. w 2x y 3z 3
2w x y z 4
w x 2y 2z 3
w x 2y 2z 2
2w 2x 2y z 6
3w 2x y z 7
3w x y 4z 12
Polynomial Curve Fitting In Exercises 15–18, use the following information.
You can use a system of equations to find a polynomial of degree n whose
graph passes through points. Consider a polynomial of degree 2,
y ax Suppose 1, 3, 1, 3, and 2, 12 lie on the graph.
Using the point 1, 3,
the following equation can be derived:
2 n 1
bx c.
y ax 2 bx c
3 a1 2 b1 c
3 a b c.
The equation a b c 3 becomes the first equation in the system.
15. Write the equation in the system that corresponds to the point 1, 3.
16. Write the equation in the system that corresponds to the point 2, 12.
17. Write a system of equations for the coefficients of a polynomial of degree
2 that passes through 1, 3, 1, 3, and 2, 12. Solve the system.
18. Write the polynomial.
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Review and Assessment
Test A
10
1
10
9
10
4
3
2
0
2
8
2
8
1. 2. 3.
4. 5. 6.
1
2
6
2
2
5
6
7. 8. 3 9. 107 10. 10 11. 20
1
1
12. 15 13. 14. 15.
16. 17.
18. 19.
20. 21. 4, 1 22. 2, 0
23. SEND MONEY 24. 46
6
14
1
2
37
14
5
2
9
2
4
1
2
3
3
4
2
6, 9 2, 1 4, 5, 8
1
5
3

CHAPTER
4
NAME _________________________________________________________ DATE
Chapter Test A
For use after Chapter 4
____________
Perform the indicated operation(s).
1. 2.
3. 4.
5. 3
4
2
6
5
3 4
1
6
0
1
2 1
5
8
7
4
1 6
1
5
3
0
4
3
2
0
0
3
2
5 2
5
0
3
Solve the matrix equation for x and y.
6. 7. 0
1
2
3
3
4 x
y 8
9
Evaluate the determinant of the matrix.
8. 9. 10.
9 5
7
1 2
2 1
Find the area of the triangle with the given vertices.
11. A3, 4, B2, 1, C6, 3 12. A4, 2, B2, 2, C2, 5
Use Cramer’s rule to solve the linear system.
13. x y 15 14. 2x 3y 7 15. x 2y 14
x y 3
Copyright © McDougal Littell Inc.
All rights reserved.
0
8
3x y 5
1
4 x
y 2
9
1
2
3
1
3
2
0
4
y 2z 11
2x z 16
3
1
4
Answers
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
Algebra 2 81
Chapter 4 Resource Book
Review and Assess

Review and Assess
CHAPTER
4
CONTINUED
NAME _________________________________________________________ DATE ____________
Chapter Test A
For use after Chapter 4
Find the inverse of the matrix.
16. 17. 18.
4
3
3
3
1
5
2
Solve the matrix equation.
19. 20.
5
2
13
5X 3
4
1
0
Use an inverse matrix to solve the linear system.
21. 5x 6y 14
22. 3x 2y 6
4x y 17
23. Decoding Use the inverse of
A 1
2
2
3
to decode the message below.
9, 23, 6, 16, 26, 39, 13, 12, 45, 65
24. Numbers Solve using any method. In a certain two digit number,
the units digit is 24 less than 3 times the sum of the digits. If the
digits are reversed, the new number is 18 more than the original
number. Find the two digit number.
82 Algebra 2
Chapter 4 Resource Book
2
11
2
x y 2
1
2
5
1X 4
2
4
9
1
0
16.
17.
18.
19.
20.
21.
22.
23.
24.
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Test B
1. 2.
3. 4.
5. 6.
7. 8. 9. 1 10.
11. 17 12. 13. 14.
15. 16.
17.
18. 19.
2 7
3 16
1
7
2
1
3
3
3
2
5
4
7
1
10 3, 1 5, 1
1, 1, 2
2
2
1
1
x 2; y 1
x 3; y 24 5
12
2
10
2
13
6
3
4
16
1
7
10
3
27
9
3
18
12
2
1
7
1
7 2 6
20. 21. 1, 2 22. 4, 4
10 3 10
23. AN APPLE A DAY
24. A $3000; B $2000; C $4000

CHAPTER
4
NAME _________________________________________________________ DATE
Chapter Test B
For use after Chapter 4
____________
Perform the indicated operation.
1. 2.
3. 4. 1
4
4
3
9
2
4
8
1
9
1
3
2
1 1
2
5
0
5.
3
4
Solve the matrix equation for x and y.
6.
x
7. 46
2x
4
0
y 4
4
0
Evaluate the determinant of the matrix.
2
5 2
2
6
5
8
3 4
1
0
1
3
1
8. 9. 10.
1 4
6 1
1
3
2
Find the area of the triangle with the given vertices.
11. A4, 2, B3, 4, C1, 2 12. A5, 2, B0, 0, C3, 3
Copyright © McDougal Littell Inc.
All rights reserved.
5
3
1
2
3 4
0
6
4
1
1
2
2 12
y
8
8
2
3
1
1
1
0
Answers
1.
2.
3.
4.
5.
6.
7.
8.
9
10.
11.
12.
Algebra 2 83
Chapter 4 Resource Book
Review and Assess

Review and Assess
CHAPTER
4
CONTINUED
Chapter Test B
For use after Chapter 4
Use Cramer’s Rule to solve the linear system.
Find the inverse of the matrix.
2
7
4
4
16. 17. 18.
1
5
3
NAME _________________________________________________________ DATE ____________
13. x 5y 8
14. 2x y 9 15. 3x 5y 8
4x 2y 10
5x 2y 27 4x 7z 18
y z 3
Solve the matrix equation.
19. 20.
5
2
2
1x 4
1
3
2
Use an inverse matrix to solve the linear system.
21. 3x y 5
22. 3x 7y 16
5x 2y 9
2x 4y 8
23. Decoding Use the inverse of A to decode the message
below.
2 1
3 1
44, 15, 3, 1, 80, 32, 39, 17, 3, 1, 12, 4, 77, 26
24. Stock Investment You have $9000 to invest in three Internet
companies listed on the stock market. You expect the annual returns
for companies A, B, and C to be 10%, 9%, and 6%, respectively. You
want the combined investment in companies B and C to be twice that
of company A. How much should you invest in each company to
obtain an average return of 8%?
84 Algebra 2
Chapter 4 Resource Book
3
3
1
2
1x 1
3
6
7
0
1
2
2
2
4
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Test C
1. 2. 3. cannot
4. 5. 6.
7. 8. 1 9. ab cd 10. 16
11. 31 12. 26 13. 3, 2 14. 4, 5, 10
1
4
2
2
1
5
7
9
0
0
16
32
4
56
16
10
10
6
4
4
9
2
1
1
15. 4, 1, 4 16.
5
14
17. cannot 18.
19.
20. 21. 1, 1 22. 7, 2
23. 16, 50, 4, 7, 11, 22, 1, 2, 7, 9,
7, 14 24. Macadamia nuts: 6 oz;
Peanuts: 10 oz; Cashews: 4 oz
1
1
9
22
2
4
15
26
17
29
2
5
1
3
1
7
3
14
2 7

CHAPTER
4
NAME _________________________________________________________ DATE
Chapter Test C
For use after Chapter 4
____________
Perform the indicated operation(s), if possible.
1. 2.
1 4
5 6 8 5
3 7
3. 4.
5. 4
1
0
5 6
3
2
4 3
1
1
9
5
6
7
3 0
1
2
3
4
5
6
7
8
Solve the matrix equation for x and y.
6. 7. 1
2
2
5
3
8 x
y 10
26
Evaluate the determinant of the matrix.
8. 9. 10.
a c
d
3 1
7 2
Find the area of the triangle with the given vertices.
11. A8, 6, B0, 0, C5, 4 12.
Use Cramer’s Rule to solve the linear system.
13. 3x 5y 1
14. 5x 10y 70
15.
2x 3y 12
4x 3y z 9
3x 2y 5z 10
2x 4y 3z 8
Copyright © McDougal Littell Inc.
All rights reserved.
b
8 0
2
4
2
5
5
8
1
8
1
2
7
2
2
3 x
y 9
14
1
2
3
A3, 2, B5, 5, C1, 8
5x 25z 270
7
2 2
5
10y 25z 300
2
0
4
9
2
3
2
1
0
2
Answers
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
Algebra 2 85
Chapter 4 Resource Book
Review and Assess

Review and Assess
CHAPTER
4
CONTINUED
NAME _________________________________________________________ DATE ____________
Chapter Test C
For use after Chapter 4
Find the inverse of the matrix, if it exists.
16. 17. 18.
1
2
4
2
2
3
4
2
3
5
Solve the matrix equation.
19.
20.
12
5
6
3
7
3X 2
3
3
1X 9
4
Use an inverse matrix to solve the linear system.
21. 2x 3y 5
22. 2x 3y 8
3x y 4
x 2y 3
23. Encoding Use the matrix
A 1
1
2
3
1
2
12
5
to encode the message BREAK A LEG.
24. Mixed Nuts Macadamia nuts cost $.90 per ounce, peanuts cost
$.30 per ounce, and cashews cost $1.30 per ounce. You want a
20-ounce mixture of macadamia nuts, peanuts, and cashews that
costs $.68 per ounce. If the combined weight of the macadamia nuts
and cashews equals the weight of the peanuts, how many ounces of
each nut should be used?
86 Algebra 2
Chapter 4 Resource Book
0
2
3
5
1
2
16.
17.
18.
19.
20.
21.
22.
23.
24.
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Cumulative Review
1. 2. 3. 4. 2 5. 4 6. 4
7. 2 8.
1
9. x ≥ 1 10. 3 x 2
1
11 11
9
13
11. 12. 13. x
14. x 4 15. no 16. yes 17. yes 18. no
19. yes 20. yes
21. 22.
5
x ≥ 2
5
x ≤ 2 or x ≥ 5
2
1
23. 24.
(2, 0)
y
1
5
(0, 5)
1
(2, 1)
y
(0, 4)
1
x
x
25. 26.
27. 28.
29. 30. 31.
32. 33. 34.
35.
39.
36. 37. 38.
40.
41.
42.
43.
44.
45.
46. 47. 48.
49. 50. 51. 1, 5 52. 7, 4
53. 54.
56. 236 57. 48
0, 55. 5, 1, 0
1
f x, y
0, 1, 2 3, 4, 7 2, 0, 3
5, 9 3, 5
5, 1
2
2
fx, y
4
3x 3y 3; 11
3
fx, y
2x 3y 5; 14
2
f x, y x
5
3x 3y 2; 8
3
10, 6
fx, y x 6y 12; 20
f x, y x 2y 8; 9
2y 4; 16
1 2
3 , 3
1
y y 5x 6 5, 1
4, 2 1, 0 2 , 1
2
y y 3 y 3x
3x 5
2
y
5x 3
2
y 5x 2 y 5x 3
1
y 2x 4
3x 6
1
y
1
(0, 5)
1
y
1
(6, 1)
(0, 3)
(4, 0)
x
x

Review and Assess
CHAPTER
4
NAME _________________________________________________________ DATE
Cumulative Review
For use after Chapters 1–4
____________
Evaluate the expression for the given values of x and y. (1.2)
x 2
1. when and 2. x when x 3and
y 2
3 2y3 x 3 y 5
3y 2
3. when and 4. x when x 4and
y 2
2 x y
x 5 y 6
2x 3y
x y
Solve the equation. (1.3)
5. 3x 2 4x 7 18
6.
1 1 7
2x 3 x 3
7. 1.5x 8 11 0.5x 1
8. x 2 3x 3x 4 15
Solve the inequality. (1.6)
9. 3x 1 8x 4
10. 10 3x 1 7
11. 2x 8 or 2x 3 7
12.
13. 2x 3 8
14.
Tell whether the relation is a function. (2.1)
15. x 1 2 4 5 5
16.
y 2 3 3 4 6
17. x 0 1 4 9 16
18.
y 0 1 2 3 4
19.
x 2 1 0 1 2
20.
y 4 1 0 1 4
Draw the line with the given information. (2.3)
21. 22. m
23. x-intercept is 2, y-intercept is 4 24. x-intercept is 4, y-intercept is 3
2
m 3, b 5
, b 5
3
Write an equation of the line that has the given slope and
y-intercept. (2.4)
25. 26. 27.
28. 29. m 30.
2
m 5, b 2
m 5, b 3
m 2,
b 6
, b 3
3
Write an equation of the line. (2.4)
31. 32. 33.
92 Algebra 2
Chapter 4 Resource Book
y
(2, 6)
2
(0, 0)
2
x
2
5
y
(0, 5)
2
4x 2 8
1
x 4 6
2
x 2 1 3 4
y 0 0 0 0
x 0 1 1 4 4
y 0 1 1 2 2
x 2 1 0 1 2
y 6 3 1 3 6
(6, 1)
x
m
m 0, b 3
1
, b 4 2
2
y
2
(2, 4)
(0, 6)
Copyright © McDougal Littell Inc.
All rights reserved.
x

CHAPTER
4
CONTINUED
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ____________
Cumulative Review
For use after Chapters 1–4
Solve the system using the substitution method or the linear
combination method. (3.2)
34. x 5y 10
35. 3x 4y 20
36.
2x 3y 13
37. 4x 3y 5
38. 3x 6y 5
39.
6x 2y 5
Write the linear equation as a function of x and y. Then evaluate the
function for the given values. (3.5)
40. x 6y z 12, f4, 2
41. x 2y z 8, f3, 2
42. 2x 3y 2z 8, f3, 6
43. 2x 5y 3z 6, f9, 0
44. 3x 6y 2z 10, f 2, 4
45. 2x 4y 3z 9, f3, 9
Use any algebraic method to solve the system. (3.6)
46. 5x 2y 2z 6
47. x 2y 3z 10
48.
3x 3y z 1
5x 5y z 7
Solve the matrix equation for x and y. (4.1)
49. 50.
51. 3x 52.
3
2
4 12
6 15
3x
8
9
7 15
8
y
7
Use Cramer’s rule or an inverse matrix to solve the system. (4.3, 4.5)
53. 2x y 11
54. 3x 6y 3
55.
3x 8y 7
y 9
2x 3y 14
x y 1
2x 2y z 9
4x y 3z 5
5x 8y 4
4x
2
56. Tickets Tickets to the Spring Concert cost $3 for students and $5 for
adults. Sales totaled $1534. Twice as many adult tickets as students tickets
were sold. How many adult tickets were sold? (3.2)
57. Kelvin According to kinetic theory, 273degrees
Celsius is the temperature
at which gas molecules would cease to move; this is called the absolute
zero of temperature. In practice all gases, on cooling, liquefy or solidify
before that temperature is reached. This temperature, 273C,
is taken as
the zero point on the Kelvin scale, so Kelvin temperature is 273 higher than
Celsius temperature. If the Kelvin temperature of a gas is 33 more than six
times the Celsius temperature, what is the temperature of the gas in degrees
Celsius? (4.3)
3
1
3
8 4
3
2
3 5
3
5x 4y 5
2x 5x 2
0.2x 0.3y 3.8
0.5x 0.7y 0.8
2x 3y z 7
2x 5y 3z 13
3x 3y 2z 12
2
1 16
y
x
7 8
2
x 5y 2z 10
2x 8y 3z 2
x y z 6
1
9
9
y
Algebra 2 93
Chapter 4 Resource Book
Review and Assess

Answer Key
Practice A
1. 2. 3. 4.
5. not equal 6. not equal 7. equal
8. 9. 10.
11. The operation is not possible because the
matrices do not have the same dimensions.
12. 13. 14.
15. The operation is not possible because the
matrices do not have the same dimensions.
16. 17.
18. 19.
20. 21.
22. 23.
24. 25.
26. 435
x 2; y 4
x 5; y 1 x 7; y 3
525
562
3
2
6
0
5
1
0
3
7
9
24
12 24 4 0
40
10
25
3
9
0
18
2
6
12
4
13
1
2
3
0
0
0
0
1
11
2
6 4
1
3
3
1
6
3
4 3
3 2 2 1 3 4
6
3
5

Lesson 4.1
LESSON
4.1
14 Algebra 2
Chapter 4 Resource Book
NAME DATE
Practice A
For use with pages 199–206
Determine the dimensions of the matrix.
1. 2. 3. 4.
4
3
4
3 5 7
9
1 2 9
5
5 1
2 6 1
2 6
4 3
Tell whether the matrices are equal or not equal.
5. 6. 2 1 6, 7.
2
1
3 4 4
7 7 1
1 , 3
Perform the indicated operation, if possible. If not possible, state
the reason.
8. 9. 10.
11. 12. 13.
14. 15. 16.
1
2
1
3
1 5
1
5
4
8 1
5
4
8
0
3
4
1 2
4
1
2
2
3
7 4
2
5 3
1
1
2
3
4 2
4
0
1
Perform the indicated operation.
17. 18. 19.
20. 8 21. 22.
3
3
43 6 1
0
5
1
2 3
0
6
1
3
6
2
Solve the matrix for x and y.
23. 24. 25.
26. Endangered and Threatened Species The matrices below show the number
of endangered and threatened animal and plant species as of June 30,
1996. Use matrix addition to find the total number of endangered and
threatened species. (Source: 1997 Information Please Almanac)
ENDANGERED THREATENED
U.S. Foreign U.S. Foreign
Animal
Plant 115
Animal
Plant 94
41
2
320
431
521
1
2x
3
4 10
3
4y
x
5
3
y 2
5
3
4
6
1
4
4 0 2 4
3
4 4
0
0
5 2
5
1 2
6
0
1
6
3
4
2
8
0
3 , 2
2
7
0
4 13
1
5
1
0
8
2
5
0
1
0
3
1 3
7
9
2
3
4
2
7
3x 21 21 7y
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice B
1. 2. 3.
4. The operation is not possible because the matri-
3
1 7
3 6 1
4 0 3
5 12
5 6
0 10
6 1
5 3
ces do not have the same dimensions.
5. 6.
7. 8. 3
13 3 2 10
9
8
9
0
12
16
9
2
0
13
15
9
3
9.
1
6
4
5
0
8
3
4
2
10
20 10 15
10. 11.
0 25 5 20
12
6
6
1
12. 13.
14. 15. $1704 16. $1753
0
2
4
6
8
6
2
19
12
4
1
2
3
2
0
2
1
4
0
9
5
0
11
3

LESSON
4.1
Copyright © McDougal Littell Inc.
All rights reserved.
NAME DATE
Practice B
For use with pages 199–206
Perform the indicated operation, if possible. If not possible, state the reason.
1. 2.
3. 4.
5. 6.
7. 6 2 1 87 5 3 2
7
1
8
2
7
10
5
3
13 1
10
8
8
4
4
3
12
6
9
1
8 4
3 0 10 8
12
5
1
12
7
6
10
11
1
7
11
4
1
2
3
5
7
2
4
6 1
4
6
2
1
7
5
3
9
1
2
2
3
5
4 4
7
2
9
1
6
1
2
3
4 5
7
2
1
Perform the indicated operation.
8. 3
2
9. 21
3
2
0
4
3
2
2
5 1
10.
1
3
4
2
Perform the indicated operations.
11. 12.
13. 3 14.
1
3
4 1
5 2
0
4
1
0
2
1 3
2
4
5 2
3
5
9
Health Club Membership In Exercises 15 and 16, use the following
information.
A health club offers three different membership plans. With Plan A, you can use
all club facilities: the pool, fitness center, and racket club. With Plan B, you can
use the pool and fitness center. With Plan C, you can only use the racket club
facilities. The matrices below show the annual cost for a Single and a Family
membership for the years 1998 through 2000.
1998 1999 2000
Single Family Single Family Single Family
Plan A
Plan B
Plan C
336
228
216
8
624
528
385
Plan A
Plan B
Plan C
384
312
240
720
576
432
2 2
0
Plan A
Plan B
Plan C
420
360
288
15. You purchased a Single Plan A membership in 1998, a Family Plan B
membership in 1999, and a Family Plan A Membership in 2000. How
much did you spend for your membership over the three years?
16. You purchased a Family Plan C membership in 1998, and upgraded to the
next highest plan each year. How much did you spend for your membership
over the three years?
1
2
5
3
0
6
9
4
3
8
2
1
0 2
1
792
672
528
5 1
0
4
5
2
1
1 7
0
5
6
1
3
11
10
2
1
3
1
3
3
3
4
8
13
3
4
Algebra 2 15
Chapter 4 Resource Book
Lesson 4.1

Answer Key
Practice C
1. 2. 3.
0
4
4
14
1
3
3
0
4
4
18
4. 5.
9 15
6. Not possible. The matrices cannot be added
because they do not have the same dimensions.
7. 8.
1
2 6
3 11 7
9. 6 3 10.
4
0
11. 12.
0 1
11 1
13
2
13.
14.
15.
18
1
2
1
6
3
4
5
4
1
Patrick
Mark
Joe
Craig
Daryl
Mike
Patrick
Mark
Joe
Craig
Daryl
Mike
71
12
143
16
1
2
5 2
2
3-point
2
1
3
0
0
0
3-point
30
15
45
0
0
0
8
3
26
3
43 3
4
5
33
70
5
4
12
12
field goals
10
6
5
4
4
3
field goals
150
90
75
60
60
45
16. New York
13 32 11
26 43 25 ;
13
6
13
70
12
6
12
7 60
rebounds
3
3
1
6
5
5
rebounds
45
45
15
90
75
75
16
14

Lesson 4.1
LESSON
4.1
16 Algebra 2
Chapter 4 Resource Book
NAME DATE
Practice C
For use with pages 199–206
Perform the indicated operations, if possible. If not possible, state
the reason.
1. 2. 3.
4. 5. 6.
2
3 1 1
3 5 4 6
3 1
4
1
2 1
5 6 2
2
0
3
4
1 1 1
2 3 0 4
2
4
3
2
1
5 1
7
0
2
3
1
7. 8. 9.
10. 3 11.
2
8
1 3 4
2 412
0
4
1
2
0
1 4
0
2
3 1
1
3
3
1
2
3
1
0
2
1
4
2 2 2
2
5
1
2
3
0
10
7
5
1
1
10 10
1
4
1
2
2
1
3
4
8
31
1 1
9
2
3
1
5
7
3
15
3
1 4 2 2
12. 2 13.
3 0 7 7 14 0
7 7
1
Basketball In Exercises 14 and 15, use the following information.
A high school basketball coach helps the six seniors on the team to set goals for
the season. The goals per game for each senior are as follows.
Patrick: 2 3-pointers, 10 field goals, 3 rebounds Craig: 4 field goals, 6 rebounds
Mark: 1 3-pointer, 6 field goals, 3 rebounds Daryl: 4 field goals, 5 rebounds
Joe: 3 3-pointers, 5 field goals, 1 rebound Mike: 3 field goals, 5 rebounds
14. Write a matrix that represents the game goals for the six seniors.
15. If there are 15 games in a season, write a matrix that represents their
season goals.
16. World Series The New York Yankees won the 1998 World Series in four
games. The matrices below show the statistics for runs, hits, and RBIs for
each team in each game. Write a matrix that gives the series statistics for
runs, hits, and RBIs for each team. Which team had the most hits for the
series?
Game 1 Game 2
R H RBI
R H RBI
San Diego 6
New York
9
8
9
5
9
San Diego 3
New York
9
10
16
3
8
San Diego
New York
R
4
5
Game 3 Game 4
H
7
9
3
RBI
3
5
1
1
2
2
2
6
4
San Diego
New York
4
3
1
1
2 2
3
1
R
0
3
H
7
9
2 1 6
4 32 1
3 3
0
RBI
0
3
1
1
2
4 3
1
8
4
0
1
4
3
2 1
3
2
1
6
1
2
4
4
6
2
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice A
1. AB is not defined. 2. AB is defined; AB:
3. AB is defined; AB:
4. AB is defined; AB: 5. AB is not
defined. 6. AB is defined; AB: 7. AB is
not defined. 8. AB is defined; AB: 9. AB
is defined; AB: 10.
11.
12.
13. 14. 15.
16. 17.
18. The matrices cannot be multiplied because
the number of columns in does not equal the
2
2
4
3
6
3
3 3
2 1
3 2
3 5
2 4
1 1 42 23;
41 22; 40 24
24; 26; 34; 36
21 14; 01 34
14 1 0 2 1
1
12
4
number of rows in
19. 20. 13 21.
1
2
3
1
3
2
1 .
22.
5
3
Opening night
$2220
Second night $2525
Final night $2972.50
3
1
2
4

Lesson 4.2
LESSON
4.2
28 Algebra 2
Chapter 4 Resource Book
NAME DATE
Practice A
For use with pages 208–213
State whether the product AB is defined. If so, give the dimensions of AB.
1. A: 2 2, B: 3 2
2. A: 3 4, B: 4 3
3. A: 2 5, B: 5 1
4. A: 3 2, B: 2 2
5. A: 4 1, B: 4 1
6. A: 3 4, B: 4 5
7. A: 3 5, B: 3 3
8. A: 2 4, B: 4 4
9. A: 1 6, B: 6 1
Complete the next step of the matrix multiplication.
10.
11.
12. 2
0
1
3 2
1
1
4
22 11
02 31
?
?
1
2
3 4 6 14
16
? ?
? ? 3
4
1
2 2
3
1
2
0
4 32 13
?
31 12
?
Find the product. If it is not defined, state the reason.
13. 14. 1 0 15.
1
2 3 2
0
1
16. 17. 18.
1
2 3
2 3
1 4
1
4
19. 20. 1 2 4 21.
3
2
1 0 3
0 2
1 1
5
22. Senior Play The senior class play was performed on three different
evenings. The attendance for each evening is shown in the table below.
Adult tickets sold for $3.50. Student tickets sold for $2.50. Use matrix
multiplication to determine how much money was taken in each night.
Performance Adults Students
Opening night 420 300
Second night 400 450
Final night 510 475
1
5
30 14
?
1 1 1
1
2
3 1
3
3
1
2
1
2
4 1
0
2
1
0
1
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice B
1. A: 3 2;
B: 1 3; AB is not defined.
2. A: 2 3;
B: 3 3;
AB is defined; AB: 2 3
3. A: ; B: AB is defined; AB:
4. A: ; B: ; AB is not defined. 5.
6. 7. 8.
9. 10. 7
2
3
6
11
18
4
7
0
6
5
16
5
1
7
38
3
14
1
0
1
3
0
3
1
4 1 1 2;
4 2
4 2 3 4
11
0
0
1
11. 12. 13.
0 1 6 8
6 6 3 12 6
8 2 28 8
18
14. 15.
33 27
16. 17.
20 6
45 42
10 15
18.
22
4
11
4
20
16
4
20
16
Opening night
$2220
Second night $2525
Final night $2972.50
2
14
4
10
4
11
14

LESSON
4.2
Copyright © McDougal Littell Inc.
All rights reserved.
NAME DATE
Practice B
For use with pages 208–213
State the dimensions of each matrix and determine whether the
product AB is defined. If it is, state the dimensions of AB.
1. 2. A
5
2
3. A B 1
3
1, 7
2
3
4. A
1
0
1
A
3
4
1
1
3
4
2
4
1 , B 4 9 3
Find the product. If it is not defined, state the reason.
5. 6. 7.
8. 9. 10.
11. 12. 13.
4
0
3
6
1
2
1
2 3
2
1
3
2
2
0
4 2
3 4 1
1
2
2
3 5
1
1
0
4
5
2
3
1
2
3
2 1
2
2
3
0
0
1
0
1
2
4 2
1
0
1
0
4
2
3
1
1
6
2
4 3
5
1
2
1
0
1 1 3
2
1
1
1 1
3 5 1
1
2
2
1
Simplify the expression.
4
1
2 1 5
14. 15.
3 4
3
4
2 3
2
16. 17.
2 4 0
0 3 6
1 1 5
1 2
3 0
1 5
3 1
0 2
4
5
1
2
3
0 5
1
3
1
0 2
5
18. Senior Play The senior class play was performed on three different
evenings. The attendance for each evening is shown in the table below.
Adult tickets sold for $3.50. Student tickets sold for $2.50. Use matrix
multiplication to determine how much money was taken in each night.
Performance Adults Students
Opening night 420 300
Second night 400 450
Final night 510 475
4
2
B
6
3, 1
6
5
1
2
0 , B 3
5
3
2
1 1
2
4 4
7
2
4
1
2
6
3
6
8
3
0
3
0 3
2
2
4
7
4
1
0
4
5
5
2
Algebra 2 29
Chapter 4 Resource Book
Lesson 4.2

Answer Key
Practice C
1. 2.
4 8
3 11
3. 4.
11 16
24 16
9 20
5. Not defined. The number of columns of the
first matrix does not equal the number of rows of
the second matrix.
6. 7. 8.
9. 10. 15
20
4
96
68
12
12
16
40
220
136
45
16
2
7 1 114
1
26
32
40
11. x 2, y 3 12. x 5, y 1
13.
0
1
2
3
12
0
3
5
1 ;
8
3
5
9
3
2
14. Rebecca: 380; Craig: 370
16
12
2
2
6
6
93
2
5 2
reflection across x-axis
35
17

Lesson 4.2
LESSON
4.2
30 Algebra 2
Chapter 4 Resource Book
NAME DATE
Practice C
For use with pages 208–213
Find the product. If it is not defined, state the reason.
1. 2. 3.
1
4
6
3
2
1
2
1
3 1
3
2
0
2
1
2
1
4
3 0
1
2
3
4. 5. 6.
1 0 4
3 2 2 1
4
2 5
1 4
3 0
2 2 1 4 2
2 3 1
Simplify the expression.
3
1
7. 8.
1 4 2 0
1 4 3 1 4
6 2 1
9. 4
10.
2 0 1
3 2 6
5 1 1
2 1 1
0 0 5
8
3 1
Solve for x and y.
11. 12.
13. Geometry Matrix B contains the coordinates of vertices of the triangle
shown in the graph. Calculate AB and determine what effect the
multiplication of matrix A has on the graph.
2
1
3
4
1
5 1
3
4
1
2
3
1
1
0
3
4
2 2
1
x 5
2 y
B 0
A
1
1
0
0
1
2
3
5
1
14. Class Election Rebecca and Craig are running for student council
president. After attending a debate, some students change their minds about
the candidate for whom they will vote. The percent of students who will
change their support is shown in the given matrix. Rebecca estimated that
prior to the debate she would lose the election 350 votes to 400 votes. After
the debate, how many votes will Rebecca and Craig receive?
Students who change their support
To
Rebecca
From Craig
Rebecca
0.80
0.25
Craig
0.20
0.75
y
1
(0, 1)
1
(2, 3)
3
1
21
2
3
4
(5, 1)
x
2
1
3
2
2 1
2
1
0
3
2
1
2
1
2
4 1
2
3
2 1
2
4
1 1
6
3
1
0
4
3
0
31
3
1
4
3
0
0
x
1
2 15
31
8
4
1
2 3
1 5 1
32
3
1 4
2
5
6
3
9
y
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice A
1. 20 2. 19
3. 0 4. 7 5. 12 6. 16
7. 15 8. 14 9. 10 10. 20 11. 20
12. 24 13. 4 14. 8 15. 4 16. 1, 4
17. 2, 1 18. 3, 2 19. 0, 3
20. 4, 0 21. 1, 3 22. 0, 0
23. 3, 4 24. 2, 5 25. x 1926; y 1928

Lesson 4.3
LESSON
4.3
42 Algebra 2
Chapter 4 Resource Book
NAME DATE
Practice A
For use with pages 214–221
Evaluate the determinant of the matrix.
1. 2. 3.
1 5
3
6 2
1
3
4. 5. 6.
2 1
4
0 1
7
8
1
7. 8. 9.
2 4
6
1 4
4
Evaluate the determinant of the matrix.
10. 11. 12.
1
0 0
0 4 0
0 0
2 0 0
0 5 0
0 0 2
13. 14. 15.
2
0 0
1 2 0
2 3
2 1 1
0 2 1
0 0
1
Use Cramer’s rule to solve the linear system.
16. x y 5
17. 2x 3y 1
18. 2x y 8
2x y 6
x 5y 3
3x 2y 5
19. 4x 2y 6
20. 2x 5y 8
21. 2x y 5
x 3y 9
x y 4
3x 2y 3
22. 2x 5y 0
23. x 4y 19
24. 3x y 1
3x 7y 0
2x y 2
3x 2y 16
25. Children’s Literature A. A. Milne (1882–1956), an English author,
became famous for his children’s stories and poems. One of Milne’s most
famous works, Winnie-The-Pooh, is based on his son Christopher Robin,
and the young boy’s stuffed animals. Two years after the first book was
published, the Pooh stories continued in the book The House at Pooh
Corner. Solve the linear system given below to find the year that each of
these books were published. (Use Cramer’s rule.)
x y 2
1 1
x y 80
6 8
4
4
5
5
2
4
2
3
5
0
2
2
0
0
1
1
0
5
3
6
3
5
9
0
2
0
2
4
0
0
0
6
2
1
2
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice B
1. 44 2. 32 3. 8 4. 5.
6. 7. 8. 357 9.
10. 11. 12. 13.
14. 1, 1, 2 15. 1, 2, 0 16. 3 17. 4
18. 8.5 19. x y z 538 20. x y 110
21. x z 255 22. 301, 191, 46
3
215
222
20 129
15
2, 5 1, 1 3, 6
1
4 , 4 , 0

LESSON
4.3
Copyright © McDougal Littell Inc.
All rights reserved.
NAME DATE
Practice B
For use with pages 214–221
Evaluate the determinant of the matrix.
1. 2. 3.
1
5
7
3
3
4
5
8
Evaluate the determinant of the matrix.
4. 5. 6.
0
3 2
10 14 2
1 1
5 8 4
4 2 1
1 1 5
7. 8. 9.
10
7 8
4 2 5
3 2 5
13 4 7
1 3 4
0 1 2
Use Cramer’s rule to solve the system of equations.
10. 2x y 9
11. 6x 11y 5
12. x 7y 39
2x 3y 19
6x 5y 1
2x 9y 48
13. 2x 2y 5z 1
14. x y 2z 6
15. 2x y 3z 0
8x z 6
2x 3y z 7
3x 2y z 7
x y 2z 1
3x 2y 2z 5
2x 2y z 2
Use a determinant to find the area of the triangle.
16. y
17. y (2, 3)
18.
(0, 2)
1
(0, 0)
1
(3, 1)
x
(2, 1)
Electoral Votes In Exercises 19–22, use the following information.
In the 1968 presidential election, 538 electoral votes were cast. Of these, x went
to Richard M. Nixon, y went to Hubert H. Humphrey, and z when to George C.
Wallace. The value of x is 110 more than y. The value of y is 145 more than z.
(Source: 1997 Information Please Almanac)
19. Write an equation involving the variables x, y, and z, that represents the
total number of electoral votes.
20. Write an equation that relates the number of electoral votes received by
Nixon, x, to the number of electoral votes received by Humphrey, y.
21. Write an equation that relates the number of electoral votes received by
Nixon, x, to the number of electoral votes received by Wallace, z.
22. Use Cramer’s rule to find the values of x, y, and z.
1
6
1
(3, 2)
x
2
3
1
2
1
0
1
1
0
5
4
9
20
5
15
(1, 3)
(2, 0)
4
3
0
1
Algebra 2 43
Chapter 4 Resource Book
y
1
1
4
2
0
5
1
(4, 1)
x
Lesson 4.3

Answer Key
Practice C
1. 10 2. 7 3. 10 4. 36
5. 104 6. 28
7. 3, 2 8. 1, 4 9. 4, 15
10. 2, 1, 3 11. 1, 0, 2 12. 2, 4, 1
13. 1, 3, 2 14. 3, 2, 4 15. 1, 1, 5
16. det AB det BA 17. det A 0
18. Carbohydrates contain 4 calories per gram. Fat
contains 9 calories per gram. Protein contains 4
calories per gram.

Lesson 4.3
LESSON
4.3
44 Algebra 2
Chapter 4 Resource Book
NAME DATE
Practice C
For use with pages 214–221
Evaluate the determinant of the matrix.
1. 2. 3.
3 5
2 1
4 2
3
1
4. 5. 6.
1
5 3
2 0 0
1 4
6 0 0
0 3 0
0 0 2
Use Cramer’s rule to solve the linear system.
7. 8. 9.
x
10. 2x 4y z 11
11. x 2y z 1
12. 3x y 5z 3
x 3z 7
x 3y 2z 5
2x y z 9
2y 4z 14
x y z 3
x 4y 3z 15
1
1
2x
3x y 7
5x 6y 19
5y 7
2
4x 2y 16
3x 2y 11
3y 8
13. 14. 15.
16. Determiniant Relationships
is det AB related to det BA?
Let A How
2
1
4
3 and B 1
3
1
2 .
x y z 6
2x 2y 7z 30
3x y 2z 12
2x y 3z 1
3x 4y 2z 9
x 4y z 0
3x 2y z 1
5x y z 9
x y 3z 17
17. Determinant Relationships Explain what happens to the determiniant of
any matrix that includes a row of zeros.
18. Nutrition For lunch you eat a peanut butter sandwich on wheat bread
and carrot sticks. The nutritional content for the peanut butter, wheat
bread, and carrots is shown in the table. Use Cramer’s rule to determine
how many calories are in a gram of carbohydrates, fat, and protein.
Carbohydrates Fat Protein Calories
Serving per serving per serving per serving per serving
Peanut butter 7 g 16 g 8 g 204
Wheat bread, 26 g 1 g 6 g 137
2 slices
Carrots 8 g 0 g 1 g 36
8
2
1
2
1
1
3
0
4
2
4
3
0
1
3
4
2
1
2
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice A
1. yes 2. no 3. yes 4. yes 5. no
6.
9.
7. 8.
1
5
3
1
2
1
0
0
1
3
2
4
3
9
7
5
4
10. The matrix does not have an inverse.
11. 12.
13.
14. The matrix does not have an inverse.
15. 16.
17. 18. 15
13
7
6
40
34
15
26
17
29
3
4
8
10
2
3
7
4
3
5
4
7
2
3
3
4
19. 20.
21.
19
10
7
10
13 5, 5 20, 0 13, 5 0, 1 20,
0 19, 21 14, 19 5, 20 0
22. 75 44, 65 35, 26 13,
25 15, 45 23, 38 19, 133 77,
105 62, 100 60
23. 75, 44, 65, 35, 26, 13, 25, 15, 45,
23, 38, 19, 133, 77, 105, 62, 100, 60
1
3
10
9
10
3
24. 25. NOT TONIGHT
2
5
15
4
5
7
5
2
5
3
5
9
6
0
1
2

LESSON
4.4
Copyright © McDougal Littell Inc.
All rights reserved.
NAME DATE
Tell whether the matrices are inverses of each other.
1. 2. 3.
4. 5.
1
0
2
0
3
4
2
6
8 , 0
1
2
1
3
3
4
0
1
2
5
4 , 5
3
3
18
10
11
20
11
12
4
7
2
1
1
1 , 1
1
1
2
5
3
3
2 , 2
3
3
5
Find the inverse of the matrix, if it exists.
6. 7. 8.
3 4
2 3
4 5
7
9
9. 10. 11.
3 4
6 8
6 3
5 3
12. 13. 14.
7 4
5
3 2
4
1
Practice A
For use with pages 223–229
Solve the matrix equation.
15. 16.
17. 18.
19. 20.
6
4
2
2X 2
3
2
1 8
6
2
4
12
5
7
3X 2
3
1
2
1
2
2
3X 4
5
1
2
Encoding Messages In Exercises 21–25, use the following information.
The message, MEET ME AT SUNSET, is to be encoded using the matrix A
21. Convert the message into 1 2 uncoded row matrices.
22. Multiply each of the uncoded row matrices found in Exercise 20 by A to
obtain the coded row matrices.
23. Write the message in code.
24. Find the inverse of A.
5
2
25. You receive the following response: 100, 57, 100, 60, 130, 75, 88,
51, 51, 29, 100, 60. Use the inverse of A to decode the response.
3
5
11
6
5
3
4
4
9X 1
3
7
6X 1
3
1
0
4
3
4
4
0
1
4
6X 1
2
1
2 , 2
7
3
1
3
0
2
3
3
2
4
3
0
3
1 .
3
2
0
2
2
2
4
4
6
1
4
Algebra 2 57
Chapter 4 Resource Book
Lesson 4.4

Answer Key
Practice B
1. No inverse exists. 2. Inverse exists.
3. Inverse exists. 4.
1 5
17 17
5. 6. 7.
2
1
1
0
1
2
8. The matrix does not have an inverse.
9. 10.
2 3
3 4
1
5
4
11. 12.
2
1
1
5 2 5
2
5 1 1 5
13. 14.
3 1
2
5
15. 16.
1 3
0
1
17.
18. ,
19. 75, 65, 26, 25, 45,
38, 133, 105, 100,
20. 21. NOT TONIGHT
1
13 5, 5 20, 0 13, 5 0, 1 20,
0 19, 21 14, 19 5, 20 0
75 44 65 35, 26 13,
25 15, 45 23, 38 19,
133 77, 105 62, 100 60
44, 35, 13, 15,
23, 19, 77, 62, 60
2
3
5
2
5
46
25
3
17
2
11
1
11
1
2
0
0
19
10
7
10
17
5
11
3
11
1
2
1
4
0
7
4
1
1
2
11
8
3
10
9
10
1
5
3
1
2
1
8
1
2
1
2
0
0
14
8
1
2
11
2
3
1

Lesson 4.4
LESSON
4.4
58 Algebra 2
Chapter 4 Resource Book
NAME DATE
Tell whether the matrix has an inverse.
1. 2. 3.
2
1 2
1 0 1
3 2 1
8 2 0
4 1 1
0 0
4
Find the inverse of the matrix, if it exists.
4. 5. 6.
7. 8. 9. 4
3
3
6
4
8
6
5
3
3
2
3
1
2
0
4
3
1
5
2
Use a graphing calculator to find the inverse of the matrix.
10. 11. 12.
1
3 5
0 1 1
2 1
2 4 1
0 4 1
0 0
2
Practice B
For use with pages 223–229
Solve the matrix equation.
13. 14.
15. 16.
4
1
7
2X 2
3
7
4 6
2
2
3
4
8
2
1X 16
22
6
13
Encoding Messages In Exercises 17–21, use the following information.
The message, MEET ME AT SUNSET, is to be encoded using the matrix A
17. Convert the message into 1 2 uncoded row matrices.
18. Multiply each of the uncoded row matrices found in Exercise 20 by A to
obtain the coded row matrices.
19. Write the message in code.
20. Find the inverse of A.
5
2
21. You receive the following response: 100, 57, 100, 60, 130, 75, 88,
51, 51, 29, 100, 60. Use the inverse of A to decode the response.
0
4
1
6
4
7
2X 9
4
2
2X 2
3
5
2
1
0
2
0
1
3
3
12
5
2
4
1
2
1 8
6
3
1 .
0
2
1
5
1
3
2
6
1
2
0
2
2
4
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice C
1. 2.
3. The matrix does not have an inverse.
4.
5.
6.
7.
8
13
1
13
0.2
0.4
0.2
0.8125
1.375
0.75
0.2
0.2
0.2
5
6
1
3 5 15
8. 9.
5 2 8 22
10
4
3
13
2
13
0.12
0.44
0.08
0.1
0.1
0.6
3
4
10. 12 11.
0.1875
0.625
0.25
8.5
11
0.6
0.1
0.6
6
5
47
1
7
0.32
0.16
0.12
12. 13.
14. AB
15. LIVE LONG AND PROSPER
1 B1 A1 A11 A
15.5
4.5
3.5
20.5
6.5
4.5
7.3
2.6
3
9
8
3
14
1
14
0.875
1.25
0.5
11
10
11
4
10
3

LESSON
4.4
Copyright © McDougal Littell Inc.
All rights reserved.
NAME DATE
Practice C
For use with pages 223–229
Find the inverse of the matrix, if it exists.
1. 2. 3.
1
2
3
2
1
3
Use a graphing calculator to find the inverse of the matrix, if it
exists.
4. 5. 6.
0
2 5
4 4 3
2 1
1 1 4
2 1 4
3 1
Solve the matrix equation.
7. 8.
4
2
3
1X 2
4
0
2
1
6
9. 10.
1 4
4 12X 2 0
1 3 7 2
3 1
11.
2
3
8
1
2
4X 1
2
3
0
1
4 3
0
12.
13. Inverse Properties Let How is A related to
14. Inverse Properties Let Calculate
How are A related?
1 , B1 , and AB1 AB, A1 , B1 , and AB1 A
.
1
0
3
4 and B 2
1
1
4 .
A11 A ?
5
2
3
2 .
2
2
4
4
2
8
2
8
6X 1
6
2
4
9
1
1
1
4 7
6
3
2
9
4
1
5
6
15. Cryptography Use the inverse of A to decode 12, 65, 87,
5, 29, 41, 15, 43, 50, 0, 29, 43, 4, 36, 52, 18, 71, 90, 16, 57, 75.
1
0
0
1
1
2
1
1
3
1
5
1
3
8
4
2
1
1
0
2
1
1X 3
4
2
1
2
1
3
2
0
2
2
4
1
1
6
6
0
2
2
3
1
2
0
8
7
1
2
1X 4
1
3 6
19
3
Algebra 2 59
Chapter 4 Resource Book
Lesson 4.4

Answer Key
Practice A
1.
2.
3.
4.
5.
3
1
1
1
2
4
2
1 y
1
12
18
1
2
0
1
0
3
1
3
1 x
y
z 2
4
7
6
5
3
9 x
y 39
25
3
4
1
1 x
y 1
15
1
2
1
1 x
y 3
4
0 x
z
6.
7.
8.
9. 10.
11. 12. 13. 14.
15. 16. 17. 18.
19. 20. 21.
22.
23.
24. 5000, 5000 25. Invest $5000 in Stock A
and $5000 in Stock B.
1
0.1
1
0.06 x
y 10,000
3, 5
4, 2 1, 7 2, 1 6, 2
11, 6 2, 1 5, 0 1, 3
1, 3, 2 5, 0, 3 9, 12, 6
x y 10,000
0.1x 0.06y 800
800
5
6
3
3
1
5
1
3 1
x
y
z 3
7
5
5
2
3
3
2
2
1
4 4
x
y
z 6
6
1
2
3
2
1
1
1
3
4 5
x
y
z 4
9
1
5
2
1
3
2
5
1
3
4 x
y
z 6
1
9

Lesson 4.5
LESSON
4.5
70 Algebra 2
Chapter 4 Resource Book
NAME DATE
Practice A
For use with pages 230–236
Write the linear system as a matrix equation.
1. x y 3
2. 3x y 1
3. 6x 3y 39
2x y 4
4x y 15
5x 9y 25
4. x y z 2
5. 3x y 2z 1
6. 5x 3y z 6
2x 3z 4
x 2y z 12
2x 2y 3z 1
3y z 7
x 4y 18
x 5y 4z 9
7. 2x y 3z 4
8. 5x 3y z 6
9. 5x 3y z 3
3x y 5z 9
2x 2y 4z 6
6x y z 7
2x y 4z 1
3x 2y 4z 1
3x 5y 3z 5
Use an inverse matrix to solve the linear system.
10. x y 2
11. 3x 2y 8
12. 5x 2y 9
2x y 1
4x 3y 10
7x 3y 14
13. 4x 5y 13
14. 3x 7y 4
15. 2x y 16
3x 4y 10
x 3y 0
6x 2y 78
16. 5x 3y 7
17. 4x y 20
18. x 2y 7
3x 2y 4
7x 2y 35
2x 3y 11
Write the linear system as a matrix equation. Then use the given
inverse of the coefficient matrix to solve the linear system.
19. 20. 21.
A1 2
A 3
0
1
1
2
1
2
3
1 2
2x y z 3
x y z 2
3x z 5
9x 6y 7z 24
5x 2y 2z 5
6x 4y 5z 15
11
6
0
1
1
1
5
3
Stock Investment In Exercises 22–25, use the following information.
You have $10,000 to invest in two types of stock. The expected annual returns for
the stocks are shown in the table below. You want the overall annual return to be 8%.
Investment Expected return
Stock A 10%
Stock B 6%
22. Write a linear system of equations that represents the given information.
23. Write the system as a matrix equation.
24. Use an inverse matrix to solve the system.
25. How much should you invest in each type of stock?
x y 2z 9
2x y z 0
x 2y 6z 21
A1
8
13
3
2
4
1
3
5
1
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice B
1.
2.
3. 4.
5. 6. 7. 8.
9. 10. 11.
12. 13. 14.
15. 16. 17.
18.
19.
1
20. 0.12
3
1
0.10
1
1
0.06
1
21. 5000, 7500, 7500 22. Invest $5000 in Stock
X, $7500 in Stock Y, and $7500 in Stock Z.
23. You can make 300 pounds of alloy X, 700
pounds of alloy Y, and 400 pounds of alloy Z.
x
y
z 20,000
5, 0
9, 8 1, 2, 0 1, 4, 3
2, 3, 1 5, 0, 3 1, 3, 1
6, 4, 4
x y z 20,000
0.12x 0.10x 0.06z 1800
3x y z 0
1800
0
44
5 , 26
51, 18
1, 3 2, 1 8, 4 4, 4
1, 5
5
1
2
3
2
1
5
3
2
9 x
y
z 14
16
36
1
2
9
4 x
y 20
15
2
3
4
1 x
y 7
12

LESSON
4.5
Copyright © McDougal Littell Inc.
All rights reserved.
NAME DATE
Practice B
For use with pages 230–236
Write the linear system as a matrix equation.
1. 2x 4y 7
2. x 9y 20
3. x 2y 3z 14
3x y 12
2x 4y 15
2x y 2z 16
3x 5y 9z 36
Use an inverse matrix to solve the linear system.
4. 2x 5y 12
5. 2x y 5
6. 2x 6y 2
x 3y 3
x 4y 11
x 5y 3
7. 5x 3y 52
8. 3x 7y 16
9. 2x 3y 13
3x 2y 32
2x 4y 8
x y 4
10. 2x 3y 2
11. 2x 7y 10
12. x y 1
x 4y 12
3x 4y 15
2x 3y 6
Use an inverse matrix and a graphing calculator to solve the linear system.
13. 2x 6y 4z 10
14. 5x 4y z 14
15. x y 2z 7
3x 10y 7z 23
5x 2y 3
2x z 5
2x 6y 5z 10
2x 5y 2z 24
9x 2y z 25
16. x y z 2
17. x 2y 7
18. 2x y 3z 4
x 2y z 8
3x 5y z 11
x 2y z 2
y z 3
5x 2y z 0
x 3y 4z 10
Stock Investment In Exercises 19–22, use the following information.
You have $20,000 to invest in three types of stocks. You expect the annual
returns on Stock X, Stock Y, and Stock Z to be 12%, 10%, and 6%, as
respectively. You want the combined investment in Stock Y and Stock Z to be
three times the amount invested in Stock X. You want your overall annual return
to be 9%.
19. Write a linear system of equations that represents the given information.
20. Write the system as a matrix equation.
21. Use an inverse matrix and your graphing calculator to solve the system.
22. How much should you invest in each type of stock?
23. Pewter Alloys Pewter is an alloy that consists mainly of tin. It also
contains small amounts of antimony and copper. Three pewter alloys
contain percents of tin, antimony, and copper as show in the matrix below.
You have 1296 pounds of tin, 69 pounds of antimony, and 35 pounds of
copper. How much of each alloy can you make?
PERCENTS ALLOY BY WEIGHT
X Y Z
Tin
Antimony
Copper
0.90
0.08
0.02
0.94
0.03
0.03
0.92
0.06
0.02
Algebra 2 71
Chapter 4 Resource Book
Lesson 4.5

Answer Key
Practice C
1.
2.
1
2
3.
1
1
1
1
1
2
1
3
1
4
1 4
1 x
z
8
6
2 y 3
1w
4. 2, 1 5. 3, 6 6. 25, 50
7. 6, 12, 6 8. 10, 3, 2
9. 3, 6, 12 10. 10, 5, 0
11. 6, 2, 1, 3 12. 150, 300, 300, 600
13. 3 lb ham, 3 lb turkey, 2 lb roast beef, 4 lb
cheese
14. f s j s 690 ;
f s j s 10
0.05f 0.05s 0.1j 0.16sn 61
2
3
1
1
1
1
1
4
1 x
y
z 4
2
6
1
2
4
3 x
y 3
1
0.1f 0.15s 0.12j 0.08sn 78
180 freshmen, 160 sophomores, 200 juniors,
150 seniors

Lesson 4.5
LESSON
4.5
72 Algebra 2
Chapter 4 Resource Book
NAME DATE
Practice C
For use with pages 230–236
Write the linear system as a matrix equation.
1. x 4y 3
2. 2x y z 4
3. w x y z 4
2x 3y 1
3x y 4z 2
2w x 3y z 8
x y z 6
w x y 2z 3
w 2x 4y z 6
Use an inverse matrix to solve the linear system.
4. 2x 3y 7
5. x 3y 21
6. 2x 9y 400
4x 4y 4
x 2y 15
3x y 25
Use an inverse matrix and a graphing calculator to solve the linear system.
7. 2x y 4z 48
8. x y z 9
9. x y z 3
x 2y 2z 6
2y z 4
x 2z 27
x 3y 4z 54
3y z 7
x y 2z 21
10. 2x y 2z 15
11. w x y z 10
3x 3y z 15
w 2y z 7
x 3y z 5
w x 3y z 8
w x 4y 4z 16
12.
w 2x 4y 3z 1350
w 2x y 4z 3150
2w 3x y z 900
2w x y 3z 2100
13. Deli Platter You want to order a deli platter for a sports banquet. You
need 12 pounds of meat and cheese. You want twice as much meat as
cheese on the platter and the same amount of ham and turkey. The price
per pound is $4.95 for ham, $6.99 for turkey, $7.99 for roast beef, and
$4.36 for cheese. How many pounds of each should you order if you plan
to spend $69.24?
14. School Population Six hundred ninety students attend your high
school. There are 10 more upper classmen (juniors and seniors) than under
classmen (freshmen and sophomores). Five percent of the freshmen, 5%
of the sophomores, 10% of the juniors, and 16% of the seniors are
members of the student government. The student government has 61
members. During the last grading period 78 students were named to the
honor roll. Ten percent of the freshmen, 15% of the sophomores, 12% of
the juniors, and 8% of the seniors made the honor roll. Write and solve a
system of equations to find the number of students in each class.
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Test A
1. y 2.
3. y
4. 0, 4 5. 7, 7
2
6. 4, 3 7. 8.
9. 10. 11.
12. 13. 14.
15. 16. 17. 18.
19. 20.
3 29
,
2
21. 100; 2 real solutions 22. 81; 2 real solutions
3 29
3i, 3i i6, i6
5 13 3, 1 2 ± 7
1, 9
2
5i
12, 12 22, 22
3, 5 3 2i 4 2i
7
23. y 24.
25. 1.84 seconds
2
1
1
1
1
x
x
x
1
y
1
y
1
2
x
x

CHAPTER
5
NAME _________________________________________________________ DATE
Chapter Test A
For use after Chapter 5
____________
Graph the quadratic function.
1. 2. y x2 y x 1
2
3.
2
y
Solve the quadratic equation by factoring.
4. 5. 6. 3x2 x 21x 36 0
2 x 49 0
2 4x 0
Solve the quadratic equation using any appropriate method.
7. 8. 9. 4x 12 x 64
2 x 8 0
2 144
Simplify the expression.
10. 3 4 11. 7 8i 3 6i 12. 5 7i
Solve the equation.
13. 14. 2y2 6 y2 x2 9
Find the absolute value of the complex number.
15. 2 i
16. 3i 2
Solve the equation by completing the square.
17. 18. x2 x 4x 3 0
2 4x 3 0
Use the quadratic formula to solve the equation.
19. 20. x2 x 3x 5 0
2 10x 9 0
Copyright © McDougal Littell Inc.
All rights reserved.
2
1
y x 2 10x 25
y
1
x
x
1
y
1
x
Answers
1. Use grid at left.
2. Use grid at left.
3. Use grid at left.
4.
5.
6.
7.
8.
9.
10
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
Algebra 2 119
Chapter 5 Resource Book
Review and Assess

Review and Assess
CHAPTER
5
CONTINUED
NAME _________________________________________________________ DATE ____________
Chapter Test A
For use after Chapter 5
Find the discriminant of the equation and give the number
and type of solutions of the equation.
21. 22. 2x2 x 5x 7 0
2 6x 16 0
Graph the quadratic inequality.
23. 24. y ≤ 2x2 y > x 1
2
1
y
25. Ball Toss You toss a ball into the air at a height of 5 feet.
The velocity of the ball is 30 feet per second. You catch the ball
6 feet from the ground. Use the model
6 16t 2 30t 5
to find how long the ball was in the air.
120 Algebra 2
Chapter 5 Resource Book
1
x
1
y
1
x
21.
22.
23. Use grid at left.
24. Use grid at left.
25.
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Test B
1. y 2.
3. y
4. 0, 8 5. 3, 3
1
6. 7. 8.
9. 10. 11.
12. 13. 14.
15. 16. 17.
18. 19.
20.
3 i11
,
2
21. 19; two imaginary solutions
22. 84; two real solutions
23. y 24.
y
3 i11
3, 5 9, 9 23, 23
0, 4 4 3i 1 i
21 3i
50
3i, 3i 2i, 2i
25 26 3, 4
2 2, 2 2 7, 3
2
25. 1.84 seconds
1
1
1
1
2
x
x
x
1
y
1
1
2
x
x

CHAPTER
5
NAME _________________________________________________________ DATE
Chapter Test B
For use after Chapter 5
____________
Graph the quadratic function.
1. 2. y 2x2 y x2 1
3.
Solve the quadratic equation by factoring.
Solve the quadratic equation using any appropriate method.
Simplify the expression.
12.
1
7. 8. 9. 4x 22 4x 16
2 x 48
2 81 0
10. 4 4 i
11. 9 7i 10 6i
3
7 i
y
4. 5. 6. 2x2 3x 4x 30 0
2 x 27 0
2 8x 0
Solve the equation.
13. 14. 4y2 8 2y2 x2 1 8
Find the absolute value of the complex number.
15. 2 4i
16. i 5
Solve the equation by completing the square.
17. 18. x2 x 4x 2 0
2 7x 12 0
Copyright © McDougal Littell Inc.
All rights reserved.
1
1
y x 2 4x 4
y
1
x
x
1
y
1
x
Answers
1. Use grid at left.
2. Use grid at left.
3. Use grid at left.
4.
5.
6.
7.
8.
9.
10
11.
12.
13.
14.
15.
16.
17.
18.
Algebra 2 121
Chapter 5 Resource Book
Review and Assess

Review and Assess
CHAPTER
5
CONTINUED
NAME _________________________________________________________ DATE ____________
Chapter Test B
For use after Chapter 5
Use the quadratic formula to solve the equation.
19. 20. x2 x 3x 5 0
2 10x 21 0
Find the discriminant of the equation and give the number
and type of solutions of the equation.
21. 22. 4x2 x 2x 5 0
2 7 3x
Graph the quadratic inequality.
23. 24. y < 2x2 y ≥ x 3
2
1
y
25. Vertical Motion An object is released into the air at an initial
height of 6 feet and an initial velocity of 30 feet per second. The
object is caught at a height of 7 feet. Use the vertical motion model,
h 16t 2 vt s,
where h is the height, t is the time in motion, s is the initial height,
and v is the initial velocity, to find how long the object is in motion.
122 Algebra 2
Chapter 5 Resource Book
1
x
1
y
1
x
19.
20.
21.
22.
23. Use grid at left.
24. Use grid at left.
25.
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Test C
1. y 2.
3. y 4. , 5 5. 6. 2, 3
7. 25, 25 8. 1 6, 1 6
9. 1 i19, 1 i19 10. 3 3i 11. 1
12.
3 4i
5
13. 2i2, 2i2
14. 82, 82 15. 65 16. 10
17.
18.
1 3i, 1 3i
9 105
,
4
9 105
4
19.
3 i11
,
2
20. 2 2i, 2 2i
21. 121; 2 real solutions
22. 23; 2 imaginary solutions
23. y 24. y
3 i11
2
25. 1.84 seconds
2
2
1
2
1
1
x
x
x
5
2
2
1
1
y
1
1
2
3
x
x

CHAPTER
5
NAME _________________________________________________________ DATE
Chapter Test C
For use after Chapter 5
____________
Graph the quadratic function.
1. 2. y x2 y x 2x 5
2 1
3.
Solve the quadratic equation by factoring.
Solve the quadratic equation using any appropriate method.
7. 8. 9.
3x 12 5x 4 22
2 100
Simplify the expression.
10. i 3 4
11. 5 8i 4 8i
12.
2 i
2 i
2
4. 5. 6. 6 x2 9x x
2 4x 12x 4 0
2 25 0
Solve the equation.
13. 2x 14.
2 1 15
Find the absolute value of the complex number.
15. 8 i
16. 5 i5
Solve the equation by completing the square.
17. 18. 2x2 x 9x 3
2 2x 10 0
Copyright © McDougal Littell Inc.
All rights reserved.
y
1
y x 2 2 4
2
y
1
x
x
1
y
1
1
4 x2 1 33
x
x2 x
2 0
10 5
Answers
1. Use grid at left.
2. Use grid at left.
3. Use grid at left.
4.
5.
6.
7.
8.
9.
10
11.
12.
13.
14.
15.
16.
17.
18.
Algebra 2 123
Chapter 5 Resource Book
Review and Assess

Review and Assess
CHAPTER
5
CONTINUED
NAME _________________________________________________________ DATE ____________
Chapter Test C
For use after Chapter 5
Use the quadratic formula to solve the equation.
19. 20. 2x2 x 8x 16
2 3x 5
Find the discriminant of the equation and give the number
and type of solutions of the equation.
21. 22. 2y2 6x 3y 4
2 4 5x
Graph the quadratic inequality.
y ≤ 2x 2 1
23. 24.
1
y
25. Vertical Motion An object is released into the air at an initial
height of 9 feet and an initial velocity of 30 feet per second.
The object is caught at a height of 10 feet. Use the vertical
motion model,
where h is the height, t is the time in motion, s is the initial height,
and v is the initial velocity, to find how long the object is in motion.
124 Algebra 2
Chapter 5 Resource Book
1
h 16t 2 vt s,
x
y ≥ x 2 5x 6
1
y
1
x
19.
20.
21.
22.
23. Use grid at left.
24. Use grid at left.
25.
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Cumulative Review
1. 24 2. 25 3. 25 4. 14 5. 12 6. 12
7. 8. 2
9. x < 2
10.
11.
16
45
3 2 1 0 1 2 3
x < 3
7
12. 13.
14. 5, 15. x > 3 or x < 2
16. 4 < x < 8 17. 23 18. 27 19. 9
5
x < 10 4 < x < 4
3
20. 4 21. 0 22. undefined
23. perpendicular 24. neither 25.
26. 27. y
28. 29.
2
y 5x 3
y 4
3x 2
1
y
(0, 5)
1
30. 31.
y
1 (0, 0)
1
3 2 1 0 1 2 3
(3, 3)
(1, 5)
32. y 2x 12 33. y x 1
x
x
3
7
x ≤ 4
3
4
3
3 2 1 0 1 2 3
1
y
1
(0, 6)
(2, 2)
y 1 8
3x 3
x
34. 35.
1
y
1
36. 37.
y
38.
39.
1
40. 41.
1
y
42. 43.
1
1
1
y
1
x
x
x
x
1
y
1
1, 4
2, 4
2, 1, 4
1
8
12
1
y
12
2
x
x

Answer Key
44. 1, 3
45. 2, 2 46. 3, 1, 0
47. 3, 4 48. 1, 2 49. 1, 0, 3
50. 51.
(2, 6)
2
52. 53.
x 1
y
(2, 2) (0, 2)
(1, 5)
(3, 5)
y
1
x 3
(4, 6)
y (x 3)
2
x
2 5
1
y 3x 2 6x 2
x
x 0
(1, 0)
(0, 3)
x 8, 2
54. 55.
56. 57. 58.
59. 60. 61. 15 8
17 17i 10 11
17 17i 6 33, 6 33 4, 2
2 8i 17 i 3 3i
2 23i
2
y
(1, 0)
2
y 3(x 1)(x 1)
x

Review and Assess
CHAPTER
5 Cumulative Review
NAME _________________________________________________________ DATE ____________
For use after Chapters 1–5
Evaluate the expression. (1.1)
1. 3 32 5 2. 3.
2
Simplify and evaluate the expression for the given value of the
variable. (1.2)
4. when 5. 3a when
6. 2n 1 4n 2 when n 1
2 a 2a2 x x 2
2 8 x
Solve the equation. (1.3)
7.
1 1
1
x 2x 8. 32x 1 4x 1 5
2
Solve the inequality and draw its graph. (1.5)
9. 3x 1 < 2x 3
10. 2x 3 ≥ 5x 1
11. 4x 3 > 3x
Solve the compound inequality. (1.6)
12. 3x 1 < 2x 9 or 5x 3 < 53
13. 4 < 2x 4 < 12
Solve the absolute value equation or inequality. (1.7)
14. 3x 5 10
15. 4x 2 > 10
16.
Evaluate the function when x 5. (2.1)
17. 18. f x x 19.
2 gx x 2
2 2
Find the slope of the line passing through the points. (2.2)
20. 4, 3 and 6, 5
21. 2, 0 and 8, 0
22. 5, 8 and 5, 14
Tell whether the two lines are parallel, perpendicular, or neither. (2.2)
23. Line 1: through 5, 3 and 8, 4
24. Line 1: through 5, 9 and 2, 5
Line 2: through 2, 7 and 1, 20
Line 2: through 6, 3 and 9, 9
Write the equation with the given slope and y-intercept. (2.3)
25. m 5; b 3
26. m 0; b 4
27.
Graph the equation. (2.3)
28. y 29. y 4x 6
30. y 5x
2
x 5
Write the equation of the line that passes through the given point
and has the given slope. (2.4)
31. m 32. 6, 0; m 2
33. 4, 5; m 1
1
5, 1;
Graph the inequality. (2.6)
34. y ≥ 35. y < x 5
36. 2x y < 4
2
x 3
3
3
3
130 Algebra 2
Chapter 5 Resource Book
3
5
5 2
5 2
a 3
x 2 < 6
f x x 3 2 5
m 2
3 ;
b 2
Copyright © McDougal Littell Inc.
All rights reserved.

CHAPTER
5
CONTINUED
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ____________
Cumulative Review
For use after Chapters 1–5
Solve the linear system. (3.2, 3.6)
37. 2x 3y 14
38. 3x 5y 14
39. 2x 3y z 11
Perform the indicated operation. (4.1)
43.
x 5y 19
1
6
3 3
2 3 2
Use Cramer’s Rule to solve the system. (4.3)
44. 2x 3y 11
45. 2x 2y 0
46. 4x 2y 3z 14
x 4y 11
Use matrices to solve the linear system. (4.5)
47. 2x 4y 22
48. 3x 2y 7
49. x 2y 3z 10
3x y 13
5
0
2x 3y 16
Graph the system of linear inequalities. (3.5)
40. y < x 2
41. y > 3x 2
42. 3x y ≥ 5
y > 3x 1
y > 2x 1
2x y ≤ 3
5x 3y 4
5x 4y 3
4x y 2z 1
3x 2y 2z 0
2x y 5x 5
3x 2y 5z 7
2x 3y 4z 10
2x 3y 5z 13
Graph the quadratic function. Label the vertex and the axis of
symmetry. (5.1, 5.3)
50. 51. 52. y 3x2 y x 3 y 3x 1x 1
6x 2
2 5
Solve the equation. (5.3, 5.5)
53. 54. 55. x2 x 6x 8 0
2 3x 5 12x 3 0
2 27
Write the expression as a complex number in standard form. (5.4)
56. 4 3i 2 5i
57. 7 3i2 i
58. 6 2i 3 5i
59. 3 2i4 5i
60.
3 2i
4 i
4 i
61.
4 i
Algebra 2 131
Chapter 5 Resource Book
Review and Assess

Answer Key
Practice A
1. y 2x opens up
2 x 1;
2. y x ; opens down
2 x 3
3. y 5x ; opens down
2 3x 4
4. y x opens up
2 2x 1;
5. y 3x opens down
2 4;
6. y 9x opens up
2 x;
7. y x opens up
2 5x 3;
8. y 3x opens down
2 4x 1;
9. opens down
10. 11. 12.
13. 14. 15.
16. 17. 18.
19. 20. 21. 22. B
23. A 24. C 25.
26.
27.
28. 29.
30. y 4x
31. y
32.
y
2 y x
12x 8
2 y 2x 9x 18
2 y 2x
4x 6
2 y x
12x 19
2 y 3x
2x 3
2 x x 0
1, 2 2, 5 3, 17
0, 5 0, 4 1, 2
12x 13
1
x
x 3
2
4
y 2x
x 1 x 1
3
2 3x 3;
33. y
34. 14 ft
1
1
1
x = 1
(1, 3)
1
(2, 1)
x = 2
x
x
x = 2
(2, 1)
3
1
x

LESSON
5.1
2
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice A
For use with pages 249–255
Write the quadratic function in standard form. Determine whether
the graph of the function opens up or down.
1. 2. 3.
4. 5. 6.
7. 8. 9. y 3x 2x2 y 3x 3
2 y x 1 4x
2 y x 9x
3 5x
2
y 4 3x2 y 2x 1 x2 y 4 3x 5x2 y 3 x x2 y 2x2 x 1
Find the axis of symmetry of the parabola.
10. 11. 12.
13. 14. 15. y 3x2 y 2x 5
2 y x 2x 3
2 y 3x
6x
2 y x 8x 2
2 y 2x 2x 5
2 4x 1
Find the vertex of the parabola.
16. 17. 18.
19. 20. 21. y 2x2 y x 4x
2 y x 4
2 y x
5
2 y 2x 6x 8
2 y x 8x 3
2 2x 1
Match the quadratic function with its graph.
22. 23. 24. y x 1
A. B. C.
2 y x y x 3x 5
12
2 2x 15
y
2
x
Write the quadratic function in standard form.
25. 26. 27. y 2x 3
28. y 2x 3x 1
29. y x 3x 6
30. y 4x 1x 2
2 y x 1 1
2 y 3x 2 2
2 1
Graph the quadratic function. Label the vertex and axis of symmetry.
31. 32. 33. y x 22 y x 2 1
2 y x 1 1
2 3
34. Maximum Height The path that a diver follows is given
by y 0.4x 4 where x is the horizontal distance
(in feet) from the edge of the diving board and y is the height
(in feet). What is the maximum height of the diver?
2 14
2
y
2
x
2
y
2
2
Algebra 2 15
Chapter 5 Resource Book
y
2
x
x
Lesson 5.1

Answer Key
Practice B
1. y x ; opens down
2 2x 3
2. y 3x opens up
2 3x 4;
3. y 4x opens down
2 5;
4. 5.
6.
7. y
8.
1 15
2 , 4 ; x 1
2, 4; x 2
2
9. y
10.
11. y
12.
3
13. y 14.
x = 7
30 10
(7, 58)
15. y 16.
x = 1
2
1
1
1
1 7
( ,
2 4)
x = 0
(0, 0)
(0, 2)
1
x = 0
30
50
3
9 15 x
x = 3
(3, 18)
1
x
x
30 x
x
1 1
6 , 12; x 1
6
3
1
21
15
9
3
y
3
3
x = 1 y
10
(1, 9)
(1, 3)
x = 1
3
y
(0, 1)
x = 0
y
x = 4
(4, 18)
1
1
x = 1
(1, 1)
y
2
1
x
x
15 x
x
x
17. y
18.
19. y 20.
21. y
22.
23. y 24.
25. y 26.
27. y 28.
x = 1
1
3
1
5 9
( ,
2 4 )
5
x =
2
(1, 3)
1
(2, 1)
x = 2
( , )
3 25
2 4
1
1
1
(3, 2)
x = 3
1
3
x = 1
(1, 4)
1
x
1 x
x
x
x = 3
2
1 x
x
29. $700 30. 20 31. March 16 32. $1.26
100
( , )
7 1
2 4
y
4
1
y
y
1
1
x = 2
(2, 3)
y x = 1
(1, 8)
2
1
x = 2
(2, 5)
1
2
y
(20, 700)
1
x = 7
2
1
y
x = 3
x
x
x
1 x
x
(3, 1)
x

Lesson 5.1
LESSON
5.1
Practice B
For use with pages 249–255
16 Algebra 2
Chapter 5 Resource Book
NAME _________________________________________________________ DATE ___________
Write the quadratic function in standard form. Determine whether
the graph of the function opens up or down.
1. 2. 3. y 5 4x2 y 3x 3x2 y 3 2x x 4
2
Find the vertex and axis of symmetry of the parabola.
4. 5. 6. y x2 y 3x x 4
2 y x x
2 4x 8
Graph the quadratic function. Label the vertex and axis of symmetry.
7. 8. 9.
10. 11. 12.
13. 14. 15. y 3x2 y 2x 3x 1
2 y x 4x 7
2 y x
14x 9
2 y 2x 8x 2
2 y x 12x
2 y x
2x
2 y x 2
2 y x 1
2
Graph the quadratic function. Label the vertex and axis of symmetry.
16. 17. 18.
19. 20. 21. y 3x 12 y 2x 2 4
2 y x 2 3
2 y x 2
1
2 y x 3 5
2 y x 1 2
2 3
Graph the quadratic function. Label the vertex and axis of symmetry.
22. y x 3x 4
23. y x 4x 1
24. y x 2x 4
25. y x 4x 1
26. y 2x 3x 1 27. y 3xx 2
Minimum Cost A manufacturer of lighting fixtures has daily production costs
modeled by y 0.25x where y is the total cost in dollars and x
is the number of fixtures produced.
28. Sketch the graph of the model. Label the vertex.
29. What is the minimum daily production cost, y?
2 10x 800
30. How many fixtures should be produced each day to yield a
minimum cost?
Price of Gasoline The price of gasoline at a local station throughout the month
of March is modeled by y 0.014x where x 1 corresponds
to March 1.
31. On what day in March did the price of gasoline reach its maximum?
32. What was the highest price of gasoline in March?
2 0.448x 2.324
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice C
1. y
2.
x 0
1
(0, 0)
1
3. y
4.
5. y
6.
7. y 8.
x 5
4
(0, 8)
1
x 2
3
5 49
( ,
4 8 )
9. y 10.
5 49
( ,
8 8 )
x 0
2
11. y
12.
2
1
1 81
( ,
4 8 )
2
2
2
2 4
,
3 3
( )
1
1
1
x = 5
8
x = 1
4
x
x
x
x
x
x
y
2
x =
23
10
1
2
23 , 319
(
10 10 )
y
y
x = 3
3 5
( ,
2 4)
2
x 0
1
1
(0, 5)
x 7
2
x 0
(0, 1)
7 49
( ,
2 4 )
( )
5 1
1 ,
12 24
1
x = 5
12
1
2
5
y
1
y
x
x
x
x
x
1
x
13. y 14.
15. y 16.
17. y
18.
19. 20.
21. 22. y 1
y
26. 27. y
28. y
As a increase the graph
becomes more narrow.
3
2x2 9x 31
y 2
5
3x2 20 41
3 x 6
1
29. 1996
1
(1, 1)
x = 1
x = 2
(2, 3)
1
3 25
( ,
2 8 )
x = 3
2
1
6
1
1
x
23 25
( ,
12 24 )
y (2, 36)
x = 2
1
1
4
1
x = 23
12
1
x
x
x
x
x
y
1
x = 1
15 169
( ,
4 8 )
x = 15
4
y
5
(1, 4)
15
2x2 3
2
23.
24.
25. y 1
y x
5
x 2 13
y 2x
2
15x 15
2 1 3
x 2 4
1
1
x = 17
10
1
8x2 1
4
(3, 2)
x = 3
17 529
( ,
10 20 )
y
y
1
2
x 2
8
x
x
x
x

LESSON
5.1
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice C
For use with pages 249–255
Graph the quadratic function. Label the vertex and axis of
symmetry.
1. 2. 3.
4. 5. 6.
7. 8. 9.
10. 11. 12.
13. 14. 15.
16. 17. 18.
19. 20. 21. y 1
y
y 5x 3x 4
y 3x 72x 3
y 3x 13x 5
y x 4x 8
y 2x 1x 7
2x 4x 1
5
4x 22 y 3
2
3x 32 y 2x 1 2
2 y x
1
2 y 2x 3x 1
2 y 10x x 10
2 y 8x
46x 21
2 y 6x 10x 3
2 y 2x 5x 1
2 y 2x
5x 3
2 y 3x 1
2 y x 4x
2 y 2x
7x
2 y x 8
2 y 3x 5
2
Write the quadratic function in standard form.
22. 23. 24.
25. 26. 27.
28. Visual Thinking Use your graphing calculator to graph y ax 3
where a 2, 3, and 4. Use the same viewing window for all three graphs.
How do the graphs change as a increases?
2 y
1
3
2x 32 y 2
5
3x 22 1
y 6
1
8x 12 1
y x
2
2
y 2x 1
2x 3
y 4
1
2x 4x 1
29. Poultry Consumption From 1990 to 1996, the consumption of poultry
per capita is modeled by y 0.2125t where t 0
corresponds to 1990. During what year was the consumption of poultry per
capita at its maximum?
2 2.615t 56.33,
3x 1
5
Algebra 2 17
Chapter 5 Resource Book
Lesson 5.1

Answer Key
Practice A
1. x 2x 3
2. x 5x 1
3. x 3x 1 4. x 3x 2
5. x 6x 3 6. x 3x 1
7. x 4x 2 8. x 4x 1
9. x 4x 1 10. x 4x 4
11. x 2x 2 12. x 3x 3
13. x 1x 1 14. x 3x 3
15. x 2x 2 16. x 8x 8
17. x 4x 4 18. x 8x 8
19. 2x 1x 1 20. 3x 2x 2
21. 2x 1x 1 22. 3x 1x 1
23. x 3x 3 24. 2x 4x 4
25. 2x 1x 2 26. 3x 1x 2
27. x 2x 3 28. 1, 3 29. 2, 1
30. 4, 5 31. 2 32. 1 33. 3 34. 5
35. 4, 4 36. 9, 9 37. 5, 2 38. 6, 6
39. 7 40. 12 ft by 3 ft 41. 17 ft by 3 ft
42. 2 seconds 43. 1 second 44. 3 seconds

Lesson 5.2
LESSON
5.2
28 Algebra 2
Chapter 5 Resource Book
NAME _________________________________________________________ DATE ___________
Practice A
For use with pages 256–263
Factor the expression. If the expression cannot be factored, say so.
1. 2. 3.
4. 5. 6.
7. 8. 9.
10. 11. 12.
13. 14. 15.
16. 17. 18. x2 x 16x 64
2 x 8x 16
2 x
64
2 x 4
2 x 6x 9
2 x
2x 1
2 x 6x 9
2 x 4x 4
2 x
16
2 x 3x 4
2 x 3x 4
2 x
6x 8
2 x 4x 3
2 x 9x 18
2 x
5x 6
2 x 4x 3
2 x 6x 5
2 x 6
Factor the expression.
19. 20. 21.
22. 23. 24.
25. 26. 27. x 2 3x 5x 6
2 2x 9x 6
2 2x
2x 4
2 x 16x 32
2 3x 6x 9
2 2x
6x 3
2 3x 2
2 2x 12
2 4x 2
Solve the equation.
28. 29. 30.
31. 32. 33.
34. 35. 36.
37. 38. 39. x2 x 14x 49
2 x 36
2 x
3x 10
2 x 81 0
2 x 16 0
2 x
10x 25 0
2 x 6x 9 0
2 x 2x 1 0
2 x
4x 4 0
2 x 9x 20 0
2 x 3x 2 0
2 2x 3 0
Find the dimensions of the figure.
40. Area of rectangle 36 square feet 41. Area of rectangle 51 square feet
x 9
x
Find the time (in seconds) it takes an object to hit the ground
when it is dropped from a height of s feet. Use the falling-object
model h 16t2 s.
x 14
42. s 64
43. s 16
44. s 144
x
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice B
1. 2. cannot be factored
3. 4.
5. 6.
7. cannot be factored 8.
9. 10.
11. 12.
13. 14.
15. cannot be factored 16.
17. 18.
19. 20.
21. 22. cannot be factored
23. cannot be factored 24.
25. 26.
27. 28.
29. 30.
31.
32.
33. 34.
35. 36. 4, 8 37. 4, 38.
1
x 7x 3
x 3x 5 x 7x 2
x 7x 4 x 6x 4
2x 1x 3
3x 2x 1 3x 1x 2
2x 3x 1 2x 15x 1
6x 1x 2 5x 33x 1
x 8x 8
x 3x 3 x 7x 7
2x 12x 1 3x 23x 2
3x 13x 1
2x 53x 1
2x 5x 3 x 3x 7
3x 4x 1 22x 1x 3
32x 1x 5 22x 3x 4
32x 12x 1
22x 32x 3
53x 13x 1 6, 5
9, 1
39. 40. 41. 42. 43.
44. 45. 46.
1
ft 47. $2.65
4
1
7
4
5 , 5
2
5
3
5
3, 7
1,
2
2
5
1,
1
2 , 3
5
2
2
3, 1
3

LESSON
5.2
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice B
For use with pages 256–263
Factor the expression. If the expression cannot be factored, say so.
1. 2. 3.
4. 5. 6.
7. 8. 9.
10. 11. 12.
13. 14. 15.
16. 17. 18.
19. 20. 21.
22. 23. 24. 6x2 4x 17x 5
2 x 7
2 9x
8x 5
2 9x 1
2 4x 12x 4
2 x
4x 1
2 x 49
2 x 6x 9
2 2x
16x 64
2 15x 7x 1
2 6x 14x 3
2 10x
13x 2
2 2x 3x 1
2 3x 5x 3
2 3x
7x 2
2 2x x 2
2 x 5x 3
2 x
3x 1
2 x 10x 24
2 x 11x 28
2 x
9x 14
2 x 8x 15
2 x 6x 2
2 4x 21
Factor the expression.
25. 26. 27.
28. 29. 30.
31. 32. 33. 45x2 8x 30x 5
2 12x 24x 18
2 4x
3
2 6x 10x 24
2 4x 33x 15
2 3x
14x 6
2 x 15x 12
2 2x 10x 21
2 4x 30
Solve the equation.
34. 35. 36.
37. 38. 39.
40. 41. 42.
43. 44.
45. 8x
46. Furniture Manufacturing You are making a coffee
table with a glass top surrounded by a cherry border.
The glass is 3 feet by 3 feet. You want the cherry border
to be a uniform width. You have 7 square feet of cherry
x
to make the border. What should the width of the border be?
3 ft
2 5x 4 2x2 2x
8x 1
2 25x x 21
2 49x
16
2 25x 14x 1 0
2 3x 20x 4 0
2 5x
8x 5 0
2 3x 3x 2 0
2 2x 8x 3 0
2 x
7x 4 0
2 x 12x 32 0
2 x 10x 9 0
2 x 30 0
47. A magazine has a circulation of 140 thousand per month when they charge
$2.50 for a magazine. For each $.10 increase in price, 5 thousand sales are
lost. How much should be charged per magazine to maximize revenue?
x
x
3 ft x
Algebra 2 29
Chapter 5 Resource Book
Lesson 5.2

Answer Key
Practice C
1. 2.
3. 4.
5. 6.
7. 8.
9. 10.
11. 12.
13. 14.
15. 16. Cannot be factored
17. 18. Cannot be factored
19. 20. 21.
22. 23.
24. 25.
26. 27.
28. 29.
30. 31. 32.
33. 34. 35. 36.
37. 38. 39. 5, 7
40. No solution 41. 2 42. 1, 1
43. $350; $306,250
7
1
4, 3
2 , 5
9
11
2 , 3
1
3
3 , 2
5
3, 2
1
7,
5
3
x 10, 12
2
28x2 x
2x 1
33x 12 4x 3 3x 9x 9
5x 11x 11 23x 7x 2
62x 1x 5 2x3x 42x 1
2x5x 32x 7
2
2x 82 5x 22 3x 72 x 9x 10
x 5x 11
x 7x 13 x 13x 15
x 17x 12 x 11x 14
2x 7x 6 x 33x 4
x 95x 2 3x 72x 5
2x 14x 3 3x 15x 2
2x 54x 1 x 82x 11
3x 2x 15
2x 135x 12

Lesson 5.2
LESSON
5.2
Practice C
For use with pages 256–263
30 Algebra 2
Chapter 5 Resource Book
NAME _________________________________________________________ DATE ___________
Factor the trinomial. If it cannot be factored, say so.
1. 2. 3.
4. 5. 6.
7. 8. 9.
10. 11. 12.
13. 14. 15.
16. 17. 18. 4x2 10x 11x 13
2 3x 89x 156
2 3x
7x 2
2 2x 43x 30
2 8x 5x 88
2 15x
18x 5
2 8x x 2
2 6x 10x 3
2 5x
29x 35
2 3x 43x 18
2 2x 13x 12
2 x
5x 42
2 x 3x 154
2 x 29x 204
2 x
28x 195
2 x 6x 91
2 x 16x 55
2 19x 90
Factor the expression.
19. 20. 21.
22. 23. 24.
25. 26. 27.
28. 29. 30. 8x4 2x3 x2 9x5 6x4 x3 20x3 58x2 12x
42x
3 10x2 12x 8x
2 6x 54x 30
2 5x
26x 28
2 3x 605
2 4x 243
2 2x
24x 36
2 5x 32x 128
2 3x 20x 20
2 42x 147
Solve the equation.
31. 32. 33.
34. 35. 36.
37. 38. 39.
40. 41. 42. 2x 12 x 22 x 12 3x 12 x 2 6
2 x 3
xx 3 1
2 3x 411 x
2 x 40 x2 4x 2x 5
2 10x x2 6x
x 4
2 6x 5x 99
2 4x 7x 3
2 5x
20x 25 0
2 2x 14x 3 0
2 x 17x 21 0
2 22x 120 0
43. Business If a gym charges its members $300 per year to join, they get
1000 members. For each $2 increase in price they can expect to lose
5 members. How much should the gym charge to maximize its revenue?
What is the gym’s maximum revenue?
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice A
1. 42
2. 23 3. 35 4. 55 5. 12
7 10 1
6. 36 7. 8. 9. 10.
2 3 11
23
5
11.
610
5
12.
22
3
13. 3, 3 14. 12, 12
15. 82, 82 16. 6, 6 17. 1, 1
18. 22, 22 19. 1, 1 20. 3, 3
21. 8, 8 22. 2, 2 23. 5, 5
24. 5, 5 25. 2, 2 26. 9, 9
27. 4, 4 28. 2.24 seconds 29. 3.16 seconds
30. 4.47 seconds
33. 1986
31. 8.06 32. 7.21

LESSON
5.3
Simplify the expression.
Solve the equation.
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice A
For use with pages 264–270
1. 2. 3.
4. 5. 6.
7. 8. 9.
10. 11. 12. 2
4 3 3
72
5
12
25
1
121
100
9
49
32
12
45
125
218 2 54 26
4
13. 14. 15.
16. 17. 18.
19. 20. 21.
22. 23. 24.
25. 26. 27. 2x2 11 x2 1
3 5
x2 3x 5 32
2 16 x
1 5
2 x 9
2 x 2 7
2 1
2x
3 1
2 4x 32
2 2x 36
2 x
2
2 x 8 0
2 x 1 0
2 x
36 0
2 x 128
2 x 144
2 9
Find the time it takes an object to hit the ground when it is
dropped from a height of s feet. Use the falling-object model
h 16t2 s.
28. s 80
29. s 160
30. s 320
Use the Pythagorean theorem to find x. Round your answer to the
nearest hundredth.
31. 32.
x
7
4
33. Cost of a New Car From 1970 to 1990, the average cost of a new car, C
(in dollars), can be approximated by the model C 30.5t where
t is the number of years since 1970. During which year was the average
cost of a new car $12,000?
2 4192,
x
14
12
Algebra 2 41
Chapter 5 Resource Book
Lesson 5.3

Answer Key
Practice B
1. 2. 3. 4.
5. 120 6. 7. 8. 9.
10. 11. 12.
13. 14. 15.
16. 17. 18.
19. 20. 21. 22. 1, 4
23. 0, 8 24. 9, 7 25. 2.5 seconds; 3.54
seconds; no; doubling the height increases the time
by the factor 2 . 26. 1992
29. 14 ft
27. 7 28. 49 ft
7
73
215 37 966
56
15
17
72
3
57
2
18, 18 9, 9 6, 6
12, 12 6, 6 25, 25
7, 7 1, 1 2, 2
5, 1 2, 6
5
3 , 3

Lesson 5.3
LESSON
5.3
Practice B
For use with pages 264–270
42 Algebra 2
Chapter 5 Resource Book
NAME _________________________________________________________ DATE ___________
Simplify the expression.
1. 2. 3.
4. 5. 6.
7. 8. 9. 15 35
12
7
14 3 3
225
147
60
63
418 248 8 18 54 10 15
289
Solve the equation.
10. 11. 12.
13. 14. 15.
16. 17. 18.
19. 20. 21.
22. 23. 24.
1
4x 12 1
2x 4 16 0
2 2x 3 8
2 3x 1
25
2 3x 2 36 0
2 2x 3 4 52
2 3x
8
2 2x 1 9
2 x 4 10
2 1 3x2 1
2
13
x2 2
3 5 5
x2 3x 8 16
2 5x
100 332
2 x 180 0
2 x 81 0
2 324
25. Falling Object Use the falling-object model where t is
measured in seconds and h is measured in feet to find the time required
for an object to reach the ground from a height of feet and
feet. Does an object that is dropped from twice as high take twice
as long to reach the ground? Explain your answer.
26. Truck Registrations From 1990 to 1993, the number of truck registrations
(in millions) in the United States can be approximated by the model
R 0.29t where t is the number of years since 1990. During which
year were approximately 46.16 million trucks registered?
Short Cut Suppose your house is on a large corner lot. The children
in the neighborhood cut across your lawn, as shown in the figure at
the right. The distance across the lawn is 35 feet.
27. Use the Pythagorean theorem to find x.
2 h 16t
s 100
s 200
45
2 s
28. Find the distance the children would have to travel if they did
not cut across your lawn.
29. How many feet do the children save by taking the “short cut?”
4x
3x
35
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice C
1. 2. 3. 270 4.
5. 6. 7. 8. 9.
10. 11. 12.
13. 14.
15. 16.
17. 18.
19.
20.
21. 22. 0,4
23.
24.
25.
26. 27. 2
28. a > 0 29. a > 2 30. a > 1
31. a < 2 32. a > 4 33. a < 5 34. 6%
7
5
2 2
3, 3
3 3
3 26, 3 26
1 2, 1 2
7
, 2
2 2
6
1
3 23, 3 23
6
, 5
12 12
5
76
67
614
45
9
7105
1
3
43
27
43
3
17, 17 13, 13 5, 5
5, 5 23, 23
10, 10 5, 5
11, 11 1, 3
4 3, 4 3
5
, 1
10 10

LESSON
5.3
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice C
For use with pages 264–270
Simplify the expression.
1. 2. 3.
4. 5. 6.
7. 8. 9.
20
8 54 45
12
35 21 7
1 27 4
160
294
252
312 527
21 24
162
Solve the equation.
10. 11. 12.
13. 14. 15.
16. 17. 18.
19. 20. 21.
22. 23. 24.
25. 26. 27.
2x 22
5
1
x 1 3
10 5
2
3
1
x 3 5
6 6
2
4
1
3x
6
2 2
3 2 2x 5 4 13
2 2
3
2x 2
3
3 4
2
4 2
1
4x 32 5x 1 5 2
2 1
3x 4 4
2 2x 1
9
2 3x 8
2 4 2x2 2x 1
2 7 x2
12
2
5x2 1
3x 3 7
2 2x 4 8
2 1
5x
10 0
2 x 5 0
2 x 13 0
2 289 0
Find the values of a for which the equation has two real-number
solutions.
28. 29. 30.
31. 32. 33. 2x2 a x a 5
2 x 4
2 3x
a 2
2 x 1 a
2 x 2 a
2 a
r
34. Compound Interest The formula A P1 gives the amount of
n
money in an account, A after t years if the annual interest rate is r (in
decimal form), n is the number of times interest is compounded per year,
and P is the original principle. What interest rate is required to earn $1 in
two months if the principle is $100 and interest is compounded monthly?
nt
32 12 75
15 5 72
Algebra 2 43
Chapter 5 Resource Book
Lesson 5.3

Answer Key
Practice A
1. 2. 3. 4.
5. 6.
7.
8.
9. 10.
11. 12. 13. 14.
15. 16. 17.
18. 19. 20.
21. 22.
3 3
2 2 23. 2 i
24. 1 i 25. 2 26. 5 27. 37
28. 5 29. 5 30. 41
31. 32.
i
4i, 4i
9i, 9i 12i, 12i i, i
2, 2 2i, 2i
A 2 3i, B 4 i, C 1 3i
A 4i, B 3 3i, C 3 i
A 2 4i, B 2i, C 4 7 7i
4 i 4 i 2 9i 11 4i
2 2i 1 4i 6 3i
28 12i 4 2i 3 11i
6 17i
1
33. 34.
1
35. 36.
1
imaginary
1
imaginary
1
imaginary
1
real
real
real
1
1
1
imaginary
1
imaginary
1
imaginary
1
real
real
real

LESSON
5.4
Solve the equation.
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice A
For use with pages 272–280
1. 2. 3.
4. 5. 6. x2 7 4x2 x 5
2 x 1 3
2 x
5 4
2 x 144 0
2 x 81
2 16
Identify the complex numbers plotted in the complex plane.
7. 8. 9.
B
1
imaginary
A
1
C
real
Write the expression as a complex number in standard form.
10. 5 3i 2 4i
11. 3 2i 1 i
12. 7 2i 3 3i
13. 5 i 3 8i
14. i 11 5i
15. i 6 i 4 2i
16. i4 i
17. 3i1 2i
18. 4i3 7i
19. 1 3i1 i
20. 5 i1 2i
21. 2 3i3 4i
22.
3
1 i
23.
5
2 i
24.
3 i
2 i
Find the absolute value of the complex number.
25. 1 i
26. 2 i
27. 6 i
28. 1 2i
29. 3 4i
30. 5 4i
Plot the numbers in a complex plane.
31. 2i
32. 3
33. 1 3i
34. 4 3i
35. 1 2i
36. 2 4i
B
A
1
imaginary
1
C
real
A
1
B
Algebra 2 55
Chapter 5 Resource Book
1
imaginary
C
real
Lesson 5.4

Answer Key
Practice B
1. 2. 3.
4. 5.
6. 7. 8.
9. 10.
11. 2 12. 5 7i, 5 7i
13. 14.
1 1
2i, 2 2i 1 6i, 1 6i
1 1
3i, 3i 8i, 8i i, i 3, 3
2i3, 2i3 4i3, 4i3
3i3, 3i3 3i, 3i 2i, 2i
1
15. 16.
1
17. 18.
1
imaginary
1
imaginary
1
imaginary
1
real
real
real
1
1
1
imaginary
1
imaginary
1
imaginary
1
real
real
real
19. 20. 21.
22. 23. 24.
25. 26. 27. 80
28. 29.
30. 31. 4
32. 33. 34. 5
35. 36. 37. i 38. 39.
40. 1 41. i 42. 43. 44. 1
45. If the exponent of i is a factor of 4, the expression
can be reduced to 1. Therefore, to simplify i
raised to any natural number, factor out the multiples
of 4 in the exponent and simplify the remaining
expression; i 231 i 228 i 3 1i3 3 12i
3 5
1 i
1 i
i.
201 73
34 34 i
12 18
13 13 1 i
23 1 2 3
i
4 4
i
39 18i 21 20i
1 5
6 12i 1
5 3i 3 17i
3
2i 2 10i
1 10i

Lesson 5.4
LESSON
5.4
Solve the equation.
Practice B
For use with pages 272–280
56 Algebra 2
Chapter 5 Resource Book
NAME _________________________________________________________ DATE ___________
1. 2. 3.
4. 5. 6.
7. 8. 9.
10. 11. 12. 3x 52 4x 2 147 0
2 2x 1 1
2 11x
72
2 1 2x2 x2 16 5x2 2x2 9 3x2 x2 x 3 24
2 x 48 0
2 x
12
2 x 5 14
2 x 1 0
2 64
Plot the number in a complex plane.
13. 3i
14. 2
15. 2 4i
16. 3 4i
17. 2 i
18. 4 3i
Write the expression as a complex number in standard form.
19. 20. 21.
22. 23. 24.
25. 26. 2 5i 27. 4 8i4 8i
28.
6
2 3i
29.
3 i
2 i
30.
2 i
3 i
2
5 4i3 6i
1 2
1
2 3i 23
4i
4 2i 1 5i
5 8i 2 9i
1
3 2i 5 8i
2 4i 3 6i
1
3 2i 23
2i
31. 22 i 1 i2
32.
33.
1 5i2 i i3 4i
Find the absolute value of the complex number.
34. 4 3i
35. 2 i
36. 3 2i
Write the complex number in standard form.
1
6 2i
3 5i
37. i 38. 39. 40.
41. 42. 43. 44. i8 i7 i6 i5 i4 i3 i2 45. Pattern Recognition Using the information from Exercises 37–44, write
a general statement about the standard form of where n is a positive
integer. Use this statement to write i in standard form.
231
in Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice C
1. 2.
3. 4.
5.
6. 1 7. a > 0,
b > 0
6 6
i, 1
2 2 i
6 21 21
i, 6
3 3 i
4 2i, 2i
2 2
i, 4
2 2 i
1 3i, 1 3i
14 14
i,
2 2 i
8. a < 0,
b > 0 9. a < 0, b < 0
10. a > 0, b < 0 11. a > 0, b 0
12. a 0, b < 0 13. 1 3i, 10
14. 8 7i, 113 15. 3 i, 10
16.
1 3i, 10 17. 1 ,1
18. 14 2i, 102 19. 4 7i, 65
11 10 221 13 i 170
20. i, 21. ,
17 17 17 34 34 34
22. z0 0, z1 3, z2 6, z3 33;
Not a member. 23. z0 0, z1 5,
z2 52, z3 2605; Not a member.
24. z0 0, z1 2, z2 25, z3 285;
Not a member. 25. real 26. pure imaginary
27. real 28. imaginary

LESSON
5.4
Solve the equation.
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice C
For use with pages 272–280
1. 2. 3.
4. 5. 6. 2x 12 3x 6 3 6
2 2x 7 0
2 7 x2 6x 4
10
2 4x 1 3 0
2 3x 12 0
2 5 x2 2
Determine whether a and b are greater than zero, less than zero or
equal to zero for the given complex number a bi .
7. a bi lies in the first quadrant 8. a bi lies in the second quadrant
of the complex plane of the complex plane
9. a bi lies in the third quadrant 10. a bi lies in the fourth quadrant
of the complex plane of the complex plane
11. a bi lies on the positive real 12. a bi lies on the negative imaginary
axis of the complex plane axis of the complex plane
Perform the given operation and find the absolute value of the
complex number.
13. 3 2i 4 i
14. 5 2i 3 5i
15. 6 i 3 2i
16. 3 2i 4 5i
17. 2 i 3 4i 3i 18. 2 6i1 2i
19. 2 3i1 2i
20.
2 3i
4 i
21.
1 2i
3 5i
Determine whether the complex number c belongs to the
Mandelbrot set. Use absolute value to justify your answer.
22. c 3
23. c 2 i
24. c 2i
Determine whether the complex number is real, imaginary, pure
imaginary, or neither.
25. The sum of a complex number 26. The difference of a complex number
and its conjugate. and its conjugate.
27. The product of a complex number 28. The quotient of a complex number
and its conjugate. and its conjugate.
Algebra 2 57
Chapter 5 Resource Book
Lesson 5.4

Answer Key
Practice A
1. 2. 3.
4. 5. 6.
7. 9; 8. 49;
9. 16; 10.
11. 121; 12. 36;
13.
15.
14.
16.
17. 18.
19.
20.
21. 22. 1, 15
23. 24.
25.
26.
27. y x 1
28. 16.675 ft by 10.675 ft
29. 4.782 ft by 8.782 ft
31. 3.662 ft by 19.662 ft
30. 8 ft by 6 ft
2 y x 5
4; 1, 4
2 y x 4
18; 5, 18
2 49 7
4 ; x 2 1 3, 1 3
2 5, 2 5 3 7, 3 7
6 33, 6 33
1 3, 1 3
4 17, 4 17
2, 1
1 5 1 5
,
2 2 2 2
11; 4, 11
2
9 3
4 ; x 2 2
100; x 102 x 62 x 112 1 1
4 ; x 2 2
x 42 x 72 x 32 x 5
2 2
x 1
2 2
x 3
2 2
x 82 x 22 x 12

LESSON
5.5
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice A
For use with pages 282–289
Write the expression as the square of a binomial.
1. 2. 3.
4. 5. 6. x2 5x 25
x 4
2 x 1
x 4
2 3x 9
x
4
2 x 16x 64
2 x 4x 4
2 2x 1
Find the value of c that makes the expression a perfect square
trinomial. Then write the expression as the square of a binomial.
7. 8. 9.
10. 11. 12.
13. 14. 15. x2 x 7x c
2 x 3x c
2 x
20x c
2 x 12x c
2 x 22x c
2 x
x c
2 x 8x c
2 x 14x c
2 6x c
Solve the equation by completing the square.
16. 17. 18.
19. 20. 21.
22. 23. 24. x2 x x 1 0
2 x x 2 0
2 x
16x 15 0
2 x 8x 1 0
2 x 2x 2 0
2 x
12x 3 0
2 x 6x 2 0
2 x 4x 1 0
2 2x 2 0
Write the quadratic function in vertex form and identify the vertex.
25. 26. 27. y x2 y x 2x 3
2 y x 10x 7
2 8x 5
Find the dimensions of the figure. Round your answer to the
nearest thousandth.
28. Area of rectangle 178 square feet 29. Area of triangle 21 square feet
x
30. Area of rectangle 48 square feet 31. Area of triangle 36 square feet
x
x 6
x 2
x
x
x 4
x 16
Algebra 2 69
Chapter 5 Resource Book
Lesson 5.5

Answer Key
Practice B
1.
4.
2. 3.
5. 6.
7. 144; 8. 225;
9. 10.
11. 4; 12. 1; 13.
14. 15.
16. 17.
18. 19.
20.
21. 22.
23. 24.
25.
26.
27.
28. 6.275 ft by 1.275 ft
29. 4.490 ft by 10.245 ft
30.
5x
32. 33.656 ft
31. 16.828, 22.428
2 x
28x 1887 0
2 2x 72 442 y 3x 1
⇒
2 y 2x 1
5; 1, 5
2 y x 4
9; 1, 9
2 2
1, 5 2 7, 2 7
5; 4, 5
33
1, 2
4, 1 1 6, 1 6
1 5, 1 5
1 3 1 3
,
2 2 2 2
, 2 33
3 3
9
3x 1 7, 1
7 43, 7 43 1, 4
57 57
, 9
2 2 2 2
2
2x 22 81 9
4 ; x 2 2
25 5
4 ; x 2 2
x 152 x 122 3x 1
4 2
3x 12 2x 32 x 1
4 2
x 52 x 42

Lesson 5.5
LESSON
5.5
70 Algebra 2
Chapter 5 Resource Book
NAME _________________________________________________________ DATE ___________
Practice B
For use with pages 282–289
Write the expression as the square of a binomial.
1. 2. 3.
4. 5. 9x 6.
2 4x 6x 1
2 x
12x 9
2 x 10x 25
2 8x 16
Find the value of c that makes the expression a perfect square
trinomial. Then write the expression as the square of a binomial.
7. 8. 9.
10. 11. 12. 9x2 4x 6x c
2 x 8x c
2 x
9x c
2 x 5x c
2 x 30x c
2 24x c
Solve the equation by completing the square.
13. 14. 15.
16. 17. 18.
19. 20. 21.
22. 23. 24. x2 2x 4x 3 0
2 3x 8x 10 0
2 4x
12x 1 0
2 5x 4x 2 0
2 2x 10x 20 0
2 3x
4x 10 0
2 2x 9x 12 0
2 x 2x 4 0
2 x
9x 6 0
2 x 3x 4 0
2 x 14x 1 0
2 6x 7 0
Write the quadratic function in vertex form and identify the vertex.
25. 26. 27. y 3x2 y 2x 6x 8
2 y x 4x 7
2 8x 11
Find the dimensions of the figure. Round your answer to the
nearest thousandth.
28. Area of rectangle 8 square feet 29. Area of triangle 23 square feet
x
x 5
No Passing Zone A “No Passing Zone” sign has the shape of an
isosceles triangle. The width of the sign is 7 inches greater than its height.
The top and bottom edges of the sign are 44 inches.
30. Use the Pythagorean theorem to write an equation that relates x,
2x 7, and 44.
31. Solve the equation in Exercise 30 by completing the square.
(Hint: Use decimal representations and a calculator to simplify
your work.)
32. What is the height of the sign?
x
x
x
1
x 8
2
9x2 3
x
1
2x 16
2 1 1
2x 16
2x 7
NO
PASSING
ZONE
44 in.
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice C
1. 2. 3.
4. 5. 6. 0.3x 0.42 x 0.82 3x 1
2x 1
5 2
2x 52 x 1
3 2
7. 4 19, 4 19
8. 5 19, 5 19
9.
5 21 5 21
,
2 2 2 2
10.
11.
12. 1 5, 1 5 13. 5, 1
14.
15.
7
2
5
2
3
2
2 2
65 65
, 7
2 2 2
57 57
, 5
2 2 2
21 3 21
,
2 2 2
1 215
, 1
5
215
5
16. 17. 2, 1
3 33 33
, 3
2 2 2 2
18.
19. 20.
21.
22.
23.
24.
25.
26.
27. y 4x
28. 10 ft; 30.03 ft 29. 204.96 ft/s
1
4 2 11
y x 2
4 ; 14
, 11 4
2 y 2x
3; 2, 3
3
4 2 1
y 3x
8 ; 34
, 18
5
2 2 71
y 2x 3 3, 23
4 ; 52
, 71 4
2 y x 8 8, 62
23;
2 1 3 1 3
i,
2 2 2 2
5 5 5 5
,
2 2 2 2
2 2, 2 2
62;
i
5 3
3
i, 5 2 2 2 2i

LESSON
5.5
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice C
For use with pages 282–289
Write the expression as the square of a binomial.
1. 2. 3.
4. 5. 6. 0.09x2 x 2.4x 0.16
2 9x 1.6x 0.64
2 3x 1
4x2 4
4x
1
5x 25
2 x 20x 25
2 2 1
3x 9
4
Solve the equation by completing the square.
7. 8. 9.
10. 11. 12.
13. 14. 15.
16. 17. 18.
19. 20. 21. 3x2 2x 1 x2 x 6x 3
2 3x 3x 7 8x 2
2 4x 2 x2 2x
6x
2 2x 10x 17
2 x 6x 4 0
2 5x
3x 6 0
2 3x 2x 3 10 8x
2 2x 9x 4 5
2 4x
8x 10 0
2 2x 1 3x2 2x 4x 5
2 5x 3 x2 x 5
2 x
7x 4 0
2 x 5x 1 0
2 x 10x 6 0
2 8x 3 0
Write the quadratic function in vertex form and identify the vertex.
22. 23. 24.
25. 26. 27. y 4x2 y x 2x 3
2 y 2x 4x 1
2 y 3x
3x 1
2 y 2x 15x 1
2 y x 12x 5
2 16x 2
28. Biology The impala is the most powerful jumper of the antelope family.
When an impala jumps, its path through the air can be modeled by
where x is the impala’s horizontal distance
traveled (in feet) and y is its corresponding height (in feet). How high can
an impala jump? How far can it jump?
29. Falling Object An object is propelled upward from the top of a 500-foot
building. The path that the object takes as it falls to the ground can be
modeled by y 16t where t is time (in seconds) and y
is the corresponding height (in feet) of the object. The velocity of the
object can be modeled by v 32t 100 where t is time (in seconds)
and v is the corresponding velocity of the object. With what velocity does
the object hit the ground?
2 y 0.0444x
100t 500
2 1.3333x
Algebra 2 71
Chapter 5 Resource Book
Lesson 5.5

Answer Key
Practice A
1.
2.
3.
4.
5.
6.
7. 8. 0 9. 28 10. 21 11.
12. 0 13. 16; 2 14. 17; 2 15.
16. 1; 2 17. 18. 41; 2 19. 0; 1
20. 0; 1 21. 22. 23. 84; 2
24. 0; 1 25.
26.
27. 28. 0, 7 29.
30. 31.
32.
33.
34.
35.
36.
37.
38.
39. x
40. 3.28 in.
41. 5.38 in.
2 x
3x 0; 3, 0
2 x 1
x
1
0;
4 2
2 x
6x 11 0; 3 i2, 3 i2
2 x
2x 15 0; 3, 5
2 x
2x 1 0; 1
2 1 i55
,
2
2x 4 0; 1 5, 1 5
1 i55
3 i11
,
2
2
3 i11
3 13
,
2
3 7, 3 7
3, 0
i6, i6 6, 6
2
3 13
1 5
,
2
2
1 5
6x
11
24
11; 0
31; 0
11; 0 12; 0
2
2 x
3 0; a 6, b 0, c 3
2 2x
9x 2 0; a 1, b 9, c 2
2 3x
4x 5 0; a 2, b 4, c 5
2 x
3x 4 0; a 3, b 3, c 4
2 3x
3x 2 0; a 1, b 3, c 2
2 4x 3 0; a 3, b 4, c 3

LESSON
5.6
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice A
For use with pages 291–298
Write the equation in standard form. Identify a, b, and c.
1. 2. 3.
4. 5. 6. 5x2 2 x2 2 x 8x x 1
2
3x2 5 x2 3x 4 3x
4x
2
x2 3x 3x 2
2 4x 3 0
Find the discriminant of the quadratic equation.
7. 8. 9.
10. 11. 12. x2 x 6x 9 0
2 x 2x 7 0
2 x
5x 1 0
2 x 2x 6 0
2 x 2x 1 0
2 x 3 0
Find the discriminant and use it to determine the number of real
solutions of the equation.
13. 14. 15.
16. 17. 18.
19. 20. 21.
22. 23. 24. 5x2 x 0
2 x 21 0
2 x
3 0
2 x 3x 5 0
2 x 4x 4 0
2 2x
18x 81 0
2 2x x 5 0
2 x x 4 0
2 x
5x 6 0
2 x 3x 5 0
2 x 5x 2 0
2 2x 3 0
Use the quadratic formula to solve the equation.
25. 26. 27.
28. 29. 30.
31. 32. 33. x2 x x 14 0
2 x 3x 5 0
2 x
36 0
2 x 6 0
2 x 3x 0
2 x
7x 0
2 x 6x 2 0
2 x 3x 1 0
2 x 1 0
Write the equation in standard form. Use the quadratic formula to
solve the equation.
34. 35. 36.
37. 38. 39. x2 3x 2x2 x2 1 x 3
x2 x
11 6x
2 3x 2x 15
2 2x 2x2 x 1
2 5 2x 1
Find the value of x. Round your answer to the nearest hundredth.
40. Area of rectangle 24.5 square inches 41. Area of parallelogram 63.9 square inches
x 4.2
x
4
x 6.5
x
Algebra 2 83
Chapter 5 Resource Book
Lesson 5.6

Answer Key
Practice B
1. 11
2. 25 3. 0 4. 76 5. 49
6. 100 7. 1; 2 8. 0; 1 9.
10. 11. 37; 2 12. 9; 2 13.
14. 15.
16. 17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28. Yes; Your garden should be approximately
12.93 ft by 27.07 ft. 29. No; The area of the
room can be expressed as The equation
has no real solution.
30. 10.22 seconds
32. 1.89 seconds
31. h 16t2 4.2x
x8 x.
x8 x 20
27t 6
2 2.4x
6.8x 2 0; 0.386, 1.233
2 2x
3.5x 2.2 0; 1.933, 0.474
2 15 89
15x 17 0; ,
4
15 89
4x
4
2 3 41
3x 2 0; ,
8
3 41
2x
8
2 5 33
5x 1 0; ,
4
5 33
3x
4
2 3 69
3x 5 0; ,
6
3 69
2x
6
2 1 57
x 7 0; ,
4
1 57
x
4
2 x
3x 4 0; 1, 4
2 7 113
,
16
4x 2 0; 2 6, 2 6
7 113
1 51
,
10
16
1 51
1 33
,
4
1
, 2
4 10
1 33
4
1
8; 0
47; 0
4, 5
, 2
2

Lesson 5.6
LESSON
5.6
84 Algebra 2
Chapter 5 Resource Book
NAME _________________________________________________________ DATE ___________
Practice B
For use with pages 291–298
Find the discriminant of the quadratic equation.
1. 2. 3.
4. 5. 6. 3x2 2x 2x 8 0
2 5x 3x 5 0
2 4x
2x 4 0
2 3x 12x 9 0
2 x x 2 0
2 3x 5 0
Find the discriminant and use it to determine the number of real
solutions of the equation.
7. 8. 9.
10. 11. 12. 4x2 x 3x 0
2 3x 4 2x2 3x 3
2 3x
x 4 0
2 4x 2x 1 0
2 x 20x 25 0
2 3x 2 0
Use the quadratic formula to solve the equation.
13. 14. 15.
16. 17. 18. 8x2 10x 7x 2 0
2 4x 2x 5 0
2 2x
9x 2 0
2 2x x 4 0
2 x 3x 2 0
2 x 20 0
Write the equation in standard from. Use the quadratic formula to
solve the equation.
19. 20. 21.
22. 23. 24.
25. 26. 27. 6.8x 2 4.2x2 2.4x2 2x 3 3.5x 2.2
2 6x
3x 1
2 5 2x2 9x x 3x 7
2 x2 x 4x 1
2 3x 2 4x2 4 2x
3
2 x x 3
2 3x 5 3x 1
2 4x 2x2 2
28. Fencing Your Garden It takes 80 feet of
fencing to enclose your garden. According to
your calculations, you will need 350 square
feet to plant everything you want. Is your garden
big enough? Explain your answer.
40 x
x
29. New Carpeting You have new carpeting
installed in a rectangular room. You are
charged for 20 square yards of carpeting and
16 yards of tack strip. Do you think these
figures are correct? Explain your answer.
Tack strip
8 x
Throwing an Object on the Moon An astronaut standing on the moon throws a
rock upwards with an initial velocity of 27 feet per second. The astronaut’s hand
is 6 feet above the surface of the moon. The height of the rock is given by
h 2.7t
30. How many seconds does it take for the rock to fall to the ground?
31. Suppose the astronaut had been standing on Earth. Write a vertical motion
model for the height of the rock after it is thrown.
32. Use the model in Exercise 31 to determine how many seconds it takes for
the rock to fall to the ground on Earth.
2 27t 6.
x
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice C
1. 13 2. 25 3. 169 4. 24 5.
6. 7. 5
31
24
37 37
, 5
2 2 2 2
8.
9. 10.
11.
12.
13. 14.
15. 16.
17.
18. 19.
20. 21. No solution
In Exercises 22–24, answer may vary. Sample
answers are given.
22. 1, 2 23. 1, 2 24. 2, 3
25. Object launched downward
26.
27.
28. h 16t
29. launched upward: 2.8 s, dropped: 2.5 s,
launched downward: 2.2 s The object launched
downward reaches the ground first.
2 h 16t
10t 100
2 h 16t
100
2 4, 4
26, 26
10t 100
1 87 87
i, 1
2 6 2 6 i
20
19.11, 1.39 0.71, 0.51
0.08 0.53i, 0.08 0.53i
1 19 1 19
i,
10 10 10 10 i
6 33, 6 33
1
2, 1
5 37 5 37
,
2 2 2 2
5 19, 5 19
3 17 17
, 3
4 4 4 4

LESSON
5.6
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice C
For use with pages 291–298
Find the discriminant of the quadratic equation.
1. 2. 3.
4. 5. 6. 6x 3 5x2 10 3x x 0
2 2x x 0
2 8x
5 0
2 3x 3x 5 0
2 x 7x 2 0
2 3x 1 0
Use the quadratic formula to solve the equation.
7. 8. 9.
10. 11. 12.
13. 14. 15.
16. 17. 18.
1
5x 12 1
7.3x
1
5x 3
2 4.5x 2.1 1.1x
2 1.2x 2.1 1.3x2 2.3x2 4.1x 2.1x2 1
16 5.3
x2 5
2x 25
5x2 1
2
9 x 8
x2 x 2x 5 2 3x
2 3 2x2 3x 5x
2 2x x2 1
3
5x 1
x2 2x 4x 3 0
2 x 3x 1 0
2 5x 3 0
Find all values of b for which the equation has one real solution.
19. 20. 2x 21.
2 x bx 3 0
2 bx 4 0
Give two examples of values of b for which the equation has two
imaginary solutions.
2
22. 23. 24. 5x2 2x bx 10 0
2 x bx 1 0
2 bx 5 0
Vertical Motion In Exercises 25–29, use the following information.
Three objects are launched from the top of a 100-foot building. The first object is
launched upward with an initial velocity of 10 feet per second. The second object
is dropped. The third object is launched downward with an initial velocity of
10 feet per second.
25. Without doing any calculations, which object do you think will hit the
ground first?
26. Write a height model for the object launched upward.
27. Write a height model for the dropped object.
28. Write a height model for the object launched downward.
29. Use the quadratic formula to verify your answer in Exercise 25.
3x 2 bx 5 0
Algebra 2 85
Chapter 5 Resource Book
Lesson 5.6

Answer Key
Practice A
1. 1, 2 is a solution 2. 2, 1 is not a solution
3. 4, 4 is not a solution 4. 3, 6 is
a solution 5. 1, 1 is not a solution
6. 2, 3 is a solution 7. C 8. A 9. F
10. E 11. B 12. D
13. 14.
1
15. 16.
1
y
y
1
1
17. 18.
y
1
19. 20.
y
1
x
x
1 x
1 x
3
1
y
y
1
1
1
y
1
1
y
1
x
x
x
x
21. 22. B 23. C 24. A
1
y
1
x

LESSON
5.7
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice A
For use with pages 299–305
Determine whether the ordered pair is a solution of the inequality.
1. 2.
3. 4.
5. 6. y ≥ x2 y < 2x 3x 5, 2, 3
2 y ≥ 3x
3x 4, 1, 1
2 y ≤ 2x 4x 1, 3, 6
2 y > 2x
5x 6, 4, 4
2 y < x x 5, 2, 1
2 2x 4, 1, 2
Match the inequality with its graph.
7. 8. 9.
10. 11. 12. y > x
A. B. C.
2 y > x 2x 3
2 y < x 4x 3
2 y ≤ x
4x 3
2 y ≤ x 2x 3
2 y ≥ x 4x 3
2 4x 3
D. y
E. y
F.
1
Graph the inequality.
13. 14. 15.
16. 17. 18.
19. 20. 21. y ≤ x2 y ≤ x 6x 8
2 y ≥ x 2x 1
2 y > x
5x 6
2 y < x 2x
2 y > 3x 5x
2 y < x
2
2 y ≥ x 3
2 y ≤ 2x 2x
2 1
Match the system of inequalities with its graph.
22. 23. 24. y > x2 y < x 1
2 y < x 1
2 1
y > x 2 1
A. y
B. y
C.
2
1
1
y
1
2
x
x
x
1
1
1
y
y > x 2 1
2
1
2
x
x
x
1
1
1
y < x 2 1
Algebra 2 97
Chapter 5 Resource Book
y
2
1
y
y
2
x
x
x
Lesson 5.7

Answer Key
Practice B
1. 1, 1 is not a solution 2. 1, 6 is not a
solution 3. 2, 7 is a solution
4. 3, 3 is a solution
5. 6.
12
7. 8.
9. 10.
1
y
1
1
y
12
1
11. 12.
y
1
y
x
x
x
1 x
5
1
y
y
y
1
1
5
1
y
1
1
x
x
x
x
13. 14.
15. 16.
16
17. 18.
1
19. 20.
1
y
y
y
21. 22.
y
1
1
1
1
4
1
y
1
x
x
x
x
x
1
y
1
1
14
1
1
y
y
y
y
1
1
1
4
x
x
x
x
x

Answer Key
23. 24.
25. 26.
27. 28.
29. 30.
31.
32.
33. 34. x < 0 or x >
35. a. b.
5
1 ≤ x < 2
4
x ≤
3 ≤ x ≤ 7
x ≤ 2 2 or x ≥ 2 2
3
2
3 or x ≥ 4
1
3 < x < 5
x < 2 or x > 8
4 ≤ x ≤ 1 x ≤ 4 or x ≥ 3
4 < x < 7 x ≤ 3 or x ≥ 6
2 ≤ x ≤ 3
1
y
1
36. b 37. a 38.
y ≥ 0.33x 2 2x 4
x
y ≥ 0.33x 2 2x 4,
y
1
1 x

Lesson 5.7
LESSON
5.7
98 Algebra 2
Chapter 5 Resource Book
NAME _________________________________________________________ DATE ___________
Practice B
For use with pages 299–305
Determine whether the ordered pair is a solution of the inequality.
1. 2.
3. 4. y ≥ 3 2
3x2 y ≤ , 3, 3
1
2x2 y > 5x
3x 1, 2, 7
2 y < 2x 7x 4, 1, 6
2 2x 5, 1, 1
Graph the inequality.
5. 6. 7.
8. 9. 10.
11. 12. 13.
14. 15. 16. y < 12 3x2 y ≤ 4x2 y > 3x 16
2 y < 2x
5x 2
2 y ≥ 2x 8x 5
2 y > x 4x 2
2 y ≥ 3x
6x 9
2 y ≤ x 6x 2
2 y < x 6x 7
2 y > 3x
2x 1
2 y > x 6x
2 y < x 4x 21
2 10x 9
Graph the system of inequalities.
17. 18. 19. y ≤ x2 y ≥ 2x 4
2 y ≥ x 4
2
y ≤ x 2 3
20. 21. 22. y ≥ 2x2 y > x 12x 16
2 y ≤ x 4x 1
2 4
y ≥ x 2 2x 1
Solve the inequality algebraically.
23. 24. 25.
26. 27. 28.
29. 30. 31.
32. 33. 34.
Gift Shop Logo You are using a computer to create a logo for a gift
shop called On the Wings of a Dove. The logo you have designed
is shown at the right.
35. Sketch the intersections of the graphs of the inequalities.
a. b. y ≥ 0.33x2 y ≥ 0.33x 2x 4
2 2x
2x 4
2 3x > 5x
2 2x 4 < 7x
2 x
≥ 8x 4
2 3x 4x ≤ 21
2 2x ≥ 10x 8
2 x
5x 3 ≤ 0
2 x 9x 18 ≥ 0
2 x 11x 28 < 0
2 x
7x 12 ≥ 0
2 x 5x 4 ≤ 0
2 x 6x 16 > 0
2 2x 15 < 0
y ≤ 0.09x 2 1.3x
y ≤ x 2 1
y ≤ x 2 2x 1
y ≤ 0.09x 2 1.3x
36. Which region in Exercise 35 represents the dove’s left wing?
37. Which region in Exercise 35 represents the dove’s right wing?
38. Which two inequalities (when intersected) make up the dove’s tail?
y ≥ x 2 2x 1
y < x 2 2x 3
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice C
1. y
2.
3. y 4.
5. y 6.
7. y
8.
1
9. y
10.
2
5
1
2
11. y 12.
1
1
2
10
1
1
x
x
2
x
x
x
x
2
y
2
1
6
y
1
6
y
y
y
1
2
1
2
1
y
1
x
x
x
x
x
x
13. 14. or
15. 16. x < or x > 6
8
7
10 ≤ x ≤ 7
x ≤ 12 x ≥ 3
< x < 4
2
17. 18. x ≤ or
3
1 7
≤ x ≤
4
19. or x > 20.
5 89
x ≤ or
4
5 89
x ≥
4
21. No solution
5
x < 3
5
3
22. or
23. 24. All real numbers
25
1 13 1 13
x < x
6
6
25
< x <
5 5
3, 1
2
25. 26.
3
27.
28. y x 29.
343
24 square units
125
30. 6 square units
2 y x
3x 1
2 2x 4
3
1
y
2
1
x
x ≥ 1
2

LESSON
5.7
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice C
For use with pages 299–305
Sketch the graph of the inequality.
1. 2. 3.
4. 5. 6.
7. 8. 9. y ≤ 4x2 y > 2x x 6
2 y ≥ 2x 5x 4
2 y < x
3x 1
2 y ≥ x 4x 6
2 y > 6x 3x 1
2 y ≤ 2x
x 2
2 y ≥ x 19x 35
2 y < x 12x 27
2 2x 35
Graph the system of inequalities.
10. 11. y > 2x 12.
2 y ≥ x 5x
2 3x 4
y ≤ x 2 4x 5
Solve the inequality algebraically.
13. 14. 15.
16. 17. 18.
19. 20. 21. x
22. 23. 24.
2 2x 2x 6 ≥ 0
2 9x 5x 8 ≥ 0
2 12x
30x 25 < 0
2 12x 12x 9 ≥ 0
2 3x 25x 7 ≤ 0
2 2x
26x 48 > 0
2 x x 28 < 0
2 x 15x 36 ≥ 0
2 3x 70 ≤ 0
3x 2 x 1 < 0
Geometry In Exercises 25–30, use the following information.
The area of a region bounded by two parabolas is given by
a d
Area 3 B3 A3 b e
2 B2 A2 c fB A
where is the top parabola,
is the bottom parabola, and A and B are the x-coordinates of
the intersection points of the parabolas with
25. To find the x-coordinates of the intersection points of
two parabolas, set the two quadratic equations equal to
each other and solve for x. Find the x-coordinates of the
intersection points of and y x
26. Graph the system of inequalities
2 y x 2x 4.
2 y dx
A < B.
3x 1
2 y ax ex f
2 bx c
y ≥ x 2 3x 1
y ≤ x 2 2x 4
27. For the region in Exercise 26, which parabola is the top boundary?
28. For the region in Exercise 26, which parabola is the bottom boundary?
29. Find the area of the region from Exercise 26.
30. Find the area of the region.
y ≥ x 2 4x 3
y ≥ 2x 2 5x 3
y < x 2 2x 3
5x 2 4 > 0
y
y > x 2 3x 1
y < 1
2 x2 x 2
2x 2 x 1 > 0
y dx 2 ex f
y ax 2 bx c
Algebra 2 99
Chapter 5 Resource Book
x
Lesson 5.7

Answer Key
Practice A
1. 2.
3. 4.
5. 6.
7. 8.
9.
10.
y x2 y x
2x 2
2 y x 2x 3
2 y
y x 3x 2 y xx 4
2x 5
1
y x 3 3x 3x 3
2
y x 12 y x 2 2
2 1
11. y 0.52x
12.
2 2.84x 7.07

Lesson 5.8
LESSON
5.8
Practice A
For use with pages 306–312
110 Algebra 2
Chapter 5 Resource Book
NAME _________________________________________________________ DATE ___________
Write a quadratic function in vertex form for the parabola shown.
1. y
2. y
3.
(2, 1)
Write a quadratic function in intercept form for the parabola shown.
4. y
5. y
6.
1
1
Write a quadratic function in standard form for the parabola shown.
7. y
8. y
9.
(1, 4) 2
1
1
(0, 3)
(1, 8)
(0, 5)
2
x
(0, 3)
x
x
(1, 2)
(1, 0)
(2, 3)
Australia’s Unemployment Rate The following table shows the percentage of
people who were unemployed in Australia from 1990 to 1995.
Assume that t is the number of years since 1990.
10. Use a graphing calculator to make a scatter plot of the data.
11. Use a graphing calculator to find the best fitting quadratic model for the data.
12. Use a graphing calculator to check how well the model fits the data.
1
4
1
1
(0, 1)
Year, t 0 1 2 3 4 5
Percentage of people
unemployed, y 6.9 9.6 10.8 10.9 9.7 8.5
1
4
(2, 4)
x
x
x
(4, 5)
y
1
(3, 3)
(1, 1)
1
1
y
1
(4, 1)
(3, 0) x
1
1 x
(3, 1)
x
(2, 2)
Copyright © McDougal Littell Inc.
All rights reserved.
y

Answer Key
Practice B
1. 2.
3. 4.
5. 6.
7. 8.
9. 10.
11. 12.
13. 14.
15. 16.
17. 18.
19. 20.
21. 22.
23. 24.
25. 26.
27.
28.
29. V 0.03t2 P 0.23t
1.17t 70.30
2 y x
2.03t 22.93
2 y x
3
2 y x 3x 2
2 y 2x
2x 4
2 y 3x 4x 5
2 y x
x 1
2 y 2x x 4
2 y x
x 3
2 y 2x x 7
2 y
x 2
1
y x 6 y x 2x 4
y x 3x 5 y x 1x 4
y x 2x 6 y x 5x 4
y x 1x 7 y 2xx 5
y 4xx 3
2x 8x 2
2
y x 42 y x 3 5
2 y x 1
1
2 y x 3 5
2 y x 4
1
2 y x 2 2
2 y x 1
1
2 y x 2 4
2 3

LESSON
5.8
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice B
For use with pages 306–312
Write a quadratic function in vertex form whose graph has the given
vertex and passes through the given point.
1. vertex: 2, 3
2. vertex: 1, 4
3. vertex: 2, 1
point: 0, 7
point: 1, 8
point: 1, 10
4. vertex: 4, 2
5. vertex: 3, 1
6. vertex: 1, 5
point: 3, 3
point: 2, 0
point: 1, 1
7. vertex: 3, 1
8. vertex: 4, 5
9. vertex: 6, 0
point: 2, 0
point: 1, 4
point: 3, 9
Write a quadratic function in intercept form whose graph has the
given x-intercepts and passes through the given point.
10. x-intercepts: 2, 4 11. x-intercepts: 3, 5 12. x-intercepts: 4, 1
point: 1, 3
point: 2, 3
point: 3, 28
13. x-intercepts: 6, 2
14. x-intercepts: 5, 4
15. x-intercepts: 1, 7
point: 3, 3
point: 3, 8
point: 5, 12
16. x-intercepts: 5, 0
17. x-intercepts: 0, 3 18. x-intercepts: 8, 2
point: 1, 12
point: 1, 8
point: 4, 12
Write a quadratic function in standard form whose graph passes
through the given points.
19. 1, 1, 0, 2, 2, 8
20. 1, 7, 1, 5, 2, 1 21. 1 2, 0, 3, 1, 0
22. 1, 4, 1, 6, 2, 10
23. 0, 1, 1, 3, 2, 11
24. 2, 11, 1, 1, 1, 7
25. 1, 7, 1, 3, 2, 4
26. 1, 2, 1, 4, 2, 4 27. 1, 2, 2, 1, 3, 6
28. Population Model The table shows the population of a town from 1990
through 1998. Find a quadratic model in standard form for the data. Assume
that t is the number of years since 1990 and that P is measured in thousands
of people.
Year, t 0 1 2 3 4 5 6 7 8
Population, P 23.2 24 26.5 27.2 27.1 27.3 26.8 25.9 24.4
29. Voter Turn-out The table shows the percentage of eligible voters that
participated in presidential elections from 1964 through 1992. Find a
quadratic model in standard form for the data. Assume that t is the number
of years since 1964.
Year, t 0 4 8 12 16 20 24 28
Percent voted, V 69.3 67.8 63.0 59.2 59.2 59.9 57.4 61.3
Algebra 2 111
Chapter 5 Resource Book
Lesson 5.8

Answer Key
Practice C
1. 2.
3. 4.
5.
7.
6.
8.
9.
10.
11.
12.
13. 14.
15. 16.
17.
18. 19.
20. 21.
22.
23. A 3.142r 2 F 0.498t
; 3.142
2 y 2x
22.103t 768.941
2 y 3x 3x
2 2
y x
3
2 y 3x 6x 9
2 5x 3
y 2x
8
2 1
y
3x 6
3
4x2 x 1
y 4
1
2x2 y x
2x 5
2 y 7x 3x 1
2 y
21x 27
7 2
y 4x 3x x 7
3
5x 5
y
8
6
5x 3
4x 1
y
2
1
4x 1
y
2x 3
1
y 2x 7x 6
y
3x 4x 2
2
3x 1
2 2 3
y x 2
1
3 2 y
5
2
5x 32 1
y 2
1
3x 22 y 3x 6
5
2 y 2x 1 2
2 3

Lesson 5.8
LESSON
5.8
Practice C
For use with pages 306–312
112 Algebra 2
Chapter 5 Resource Book
NAME _________________________________________________________ DATE ___________
Write a quadratic function in vertex form whose graph has the
given vertex and passes through the given point.
1. vertex: 2. vertex: 3. vertex:
point: point: point:
4. vertex: 5. vertex: 6. vertex:
point: point: point:
1
1, 3
6, 2
2, 5
4, 14
1
3, 2
3 , 5
2, 9
10
Write a quadratic function in intercept form whose graph has the
given x-intercepts and passes through the given point.
7. x-intercepts: 8. x-intercepts: 9. x-intercepts: 3,
point: 2, 80
point: 5, 1
point: 5, 11
1
6, 7
2, 4
2
1
2 10
1 3
,
10. x-intercepts: 2 4
11. x-intercepts: 8 5
12. x-intercepts:
point:
3
, point: point:
Write a quadratic function in standard form whose graph passes
through the given points.
13. 14. 15.
16. 17. 18.
19. 20. 21. 1
11
1, 3 , 2 , 2, 12
, 1, 32
, 0
1
3 , 1, 23
, 2
12
, 23 4 , 1, 2, 3
9
2 , 1 67
8 , 64, 1, 13
8 , 5 2, 3, 13, 0, 6, 3, 11
4 , 19
21
4 , 1 2, 13, 3, 27, 4, 55
2, 9, 0, 1, 1, 3
2, 3, 2, 11, 4, 21
1
2 , 16, 1, 0
4
1, 41
9
2, 77
5 3
,
10
22. Average Fuel Consumption The table shows the average fuel consumption
(in gallons) of a passenger car between 1970 and 1996. Use a system of
equations to write a quadratic model for average fuel consumption F as a
function of time t, where t is the number of years since 1970. Check your
model using the quadratic regression feature of a graphing calculator.
Year, t 0 5 10 15 20 25 26
Average Fuel 760 695 576 559 520 530 531
Consumption, F
23. Geometry The table shows the areas of a circle with a given radius. Use
the quadratic regression feature of a graphing calculator to write a quadratic
model for the area of a circle A as a function of its radius r. Round the values
for a, b, and c to three decimal places. Using A r what is a three
decimal approximation of ?
2 ,
Radius, r 2 3 4 5
Area, A 12.5664 28.2743 50.2655 78.5398
2, 5
5, 2
1 3
2 ,
1, 3
2
5 7 , 53
2
7 , 0
Copyright © McDougal Littell Inc.
All rights reserved.
16

Answer Key
Test A
1. 2. 3. 4. 5x
5. f x → as x →
and f x → as x → ;
2 y y
6
8x3y3 1
x
x 2 1 0 1 2
y 5 7 1 5 7
6. f x → as x →
and f x → as x → ;
x 2 1 0 1 2
y 0 3 0 3 0
7. 8. 9.
10. 11.
12. 13.
14. 15.
16. 17.
18. Possible zeros: ; Zeros:
19. Possible zeros:
Zeros:
20.
21. f x x 22. 1.29, 2, 3.24
23. x-intercepts: 3, 0, 3, 0;
local max: 0, 27;
local mins: 3, 0, 3, 0
The graph rises to the right and to the left.
24.
2 f x x
7x 12
3 2x2 2x
1, 1, 3, 3 1, 3
1, 1, 2, 2, 4, 4, 8, 8
4, 1, 2
11x 12
2 x 8x 8
2 4x 4, 4
2, 2, 3, 3 1, 1, 4
2x 3
2y3x2y2 x 1x
5y 6
2 x
5x 15x 1
x 1
3 4x 1
2 y2 2x2 2x 2
f 1
f 2
1 0
1
2
f 3 f 4 f 5
1 4 9
1 3 5 7
2 2 2
2
1
y
y
1
6
f 6
16
x
x

Review and Assess
CHAPTER
6
NAME _________________________________________________________ DATE
Chapter Test A
For use after Chapter 6
____________
Simplify the expression.
1. 2. 3.
y
4.
3
y3 2xy3 x5 x6 Describe the end behavior of the graph of the polynomial
function. Then evaluate for Then graph
the function.
5. 6. y x3 y 3x 4x
3 x 2, 1, 0, 1, 2.
9x 1
9.
12.
x
y
x 1x 2 x 1
2
12x 4 y 3 20x 2 y 2 24x 2 y
130 Algebra 2
Chapter 6 Resource Book
y
2
Perform the indicated operation.
7. x 8. 2x y2x y
2 x 1 x2 x 1
Factor the polynomial.
10. 11. x3 25x 1
2 1
x
Solve the equation.
13. 14.
15. x3 4x2 x
x 4 0
4 13x2 x 36 0
2 16
x
y
1
y
1
25x 3 y 2
5xy
x
Answers
1.
2.
3.
4.
5. Use grid at left.
6. Use grid at left.
7.
8.
9.
10.
11.
12.
13.
14.
15.
Copyright © McDougal Littell Inc.
All rights reserved.

CHAPTER
6
CONTINUED
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ____________
Chapter Test A
For use after Chapter 6
Divide. Use synthetic division if possible.
16. 17. 2x3 6x2 x 8 x 1
3 7x 6 x 2
List all the possible rational zeros of f using the rational zero
theorem. Then find all the zeros of the function.
18. 19. f x x3 x2 f x x 10x 8
2 4x 3
Write a polynomial function of least degree that has real
coefficients, the given zeros, and a leading coefficient of 1.
20. 21.
22. Use technology to approximate the real zeros of
23. Identify the x-intercepts, local maximum, and local minimum of the
graph of f x Then describe the behavior of
the graph.
1
3x 32x 32 f x 0.25x
.
3 x2 4, 1, 3
4, 3
2.
24. Show that the nth-order finite differences for the function
f x x of degree n are nonzero and constant.
2 4x 4
16.
17.
18.
19.
20.
21.
22.
23.
24.
Algebra 2 131
Chapter 6 Resource Book
Review and Assess

Answer Key
Test B
1. 2. 3. x 4. 1
5. f x → as x →
and f x → as x → ;
8y8 1
x6y9 y
x
x 2 1 0 1 2
y 8 1 0 1 8
6. f x → as x →
and f x → as x → ;
x 2 1 0 1 2
y 0 3 4 9 0
1
y
y
6
7. 8.
9. 10.
11.
12. 13.
14. 15. 16.
17.
18. Possible zeros: ; Zeros: 1, 5
19. Possible zeros:
Zeros: 20.
21. x 22. 4.66, 2.80, 1.75
23. x-intercepts: 2, 0, 2, 0;
local max: 0, 4
local mins: 2, 0, 2, 0
The graph rises to the right and to the left.
24.
3 3x2 x
4x 12
2 2x
1, 1, 5, 5
1, 1, 2, 2, 4, 4, 8, 8
4, 1, 2 x 20
2 x
5x 3
2 5xy3x 9, 9
6, 0, 1 0, 20 4x 12
2y2 y 1y
2xy 1
2 2x 10x 3y10x 3y
y 1
3 x2 x
1
2 7xy 12y2 x3 2x2 2
f 1
f 2 f 3 f 4 f 5 f 6
3 0 15 48 105 192
3 15 33 57 87
12 18 24 30
6 6 6
1
6
x
x

Review and Assess
CHAPTER
6
NAME _________________________________________________________ DATE
Chapter Test B
For use after Chapter 6
____________
Simplify the expression.
1. 2. 3. 4.
x4y4 x 4y Describe the end behavior of the graph of the polynomial
function. Then evaluate for Then graph
the function.
5. 6. y 2x3 x2 y x 8x 4
3
x 2, 1, 0, 1, 2.
9.
12.
x 3 y 2
x
y
x 12x 2 x 1
15x 3 y 3 10x 2 y 2 5xy
15. xx 5x 4 x 3
1
132 Algebra 2
Chapter 6 Resource Book
y
1
x 2 y 3 3
Factor the polynomial.
10. 11. y3 100x 1
2 9y2 Solve the equation.
13. 14. 5x3 30x 25x2 x2 81
x
x 4 y 4
Perform the indicated operation.
7. 3x 8. x 3yx 4y
3 x2 4 2x3 x2 2
x
y
2
y
2
xy
1
xy1
x
Answers
1.
2.
3.
4.
5. Use grid at left.
6. Use grid at left.
7.
8.
9.
10.
11.
12.
13.
14.
15.
Copyright © McDougal Littell Inc.
All rights reserved.

CHAPTER
6
CONTINUED
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ____________
Chapter Test B
For use after Chapter 6
Divide. Use synthetic division if possible.
16. x3 28x 48 x 4
17.
2x 3 11x 2 18x 9 x 3
List all the possible rational zeros of f using the rational zero
theorem. Then find all the zeros of the function.
18. f x x 19.
2 6x 5
f x x 3 x 2 10x 8
Write a polynomial function of least degree that has real
coefficients, the given zeros, and a leading coefficient of 1.
20. 21.
22. Use technology to approximate the real zeros of
23. Identify the x-intercepts, the local maximum, and local minimum of
the graph of f x Then describe the behavior
of the graph.
1
4x 22x 22 f x 0.35x
.
3 2x2 4, 5
2, 2, 3
8.
24. Show that the nth-order finite differences for the function
f x x of degree n are nonzero and constant.
3 4x
16.
17.
18.
19.
20.
21.
22.
23.
24.
Algebra 2 133
Chapter 6 Resource Book
Review and Assess

Answer Key
Test C
1. 2. 3. 4. x
5. f x → as x →
and f x → as x → ;
4y14 x3y3 x5y5 1
x3y2 x y
2 0
1 6
0 4
1 0
2 0
6. f x → as x →
and f x → as x → ;
x y
2 4
1 0
0 6
1 4
2 0
7. 8.
9.
10.
11.
12. 13.
14. 15. 16.
17.
18. Possible zeros: ; Zero:
19. Possible zeros:
20. 21. x 22.
9.67, 1.93, 1.61
23. x–intercepts: 4, 0, 4, 0;
local max: 0, 16;
local min: 4, 0, 4, 0
The graph rises to the right and to the left.
4 5x2 x 36
3 6x2 1, 1, 2, 2, 3, 3, 4, 4,
6, 6, 12, 12; zeros: 4, 1, 3
11x 6
1
1, 1,
2
1
x
1
,
2 2
3 3x2 x
x 1
2 2y 14y
4c dc dc 2d 6, 6
0, 3, 4
1 3
2 , 2 x 3
2 2x
42x y2x y
2y 1
3 3x2y 3xy2 y3 x2y2 x xy 12
3 6x2 2x 6
24.
f 1
f 2 f 3 f 4 f 5 f 6
0 12 40 90 168 280
12 28 50 78 112
16 22 28 34
6 6 6
y
1
1
y
1
3
x
x

Review and Assess
CHAPTER
6
NAME _________________________________________________________ DATE
Chapter Test C
For use after Chapter 6
____________
Simplify the expression.
1
1. 2. 3. 4.
xy3 x3y3 x2y2 x3y21 Perform the indicated operation.
7.
8. 9. 2x yx2 xy y2 4x
xy 4xy 3
3 3x2 x 2 5x3 3x2 x 4
12.
1
4c 3 8c 2 d 4cd 2 8d 3
Solve the equation.
13. 14.
15. 2x2 32 4xx3 4y
6
3 48y2 4y 4
2x2 72
134 Algebra 2
Chapter 6 Resource Book
y
1
Factor the polynomial.
10. 11. 8y3 16x 1
2 4y2 x
y
1
1
x2y3 y4 y
4
x2y3 Describe the end behavior of the graph of the polynomial
function. Then evaluate for Then graph
the function.
5. 6. y x 1x 2x2 y x 3
3 x2 x 2, 1, 0, 1, 2.
4x 4
x
x
y
y
x
Answers
1.
2.
3.
4.
5. Use grid at left.
6. Use grid at left.
7.
8.
9.
10.
11.
12.
13.
14.
15.
Copyright © McDougal Littell Inc.
All rights reserved.

CHAPTER
6
CONTINUED
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ____________
Chapter Test C
For use after Chapter 6
Divide. Use synthetic division if possible.
16. x3 2x2 9 x 3
17.
x 4 10x 2 2x 3 x 3
List all the possible rational zeros of f using the rational zero
theorem. Then find all the zeros of the function.
18. 19. f x x3 2x2 f x 2x 11x 12
3 x2 2x 1
Write a polynomial function of least degree that has real
coefficients, the given zeros, and a leading coefficient of 1.
20. 21.
22. Use technology to approximate the real zeros of
23. Identify the x-intercepts, local maximum, and local minimum of the
graph of f x Then describe the behavior of
the graph.
1
16x 42x 42 f x 0.2x
.
3 2x2 1, 2, 3
3, 3, 2i, 2i
6.
24. Show that the nth-order finite difference for the function
f x x of degree n is nonzero and constant.
3 2x2 x 2
16.
17.
18.
19.
20.
21.
22.
23.
24.
Algebra 2 135
Chapter 6 Resource Book
Review and Assess

Answer Key
Cumulative Review
1. 2. 3. 14 4. 5.
6.
12. 10
7. 6 8.
23
9. 11 10. 6 11. 8
13. x ≥ 2
14. x > 2
19
14 5
26 27
14
2
3 2 1 0 1 2 3
15. or x < 3 16. x > 5 or x ≤ 5
x > 3
2
3 2 1 0 1 2 3
17. 2 < x < 3 18. 2.5 ≤ x ≤ 0.5
3 2 1 0 1 2 3
19. Line 2 20. Line 2 21. Line 1 22. Line 2
23. 24.
1
25. 26.
1
y
(0, 8)
y
1
(0, 4)
1
27. 28.
2
y
( 2 , 0)
2
3
(0, 8)
2
(3, 0)
x
x
x
3 2 1 0 1 2 3
5
6 4 2
2.5
0.5
3 2 1 0 1 2 3
1
2
( 5
, 0)
2
y
y
0 2 4 6
1
2
( 3 , 0)
1
2
(0, 7)
1
y
1
( 2
0, )
1
5
(6, 0)
x
x
x
29. 30.
31. 32.
33. 34. 35. 2
36. 6 37. 38. 0
39. infinitely many solutions 40. none
41. one 42. 43. 44.
45. 46. 2, 5 47. 0.5, 0.3 48. 8
49. 6 50. 7 51. 65 52. 14 53. 1
54. 55.
1
3 , 4
1, 0
1
y
3
3, 2 2 , 4
2
y
7
3x 3
3
y x 2
2x 2
3
y
4x 5
2
y 3x 5
24
5x 5
1
56. 57.
y
2
y
1
2
58. 59.
1
1
y
x
x
x
6
1
y
y
2
1
1
1
y
x
x
x

Answer Key
60. 61. 62. 63.
64. 65. 66. 5 67. 68.
69. 70. 71.
72. 73. 74.
75. 76. 77.
78. 79.
80.
81.
82. 83. 3x2 4x 12x 3
2 1x2 3xx 3x
9
2 3x2x
3x 9
2 1x2 x
2
2 2x2 3x 1
2 13x2 25 2
26 10 11
1 ±41
4
9 ±41
20
4 ±7
4
3 , 1 ±32 2 ±3
1
2
3 , 5
±3
±3
3 ±6 ±4
84.
85. x 1 86.
4
x 1
87.
2x 2 4x 5 15
x 2
x 3 x 2 3x 10 5
x 3
88. 8 in. on each side
3
2
3x 8 38
x 4

CHAPTER
6
NAME _________________________________________________________ DATE
Cumulative Review
For use after Chapters 1–6
____________
Evaluate the expression for the given values of the variables. (1.2)
1. when 2. when 3. x when x 2
2 x 5x
1
3x 5 x 3
4x 8x 4
4. when 5. when 6. x when x 2
2 x x 3
5x
3 x x 2 2x 3
3 4x2 x
Solve the equation. (1.3)
7. 4x 8 32
8. m 15 3m 4
9. 43x 5 x 3
10.
3
2x 4 2x 1
11.
1 3 3 29
2x 4 2x 4
12.
2 2 1 11
5x 3 10x 3
Solve the inequality. Then graph the solution. (1.6)
13. 2x 5 ≥ 9
14. 5 2x < 15 3x
15. 4x 2 > 8 or 4x 2 < 10
16. 3x 7 > 8 or 2x 1 ≤ 9
17. 5 < 3x 1 < 10
18. 0.25 ≤ 0.5x 1 ≤ 0.75
Tell which line is steeper. (2.2)
19. Line 1: through 2, 5 and 3, 7
20. Line 1: through 0, 5 and 3, 8
Line 2: through 0, 8 and 4, 3
Line 2: through 7, 1 and 9, 10
21. Line 1: through 4, 6 and 5, 9
22. Line 1: through 5, 6 and 2, 3
Line 2: through 3, 1 and 5, 4
Line 2: through 2, 8 and 1, 9
Graph the equation using standard form. Label any intercepts. (2.3)
23. 3x y 8
24. 2x y 7
25. 4x 3y 12
26. 5x 4y 2
27. y 8
28. x 6
Write an equation of a line using the given information. (2.4)
29. The line passes through the point and has a slope of 3.
30. The line passes through the point and has a slope of
31. The line has a slope of and a y-intercept of 5.
3
0, 5
2
2, 4
5.
32. The line passes through the point 2, 4 and is parallel to x 7.
33. The line passes through the point and is perpendicular to the line
34. The line passes through the point and is parallel to the line y 2
y
4, 5
3x 7.
2
2, 1
3x 5.
Evaluate the function for the given value of x. (2.7)
f x 3x,
x 1,
if x ≤ 2
if x > 2
Copyright © McDougal Littell Inc.
All rights reserved.
4
35. f3
36.
37. f1
38.
Tell how many solutions the linear system has. (3.1)
39. 4x 2y 8
40. 3x 2y 6
41. 5x 6y 7
8x 4y 16
6x 4y 8
2x 3y 5
4
f2
f0
Algebra 2 141
Chapter 6 Resource Book
Review and Assess

Review and Assess
CHAPTER
6
CONTINUED
NAME _________________________________________________________ DATE ____________
Cumulative Review
For use after Chapters 1–6
Solve the system using an algebraic method. (3.2)
42. 3x 4y 17
43. 4x y 6
44. 3x 8y 3
2x y 8
45. 46. 47.
1
2x 4x 3y 1.1
2
3x 2x 5y 0.5
9x 3y 15
5y 1
1
6x 2y 6
5y 7
Evaluate the determinant of the matrix. (4.3)
48. 49. 50.
2
0
1
3
4
4
3
1
51. 52. 53.
0
1 3
5 1 2
6 1
5 4 3
2 1 0
4 2
5
Graph the quadratic function. (5.1)
54. 55. 56.
57. 58. 59. y 1
2x 52 y 2x 4 2
2 y x 1 2
2 y 2x
3
2 y x 8x 3
2 y x 4x 5
2 2x 3
Solve the quadratic equation. (5.2, 5.3)
60. 61. 62.
63. 64. 65. 3x2 x 13x 10 0
2 4x 9 0
2 x
12x 9 0
2 1
3x 3 2 14
2 2x 2
2 5 11
Find the absolute value of the complex number. (5.4)
66. 3 4i
67. 4 2i
68. 1 i
69. 1 5i
70. 3 i
71. 2 7i
Use the quadratic formula to solve the equation. (5.6)
72. 73. 74.
75. 76. 77. 2x2 4x x2 x 1
2 3x 18 0
2 x
x 4 0
2 10x 8x 9 0
2 2x 9x 1 0
2 x 5 0
Factor using any method. (6.4)
78. 79. 80.
81. 82. 83. 6x3 9x2 4x 2x 3
4 37x2 3x 9
4 6x
81x
5 15x3 x 6x
4 3x2 9x 2
4 1
Divide using synthetic division. (6.5)
84. 85.
86.
87.
88. Dimensions of a box An open box with a volume of 32 in. is made from
a square piece of metal by cutting 2-inch squares from each corner and then
folding up the sides. Find the dimensions of the piece of metal required to
make the box. (5.5)
3
x4 2x3 3x x 25 x 3
2 x
4x 6 x 4
2 2x 2x 3 x 1
3 3x 5 x 2
142 Algebra 2
Chapter 6 Resource Book
8x 2y 4
7
2x 5y 2
3 1
2
4
3
2
2
2
2
3
5
1
1
2
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice A
1. 19,683 2. 256 3. 1024 4. 64 5.
6. 5 7. 8. 9. 10.
11. 25 12. 13. 25 14. 15. 1
16. 17. 18. 15,625 19. 256
20. 729 21. 22. 23. 24.
25. 1 26. 1 27. 28. 29. 30.
31. 32. 33. 34. 35.
x4 27x
16
3
x24 x12 x8
1
9
1
64
16
9
1
1
81
27
8
4
25
64
1
1
343
32
3
1
1
216
1
243
1
128 243
32
1 9
36. 37. 38. 39.
2.47 10 10 mi2 x6 x5 x 2
40. 41.
42. 5.59 107 mi2 16
x 2
1.88 10 8 mi 2
1
4
81
16

LESSON
6.1
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice A
For use with pages 323–328
Use the properties of exponents to evaluate the expression.
3 4 3 5
54 52 13. 14. 15.
28 23 16. 17. 18.
2 4 2
19. 20. 21.
22. 23. 24.
2
3
25. 26. 27. 32 4
130 28. 29. 30.
3
43 Simplify the expression.
x 3 x 5
31. 32. 33.
3x 3
34. 35. 36.
x
37. 38. 39.
3
x3 x 9
2 3
2 6 2 2
33 34 3 2 3
4 2
x 4 x 8
Surface Area In Exercises 40–42, use the formula S 4r to find
the surface area of each planet.
40. The radius of Jupiter is approximately 44,366 miles. Find the surface area
of Jupiter.
41. The radius of Earth is approximately 3863 miles. Find the surface area of
Earth.
42. The radius of Mars is approximately 2110 miles. Find the surface area of
Mars.
2
76 79 5 0
2 4
x 2
5 2
4 3 4 2
1. 2. 3.
4. 5. 6.
7. 8. 9.
10. 11. 5 12.
658 3233 24 23 32 33 62 61 57 58 25 23 41 44 2 3 2 2
3 5
3 5
5 2 3
1
1 4 3
3 4
2
3 4
x 4 6
x 7
x 2
x
4 2
Algebra 2 13
Chapter 6 Resource Book
Lesson 6.1

Answer Key
Practice B
1. 9 2. 15,625 3.
8
27
4.
1
64 5. 1 6.
7. 9 8. 16 9. 1 10. 11.
2
12.
1
13. 14. 15. 16.
y2 256x12 y3 8
17. 18. 19. x 20. 5 3
y5
3x 2
2x 3
7.02 10 1 peoplemi 2
x 5
21. 22.
23. 580.52 computers/1000 people
y 2
5x 3
2y 2
3 x 4
1
16
9x 2
1.08 10 5 mih

Lesson 6.1
LESSON
6.1
Practice B
For use with pages 323–328
14 Algebra 2
Chapter 6 Resource Book
NAME _________________________________________________________ DATE ___________
Use the properties of exponents to evaluate the expression.
3 4 3 2
1. 2. 3.
84 86 4. 5. (7 6.
676 325 38 7. 8. 9.
1
Simplify the expression.
x 3 x 2
10. 11. 12.
y
2 3
13. 14. 15.
16. 17. 18. 3x2
5x 3xy
2y 2x 1 y 3
19. Geometry Find an expression for the
area of the triangle.
2x 3
x 2
5 2 3
2 4
2y3 y5 21. Population per Square Mile In 1996,
the population of the United States was
approximately 265,280,000 people. The
area of the United States is approximately
3,780,000 square miles. Use scientific
notation to find the population per square
mile in the United States.
23. Computers per 1000 People The population
of the United States is approximately
265,280 thousand people. It is estimated
that by the year 2000, there will be
154,000,000 computers in the United
States. How many computers will there be
per 1000 people?
4x 3 4
9x 3 y 4
2
3 3
4 4 3
4 6
5 6
5 3 2
3x 2
x 0 y 2
6x 5
20. Geometry Find an expression for the
area of the circle.
x 2 π
22. Speed of Mercury Mercury travels
approximately 226,000,000 miles around
the sun. It takes Mercury approximately
2100 hours to revolve around the sun.
Use scientific notation to find the speed
of Mercury as it revolves around the sun.
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice C
1. 16 2. 2187 3. 1
27
4. 5.
81
6. 243
7. 8. 9. 1 10. 11. 12x
5y
4
x3 2y 2
y 1
12. 13. 14. 15. 16. 2
10z2 4x2 y 4
17. 6 18. 4 19. 3 20. 21.
22.
23.
24. about 25. 345,600 in. 3
190
53.32%
4
4 3
203 6517
4 7 3 4
38,400
3
in. 3 343
48 in.3
5
3 7
3y 2
16x 5
4x 2
8
4x 2
4096
x 48
3

LESSON
6.1
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice C
For use with pages 323–328
Use the properties of exponents to evaluate the expression.
2 4 2 5
1. 2. 3.
31 23 Simplify the expression.
2x
7. 8. 9.
2
3xy3 2x1
y1 xy 2x2
4 y3 2x
10. 11. 12.
23
5
15x2
2x3 5x2y 8 2x1y x3y 13. 14. 15.
x2y5z 2x3 2
2x3
2x3 4x5 Use the properties of exponents to simplify the left side of the
equation. Then solve the equation as demonstrated below.
3
16. 17. 18.
x
2 34
32 x23 25 4x1 42 ⇒ x 1 2 ⇒ x 3
4 3
3 2 3
4. 5. 6.
1
1
1
3 8 2
2
2
3 3
2 x y 2
19. 40
20. 25
21.
4x y2 Class Project In Exercises 22–25, use the following information.
Your class project is to design a piece of playground equipment for an
elementary school. You design a romper room that will contain small plastic
balls for the children to roll around in. The room will be 10 feet by 10 feet. The
plastic balls will cover the entire floor to a depth of 2 feet. A toy distributor can
ship you 190 balls (each with a radius of 1 inches) in a cubic box, 20 inches on
a side.
22. Find an expression for the volume (in cubic inches) of one ball.
23. Find an expression that represents the ratio of the volume of 190
balls to the volume of the cubic box.
24. What percent of the volume of the cubic box is filled with plastic
balls?
25. Find the volume of the region in the romper room that will contain
plastic balls. Give your result in cubic inches.
3
4
2
2 4 2 1
2 3
3 4
3 3
3 2
x4 y2 y2
x4 x3 y 2
2x 42
(x 4 6 2
5 x 3 5 12
2x 0 3 2 3 x 3 1
10
10
Algebra 2 15
Chapter 6 Resource Book
Lesson 6.1

Answer Key
Practice A
1. yes 2. yes 3. no 4. yes 5. no 6. yes
7. 5; 3 8. 9. 4; 8 10.
11. 12. 9; 3 13.
14.
15.
16.
17.
18. 19.
20. 1 21. 34 22. 23. B 24. C
25. D 26. A
27. C 0.99x 28. 2; 0.99
2 f x 5x 1
14
14.93x 75.32
3 7x2 f x 5x
x 3
4 f x 5x
6x 2
2 f x 2x
3x 14
3 5x2 f x 5x
3x 3
2 f x 2x
2x 3
3 3x2 7; 2
2; 5
5
29. 324
2; 1
3

Lesson 6.2
LESSON
6.2
Practice A
For use with pages 329–336
26 Algebra 2
Chapter 6 Resource Book
NAME _________________________________________________________ DATE ___________
State whether the following function is a polynomial.
f x 3x 2 7x 3
1. 2. 3.
4. f x 9
5. f x 2x 5x 8
6.
State the degree and leading coefficient of the polynomial.
7. 8.
9. f x 8x 10.
11. 12.
4
f x 3x5 3x2 8
f x 3x 5 x 2 5
Write the function in standard form.
13. 14.
15. f x 3x 5x 16.
17. 18.
2 3 2x3 f x 3x2 5 2x3 f x 6x 5x 4 2
Use direct substitution to evaluate the polynomial function for the
given value of x.
f x 3 x 2 4x x 3 , x 2
19. 20.
21. 22.
f x 7x 2x 2 5, x 3
Use what you know about end behavior to match the polynomial
with its graph.
f x 2x 4 2x 1
23. 24.
25. 26.
f x x 2 3x 2
A. B. C. D.
1
y
1
Computers In Exercises 27–29, use the following information.
From 1990 to 1995, the number of computers per 1000 people in Germany
can be modeled by C 75.32 14.93t 0.99t where C is the number
of computers per 1000 people and t is the number of years since 1990.
2
27. Write the model in standard form.
x
28. State the degree and leading coefficient of the model.
29. Estimate the number of computers per 1000 people in the year 2000.
1
y
1
f x 5 3x 4
x
f x 2x 7 3x
f x 24 4x 1
3 x2
f x 4x 5 4x 7x 8 3x 9
f x 3 2x 5x 2
f x 14 3x 5x 2
f x x 3 5x 3 7x 2
f x 3x 2 5x 2x 5 x 4 , x 1
f x x 2 5x 22, x 4
f x 2x 3 x 2 3x 3
f x 2x 3 x 2 1
1
y
2
x
f x 2 x 3x 1
f x x3 x 2
1
y
1
Copyright © McDougal Littell Inc.
All rights reserved.
x

Answer Key
Practice B
1. yes; f x 2x 2. no
3 3x2 4x; 3; 2
3. no 4. yes;
5. yes; f x 1
f x 2x
2
x ; 2; 1
5 7x2 3; 5; 2
6. yes;
7. 7 8. 3 9. 23 10. 30 11. 8
12. 52 13. 6 14. 84 15. 98 16. 86
17. 5 18. 74 19. 37 20. 0 21. 72
22. 6
23. 24.
1
25. 26.
2
27. 28.
1
y
y
y
1
1
2
6x2 1
3
f x 5 x 4 2x 2 x 7; 4; 5
x
x
x
3
2
1
1
6
y
y
y
1
1
2
x
x
x
29. 30.
2
31. 32. $1.02
1
y
y
2
2
x
x
33. $491,662.20
1
y
1
x

LESSON
6.2
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice B
For use with pages 329–336
Decide whether the function is a polynomial function. If it is, write
the function in standard form and state the degree and leading
coefficient.
f x 3x 2 2x 3 4x
1. 2.
3. 4.
5. f x 6.
1
f x 4x 2x 7x
2 1
x 3 1
3
Use direct substitution to evaluate the polynomial function for the
given value of x.
7. 8.
9. 10.
11. f x 3x 12.
13. 14.
7 2x6 f x 4x
5x 8, x 0
2 f x 3x 2, x 3
5x 2, x 3
f x 2x 5 3x 3 2x 5, x 1
Use synthetic substitution to evaluate the polynomial function for
the given value of x.
f x 2x 3 3x 2 4x 2, x 4
15. 16.
17. 18.
19. f x 2x 20.
21. 22.
2 f x 5x
4x 7, x 3
4 3x2 2x 5, x 1
f x 4x 3 2x 2 6x, x 3
Graph the polynomial function.
23. 24. 25.
26. 27.
28. 29. f x 1 x
30. 31.
2 x3 f x x4 2x3 f x x
5x 1
3 f x 3 x 2x 3
2
f x 2x4 f x x 1
3 2
f x 2 x 2 x 4
3
6 x2
f x x 3 x 2 2
f x 3x 3 2x 1
f x 2x 5 3 7x 2
f x x 5 x 4 2x 2 7
f x 2x 3 3x 2 5x 1, x 1
f x 3x 4 2x 2 3x 4, x 2
f x 6x 3 2x 2 5x 2, x 2
f x x 4 2x 3 4x 2 6x 3, x 3
f x 2x 4 3x 3 5x 2 2x 6, x 2
f x x 6 3x 4, x 2
f x x 4 3x 3 2x 2 8x, x 4
f x 3x 3 5x 2 6x 8, x 1
32. Value of the Dollar From 1988 to 1998 the value of a dollar in 1998 dollars
can be modeled by where V is the value of
the dollar and t is the number of years since 1988. What was the value of a
dollar in 1996 in terms of 1998 dollars?
33. Preakness Stakes From 1990 to 1998, the money received by the winning
horse can be modeled by W 6266.2t
157,544.5 where W is the winnings and t is the number of years since 1990.
How much did Silver Charm win in 1997?
3 79,306.8t2 V 0.002t
295,834.9t
2 0.06t 1.37
f x 2x 3 1
Algebra 2 27
Chapter 6 Resource Book
Lesson 6.2

Answer Key
Practice C
1. 3 2. 15 3. 16 4. 5.
6. 7. 0 8. 45 9. 10.
11. 12.
215
27
13. 14.
9
2
61
35
8 10
13 52
3
1
15. 16.
1
17. 18.
2
19. 20.
1
y
y
y
y
1
1
1
1
x
x
x
x
1
1
2
1
y
y
y
y
1
1
1
2
103
10
x
x
x
x
21.
1
22. Sample answer:
23. Sample answer:
y
24. 20.48 years 25. older
2
x
f x 3x 4 2x 1
f x 2x 3 3x 2 x 5

Lesson 6.2
LESSON
6.2
Practice C
For use with pages 329–336
28 Algebra 2
Chapter 6 Resource Book
NAME _________________________________________________________ DATE ___________
Use direct substitution to evaluate the polynomial function for the
given value of x.
f x 3x 3 4x 2 x 7, x 2
1. 2.
3. f x 4.
5. 6.
3
2x3 1
4x2 3x 1, x 2
f x x 4 2x 2 5, x 5
Use synthetic substitution to evaluate the polynomial function for
the given value of x.
f x 2x 5 3x 4 x 3 x 2 6x 3, x 1
7.
8.
9.
2
f x 3 10.
11. 12.
x3 4x2 1
f x 3x
2x 2, x 2
4 2x2 5, x 2
f x 4x3 2x2 x 3, x 1
2
Graph the function.
13. 14. f x 3x 15.
16. 17. 18.
2 f x 4 x 5
3
f x 2x 4 3x 1
19. 20. f x 3 x 21.
4 2x 1
5
4
f x x3
22. Critical Thinking Give an example of a polynomial function f such that
f x → as x → and f x → as x →.
23. Critical Thinking Give an example of a polynomial function f such that
f x → as x → and f x → as x →.
First-time Brides In Exercises 24 and 25, use the following information.
The median age of a female when she gets married for the first time in the
United States from 1890 to 1996 can be modeled by
A 0.001t 2 0.098t 22.763
f x 2x 7 1
where A is the age and t is the number of years since 1890.
24. What was the median age of first time brides in 1950?
f x 1
2 x2 x 3, x 4
f x 2x 4 3x 2 5, x 1
2
f x 2x 6 x 4 5x 1, x 2
f x x3 3x 7, x 1
f x
3
1
5x2 3x 1
2 , x 3
25. Describe the end behavior of the graph. From the end behavior, would
you expect first time brides in 2000 to be older or younger than the brides
in 1996?
f x x 3 3x 1
f x 2
3 x2
f x 2x 3 7
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice A
1. 2.
3. 4.
5.
6. 7.
8. 9.
10. 11. 12.
13. 14.
15. 16.
17.
18. 19.
20. 21.
22. 23.
24. 25.
26. 27. 28.
29. 30.
31. 32.
33. 34. x
35. M 3052.04t 515,887.88
2 2x 10x 25
2 x
5x 3
2 x 5x
2 x
8x 16
2 x 16x 64
2 x
12x 36
2 x 6x 9
2 x 49
2 3x
16
2 2x x 2
2 2x
11x 5
2 x 5x 3
2 x
5x 6
2 x 8x 12
2 14x
x 12
2 x 9x 18
3 2x2 2x
10x 7
3 4x2 x
15x 4
12 5x8 2x 5x 4
5 5x2 x
9
3 5x2 2x 8x 5
2 x
7x 3
2 2x
x 2 x 3 2x 7
3 2x2 4x
x 4
2x 2
3 6x2 2x 2x 2
2 5x
3x 8
5 3x4 2x3 x2 4x
3x 8
2 4x 5x
4 3x3 2x2 2x
4x 8
3 5x2 3x x 4
2 5x 6

Lesson 6.3
LESSON
6.3
Practice A
For use with pages 338–344
40 Algebra 2
Chapter 6 Resource Book
NAME _________________________________________________________ DATE ___________
Find the sum.
1. x 2.
2 2x 5
3.
2x 2 3x 1
3x 4 x 3 x 2 x 9
x 4 2x 3 3x 2 5x 1
4. 5.
6. 7. 5x3 2x2 x 3 x3 4x2 x 3x 1
2 7x 1 3x2 2x
10x 7
5 3x4 2x3 x2 x 8 3x5 3x 2x
2 2x 5 x2 3x 5
Find the difference.
8. 9. 3x 10.
3 x 2x 1
2 4x 3
x 2 3x 1
11. 12.
13. 14.
15. 16. 7x12 3x8 2x 1 8x12 2x8 4x 3x 5
5 3x2 8 2x5 2x2 2x
1
3 4x2 3x 7 3x3 x2 3x 5x 2
2 2x 1 x2 x
5x 2
2 3x 1 2x2 x 7 2x 4
x 6
Find the product.
17. 2x 18. 19.
2 4x 1
x2 3x 7
x 4
20. 21. 22.
23. 24. 25.
26. 27. 28.
29. 30. 31. (x 42 x 82 x 62 x 32 x 4x 3
x 6x 2
x 3x 2
x 12x 3
2x 1x 5
3x 2x 1
x 4x 4
x 7x 7
Write the area of the figure as a polynomial in standard form.
32. 33. 34.
x 5
35. Education For 1990 through 1996, the number of bachelor degrees D earned by people in the
United States and the number of bachelor degrees W earned by women in the United States can
be modeled by
D 12829.86t 1117893
W 9777.82t 602005.12
x
x 3 2x 2 4x 3
x 1
x 1
4x 3 3x 2 2x 1
2x 3
6x 3 2x 2 x 3
6x 1
x 5
5x 3
7x 6
2x 3
x 5
where t is the number of years since 1990. Find a model that represents the number of bachelor
degrees M earned by men in the United States from 1990 through 1996.
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice B
1. 2.
3. 4.
5.
6. 7.
8.
9.
10. 11. 10 12.
13. 14. 15.
16. 17.
18. 19.
20. 21.
22. 23.
24. 25.
26. 27.
28. 29.
30. 31.
32. 33.
34.
35. v 16.2t3 183t2 x
1352.5t 11504.1
2 9x
42x 360
2 x 48x 64
2 16x
24x 144
2 x 24x 9
2 4x
20x 100
2 x 25
2 x
81
3 3x2 x 10x
3 x
7x 6
3 2x2 15x 1
2 8x
17x 4
2 6x 10x 3
2 2x
13x 5
2 3x 5x 3
2 2x
11x 4
2 x 11x 5
2 x
5x 4
2 x 4x 3
2 3x
3x 10
3 x2 2x 5x
3 6x2 3x2 8x
x
2
x3 3x2 2x
8x 5
5 3x4 x2 2x
5x 4
5 x3 x2 3x
7x 4
4 2x2 2x x 5
3 4x2 7x
3x 1
3 3x2 4x
2x 1
2 2x 2x 4
2 3x
6x 4
3 3x2 2x x 4
2 2x 2

LESSON
6.3
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice B
For use with pages 338–344
Find the sum or difference.
1. 2.
3. 4.
5. 6.
7. 8.
9. 10.
11.
12. 6x2 3x 7 2x2 3x
3x 7
3 2x2 7x 5 3x3 2x2 6x
7x 5
3 3x2 5x 1 7x3 4x 3x 6
5 3x4 5x 1 2x5 x2 1 3x x
3
2 x3 3 2x5 2x 4x
2 5 x 4x2 3x4 2x
3 3x2 x 3 x2 4x 2x 4
3 2x 3x3 3x2 x
1
2 2x 7 5x2 4x 3
2 x 3 2x2 3x
5x 1
3 2x2 x 1 x2 x 2x 3
2 2x 3 x2 5
Find the product.
13. 14. 15.
16. 17. 18.
19. 20. 21.
22. 23. 24.
25. 26. 27.
28. 29. 30.
31. 32. 33. 3x 82 x 122 4x 32 x 102 x 2x
x 9x 9
2x 52x 5
2 x 3x 5x
2 x 1x 3x 2
2 x3x
x 5x 2
(x 3x 1
x 4x 1
2x 1x 5
3x 1x 4
2x 3x 1
2x 53x 1
4x 12x 3
5x 43x 1
x 1
2 2x x 5
2 x3x 1
x 3)
34. Floor Space Find a polynomial that represents the total number of
square feet for the floor plan shown below.
12 ft
x ft
x 6 ft
24 ft
35. Advertising For 1980 through 1990, the amount of money A (in
millions of dollars) spent on television and newspaper advertising
can be modeled by
A 16.2t 3 153t 2 3609.5t 26,265.9
where t is the number of years since 1980. The amount of money n (in
millions of dollars) spent on newspaper advertising can be modeled by
n 30t 2 2257t 14,761.8
where t is the number of years since 1980. Write a model that represents
the amount of money v (in millions of dollars) spent on television
advertising.
Algebra 2 41
Chapter 6 Resource Book
Lesson 6.3

Answer Key
Practice C
1.
2. 3.
4. 5.
6.
8.
7.
9.
10. 11.
12. 13.
14. 15.
16.
17.
18.
19. 20.
21. 22.
23. 24.
25.
26.
27.
28.
29.
30. 31.
32. 33.
34.
35.
36.
37. I 814,536.25t
17,858,746.41t 560,699,692.4
3 4,028,984.354t2 4x
3 20x2 2x
31x 15
3 9x2 x
10x 3
3 4x2 x
11x 30
3 4x2 x x 6
2 8xy 16y2 36x2 12xy y2 16x2 9y2 8x3 36x2y 54xy2 27y3 27x3 135x2 8x
225x 125
3 12x2 x
6x 1
3 9x2 x
27x 27
3 6x2 1
9
12x 8
x2 4
25x
4
9x 9
2 16
9
20x 4
x2 40
1
4 3 x 25
x2 36x
49
2 2x 25
7 6x6 3x5 3x4 x
x
6 x5 2x4 6x3 x2 x
10x 5
5 3x4 x3 6x2 x
12x 9
4 6x3 5x2 2x
18x 6
3 x2 2x 7x 3
3 5x2 2x
x 2
3 5x2 x x 4
3 x2 24x
x 1
2 5x 35x 4
2 6x
32x 21
2 25x 25
3
8x2 1
6x 5
3
10x3 3x2 x 2x 1
2 5x 2
3
2
3
x2 11
3 x 2
3x4 4x2 5x
6x 5
2 x 5x 6
3 3x2 x
2x 3
3 3x2 5x 4

Lesson 6.3
LESSON
6.3
Practice C
For use with pages 338–344
42 Algebra 2
Chapter 6 Resource Book
NAME _________________________________________________________ DATE ___________
Find the sum or difference.
1. 2.
3. 4.
5. 6.
7. 8. 3 8x2 2
3x 5 34
x2 1
2x 15
x3 3x2 4
2x3 2x 1
2 5x2 2x 1 3 5x2 7x 1
3
1
2x2 3x 1 x2 2
2x
3x 3
3 6x 4 3x4 2x3 4x2 2x 1
2 7x 7 3x2 4x
2x 1
2 5x 1 x3 x2 2x 3x 4
3 3x2 5x 2 3x3 6x2 2
3 1
Find the product.
9. 10. 11.
12. 13. 14.
15. 16.
17. 18.
19. 20.
21. 22. 23.
24. 25. 26.
27. 28. 29.
30. 31. 32. (x 4y2 6x y2 2x 3y
4x 3y4x 3y
3
3x 53 2x 13 x 33 x 23 1 2
3x 3 2
5x 22 4 3x 52
1
2x 6x 56x 5
2x 712
x 7
3 xx4 3x3 2x2 x
1
3 2x 1x3 x2 x 5
3 x2 3x2 x
4x 3
2 3x2 2x 1x 6x 2
2 2x 1x
x 3
2 x 12x 3x 2
2 x 1x 3x 4
2 3x 52x 5
x 75x 3
3x 48x 1
2x 1
Find the product of the binomials.
33. x 3x 2x 1
34. x 5x 3x 2
35. 2x 1x 3x 1
36. 2x 32x 5x 1
37. IRS Collection The principal source of collections by the IRS include
individual income and profit taxes, corporation income and profit taxes,
employment taxes, estate and gift taxes, and other taxes. From 1992
through 1996, the amount of taxes collected in each of these categories
can be modeled by
T 7,810,103.714t 2 61,813,629.34t 1,116,758,213
C 18,508,265.4t 116,419,459.8
E 23,846,333.7t 394,945,983.6
3
G 133,820.25t 3 881,998.57t 2 2,915,045.54t 11,328,112.36
O 948,356.5t 3 4,663,117.93t 2 1,314,761.71t 33,364,964.86
(Total collected)
(Corporate income and profit)
(Employment)
(Estate and gift tax)
(Other taxes)
where T, C, E, G and O are in thousands of dollars and t is the number of years since 1992.
Write a model that represents the individual income and profit taxes I (in thousands of dollars)
from 1992 to 1996.
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice A
1. D 2. C 3. E 4. F 5. A 6. B 7. G
8.
9.
10.
11.
12.
13. 14.
15. 16.
17. 18.
19. x 5x 20. 2, 0 21. 0, 3
22. 4, 1 23. 3, 2 24. 7, 7
25. 10, 10 26. 2, 1, 1 27. 2, 1, 2
28. 3, 1, 3 29. C 30. A 31. B
2 x 4x
2
2 x 6x 3
2 x 5x
1
2 x 1x 1
2 x 3x
4
2 x 4x 2
2 x 2x
4x 16
2 x 1x
2x 4
2 x 5x
x 1
2 x 3x
5x 25
2 x 1x
3x 9
2 x 1

LESSON
6.4
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice A
For use with pages 345–351
Match the polynomial with its factorization.
1. A.
2. B.
3. C.
4. D.
5. E.
6. F.
7. G. 4x2 16x 92x 32x 3
4 5x 1x
81
2 8x x 1
3 x x 3x 2x 2
1
3 x 2x 2x
27
2 5x 4
3 x 2x
5
2 x 6
3 3x2 2x 14x
4x 12
2 x 2x 1
3 2x2 x 3x
6x 12
2 x 3x 9
4 16
Factor the sum or difference of cubes.
8. 9. 10.
11. 12. 13. x3 x 64
3 x 8
3 x
1
3 x 125
3 x 27
3 1
Factor the polynomial by grouping.
14. 15. 16.
17. 18. 19. x3 5x2 x 2x 10
3 4x2 x 3x 12
3 6x2 x
x 6
3 5x2 x x 5
3 x2 x 4x 4
3 3x2 2x 6
Find the real-number solutions of the equation.
20. 21. 22.
23. 24. 25.
26. 27. 28. x3 x2 x 9x 9 0
3 x2 x 4x 4 0
3 2x2 x
x 2 0
2 x 100 0
2 x 49 0
2 x
5x 6 0
2 x 3x 4 0
3 3x2 x 0
2 2x 0
Match the equations for volume with the appropriate solid.
29. 30. 31. V x
A. B. C.
4 V x 16
3 4x2 V x 4x
3 4x
x 2
x
x 2
x 2 4
x 2
x 2
x 2
Algebra 2 53
Chapter 6 Resource Book
x
x 2
Lesson 6.4

Answer Key
Practice B
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13. 14.
15. 16.
17. 18.
19. 20.
21.
22.
23.
24.
25.
26. 27.
28. 29.
30. 31.
32.
33.
34.
35. 36.
37. 38. 2 39. 40. 41.
42. 43. 44. No real solutions
45. 46.
47.
48. 49. 750
50. x 51. 15
52. 10 ft by 15 ft by 5 ft
3 15x2 ft
50x 750
3
1
3 7
3, 3, 5 2, 2
3, 1, 1, 3 5, 5
6, 2, 2, 6
22, 2, 2, 22
3
x
6, 2, 2
2
2 7x2 2x 3
2 2x2 3x 1x 1x
6
2 3x
1
2 2x
3x 13x 1
2 2x
2x 32x 3
2 x x 10x 10
2 5x2 x
2
2 3x2 x 8
2 3x2 x
2
2 3x2 x 2
2 3x2 2x 32x 34x
3
2 x 2 x 5x 3x 3
x 1x 4x 4
x 12x 32x 3
x 34x 14x 1
x 23x 23x 2
9
2 x 62x
x 2
2 x 15x 5
2 x 43x
1
2 x 2x 2
2 x 4x
7
2 x 3x 2
2 5x 425x
5
2 10x 1100x
20x 16
2 4x 316x
10x 1
2 3x 89x
12x 9
2 2x 104x
24x 64
2 3x 29x
20x 100
2 2x 54x
6x 4
2 2x 14x
10x 25
2 x 7x
2x 1
2 x 10x
7x 49
2 x 6x
10x 100
2 x 4x
6x 36
2 4x 16

Lesson 6.4
LESSON
6.4
Practice B
For use with pages 345–351
54 Algebra 2
Chapter 6 Resource Book
NAME _________________________________________________________ DATE ___________
Factor the sum or difference of cubes.
1. 2. 3.
4. 5. 6.
7. 8. 9.
10. 11. 12. 125x3 1000x 64
3 64x 1
3 27x
27
3 8x 512
3 27x 1000
3 8x
8
3 8x 125
3 x 1
3 x
343
3 x 1000
3 x 216
3 64
Factor the polynomial by grouping.
13. 14. 15.
16. 17. 18.
19. 20. 21.
22. 23. 24. 9x3 18x2 16x 4x 8
3 48x2 4x x 3
3 4x2 x
9x 9
3 x2 x 16x 16
3 5x2 x 9x 45
3 2x2 2x
4x 8
3 12x2 5x 5x 30
3 5x2 3x x 1
3 12x2 x
2x 8
3 2x2 x 7x 14
3 4x2 x 2x 8
3 3x2 5x 15
Factor the polynomial.
25. 26. 27.
28. 29. 30.
31. 32. 33.
34. 35. 36. x4 10x2 2x 21
4 16x2 3x 24
4 27x
3
4 3x2 8x4 18x2 2x4 200x2 x4 7x2 x 10
4 5x2 x 24
4 x2 x
6
4 5x2 x 6
4 16x 9
4 81
Find the real-number solutions of the equation.
37. 38. 39.
40. 41.
42. 43. 44.
45. 46.
47. 48. x4 10x2 x 16 0
4 10x2 x
24 0
4 4x2 x 5 0
4 10x2 x
9 0
4 6x2 x 5 0
4 x2 x 12 0
3 5x2 x
9x 45 0
3 7x2 3x 4x 28 0
3 x2 8x
3x 1 0
3 x 27 0
3 x 8 0
3 6x2 4x 24 0
Aquarium In Exercises 49–52, use the following information.
The aquarium shown at the right holds 5610 gallons of water.
Each gallon of water occupies approximately 0.13368 cubic feet.
49. How many cubic feet of water does the aquarium hold?
(Round the result to the nearest cubic foot.)
50. Use the result from Exercise 49 to write an equation that
represents the volume of the aquarium.
51. Find all real solutions of the equation in Exercise 50.
52. What are the dimensions of the aquarium?
x 5
x
x 10
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice C
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19. 20.
21. 22. 11 23. 24. 3
25. 26. 27. 28.
29. 30. 2, 5 31. 32. 3
33. 34. 35.
36. 37. 38.
39. 40.
41. 42.
43. 44. 45.
46. 99 in. 3
6, 6
10, 0, 10 2, 2 2, 2
5
2 , 5
1,
1, 5 6, 3, 0, 3 1, 0, 1
3, 0, 2 2, 0, 1, 2 1, 0, 1, 3
3, 3, 2 4, 7, 7
, 1
2 2
3, 3
2
2, 2, 3 8
2
3 , 3
1
2, 2
1
2 , 2
2
x 3
2x 1x4 6xx 2x
1
2 x 2
3x 12 3x 2x 2x
xx 3x 2x 2
x 1
2 8x 1x 2x
3x 4x 1x 1
2x 4
2 x 5x 1x
2x 4
2 x 12x 14x
x 1
2 x 2x 1x
2x 1
2 x 1x
x 62x 12x 1
x 1
2 3x 2x 2x
x 2x 7x 7
3
2 x
4
2 8x2 2x 32x 34x
8
2 22x 34x
9
2 52x 14x
6x 9
2 2x 2x
2x 1
2 4x 516x
2x 4
2 x 9x
20x 25
2 9x 81

LESSON
6.4
Factor the polynomial.
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice C
For use with pages 345–351
1. 2. 3.
4. 5. 6.
7. 8. 9.
10. 11. 12.
13. 14. 15.
16. 17. 18.
19. 20. 21. x7 x6 x3 x2 6x4 12x3 12x2 x 24x
6 x5 x4 x3 x4 3x3 4x2 3x 12x
4 6x3 3x 24x 48
3 12x2 8x
3x 12
4 8x3 x 64x 64
4 5x3 8x x 5
4 8x3 x
x 1
4 2x3 4x x 2
3 24x2 x x 6
3 x2 x
3x 3
3 2x2 3x 49x 98
4 x 48
4 16x
64
4 16x 81
3 40x 54
3 2x
5
3 64x 16
3 x 125
3 729
Find the real number solutions of the equation.
22. 23. 24.
25. 26. 27.
28. 29. 30.
31. 32.
33.
34. 35. 36.
37. 38. 39.
40. 41. 42.
43. 44. 45. x8 3x 256 0
4 x 12 0
5 x
100x 0
4 2x 36 0
3 2x2 x 5x 5
3 4x2 x
7x 28
3 2x2 x 3x 6
8 3x7 x6 3x5 5x4 5x3 20x2 x
20x 0
5 3x4 8x2 x 24x
6 x5 x4 x3 x4 6x3 9x2 2x
54x
4 10x3 2x
2x 10 0
3 6x2 27x 2x 6 0
4 8 27x3 x
8x
4 5x3 9x 8x 40
3 27x2 x 4x 12
3 8x2 x
6x 48 0
3 12 3x2 32x 4x
4 x 2
4 4x
16 0
3 27x 108
3 x 8 0
3 1331 0
46. Manufacturing A tool shop is hired to make a metal mold in which
plastic is injected to make a solid block. (See diagram below.) The
finished plastic block should have a length that is 8 inches longer than
the height. It should also have a width that is 2 inches shorter than the
height. Each plastic block requires 96 cubic inches of plastic. If the
1
sides of the mold are to be 2 inch thick, how much metal is required
to make the mold?
Plastic
injection
Algebra 2 55
Chapter 6 Resource Book
Lesson 6.4

Answer Key
Practice A
1. Dividend: Divisor:
Quotient: , Remainder: 0
2. Dividend: Divisor:
Quotient: Remainder: 7
3. Dividend:
Divisor:
Quotient: Remainder: 28
4. 5. x 3 3
x 2
x 2
8
x
x 1
2 x x 3,
3x 10,
3 2x
x 2,
2 2x
x 2,
x 5,
3 3x2 x
3x 17,
2 x
x 5,
3x 1
3 2x2 14x 5,
6. x 2 7.
4
x 3
8. 9. x 2 10. x 2
5
x 2
x 5
11. x 4 12.
5
x 1
13. 14.
15. 16. x 6 15
x 5
x 1
8
x 4 x 1
x 2
8
x 3
17. x 1 18. x 2
6
x 2
19. x 5 20. x 6
2
x 1
21. x 1 22. x 7 23. x 2
24. x 3
3
x 4
25.
3
1
1
6
3
3
x 6 5
x 1
x 3 3
x 2
1
9
10
x 3 10
x 3 .
The denominator of the remainder is x 3, not
x 3.
26. As written, synthetic division cannot be used
because the divisor does not have the form x k.

LESSON
6.5
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice A
For use with pages 352–358
Write the polynomial form of the dividend, divisor, quotient, and
remainder represented by the synthetic division array.
1 2 14 5
1. 5 5 15 5
2. 2
1 3 1 0
3.
3
Divide using polynomial long division.
4. 5.
6. 7.
8. 9.
10. 11.
12. x2 x
5x 3 x 2
2 x 3x 1 x 1
2 x
2x 8 x 4
2 x 3x 5 x 5
2 x
5x 6 x 3
2 x 7x 1 x 1
2 x
5x 2 x 3
2 x x 3 x 2
2 3x 6 x 1
Divide using synthetic division.
13. 14.
15. 16.
17. 18.
19. 20.
21. x2 x
3x 1 x 4
2 x 5x 6 x 1
2 x
6x 3 x 1
2 x 7x 10 x 5
2 x
3x 8 x 2
2 x 7x 9 x 1
2 x
3x 2 x 2
2 x 2x 1 x 1
2 7x 4 x 3
You are given an expression for the area of the rectangle. Find an
expression for the missing dimension.
22. 23. 24. A x2 A x 8x 15
2 A x 2x 8
2 10x 21
x 3
1
1
Find the error in the example and correct it.
25. 26. x2 x 4x 5 2x 3
2 6x 1 x 3
3 1
1
0
3
3
6
3
3
?
x 3 10
x 3
1
9
10
1
9
10
2
30
28
?
x 4
3 1
1
x 1
2
2
4
3
1
3
4
1
2
2x 3
5
3
2
3
2
5
17
10
7
?
x 5
Algebra 2 67
Chapter 6 Resource Book
Lesson 6.5

Answer Key
Practice B
1. 2. 3. x2 x 5 2x 3 x 1
21
x 3
4.
5.
6.
7.
8.
9. 2x 10.
2 x 3
11.
12.
13.
14.
15.
x2 1 16
x
3 9
2x
25
93x 1
2 x 3
5
2x 1
4x 7
2
23
22x 3
26x 11
x 4
x2 1
x 2
x
x 4
2 3x 1
x 3 4 3
x 5
3x 2 8x 21 43
x 2
5x 3 3x 2 5 6
x 1
3x 3 10x 2 40x 160 635
x 4
x 2 x 1 3
x 1
x 2 3x 7 9
x 3
16.
17. 18. 2 19. 20.
21. 22. Px 50x 5x
23. about 0.3 million
3
x 2
1
3x
8, 2
2, 1
3 6x2 12x 24 47
x 2
2
3, 1

Lesson 6.5
LESSON
6.5
Practice B
For use with pages 352–358
68 Algebra 2
Chapter 6 Resource Book
NAME _________________________________________________________ DATE ___________
Divide using polynomial long division.
1. 2.
3. 4.
5. 6.
7. 8. x3 3x2 4x 6 x2 x x 4
3 5x2 5x 3 x2 8x
3x 1
2 3x 5x 1 2x 3
3 2x2 4x
5x 1 3x 1
3 x 7x 8 2x 1
3 x2 2x
x 2 x 2
2 x x 3 x 1
2 2x 6 x 3
Divide using synthetic division.
9. 10.
11. 12.
13. 14.
15. 16. 3x4 x 1 x 2
3 3x
2 x 1
4 2x3 5x 5 x 4
4 2x3 3x2 3x
5x 1 x 1
3 2x2 x 5x 1 x 2
4 5x3 x
4x 17 x 5
3 2x 2x 12 x 3
3 7x2 x 12 x 4
Given one zero of the polynomial function, find the other zeros.
17. f x x 18.
19. 20.
3 3x2 34x 48; 3
f x 2x 3 3x 2 3x 2; 2
21. Geometry The volume of the box shown below is given
by V 2x Find an expression for the
missing dimension.
3 11x2 10x 8.
?
x 4
2x 1
f x x 3 2x 2 20x 24; 6
f x 3x 3 16x 2 3x 10; 5
Company Profit In Exercises 22 and 23, use the following information.
The demand function for a type of portable radio is given by the model
p 70 5x where p is measured in dollars and x is measured in millions
of units. The production cost is $20 per radio.
22. Write an equation giving profit as a function of x million radios sold.
2 ,
23. The company currently produces 3 million radios and makes a profit
of $15,000,000, but would like to scale back production. What lesser
number of radios could the company produce to yield the same profit?
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice C
37x 4
1. x 6
x2 3x 1
2.
3.
4.
5.
6.
2x 2 4x 9 28
2x 3
2x 2 4x 6
4x 6
2x 4 4x 15
3 33x2 x
1
3 x2 8 61
x
9 27
149
273x 2
7.
8.
9.
10.
11.
12.
13.
14. 15. 16.
17.
18. 19.
20. 21.
22. 23.
24.
25. A 0.004t3 0.082t2 1 10
,
3
1 i, 1 i
5 i, 5 i
0.268t
1 10
3
3
3 5
,
2
, 1
2 3 5
2 5, 2 5
5 17 5 17
,
2 2
5, 1
2
3
2x 1, 7
1
,
2 3
2 3x
5x 1
4 9x3 29x2 87x 256 769
4x
x 3
2 10x 20 39
2x
x 2
2 2x 1 3
6x
x 1
2 20x 65 192
5x
x 3
3 8x2 23x 52 96
1 5
x
2 4
x 2
38x 5
44x2 1 x 10
x
2 22x
2x 1
2 1
3.206 2.61t 247; 0.0118
26. 810 yearbooks
16x 19
x 2 4
5x 7
x 2 2x 1
quadrillion Btu
million people

LESSON
6.5
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice C
For use with pages 352–358
Divide using polynomial long division.
1. 2.
3. 4.
5. 6.
7. 8. 2x3 4x2 3x 5 4x2 x 2x 1
3 5 2x2 x
1
3 2x2 6x 5x 1 3x 2
3 2x2 5 3x2 4x
x
3 6x2 5 x2 2x 4
4 3x 1 x2 4x
2x 1
3 2x2 x 6x 1 2x 3
3 3x2 2x 6 x2 3x 1
Divide using synthetic division.
9. 10.
11. 12.
13. 14. 4x 2x3 7x2 3x 1 x 1
5 2x3 4x
5x 1 x 3
3 2x2 2x 1 x 2
3 6x
3x 4 x 1
3 2x2 5x 5x 3 x 3
4 2x3 7x2 6x 8 x 2
Given one zero of the polynomial function, find the other zeros.
15. f x x 16.
17. 18.
3 8x2 5x 14; 2
f x x 3 x 2 13x 3; 3
Given two zeros of the polynomial function, find the other zeros.
19. 20.
21. f x 2x 22.
23. 24.
4 9x3 4x2 f x x
21x 18; 2, 3
4 6x3 4x2 54x 45; 3, 3
f x x 4 2x 3 14x 2 32x 32; 4, 4
f x 2x3 11x2 9x 2; 1
f x 12x
2
3 8x2 13x 3; 1
2
f x x 4 3x 3 3x 1; 1, 1
25. Hydroelectric Power The amount of conventional hydroelectric power
(in quadrillion Btu) consumed from 1990 to 1997 can be modeled by
P 0.004t where t is the number of
years since 1990. For the same years, the U.S. population (in millions)
can be modeled by P 2.61t 247 where t is the number of years
since 1990. Find a function for the average amount of energy consumed
by each person from 1990 to 1997. What was the per capita consumption
of conventional power in 1992?
26. Yearbook Sales If the school charges $15 for a yearbook, 800
students will buy a yearbook. For every $.50 reduction in price two
more books are sold. It costs $10 to produce each book. How many
books must be sold to earn a profit of at least $2000?
3 0.082t2 0.268t 3.206
f x 3x 4 2x 3 12x 2 6x 9; 3, 3
f x x 4 3x 3 7x 2 15x 10; 2, 1
Algebra 2 69
Chapter 6 Resource Book
Lesson 6.5

Answer Key
Practice A
1. 2. 3.
4. 5.
6.
7.
8.
9.
10. 11. 1 12. neither 13. 1 14. neither
15. 16. 17. neither 18. 1
19. 20. 21.
22.
23. 24. x
25. ±1, ±2, ±3, ±4, ±6, ±7, ±12, ±14, ±21, ±28,
±42, ±84 26. 3 in. by 4 in. by 7 in.
3 5x2 ±1
±1, ±7 ±1, ±2, ±3, ±6
±1, ±3, ±9 ±1, ±2, ±3, ±4, ±6, ±12
±1, ±2, ±4, ±5, ±10, ±20
±1, ±2, ±3, ±4, ±6, ±8, ±12, ±24
±1, ±2, ±4, ±5, ±8, ±10, ±20, ±40
±1, ±2, ±4, ±5, ±10, ±20, ±25, ±50, ±100
1
1 and 1 1 and 1
3, 2, 4 1, 1, 2 3, 2, 2
1 6, 1, 1 6
5, 5, 3
4x 84

LESSON
6.6
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice A
For use with pages 359–365
List the possible rational zeros of f using the rational zero theorem.
f x x 3 2x 2 4x 1
1. 2.
3. 4.
5. 6.
7.
9.
f x x 8.
5 2x4 f x x
3x 24
3 3x2 f x x
12
3 2x2 5x 6
f x x 3 5x 2 2x 100
Use synthetic division to decide which of the following are zeros of
the function: 1, 1.
f x x 2 6x 5
10. 11. 12.
13. 14. f x x 15.
16. 17. 18.
3 3x2 f x x 4x 12
3 2x2 2x 1
f x x 3 5x 2 x 5
Find all the rational zeros of the function.
19. 20.
f x x 3 x 2 14x 24
10
y
2
Find all the real zeros of the function.
21.
23.
f x x 22.
3 3x2 4x 12
f x x 3 3x 2 5x 15
x
f x x 2 3x 7
f x x 4 6x 9
f x x 3 6x 2 8x
f x x 8 2x 5 x 4 3x 20
f x x 2 6x 40
f x x 3 x 2 9x 9
f x x 3 2x 2 x 2
f x x 3 3x 2 3x 5
Geometry In Exercises 24–26, use the following information.
The volume of the box shown at the right is given by
24. Write an equation that indicates that the volume of the box is 84 in.
25. Use the rational zero theorem to list all possible rational zeros of the
equation in Exercise 24.
26. Find the dimensions of the box.
3 V x
.
3 5x2 4x.
1
y
1
x
x
f x x 2 10x 21
f x x 3 x 2 x 1
f x 2x 2 x 1
x 1
x 4
Algebra 2 79
Chapter 6 Resource Book
Lesson 6.6

Answer Key
Practice B
1. 2.
3.
4. 5. 6.
7. 8.
9. 10. 11.
12. 13.
14.
15.
16. t
17. ±1, ±3, ±5, ±7, ±15, ±21, ±35, ±105
18. 1, 3, 5, 7 19. 1983
3 13t 2 2, 2, 2,
3, 2, 1, 2
1 17 1 17
3, 1, ,
4 4
65t 105 0
1
3, 1,
5
2, 2, 2
3, 3, 3
2
1
2, 1, 5 3, 1, 2, 2
2 , 1
3 1
2 , 4 , 2
8
±1, ±2, ±4, ±8, ±
1
2, 2 , 3 3 , 1, 1
1
±1, ±2, ±3, ±6, ±
2 4 8
3 , ± 3 , ± 3 , ± 3
1
±1, ±2, ±4
3
2 , ± 2
3 1
2 , 2
, 3

Lesson 6.6
LESSON
6.6
Practice B
For use with pages 359–365
80 Algebra 2
Chapter 6 Resource Book
NAME _________________________________________________________ DATE ___________
List the possible rational zeros of f using the rational zero theorem.
f x x 4 2x 3 3x 4
1. 2. 3.
Use the rational zero theorem and synthetic division to find all
rational zeros of the function.
f x 2x 3 3x 2 11x 6
4. 5.
5
6. 7.
8. 9.
Find all real zeros of the function.
10. 11.
2
y
y
1
f x 8x 3 6x 2 23x 6
f x x 4 4x 3 x 2 8x 6
f x 2x 3 5x 2 4x 10
f x x 3 3x 2 3x 9
4
12. 13.
14. 15.
f x x 4 2x 3 5x 2 4x 6
x
x
f x 2x 3 x 2 5x 6
f x 3x 3 8x 2 3x 8
f x x 3 4x 2 7x 10
f x 2x 4 5x 3 5x 2 5x 3
f x 4x 3 8x 2 15x 9
f x 2x 4 3x 3 6x 2 6x 4
f x 2x 4 5x 3 6x 2 7x 6
European College Students In Exercises 16–19, use the following information.
Many students from Europe come to the United States for their college education. From 1980 through
1990, the number S (in thousands), of European students attending a college or university in the U.S.
can be modeled by S 0.07t where t 0 corresponds to 1980.
16. Write an equation with a leading coefficient of 1 that represents the year that 31.08 thousand
European students attended a U.S. college or university.
17. Use the rational zero theorem to list all possible rational zeros of the equation in Exercise 16.
18. Which of the rational zeros listed in Exercise 17 are valid values of t?
3 13t2 65t 339
19. In what year did 31.08 thousand European students attend a U.S. college or university?
y
9
5
y
3
1
x
x
f x 3x 5 2x 8
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice C
1. 2. 3.
4. 5.
6. 7.
8.
9.
10.
11.
12.
13. 14.
15. cannot be 0. 16.
17. 18.
19. 20. The zeros of are also the
zeros of 21. To apply the rational zero theorem,
the coefficients must be integers.
22. 2f x x3 2,
2, 1, 1
f x
af x.
19x 30; 3, 2, 5
1
xx
3, 2, 6
3, 0, 2
3 x2
a0 24x 36
7
2, 3, 5
2, 1
2
9
2 , 3, 53
, 4
5 13 1 13
, 1 , ,
2 6 6
1
5 17
, 1,
4
2
2
1 6,
3 22, 1, 3 22, 3
17
3 , 5
4
4
4 14,
3 , 1 6
1
5 21
7, ,
2
6 , 4 14
5 21
2
5
3,
1
2 , 3 2 , 2
7
2 , 13
, 1
3
1,
1
4 , 1 2 , 3 , 2
1
2
4, 1, 3 , 1
5
5 , 2 , 3
3 2 , 1 2 , 4

LESSON
6.6
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice C
For use with pages 359–365
Use the rational zero theorem and synthetic division to find all
rational zeros of the function.
1. 2.
3. 4.
5. 6. f x) 8x3 28x2 f x 6x 14x 15
4 35x3 35x2 f x 24x
55x 21
4 26x3 45x2 f x 10x x 6
4 43x3 11x2 f x 3x
79x 15
4 10x3 11x2 f x 4x 10x 8
3 8x2 29x 12
Find all real zeros of the function.
7. 8.
9. 10.
11. 12.
13. f x 6x 14.
4 31x3 64x2 f x 6x
489x 540
4 25x3 32x2 f x 3x
15x 2
3 10x2 f x x
7x 20
3 2x2 34x 7
Critical Thinking In Exercises 15–18, consider the function
f x x 4 x3 24x2 36x.
15. Explain why the rational zero theorem cannot be directly applied to this
function.
16. Factor out the common monomial factor of f.
17. Apply the rational zero theorem to find all other rational zeros of f.
18. Find all the real zeros of
f x 3x 5 x 4 12x 3 4x 2 .
f x 6x 3 49x 2 20x 2
f x x 4 4x 3 14x 2 20x 3
Critical Thinking In Exercises 19–22, consider the functions
and
19. Use the rational zero theorem to find all rational zeros of each function.
20. Note that and What can you
conclude about the zeros of and
21. Explain why the rational zero theorem cannot be directly applied
to f x
22. Use the conclusion from Exercise 20 to find the rational zeros of the
function in Exercise 21.
1
2x3 19
j x 5x
gx fx, hx 2f x, jx 5f x.
f x af x?
2 x 15.
3 10x2 h x 2x 5x 10.
3 4x2 g x x 2x 4,
3 2x2 f x x x 2,
3 2x2 x 2,
f x 12x 4 28x 3 11x 2 13x 5
f x 8x 4 68x 3 178x 2 103x 105
Algebra 2 81
Chapter 6 Resource Book
Lesson 6.6

Answer Key
Practice A
1. 3 2. 5 3. 4 4. 6 5. 3 6. 2 7. 1
8. 5 9. 10. 11.
12. 13. 14.
15. 16. 17.
18. yes 19. no 20. no 21. yes 22. yes
23. no 24.
25. 26.
27.
28.
29. f x x
30. x 3x 1x 2
31. Length: x 3; Width: x 1;
Height: x 2 32. 10
3 8x2 f x x
x 42
3 7x2 f x x
12x
3 3x2 f x x
x 3
2 f x x 6x 5
2 2 i
3 5i 6 2i
7 3i 2 i 5 4i
3 2i 2 3i 3 5 i
f x x 6
x 6

Lesson 6.7
LESSON
6.7
Practice A
For use with pages 366–371
94 Algebra 2
Chapter 6 Resource Book
NAME _________________________________________________________ DATE ___________
Determine the total number of solutions (including complex and
repeated) of the polynomial equation.
1. 2.
3. 4.
5. 6.
7. 8. 2x5 3x4 6x
5x 7 0
x 9 0
2 5x 3x 1 0
3 2x2 3x
3x 1 0
6 2x5 x4 3x3 2x2 2x x 8 0
4 3x3 2x2 x
x 5 0
5 3x2 x 4x 1 0
3 3x2 4x 2 0
Given that f x has real coefficients and x k is a zero, what
other number must be a zero of f ?
9. k 2 i
10. k 3 5i
11. k 6 2i
12. k 7 3i
13. k 2 i
14. k 5 4i
15. k 3 2i
16. k 2 3i
17. k 3 5i
Decide whether the given x-value is a zero of the function.
f x x 3 2x 2 4x 7, x 1
18. 19.
20. f x x 21.
22. 23.
3 x2 4x 3, x 3
f x x 3 2x 2 2x 3, x 3
f x x 3 3x 2 2x 1, x 2
f x 2x 4 x 3 x 2 4x 4, x 1
f x x 4 2x 3 6x 2 5x 2, x 2
Write a polynomial function of least degree that has real
coefficients, the given zeros, and a leading coefficient of 1.
24. 6 25. 2, 3
26. 1, 5
27. 1, 1, 3
28. 0, 3, 4
29. 2, 3, 7
Room Dimension Riddle In Exercises 30–32, use the following
information.
One of the bedrooms of a house has a volume of 1144 cubic feet. The volume
of the bedroom is given by y x where x is the number of
rooms in the house.
30. Factor the polynomial that represents the volume of the bedroom.
31. The factors in Exercise 30 represent the length, width, and height of the
bedroom. Which do you think represents the length, the width, and the
height?
32. How many rooms does the house have?
3 2x2 5x 6,
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice B
1. 3 2. 6 3. 5 4. 4 5. yes 6. no 7. yes
8. yes 9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23. 24.
25. 26.
27. 28.
29. 4, 30. 1996 31. 5
1
1, 2, 2, i, i
, 2i, 2i
1
3, 4, 3i, 3i
2 , i, i
1
f x x 1, i, i
2 , 2
4 2x2 f x x
8x 5
3 10x2 f x x
33x 34
4 10x2 f x x
9
4 3x3 3x2 f x x
3x 2
4 x3 9x2 f x x
9x
3 2x2 f x x
x 2
3 x2 f x x
6x
3 5x2 f x x
7x 3
3 5x2 x 3, x 1, x 2
x 4, x 1, x 2, x
x 6, x 2, x 1, x 1
x 3, x i, x i
x 4, x 5, x 2i, x 2i
x 3, x 2 i, x 2 i
2x 8
3

LESSON
6.7
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice B
For use with pages 366–371
Determine the total number of solutions (including complex and
repeated) of the polynomial equation.
1. 2.
3. 4. 3x 4 2x 3 15x 2 x x 1 8
5 2x3 4x2 8x
7x 12
6 3x4 11x3 2x2 4x 4 0
3 7x2 5x 9 0
Decide whether the given x-value is a zero of the function.
5. 6.
7. f x x 8.
3 4x2 f x x
x 4, x i
4 2x3 5x2 8x 4, x 1
Identify the factors of a polynomial function that has the given
zeros.
9. 3, 1, 2 10. 4, 1, 2, 0
11. 6, 2, 1, 1
12. 3, i, i
13. 4, 5, 2i, 2i
14. 3, 2 i, 2 i
Write a polynomial function of least degree that has real
coefficients, the given zeros, and a leading coefficient of 1.
15. 1, 2, 4
16. 3, 1, 1
17. 3, 2, 0
18. 2, i, i
19. 0, 1, 3i, 3i
20. 1, 2, i, i
21. i, i, 3i, 3i
22. 2, 4 i
23. 1, 1, 1 2i
Find all of the zeros of the polynomial function.
24. 25.
26. 27.
28. f x x 29.
4 3x2 f x x
4
3 4x2 f x x
9x 36
3 x2 x 1
30. Preakness Stakes For 1990 through 1998, the value of a horse winning
the Preakness Stakes can be modeled by
V 2553x 3 25,200.56x 2 64,026.95x 428,075.56
where x is the number of years since 1990. Use a graphing calculator to
determine in what year the winnings were $488,150.
31. NBA Standings There are seven teams in the Atlantic Division of the
Eastern Conference of the NBA. During the 1997-98 season the winning
percentage of the teams in this division can be modeled by
W 0.0051x 3 0.063x 2 0.260x 0.862
f x 2x 3 3x 2 11x 6
f x 2x 4 x 3 x 2 x 1
where x is the team’s rank within the division. Orlando’s winning percent
was 0.500. Use a graphing calculator to estimate their ranking in the
division.
f x x 4 x 3 8x 2 2x 12, x 2
f x 2x 3 x 2 8x 4, x 2i
f x 3x 4 11x 3 8x 2 44x 16
Algebra 2 95
Chapter 6 Resource Book
Lesson 6.7

Answer Key
Practice C
1. 4 2. 3 3. 5 4. no 5. no 6. no
7. no 8.
9.
10.
11.
12.
13.
14.
15. 16.
17.
18.
19.
20. R 315.035t 5 5562.592t 4 1832.426t 3
118x 7, 5 i, 5 i
1, 1, 2 3, 2 3 3
2 i3, 2 i3, 2, 0
i, i, 1 2, 1 2
1 4i, 1 4i, 3, 3
2 f x 2x
174x
6 26x5 120x4 200x3 f x 2x
4 14x3 38x2 f x 2x
46x 20
3 12x2 f x 2x
50x
3 12x2 f x 2x
2x 68
4 58x2 f x 2x
200
4 4x3 32x2 64x
708,818.278t 2 6,449,569.245t
49,245,170.73; 1993 21. The fifth solution
must be a repeated solution because complex solutions
come in conjugate pairs.

Lesson 6.7
LESSON
6.7
Practice C
For use with pages 366–371
96 Algebra 2
Chapter 6 Resource Book
NAME _________________________________________________________ DATE ___________
Determine the total number of solutions (including complex and
repeated) of the polynomial equation.
1. 2. 3. 4 7x x2 3x5 3 2x2 x3 2x 0
2 3x x 4 5x 1
Decide whether the given x-value is a zero of the function.
4. 5.
6. f x x 7.
4 5x3 5x2 f x x
5x 6, x 2
3 5x2 4x 6, x 1 i
Write a polynomial function of least degree that has real coefficients,
the given zeros, and a leading coefficient of 2.
8. 4, 0, 2, 4
9. 2i, 2i, 5i, 5i
10. 4 i, 4 i, 2
11. 3 4i, 0
12. 2 i, 1, 2
13. 5 2i, i, 0, 3
Find all the zeros of the polynomial function.
14. 15.
16. f x x 17.
4 12x3 54x2 f x x
108x 81
3 17x2 96x 182
f x x 4 4x 3 4x 1
f x 2x 5 4x 4 2x 3 28x 2
Find all the zeros of the polynomial function using the given hint.
18. 19. f x x
Hint: i is a zero Hint: 1 4i is a zero
4 2x3 14x2 f x x 6x 51
4 2x3 2x 1
20. College Tuition For 1990 through 1997 the enrollment of a college can
be modeled by where t is the number
of years since 1990. For the same years, the cost of tuition at the college
can be modeled by T 10.543t
where t is the number of years since 1990. Write a model that represents
the total tuition brought in by the college in a given year. In what year did
the college take in $62,638,006 in tuition?
21. Critical Thinking The graph of a polynomial of degree 5 has four
distinct x-intercepts. Since the total number of solutions (including
complex and repeated) must be 5, is the fifth solution a complex
solution or a repeated solution? Explain your answer.
3 118.826t2 E 29.881t
921.032t 9978.758
2 190.833t 4935
f x x 3 2x 2 3x 10, x 2 i
f x x
x 3i
5 4x 4 10x3 4x 2 9x 36,
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice A
1. 4 2. 5 3. 3 4. local maximum;
local minimum 5. local minimum
6. local minimum; local
maximum; 1, 1 local minimum
7. 8.
1
1, 2
1, 4
2 , 1
1
2, 5
2 , 3
9. 10.
11. 12.
13.
y
1
y
2
1
2
Sales
(millions of dollars)
1
300
250
200
150
100
y
0
2
1 2 3 4 5 6 7 8 9
Years since 1990
14. 1996 15. $244 million
x
x
x
1
y
y
1
y
2
1
2
2
x
x
x

Lesson 6.8
LESSON
6.8
Practice A
For use with pages 373–378
108 Algebra 2
Chapter 6 Resource Book
NAME _________________________________________________________ DATE ___________
Determine the lowest-degree polynomial that has the given graph.
1. y
2. y
3.
2
Estimate the coordinates of each turning point and state whether
each corresponds to a local maximum or a local minimum.
4. y
5. y
6.
2
2
2
x
x
Graph the function.
7. f x x 2x 4
8. f x x 1x 3 9.
10. f x x 1x 2x 3 11. f x x 3x 1x 1 12.
Sales In Exercises 13–15, use the following information.
From 1990 to 1999, the annual sales S (in millions of dollars) of a certain
company can be modeled by S 0.4t where t is the
number of years since 1990.
13. Use a graphing calculator to graph the polynomial function.
14. Approximate the year in which sales reached a low point.
15. If this polynomial function continues to model the sales of the company in
the future, what can the expected sales be in 2000?
3 4.5t2 9.2t 202
1
1
1
1
x
x
2
1
y
y
f x x 2x 4
f x x 2x 2 2
2
1
Copyright © McDougal Littell Inc.
All rights reserved.
x
x

Answer Key
Practice B
1. 3 2. 2 3. 5 4. 1 5. 6 6. 8 7. B
8. C 9. A 10. 3, 2, 5 11. 4, 6, 8
12. 3, 2 13. 5, 1, 7 14. 6, 2 15. 8
16. 17.
1
y
18. 19.
3
1
y
20. 21.
1
22. 23.
y
60
1
y
2
2
x
x
x
x
y
5
1
5
1
y
y
1
1
4
y
x
2 x
x
x
24.
y
1
1
x
25. 8.78, 745.80 is a
local maximum;
19.95, 652.46 is a local
P
700
600
500
minimum; During the
400
1980 games the gold
medal winner scored
300
200
100
more points than in
0
0 3 6 9 12 15 18 21t
previous years and that
was the record for several
Years since 1972
years following 1980. Starting in 1992, the
number of points started to increase after several
years of declining scores.
26. 8.5, 122,069.35 is
a local maximum.
29.3, 96,068.15 is a local
C
140,000
120,000
100,000
minimum. In 1973, the
80,000
number of cattle on farms
60,000
40,000
reached a maximum of
20,000
122,069.35 thousand. This
0
0 5 10 15 20 25 30 35 t
number decreased to
96,068.15 in 1994 and
then started to rise again.
Years since 1965
Points
Cattle (thousands)

LESSON
6.8
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice B
For use with pages 373–378
State the maximum number of turns in the graph of the function.
f x x 4 2x 2 4
1. 2. 3.
4. 5. 6.
f x 4x 2 5x 3
Match the graph with its function.
7. 8. f x 2x 9.
A. B. C.
6 6x4 4x2 f x 2x 2
4 3x2 2
1
Determine the x-intercepts of the graph of the function.
10. 11. 12.
13. 14. f x x 6 15.
3 f x x 3x 2x 5 f x x 4x 6x 8
f x x 5x 1x 7
x 2
Graph the function.
16. 17.
18. 19.
20. 21.
22.
24.
f x x 23.
3 f x x 2
x 3)x 5
2 f x x 3
x 1
2 f x x 4x 1
x 2
f x x 2x 2 2x 2
y
25. Olympic Platform Diving The polynomial function
P 0.134t 3 5.775t 2 70.426t 481.945
models the number of points earned by the gold medal winner of the
platform diving event in the summer Olympics, where t is the number
of years since 1972. Graph the function and identify any turning points
on the interval 0 ≤ t ≤ 24. What real-life meaning do these points have?
(Hint: The Olympics only take place every four years.)
26. Livestock The polynomial function
1
x
f x 3x 3 x 2 x 5
f x 3x 7 6x 2 7
C 0.03t 4 3.53t 3 271.40t 2 3788.76t 107,148.79
f x x 3x 4x 1
f x x 6x 1x 2
f x x 1 2 x 1x 4
f x x 1x 2 x 1
models the number of cattle (in thousands) on farms from 1965 to 1998,
where t is the number of years since 1965. Graph the function and identify
any turning points on the interval 0 ≤ t ≤ 33. What real-life meaning do
these points have?
1
y
1
x
f x 2x 6 1
f x 2x 9 8x 7 7x 5
f x 2x 4 3x 2 2
f x x 3 2 x 2
f x x 8 5
Algebra 2 109
Chapter 6 Resource Book
1
y
1
x
Lesson 6.8

Answer Key
Practice C
1. 3 2. 2 3. 4
4. 5.
6. 7.
5
y
1
8. 9.
7
10. 1 11. 2, 4 12. 1, 3, 5
13. If n is even there is a turning point. If n is odd
the graph passes through the x-axis.
y
1
y
2
1
1
y
x
2
x
x
x
14. 2, 3; 3 15. 1, 7; none 16. 3, 5; 3, 5
17. 4, 3; 4 18. 1, 3; 1 19. 4, 0, 2; 4
20. 3, 2, 5; none
22. 8, 1, 4; 1
21. 3, 2, 3; 3,3
1
y
2
1
y
2
2
y
1
y
1
1
x
x
x
x
23. y
140
135
130
local minimum
0.86, 129.88, local
maximum 1.72, 130.20;
125
120
0
0 1 2 3
x
Years since 1995
In 1996 you could buy
more women’s and girls’
apparel with your money
than in previous years, but
by 1997 prices were higher than in recent years.
CPI

Lesson 6.8
LESSON
6.8
Practice C
For use with pages 373–378
110 Algebra 2
Chapter 6 Resource Book
NAME _________________________________________________________ DATE ___________
State the maximum number of turns in the graph of the function.
1. 2. f x 4 2x 3.
2 5x3 f x x4 3x3 2x 5
Graph the function.
4. 5. 6.
7. 8. f x x 2 9.
2 f x x 2 x 3x 1
3x 13 f x x 22x 52 f x x 32x 1
Critical Thinking Consider the graphs f x x 1 where
n 1, 2, 3, 4, and 5.
10. What is the x-intercept for all of the functions?
n
11. For what values of n does the graph have a turning point at the x-intercept?
12. For what values of n does the graph not have a turning point at the x-intercept?
13. Generalize your findings in Exercises 11 and 12. Test your theory for
and gx x 17 f x x 1 .
6
Find all x-intercepts and identify the x-intercepts that are also
locations of turning points for the graph of the function.
14. 15.
16. 17.
18. 19.
20. 21.
22. f x x 85x 12x 43 f x x 32x 2x 34 f x xx 2x 4
f x x 3x 2x 5
2
f x x 35x 12 f x x 48x 35 f x x 56x 32 f x x 73x 13 f x x 32x 2
23. Consumer Economics The consumer price index of women’s and girl’s
apparel from 1995 to 1998 can be modeled by
P 1.02t 3 3.95t 2 4.53t 131.5,
where t is the number of years since 1995. Graph the function and identify
any turning points on the interval 0 ≤ t ≤ 3. What real-life meaning do
these points have?
f x 2x 3x 5 2x 2 5
f x x 1 3 x 3 2
f x x 10 6
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice A
1. B 2. A 3. C
4. f x x 1x 1x 3
5. f x x 3x 2x 1
6. f x x 3x 1x 4
7. f x x 3x 1x 6
8. f x x 2x 3x 5
9. fx x 3x 4x 5
10.
11.
f x x 2x 1x 6
f 1 f 2 f 3 f 4 f 5
0
12.
f 1
f 2 f 3 f 4 f 5 f 6 f 7
2 11 34 77 146 247 386
13.
f 1
0
0
2
f 2
2
2
2
f 3
4
14.
15.
16.
17. y 0.28x3 2.10x2 y 0.58x
5.56x 1.79
3 5.07x2 y 0.22x
19.20x 53.43
3 2.51x2 y 0.33x
8.98x 20.43
3 3.25x2 8.77x 10.64
6
2
f 4
6
12
2
f 5
8
f 6
20
2
10
9 23 43 69 101 139
14 20 26 32 38
6 6 6 6
f 7
30
8 28 74 158 292 488 758
20 46 84 134 196 270
26 38 50 62 74
12 12 12 12
f 6
f 7

LESSON
6.9
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice A
For use with pages 380–386
Match the cubic function with its graph.
1. f x x 1x 2x 4 2. f x 2x 1x 2)x 4 3.
A. y
B. y
C.
4
Write the cubic function whose graph is shown.
4. 5. 6.
1
y
1
2
x
x
Write the cubic function whose graph passes through the given
points.
7. 3, 0,1, 0,6, 0,0, 18
8. 2, 0, 3, 0, 5, 0, 0, 30
9. 3, 0,4, 0,5, 0,0, 60
10. 2, 0, 1, 0, 6, 0, 0, 12
Show that the nth order differences for the given function of n are
nonzero and constant.
11. 12. 13. f x 2x3 x2 f x x 3x 2
3 x2 f x x x 1
2 3x 2
Use a graphing calculator to find a cubic function for the data.
14. x 0 1 2 3 4 5 6
15.
y 11 15 20 16 14 16 18
16. x 0 1 2 3 4 5 6
17.
y 53 40 30 24 23 10 5
2
2
1
y
2
x
x
f x 1
2 x 1x 2x 4
x 0 1 2 3 4 5 6
y 20 15 10 9 12 10 9
x 0 1 2 3 4 5 6
y 2 5 7 7 9 11 20
1
y
5
Algebra 2 121
Chapter 6 Resource Book
1
y
2
x
x
Lesson 6.9

Answer Key
Practice B
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
f x 1
f x
f x x 2x 4x 6
f x 2x 1x 3x 4
f x 2xx 1x 8
4xx 3x 9
1
f x
f x 2x 1x 3x 2
2x 4x 1x 5
1
f x x 2x 1x 2
f x 2x 1x 1x 3
2x 2x 3x 4
f 1 f 2 f 3 f 4 f 5
1
11.
f 1
3
12.
f 1
3
1 11 35 79 149 251
2 10 24 44 70 102
8 14 20 26 32
f 2
f 2
6 6 6 6
f 3
f 3
f 4
f 4
f 5
f 5
f 6
f 7
5 29 75 149 257 405
8 24 46 74 108 148
16 22 28 34 40
6 6 6 6
6 33 90 189 342 561
9 27 57 99 153 219
18 30 42 54 66
12 12 12 12
f 6
f 6
f 7
f 7
13.
14.
15.
16.
17. M 0.000127t
9.77; 13.3 thousand miles
3 0.00330t 2 f x x
0.0158t
3 x2 f x x
3x 2
2 f x x
3x 2
3 3x2 f x x
x 4
3 2x2 x 1

Lesson 6.9
LESSON
6.9
Practice B
For use with pages 380–386
122 Algebra 2
Chapter 6 Resource Book
NAME _________________________________________________________ DATE ___________
Write the cubic function whose graph is shown.
1. y
2. y
3.
1
1 x
2
Write a cubic function whose graph passes through the given points.
4. 1, 0, 3, 0, 2, 0, 0, 12
5. 4, 0, 1, 0, 5, 0, 0, 10
6. 2, 0, 4, 0, 6, 0, 0, 48
7. 1, 0, 3, 0, 4, 0, 0, 24
8. 0, 0, 1, 0, 8, 0, 2, 24
9. 0, 0, 3, 0, 9, 0, 1, 4
Show that the nth order differences for the given function of
degree n are nonzero and constant.
10. 11. f x x 12.
3 2x2 f x x 5x 1
3 2x2 x 1
Use finite differences and a system of equations to find a
polynomial function that fits the data.
13. 14.
x 1 2 3 4 5 6
f(x) 5 19 49 101 181 295
15. 16.
x 1 2 3 4 5 6
f(x) 4 4 2 2 8 16
17. Average Miles Traveled The table shows the average miles traveled per vehicle
(in thousands) from 1960 to 1996. Find a polynomial model for the data. Then
predict the average number of miles traveled per vehicle in 2000.
t 1960 1965 1970 1975 1980 1985 1990 1995 1996
M 9.7 9.8 10.0 9.6 9.5 10.0 11.1 11.8 11.8
2
x
3
y
1
f x 2x 3 3x 2 4x 6
x 1 2 3 4 5 6
f(x) 5 6 1 16 51 110
x 1 2 3 4 5 6
f(x) 1 8 25 58 113 196
Copyright © McDougal Littell Inc.
All rights reserved.
x

Answer Key
Practice C
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
f x 108x 1
3x 1
3x 5
f x x
6
2
3x 1
4x 1
f x 12x
2
1
3x 1
f x 12x
4x 1
1
2x 3
f x
2x 2
3
2x 1
f x
2x 1x 3
3
f x x 1x 2
2x 1x 2x 3
2
f x x 5x 2x 1
f x 2x 2x 1x 2
f 1 f 2 f 3 f 4 f 5 f 6
0 29 132 381 872 1725 3084
11.
f 1
2
29 103 249 491 853 1359
74 146 242 362 506
72 96 120 144
24 24 24
f 7
f 2 f 3 f 4 f 5 f 6 f 7
9 76 265 666 1393 2584
11 67 189 401 727 1191
56 122 212 326 464
66 90 114 138
24 24 24
12.
f 1
3 22 213 966 3031 7638 16617
13.
f 1
7
f 2
f 3
f 4
19 191 753 2065 4607 8979
172 562 1312 2542 4372
390 750 1230 1830
360 480 600
120 120
f 5
f 6
f 7
f 2 f 3 f 4 f 5 f 6 f 7
0 57 224 585 1248 2345
7 57 167 361 663 1097
50 110 194 302 434
60 84 108 132
24 24 24
14.
15.
16. y 1.114t
about 274,774,000 people
3 45.50t 2 f x x
2829.5t 249,915;
3 8x2 f x x
12x 13
3 10x2 8x 15

LESSON
6.9
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice C
For use with pages 380–386
Write the cubic function whose graph is shown.
1. y
2. y
3.
Write a cubic function whose graph passes through the given
points.
4. 5.
6. 7.
8. 9.
2
25
, 0, 1,
0, 1,
0, 1, 1
1, 0, 2, 0, 3, 0, 0, 9
2 , 0, 32
, 0, 2, 0, 0, 18
3
4
3
x
1
2
Show that the nth order differences for the given function of
degree n are nonzero and constant.
10. 11.
12. f x x 13.
5 4x2 f x x
6
4 2x3 3
Use finite differences and a system of equations to find a
polynomial function that fits the data. You may want to use
a calculator.
14. 15.
24
x 1 2 3 4 5 6
f(x) 16 31 54 79 100 111
, 0, 1 4 , 0, 1, 0, 2, 49
, 0, 1,
0, 5,
0, 1, 16
1
9
2 , 0, 1, 0, 3, 0, 0,
1
3 1
3
f x x 4 x 3 3x 2 2x 1
f x x 4 8x
16. The table shows the U.S. population (in thousands) from 1990 to 1997.
Find a polynomial model for the data. Then estimate the U.S. population in 2000.
t 1990 1991 1992 1993
y 249,949 252,636 255,382 258,089
t 1994 1995 1996 1997
y 260,602 263,039 265,453 267,901
3
1
x
3
6
4
3
x 1 2 3 4 5 6
f(x) 10 29 76 157 278 445
Algebra 2 123
Chapter 6 Resource Book
y
1
x
Lesson 6.9

Answer Key
Test A
1. 2. 5 3. 9 4. 5. 6 6.
7. 8. 9. Domain: all real
numbers 10. Domain: all real numbers
11. Domain: all real numbers
12. Domain: all real numbers except 5
13. Domain: all real numbers
14. 15.
16. f x
17. y
18.
y
1
3x
x 5
3x 15;
f x x 9 f x 2x 4
3x 2
;
3x2 x 72 4x 5;
2x 5;
15x;
6y6 2xy2 2
1
2
z
Domain: x ≥ 0 Domain: all real numbers
Range: y ≥ 0 Range: all real numbers
19. y
Domain: x ≥ 0
Range: y ≥ 0
1
1
1
1
20. 1 21. 6 22. ±32
23. mean 83.4
median 85
mode 84
range 30
standard deviation 9.25
24.
60 70 80
65
Exam Scores
75
x
x
90 100
85 91 95
1
1
x
25.
Frequency
0
Interval Tally Frequency
60–69 1
70–79 2
80–89 3
90–99 4
Exam Scores
y
4
3
2
1
60-69
70-79
80-89
90-99
Interval
x

Review and Assess
CHAPTER
7
NAME _________________________________________________________ DATE
Chapter Test A
For use after Chapter 7
____________
Evaluate the expression without using a calculator.
1. 2. 3. 4. 813 2723 2512 38
Simplify the expression. Assume all variables are positive.
5. 6. 7.
xy
8. 50 8
Perform the indicated operation and state the domain. Let
fx 3x and gx x 5.
9. f x gx 10. f x gx 11. f x gx
12.
fx
gx
13. fgx
3
38x3y6z3 213313 3
Find the inverse function.
14. f x x 9
15.
16.
Graph the function. Then state the domain and range.
17. 18. f x x13 f x x
19.
f x 3x 6
1
y
1
1
y
1
gx x 3
106 Algebra 2
Chapter 7 Resource Book
x
x
x 3 y 3
f x 1
2x 2
1
y
1
x
Answers
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17. Use grid at left.
18. Use grid at left.
19. Use grid at left.
Copyright © McDougal Littell Inc.
All rights reserved.

CHAPTER
7
CONTINUED
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ____________
Chapter Test A
For use after Chapter 7
Solve the equation. Check for extraneous solutions.
20. 21. 22. 3x 2 x 32x 4 12
9 3
12 3 4
Exam Scores In Exercises 23–25, suppose your exam scores on the
ten exams taken in Algebra 2 are: 65, 75, 84, 72, 90, 92, 86, 95, 84, and
91.
23. Find the mean, median, mode, and range of the exam scores.
24. Draw a box-and-whisker plot of the exam scores.
25. Make a frequency distribution using four intervals beginning with
60–69. Then draw a histogram of the data set.
20.
21.
22.
23.
24. Use space at left.
25. Use space at left.
Algebra 2 107
Chapter 7 Resource Book
Review and Assess

Answer Key
Test B
1. 4 2. 9 3. 9 4.
1
5 5. 12 6. 2xyz
7.
1
8. 82
4y 3
9. ; Domain: all real numbers
10. ; Domain: all real numbers
11. ; Domain: all real numbers
12. ; Domain: all real numbers except 0
13. ; Domain: all real numbers
14. 15.
16. f x x
17. y
18.
y
12
f x 3
f x 2x 6
1
2x
x 1
2x
2x 1
2x 2
2 3x 1
x 1
2x
Domain: x ≥ 0 Domain: all real
Range: y ≥ 1
numbers
Range: all real
numbers
19. y
Domain: x ≥ 7
Range: y ≥ 0
2
1
20. 32 21. 3 22. 4, 3
23. mean 976.4
median 971
mode 964
range 184
standard deviation 51.3
24.
900 950 1000
894
2
1
928
Polar Bears
1050
971 1005 1078
x
x
1
1
x
25.
Interval Tally Frequency
875–929 3
930–984 3
985–1039 3
1040–1094 1
Frequency
y
4
3
2
1
0
Polar Bears
875-929
930-984
985-1039
1040-1094
Interval
x

Review and Assess
CHAPTER
7
NAME _________________________________________________________ DATE
Chapter Test B
For use after Chapter 7
____________
Evaluate the expression without using a calculator.
1. 2. 3. 4. 12513 2723 8112 364
Simplify the expression. Assume all variables are positive.
5. 6. 7. 8. 98 2
4xy1
16xy2 38x3y3z3 313 4133 Perform the indicated operation and state the domain. Let
f(x) x 1 and g(x) 2x.
9. f x gx 10. fx gx 11. fx gx
12.
fx
gx
13. fgx
Find the inverse function.
14. 15. f x 16.
2
f x 2x 4
x 4
Graph the function. Then state the domain and range.
17. 18. fx 2x13 f x x 1
3
19.
2
y
1
2
y
1
f x x 7
108 Algebra 2
Chapter 7 Resource Book
x
x
3
1
y
f x x 2 , x ‡ 0
1
x
Answers
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17. Use grid at left.
18. Use grid at left.
19. Use grid at left.
Copyright © McDougal Littell Inc.
All rights reserved.

CHAPTER
7
CONTINUED
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ____________
Chapter Test B
For use after Chapter 7
Solve the equation. Check for extraneous solutions.
20. 21. 22. x2 32x 4
3x x 6
x 3 3
Polar Bears In Exercises 23–25, suppose a scientific team gathered the
weights (in pounds) of ten polar bears. The weights are 964, 1002, 1026,
978, 1078, 925, 928, 1005, 964, and 894.
23. Find the mean, median, mode, range, and standard deviation of the
weights.
24. Draw a box-and-whisker plot of the weights.
25. Make a frequency distribution using four intervals beginning with
875 929. Then draw a histogram of the data set.
20.
21.
22.
23.
24. Use space at left.
25. Use space at left.
Algebra 2 109
Chapter 7 Resource Book
Review and Assess

Answer Key
Test C
1. 5 2. 9 3. 3 4. 6 5.
6. 7. 8. 4 3 2xy 2
4 2x
9. Domain: all real numbers
10. Domain: all real numbers
11. Domain: all real numbers
12. Domain: all real numbers except
13. Domain: all real numbers
14. 15.
16. f x x
17. y
18. y
3 f x f x x 5; x ≥ 5
7
1
x 1
1
x 1
x;
2x 2
;
x2 2x;
2;
1;
Domain: x ≥ 0 Domain: x ≥ 0
Range: y ≤ 1 Range: y ≥ 2
19. y Domain: all real numbers
Range: all real numbers
20. 2, 3 21. no solution 22. 25
23.
Boys Girls
mean 70.1 65.3
median 70 65
mode 70 65
range 42 23
standard
deviation
11.7 6.87
24. girls team
25.
1
Boys Basketball Points
50
48
1
1
60 70 80
65 70
9x4 4y8 x
1 x
90
80 90
3 56
1
1
x
26.
Interval Tally Frequency
55–59 2
60–64 2
65–69 3
70–74 2
75–79 1
Frequency
Girls Basketball Score
y
4
3
2
1
0
55-59
60-64
65-69
70-74
75-79
Interval
x

Review and Assess
CHAPTER
7
NAME _________________________________________________________ DATE
Chapter Test C
For use after Chapter 7
____________
Evaluate the expression without using a calculator.
1. 2. 27 3. 481 4.
23
3125
Simplify the expression. Assume all variables are positive.
5. 6. 7. 8.
27x6
432x5y4 312 313 Perform the indicated operation and state the domain. Let
f x x 1 and gx x 1.
9. fx g(x 10. fx gx 11. fx gx
fx
12.
gx
13. fgx
Find the inverse function.
14. 4x 2y 8
15.
16.
Graph the function. Then state the domain and range.
17. f(x) 1 x 18. f x x12 f x x 7
2
13
19.
1
y
1
f x 3 x 2 1
110 Algebra 2
Chapter 7 Resource Book
1
y
x
1 x
8y 1223
f x x 2 5; x ≥ 0
1
y
1
1
216 13
354 3 2
x
Answers
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17. Use grid at left.
18. Use grid at left.
19. Use grid at left.
Copyright © McDougal Littell Inc.
All rights reserved.

CHAPTER
7
CONTINUED
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ____________
Chapter Test C
For use after Chapter 7
Solve the equation. Check for extraneous solutions.
20. 4 x 10 3x
21. 5 7y 3
22.
2x 2 13 6
Basketball In Exercises 23–26, use the tables below which give the
points scored in each game played by the boys and girls basketball
teams this season.
Boys Team
56, 81, 80, 75, 48, 65, 90,
66, 70, 70
Girls Team
60, 72, 61, 58, 78, 65, 66,
55, 65, 73
23. Find the mean, median, mode, range, and standard deviation for
each data set.
24. Interpret the data as to which team is more consistent in their
scoring (use the standard deviation).
25. Draw a box-and-whisker plot of the boys points.
26. Make a frequency distribution of the girls points using five intervals
beginning with 55–59. Then draw a histogram of this data.
20.
21.
22.
23.
24.
25. Use space at left.
26. Use space at left.
Algebra 2 111
Chapter 7 Resource Book
Review and Assess

Answer Key
Cumulative Review
1. inverse property of addition
2. commutative property of multiplication
3. associative property of multiplication
4. identity property of multiplication
5. distributive property
6. commutative property of addition
7. 4 8. 5 9. 5, 11 10. 1, 6 11. 6
1
4
12. 13. C 14. B 15. A
16. positive correlation 17. negative correlation
18. minimum: 0, maximum: 12 19. minimum: 1,
maximum: 21 20. minimum: maximum: 19
21. 22.
23. 24. 1
3
4
6
7
8
4
4
8
12
8
4
7
2
2
1
5,
2
1
1
25. not defined; number of columns of first matrix
is not equal to number of rows of second matrix
26. 27. 8 28. 19 29.
30. 31. 32.
33. 34.
35.
36.
37.
38. 3x 2y9x
39. y 40.
y
2 6xy 4y2 x
2 y2 2a 54a
x y
2 x
10a 25
2 y2 a 2
x yx y
2a 22 2x2 12 1
6
1
3
1
12
2
3
1
10
1
5
1
10
4 5
1
1
70
3
2
2
7 2
41. y
42. y
1
1
1
1
x
x
1
8
1
1
x
1 x
43. y
44.
1
1
45. 46.
47.
48.
49.
50. 51. 52. 53.
1
9x4y6 x10 1
x9y12 x3 y 2
3x2 y x 2
y 2x 4x 2
y x 2x 4
2x 1
2
y 3x 32 1
5
54. x 55. 56. 1254F
3y5 x 4
57. Drivers ≥ 35 years
x
1
y
1
x

CHAPTER
7
NAME _________________________________________________________ DATE
Cumulative Review
For use after Chapters 1–7
____________
Identify the property shown. (1.1)
Solve the equation. (1.3, 1.7)
7. 4x 5 11
8. 1.3x 3.5 10
9. x 3 8
10. 10 4x 14
11.
2 5 1 23
x x 12. 42x 3 14
Match the equation with the graph. (2.3, 2.8)
13. 14. y x 15.
1
y 1
x 1
A. y
B. y
C.
1
3
1
Draw a scatter plot of the data. Then state whether the data have
a positive correlation, a negative correlation, or relatively no
correlation. (2.5)
16. x 1 1 2 4 5 6 8
17.
y 1 2 3 5 5 7 9
Find the minimum and maximum values of the objective function
subject to the given constraints. (3.4)
18. Objective function: 19. Objective function: 20. Objective functions:
C 2x y
C x 3y
C 2x 3y
Constraints: Constraints: Constraints:
x ≥ 0
x ≤ 6
x ≥ 4
y ≥ 0
x ≥ 1
x ≤ 2
x y ≤ 6
y ≤ 5
y ≤ 5
y ≥ 0
y ≥ 1
Perform the indicated matrix operation. If the operation is not
defined, state the reason. (4.1, 4.2)
21. 22. 23.
8 3
7 1 4 5
0 3
3 2
4 1 4 3
2 0
24. 25. 26. 1
2
2 8 1
3 4 1 0
2 3
2 1 2
3 4
2
2 1
1 3
4
0 1
Copyright © McDougal Littell Inc.
All rights reserved.
x
3
6
3
1
6
1
6
x
3 5 7 3 5 7
1. 7 7 0
2. 7 9 9 7
3.
4. 91 9
5. 25 3 2 5 2 3 6. 4 7 7 4
y x 3
x 2
1 1 2 3 3 4 5
y 5 4 2 2 2 0 1 3
4 2
1
2 6
1 3
2 2
0
4
1
3 1
Algebra 2 117
Chapter 7 Resource Book
2
y
2
x
Review and Assess

Review and Assess
CHAPTER
7
CONTINUED
NAME _________________________________________________________ DATE ____________
Cumulative Review
For use after Chapters 1–7
Evaluate the determinate of the matrix. (4.3)
27. 28. 29.
2 0 1
3 1 4
1 2 2
1 2
2 4
Find the inverse of the matrix. (4.4)
7
4
1
30. 31. 32.
3
2 1
Factor the expression. (5.2)
33. 34. 35.
36. 37. 38. 27x3 8y3 x 3 x 2y y3 xy2 8a3 a
125
4 8a2 4x 16
4 4x2 1
Graph the inequality. (5.7)
39. 40. 41.
42. 43. 44. y ≥ 4x2 y ≤ x 3 3
2 y < x 2 1
2
y < 3x2 y ≥ x 12x 11
2 y ≥ x x 5
2 3
Write a quadratic function in the specified form whose graph has
the given characteristics. (5.8)
45. vertex form 46. vertex form 47. intercept form
vertex: 3, 1
vertex: 2, 0
x-intercepts: 4, 2
point on graph: 4, 2
point on graph: 3, 1
point on graph: 3, 14
48. intercept form 49. standard form
x-intercepts: 2, 4
point on graph: 1, 3
points on graph: 0, 1, 3, 11, 3, 1
Simplify the expression. (6.1)
x 5 1
50. 51. 52.
x2 3x 2 y 3 2
2
53. 54. 55.
x
56. Planet Temperatures Pluto’s surface temperature is believed to be
387F, the lowest temperature observed on a natural body in our solar
system. Measurements by the Pioneer probe indicate that Venus’ surface
temperature is 867F. What is the difference between the two
temperatures? (1.1)
4y3 57. Driving For a driver aged x years, a study found that a driver’s reaction
time (in milliseconds) to a visual stimulus such as a traffic light can be
modeled by: Vx 0.005x 16 < x < 70. At what age
does a driver’s reaction time tend to be greater than 20 milliseconds? (5.7)
2 Vx
0.23x 22,
118 Algebra 2
Chapter 7 Resource Book
8
x 3 y 4 3
x 1 y 2
1
2
2
8
4
x 4 y 4
x 7
x 3
1
2
5x 4 y 0
4
2
1
5
0
4
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice A
11 13
5 14
23 15
7 12
17 13
1. 2. 3. 4. 5.
6. 7. 8. 9. 10.
11. 12. 21 13. 32 14. 45
15. 11 16. 56 17. 723 18. 431
19. 103 20. 317 21. 34 22. 87
23. 58 24. 14 12 25. 2 26. 3 27. 2
28. 4 29. 1 30. 5 31. 1 32. 2 33. 2
34. 1.71 35. 2.88 36. 1.78 37. 1.32
38. 1.74 39. 1.52 40. 1.43 41. 2.29
42. 1.63 43. 1.32 44. 3.07 45. 2.24
46. 6 in. 47. 8.08 cm.
18
615 317 1012 1513 814 216

LESSON
7.1
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice A
For use with pages 401–406
Rewrite the expression using rational exponent notation.
1. 311
2.
45
3.
523
4. 7
5. 317
6. 62
7. 48
8. 315
9. 10
10. 73
11. 56
12. 821
Rewrite the expression using radical notation.
2 13
13. 14. 15. 16.
17. 18. 19. 103 20.
21. 22. 23. 24.
12
3114 2317 4 13
Evaluate the expression without using a calculator.
25.
38
26.
481
27.
28. 364
29.
41
30.
31. 32. 33.
1 16
Evaluate the expression using a calculator. Round the result to two
decimal places.
34. 35. 36.
37. 38. 39.
40. 41. 42.
43. 44. 29 45.
46. Geometry Find the length of an edge of the cube shown below.
13
415 1213 615 35
324
43
516
Volume 216 in. 3
47. Geometry Find the length of an edge of the cube shown below.
Volume 527 cm 3
5 14
7 18
16 14
11 12
8 15
532
3125
8 13
410
58
7 14
126 16
6 15
17 13
12 114
Algebra 2 13
Chapter 7 Resource Book
Lesson 7.1

Answer Key
Practice B
7 13
5 23
11 52
12 53
15 73
1. 2. 3. 4. 5.
6. 7. 8.
9. 10. 11. 12.
13. 14. 15.
16. 17. 16 18. 216 19. 8
20. 729 21. 16 22. 4 23. 32 24.
25. 26. 27. 3.00 28.
29. 30. 31. 2.21 32. 25.92
33. 4148.54 34. 35.
36. 37. 9.00 38. 16
39. 511.48
8.22 cm
40. 8 cm 41. 556.28 cm 42. 3
cm3
4
32 2.65
2.61
2.93 2.47
291,461.63 4.50 cm
12, 12
7 143 3 104 3 62 4 83 3 9 4
3 62 543
10
319
83
4227 953

Lesson 7.1
LESSON
7.1
Practice B
For use with pages 401–406
14 Algebra 2
Chapter 7 Resource Book
NAME _________________________________________________________ DATE ___________
Rewrite the expression using rational exponent notation.
1. 2. 3. 11 4.
5. 6. 7. 8.
5
3 52 37
3 15 7
Rewrite the expression using radical notation.
9. 10. 11. 6 12.
13. 14. 15. 16.
23
4315 1913 8 34
Evaluate the expression without using a calculator.
17. 18. 19.
20. 21. 64 22.
23. 24. 25.
23
8132 3632 843 4 52
3 9 5
6 23
64 13
7 42 2
10 43
Evaluate the expression using a calculator. Round the result to two
decimal places.
26. 27. 28.
29. 30. 31.
32. 33. 28 34.
35. Geometry Find the radius of a sphere with a volume of 382 cubic centimeters.
52
13223 11616 1513 21515 449
919,422
5122
Solve the equation. Round your answer to two decimal places
when appropriate.
36. 37. 38. x 73 5x 729
3 x 3650
2 5 139
Water and Ice In Exercises 39–42, use the following information.
Water, in its liquid state, has a density of 0.9971 grams per cubic centimeter. Ice
has a density of 0.9168 grams per cubic centimeter. You fill a cubical container
with 510 grams of liquid water. A different cubical container is filled with 510
grams of solid water (ice).
39. Find the volume of the container filled with liquid water.
40. Find the length of the edges of the container in Exercise 39.
41. Find the volume of the container filled with ice.
42. Find the length of the edges of the container in Exercise 41.
16 34
32 25
8 53
112 83
3 108 6 1210 9 43
14 37
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice C
1
100,000
1. 27 2. 729 3. 9 4. 5. 6.
7. 8. 9. 10. 3596.65
11. 12. 0.03 13. 0.15
14. 2002.65 15. 6.85 16.
17. 15.00 18. 0.10 19. 2.68 20.
21. 22. 4.61, 2.39 23.
24. 25. 26.
27. 28. 29. 30. 31.
32. 33. na when a < 0 and n
is even.
n
106.17
13,593.93
1, 1
1
2.92
0.99 0.67, 1.67 1.41, 1.41
1.33 > <
1.4 in. a
1
2
125
1
64 256 8
1
1

LESSON
7.1
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice C
For use with pages 401–406
Evaluate the expression without using a calculator.
81 34
1. 2. 3.
4. 5. 6.
7. 8. 9. 3235 25634 10052 2532 1614 Evaluate the expression using a calculator. Round the result to two
decimal places.
10. 11. 12.
13. 14. 15.
16. 17. 18.
3 267 1723 12434 2875 13653 3 302 5
Solve the equation. Round your answer to two decimal places
when appropriate.
19. 20. 21.
22. 23. 24.
25. 26. 27. 12 3x 23 3 x 20
2 2x 1 1
4 x 1
10 20
7 2x 125
3 2x 7 50
6 x 3
120
5 3x 32
4 x 2 5
5 137
Place the appropriate sign between the two expressions.
28. 29.
30. 31.
32. Volume A cylindrical can of chicken broth holds 14.5 ounces of broth.
One fluid ounce is approximately 1.8 cubic inches. What is the radius of a
can that is 4.5 inches tall? (Hint: Use the formula for the
volume of a cylinder.)
33. Critical Thinking
na
Use the following examples to determine when
n V r
a.
2 27
h
23 2723 1635 1635 823 823 3215 3215 , or =
32 3
2 2
243 65
3 64 4
4 37 3
32 3
3 27 2
5 433 5 1232 a. b. c. d. 2 2
Algebra 2 15
Chapter 7 Resource Book
Lesson 7.1

Answer Key
Practice A
4 53
1. 2. 3. 4.
5. 10 6. 7. 21 8. 65 9. 2
16
1
10. 11. 12. 13.
14. 15. 16. 17. 3x
18.
1
19. x 20.
1
21.
10
22. 63
13 3 x12 x110 x83 5
32
x 72
6 14
218 318 10 3
23. 24. 25.
26. 27. 28.
29. 30. 31.
32. 33.
y
34. 22 in.
2 6x
xz
2 3x
x
3 yz yz
2x3 x xy
yy y
y
2
2 7xx
4 3 x
3 15 5x
x
5 27 22
x 2
5 23 3 23
x 2
x 12
1
13 54
x 34

LESSON
7.2
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice A
For use with pages 407–414
Simplify the expression using the properties of rational exponents.
4 13 4 43
1. 2. 3.
4. 13 5. 6.
54
Simplify the expression using the properties of radicals.
7. 7 3
8. 9.
10. 11. 53 12.
1
25
Simplify the expression. Assume all variables are positive.
x 14 x 24
13. 14. 15.
16. 17. 18. x72 27x13 3x12 x53 x23 19. 20. 21.
Perform the indicated operation. Assume all variables are positive.
22. 23. 24.
25. 26. 27. 8 4 x 6 4 5 x
3 x 2 3 6
2x 7x
x
5 22 9 5 23 43
57 37
22
Write the expression in simplest form. Assume all variables are
positive.
49x 3
6 34 13
1056 1046 3 5
x 23 4
x12 x52 x2
y3 28. 29. 30.
31. 32. x 33.
5 5xx3 3x 3yz 3 8x3yz 34. Geometry The area of an equilateral triangle is given by A
Find the length of the side s of an equilateral triangle with an area of 12
square inches.
3
4 s 2 .
5 3 23
2
3 18
20
5
6 30
10
x 35 16
100
x 12
4x 3 y 5 z 8
x 2 y 4 z
x 5
Algebra 2 25
Chapter 7 Resource Book
Lesson 7.2

Answer Key
Practice B
1. 2. 3. 4.
5. 6. 7. 8. 9.
10. 11. 12. 13. 14.
15. 16. 17. 18. 4y 4 x x
23
x
3x 2x
12
3
4
5
3x 32 x x
2
23
12
38 2 2
14
753 312 52 25
x 35
19. 20. 21.
1
22. x 23. 24.
43 1
x 43
x 3
4 2 x 2
x 2
82 13
x 6
10 13
2x 14
25. 26. 27. 28.
29. 30.
31. diameter miles;
thickness 5.88 10 miles 32. 12.5 in.
33. 2.5 in. 34. 0.2
16
5.88 1017 2 5 3 3
3 22
5
4 3 15
3 3

Lesson 7.2
LESSON
7.2
Practice B
For use with pages 407–414
26 Algebra 2
Chapter 7 Resource Book
NAME _________________________________________________________ DATE ___________
Simplify the expression using the properties of radicals and
rational exponents.
5 23 5 43
1. 2. 3.
3
3 14 4 14
4. 5. 6.
7. 8. 9.
64
125 13
33
3
Simplify the expression. Assume all variables are positive.
9x 2
10. 11. 12.
x
12x2 4 12
13. 14. 15.
16. 17. 18.
19. 20. x 21.
33 x3 x5 1
x213 3
x3 x53 32x3 16x 14
x 2
22. 23. 24.
Perform the indicated operation.
25. 26. 27.
28. 29. 30.
31. Milky Way The Milky Way is light years in diameter and light
years in thickness. One light year is equivalent to 5.88 10 miles. What
is the diameter and thickness of the Milky Way in miles?
12
104 105 596 4 5 340 3
3 32
42 8
5
13 5213 3
4 15 2 4 2 15
3 3 3 3
Archery Target In Exercises 32–34, use the following information.
The figure at the right shows a National Field Archer’s Association
official hunter’s target. The area of the entire hunter’s target is
approximately 490.9 square inches. The area of the center white
circle is approximately 19.6 square inches.
32. Find the radius of the target.
33. Find the radius of the center white circle.
34. Find the ratio of the radius of the white circle to the radius
of the target.
3 12
32 3 4
7 23 52
4240
415
10 12 23
x 23 x 13
527x 5 9x 4
4256xy 4
4x 2
3x 6 2x 6
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice C
5 3 34
1. 2. 3. 4.
1
8
5. 6. 7. 2 8. 4 9.
x 14
24 2
2 1324
5 415
2z
10. 11. 12. 13.
18
x13y54 9y13z2 4x32 y13 14. 15. 16. 17. 5x23 y2 4x 4x 46
z
4
18. 19. 20.
21. 22. meters
23. 5.3 10 meters
12
2.7 1012 15x2
yy
5 2
y
3 y2 10 x
y
6 110
1 10
10 10
3x 12

LESSON
7.2
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice C
For use with pages 407–414
Simplify the expressions using the properties of radicals and
rational exponents.
1. 2. 3.
4. 5. 6.
7. 8. 72 9.
23 224 108
27
Simplify the expression. Assume all the variables are positive.
x
10. 11. 12 2
12.
2xy 54 y23 xy
13. 14. 15.
Perform the indicated operations. Assume all variables are positive.
16. 17. 18.
19. 20. 5y 10 y2 3 15 y3
3 5 9 y 5 x 5 38x 32x
6y2z x 3 27x3y2 46 36
z
21.
612
61335 312 52332 3xy12
27x2y121 y 2
xy3x 2 y3xy 6x 3 yx54y 2
Halley’s Comet In Exercises 22 and 23, use the following information.
Halley’s Comet travels in an elliptical orbit around the sun,
making one complete orbit every 76 years. When the comet was
closest to the sun 8.9 10 meters), it developed its tail. In the
diagram at the right, a is the length of the semi-major axis, A is the
comet’s closest distance to the sun, and B is the comet’s
farthest distance from the sun.
10
A
Sun
22. The length of the semi-major axis a can be found by the
equation where
gravitational constant
mass of sun
period 2.4 10 seconds (76 years).
Find the length of the semi-major axis.
23. The comet’s farthest distance from the sun can be calculated by
B 2a A. What’s the comet’s farthest distance from the sun?
9
1.99 10
T
30 6.67 10
M
kg
11 N m2kg2 2 GMT
a 2 13
G
4
312
12123 213 23412 3x14 y 23 z
52x 2 3 2x 2 7
5 23 15 2
4 3 2
3
18 3
x43 y 5
16z 1214
3 4 x 3 x
B
5
a
Halley's Comet
Not drawn to scale.
Algebra 2 27
Chapter 7 Resource Book
Lesson 7.2

Answer Key
Practice A
1. 2. 3.
4. 5. 6. 7.
8. 9. 10.
11. 2x 12. 6x 13.
3x
x 2
3 2x2 3x
2x
2 x 6x 3 x 2
32
x2 7x x 3 x 2 x 2
12
2x2 x 2x 2
2 3x 1
2x 2
14. 15. 16.
17. 18. 19.
20. x 21. All real numbers 22. All real
numbers 23. All real numbers 24. All real
numbers except x 3 25. All real numbers
26. All real numbers 27. All real numbers
28. All real numbers except x 0 29. All real
numbers 30. Px 0.75x 20,000; $730,000
320
x2 x
2x 10 4x 9 2x 3
16
x 2
x 2
2 x
x 4
2 1
x 2

Lesson 7.3
LESSON
7.3
Practice A
For use with pages 415–420
40 Algebra 2
Chapter 7 Resource Book
NAME _________________________________________________________ DATE ___________
Find f x g x. Simplify your answer.
1. 2.
3. f x x 4.
2 3, g x x2 f x 4x, g x 1 x
2x 1
Find f x g x. Simplify your answer.
5. 6.
7. f x x 1, g x x 8.
2 f x 2x, g x x 3
2x 3
Find f x g x. Simplify your answer.
9. 10.
11. f x x 12.
2 f x 2x 1, g x 3
x 1, g x 2x
f x
Find Simplify your answer.
gx .
13. 14.
15. 16. f x 2x12 , g x 22 x13 f x x 2, g x x2 f x x
x 4
2 f x 3x, g x x 2
1, g x x 2
Find Simplify your answer.
17. 18.
19. f x x 20.
2 f gx.
f x 2x, g x x 5
2, g x x 1
f x 2x 3, g x x 2 1
f x x 12 , gx 6x 12
f x x 2 x, g x x 2 2
f x 3x 32 , g x 4x 32
f x x 1, g x 3x 2
f x 2x 23 , g x 3x 13
f x x, g x 4x 9
f x x 15 , g x x 34
Let f x x Find the domain of the following
functions.
21. f x gx
22. f x g x
23. f x g x
24.
f x
g x
25. f gx
26. g f x
2 and g x x 3.
g x
27. g x f x
28. 29.
f x
30. Profit A company estimates that its cost and revenue can be modeled by
the functions C x 0.75x 20,000 and R x 1.50x where x is the
number of units produced. The company’s profit, P, is modeled by
P x R x C x. Find the profit equation and determine the profit
when 1,000,000 units are produced.
f f x
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice B
1.
2. 3.
4.
5.
6.
7. 8. 9.
10. 11. 12.
13.
14.
15.
16.
17. nonnegative real numbers
18. nonnegative real numbers
19. nonnegative real numbers
20. positive real numbers
21. real numbers greater than or equal
to
22. 4x nonnegative real numbers
23. f x x 100 24. gx 0.75x
25. g f x 0.75x 75
26. f gx 0.75x 100 27. Discount
12 4x 3
3.
3;
12 4x
x 3
;
4x12 ;
32 12x12 x 3 4x
;
12 4x
;
12 f g x 3x
x 3;
25 , g f x 3 x25 f g x x 412 , g f x x12 f g x x
4
2 4x 5, g f x x2 3
f g x 6x 3, g f x 6x 1
1
14
2x
x
53
3x 5
2x2 3x
1
2 8x
x 1
x 3
12 8
x12 4x712 x6 3x4 3x3 2x2 x
9x 6
3 x2 5
8
4x 2
x34 ; 3
8 x34
2x3 x2 2x
8x 5
3 x2 7x 2x 3;
23 ; x23 3x3 x2 12x 2; 3x3 3x2 2x

LESSON
7.3
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice B
For use with pages 415–420
Find and Simplify your answers.
1. 2.
3. f x 2x 4.
x 34
3 3x 4, gx x2 f x 4x
5x 1
23 , gx 3x23 f x 3x3 2x2 5x 1, gx x2 f x g x
f x g x.
7x 1
Find f x g x. Simplify your answer.
5. 6.
7. f x 2x 8.
14 , gx 2x13 f x x2 2x 2, gx x 1
Find Simplify your answer.
9. 10.
11. f x 6x 12.
73 , gx 3x23 f x 3x2 f x
gx
x 1, gx x 3
.
Find and Simplify your answers.
13. 14.
15. f x x 16.
12 f gx gf x.
f x 3x, gx 2x 1
, gx x 4
1/ 2
f x 1
2x34 , gx 1
8
f x 4x 1 , gx 2x 12
f x 3x 14 , gx x 54
f x x 2 1, gx x 2
f x 3x 45 , gx x 12
Let f x 4x and gx x 3. Perform the given operation and
state the domain.
17. f x gx
18. gx f x
19. f x gx
20.
gx
f x
21. f gx
22. g f x
Furniture Sale In Exercises 23–27, use the following information.
You have a coupon for $100 off the price of a sofa. When you arrive at the
store, you find that the sofas are on sale for 25% off. Let x represent the
original price of the sofa.
f x x 4 3x 2, gx x 2 3
f x 3x 5, gx 2x 2 1
23. Use function notation to describe your cost, f x, using only the coupon.
24. Use function notation to describe your cost, gx, with only the 25% discount.
25. Form the composition of the functions f and g that represents your cost, if
you use the coupon first, then take the 25% discount.
26. Form the composition of the functions f and g that represents your cost if
you use the discount first, then use the coupon.
27. Would you pay less for the sofa if you used the coupon first or took the
25% discount first?
Algebra 2 41
Chapter 7 Resource Book
Lesson 7.3

Answer Key
Practice C
1.
2.
3.
4.
5.
6. 5x58 5x14 3x38 x
3
5 4x4 x3 15x2 5x
16x 30
16 7x3 1; x16 3x3 x
1
2 10x 1; x2 2x 4x 3
25 8x1 x5 3x3 3x2 x
2x 7
5 x3 3x2 6x 9;
7. 3x x 8. 13
9.
10.
11.
12.
f gx x 2 4 12 ; g f x x 4
f gx
16
x 73
1
3
3x 12; g f x 1 2 x
f gx 2x 34 ; g f x 2x 34
f gx 3
23
2x12; g f x
x12 10x 25 2x 1 ;
1
13. f gx
all real numbers less
x
than 2 or greater than 0
2 2x ;
14. positive real numbers
15. positive real numbers
16. nonnegative real numbers
17. nonnegative real numbers
18. all real numbers
19. True 20. False; Examples vary.
21. True 22. False; Examples vary.
23. False; Examples vary.
vary.
24. False; Examples
25. Sample answer:
26. Sample answer: f x 1
g g x x
f x x, g x 2x 1
, g x 3x 2
x 4 4x3 6x2 f f x x
4x;
14 g x
f x
;
x52 2x32 f x
g x
;
1
x52 2x32; 1 2x12
g f x ;
x
27. Let f x 0.6x, g x x 5, h x 0.9x
f g h x 0.54x 3
f h g x 0.54x 2.7
g f h x 0.54x 5
g h f x 0.54x 5
h f g x 0.54x 2.7
h g f x 0.54x 4.5; First the store will
deduct the $5 coupon. Then it makes no difference
in what order they take the 40% and 10%
discount.

Lesson 7.3
LESSON
7.3
Practice C
For use with pages 415–420
42 Algebra 2
Chapter 7 Resource Book
NAME _________________________________________________________ DATE ___________
Find f x g x and f x g x. Simplify your answers.
1.
2.
3.
4.
f x x 3 3x 2 2x 1, gx x 5 2x 3 4x 8
f x 6x 25 3x 1 , gx 4x 25 5x 1
f x x 2 3x 1, gx 7x 2
f x 3x 16 2x 3 1, gx 2x 16 5x 3
Find f x g x. Simplify your answer.
5. f x x 6.
3 2x2 x 5, gx x2 2x 6
Find Simplify your answer.
7. f x 3x 8.
23 1, gx x13 f x
gx .
Find and Simplify your answers.
9. 10.
11. f x x 12.
34 f x 3 x
, gx 2x
12 , gx x2 f gx gf x.
1
1/ 2
f x 16x 13 , gx x 2
f x x 2 , gx 3x 1
f x 3x 1 , gx 2x 12
Let and gx x Perform the operation and state
the domain.
13. f gx
14. g f x
15.
f x
gx
16.
gx
f x
17. f f x
18. ggx
2 f x x 2x.
Critical Thinking State whether or not the following statements
are always true. If they are false, give an example.
19. 20.
21. 22.
23. 24. f f x f x2 f x gx gx f x
f x gx gx f x
f x gx gx f x
f x gx
gx f x
f gx g f x
Function Composition Find functions f and g such that hx) f gx.
25. 26. hx
1
hx 2x 1
3x 2
f x 5x 14 3, gx x 38 1
27. Holiday Sale A department store is holding its annual end-of-year sale.
Feature items are marked 40% off. In addition, a flyer was sent to the
newspapers which included a coupon for $5 off any purchase. Also, if
you open a charge account with the store, you can receive an additional
10% discount. There are six different ways in which these price reductions
can be composed. Find all six compositions. Which of the six
compositions is the store most likely to use?
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice A
1.
2.
3. no 4. yes 5. yes 6. B 7. A 8. C
9–12. Show
13.
x 3 5 7 9 11
y 2 1 0 1 2
x 1 2
4 1 0
y 0 1 2 3 4
C
i ; 16.54 in.
2.54
f gx x and g fx x.
14. r C
; 4.46 in.
2

Lesson 7.4
LESSON
7.4
Find the inverse relation.
Practice A
For use with pages 422–429
54 Algebra 2
Chapter 7 Resource Book
NAME _________________________________________________________ DATE ___________
1. x 2 1 0 1 2
2. x 0 1 2 3 4
y 3 5 7 9 11
y 1 2
4 1 0
Use the horizontal line test to determine whether the inverse of f is
a function.
3. y
4. y
5.
1
Match the graph with the graph of its inverse.
6. y
7. y
8.
1
A. y
B. y
C.
1
Verify that f and g are inverse functions.
9. f x x 5, gx x 5
10.
11. 12.
f x x 5 , gx 5 x
1
2
2
x
x
x
f x 6x, gx 1
6 x
f x 2x 1, gx 1 1
2x 2
13. Metric Conversions The formula to convert inches to centimeters is
C 2.54i. Write the inverse function, which converts centimeters to inches.
How many inches is 42 centimeters? Round your answer to two decimal places.
14. Geometry The formula C 2r gives the circumference of a circle of radius
r. Write the inverse function, which gives the radius of a circle of circumference
C. What is the radius of a circle with a circumference of 28 inches? Round your
answer to two decimal places.
1
1
2
1
1
1
x
x
x
1
1
y
1
1
y
y
Copyright © McDougal Littell Inc.
All rights reserved.
1
1
x
x
x

Answer Key
Practice B
1.
2.
x 6 3 0 3 6
y 1 2 3 4 5
x 1 2 4 6 0
y 0
1
3
2
1
3. yes 4. no 5. no 6. no 7. yes 8. yes
9–16. Show
17. 18. 19.
20. 21.
22.
23.
24.
25. y x
26. y
27.
y
2 y
y x 3, y x 3
y x 1, y x 1
, x ≥ 0
3 1
2 2x y y 2x 12
1
y
9
4x 4
1
y y x 5
1
3x 3
1
4x f gx x and g fx x.
1
1
3
x
28. 29. ,
21.85
30. R , $26.51
S
y
C K 273.15
C
1
1 x
0.75
2
1
1
x

LESSON
7.4
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice B
For use with pages 422–429
Find the inverse of the relation.
1. x 1 2 3 4 5
2.
y 6 3 0 3 6
Use the horizontal line test to determine whether the inverse of f is
a function.
3. 4. 5.
6. 7. f x 3 2x
8.
f x x f x 2x2 f x 3x 5
3
Verify that f and g are inverse functions.
9. 10.
11. 12.
13. f x 14.
15. 16.
1
f x 2x, gx
f x x 2, gx x 2
2x 4, gx 2x 8
x
2
f x x 2 , x ‡ 0, gx x
Find an equation for the inverse of the relation.
17. 18. 19.
20. 21. 22.
23. 24. y x 25. y x
2 y x 1
2 y y 3 2x
3
1
y 4x
y x 5
y 3x 1
y 4x 9
2x 6
Sketch the inverse of f on the coordinate system.
26. y
27. y
28.
1
1
x
29. Temperature Conversion The formula to convert temperatures from
degrees Celsius to Kelvins is K C 273.15. Write the inverse of the
function, which converts temperatures from Kelvins to degrees Celsius.
Then find the Celsius temperature that is equal to 295 Kelvins.
30. Sale Price A gift shop is having a storewide 25% off sale. The sale price
S of an item that has a regular price of R is S R 0.25R. Write the
inverse of the function. Then find the regular price of an item that you got
for $19.88.
1
1
x 1
3 0 2 3
y 1 2 4 6 0
f x 1 x, gx 1 x
f x 4x 1, gx 1
f x 3x 6, gx
1
4x 4
1
3x 2
f x x 3 , gx 3 x
x
2
1
f x 1 x 2
f x 1
2x 4
Algebra 2 55
Chapter 7 Resource Book
1
y
1
x
Lesson 7.4

Answer Key
Practice C
1–6. Show
7.
8.
9.
10.
11.
12.
13.
14.
15. f
16. Restrictions on the domain must be made in
inverse functions of all functions where n is even.
1 f
x x, x ≥ 0
1x 3 f
x 5
2
1 f
x x 7; x ≥ 7
1x 1
5x3 3
f
5
1x 4 x2 f
, x ≥ 0
1x 1
2x2 3
f
2 , x ≥ 0
1x x2 f
1, x ≥ 0
1x 1
f
8
3x 3
1x 1 1
4 4x f gx x and g fx x.
17. No.
g1x 3 1 3
x and
2 g x 2x
18.
19.
20. yes; f gx g fx x 21. no 22. yes
23. yes
f1x 1 1 1
x and
3 f x 3x
y
1
1
x
⇒ 3
⇒ 1
3
x
2 2x
1
x
3 3x
f f x f 1 1
x x 1
x

Lesson 7.4
LESSON
7.4
Practice C
For use with pages 422–429
56 Algebra 2
Chapter 7 Resource Book
NAME _________________________________________________________ DATE ___________
Verify that f and g are inverse functions.
1. 2.
3. f x x 4, gx x 4.
2 1 7
f x 2x 7, gx 2x 2
4, x ‡ 0
5. f x 6.
1
3x 4 2 ‡ 0, gx 4 3x 6
Find the inverse function.
7. 8. 9.
10. 11. 12.
13. 14. 15.
f x 2x3 f x x 5
2 f x 1 4x
f x 3x 8
f x 2x 3
f x 4 x
7, x ‡ 0
16. Critical Thinking Consider the basic power function for
and 5. Make a conclusion about the values of n for which a
restriction on the function’s domain must be made to ensure that the
inverse of f is a function.
17. Critical Thinking Consider the following pairs of inverse functions:
and
and
Does f ? Explain.
Visual Thinking In Exercises 18–20, consider the function f(x)
which is its own inverse.
1
,
x
1x 1
g
f x
1x 3
gx 2x
2
f
3x
1x 1
n 1, 2, 3, 4,
f x 3x
3x
18. Sketch the graph of f x to verify that it is its own inverse.
19. Verify that f x is its own inverse by showing f f x x.
20. If g(x) af(x) where a is a nonzero constant, is it true that g(x) is its own
inverse? Explain.
Use the horizontal line test to determine whether the inverse of
the function is a function.
x 2, x < 0
x 2, x < 0
21. f x 22. f x 23.
x 1, x ‡ 0
x 3, x ‡ 0
1
y
1
x
1
y
1
f x 5x 3, gx 3 1
5 5x f x 1
2 x3 , gx) 3 2x
f x 3
4 x4 2, gx 4 108x 216
3
f x x n
x
f x x 1
f x
f x x , x † 0
3 5x 3
f x x2 ,
x,
1
y
Copyright © McDougal Littell Inc.
All rights reserved.
1
x < 0
x ‡ 0
x

Answer Key
Practice A
1. F 2. C 3. B 4. E 5. A 6. D
7. Shift the graph 3 units up. 8. Shift the graph
2 units down. 9. Reflect the graph across the xaxis.
10. Shift the graph 1 unit left.
11. Shift the graph 4 units right. 12. Stretch the
graph vertically by a factor of 2. 13. Shift the
graph 3 units down. 14. Shift the graph 2 units
up. 15. Shift the graph 7 units left.
16. Shift the graph 5 units right. 17. Shrink the
1
graph vertically by a factor of 2
graph across the x-axis.
18. Reflect the
.
19. y
20.
x ≥ 0, y ≥ 4 x ≥ 0, y ≥ 3
21. y 22.
x ≥ 2, y ≥ 0 x ≥ 3, y ≥ 0
23. y 24.
x, y are all real x, y are all real
numbers. numbers.
25. Domain: 0 ≤ h ≤ 100, Range: 0 ≤ t ≤ 2.5
26. t
27. 36 ft
1
1
20
2
1
1
1
1
x
x
x
h
1
y
1
1
y
1
2
y
1
x
x
x

Lesson 7.5
LESSON
7.5
Practice A
For use with pages 431–436
68 Algebra 2
Chapter 7 Resource Book
NAME _________________________________________________________ DATE ___________
Match the function with its graph.
f x 3 x 2
D. y
E. y
F.
1
1
1
1
x
x
f x 3 x 2
Describe how to obtain the graph of g from the graph of f x x.
7. gx x 3
8. gx x 2
9. gx x
10. gx x 1
11. gx x 4
12. gx 2x
Describe how to obtain the graph of g from the graph of f x 3 x.
13. 14. 15.
16. 17. 18. gx 3 gx x
1
gx 3 gx
x 5
3 gx x 7
3 gx x 2
3 x 3
2 3 x
Graph the function. Then state the domain and range.
19. 20. 21.
22. 23. f x 24.
3 f x x 4
f x x 3
f x x 3
x 1
Falling Object In Exercises 25–27, use the following information.
A stone is dropped from a height of 100 feet. The time it takes for the stone to
reach a height of h feet is given by the function t where t is
time in seconds.
25. Identify the domain and range of the function.
26. Sketch the graph of the function.
27. What is the height of the stone after 2 seconds?
1
4100 h
1
2
1
1
x
x
f x 3 x 2
1. 2. 3.
4. f x x 1
5. f x x 1
6. f x x 1
A. y
B. y
C.
y
2
1
f x x 2
f x 3 x 2
Copyright © McDougal Littell Inc.
All rights reserved.
y
1
1
x
x

Answer Key
Practice B
1. E 2. B 3. F 4. A 5. C 6. D
7. Shift the graph 4 units left and 3 units up.
8. Shift the graph 4 units left and 2 units down.
9. Shift the graph 4 units left and reflect it across
the x-axis. 10. Shift the graph 4 units right and
3 units down. 11. Shift the graph 4 units right
and 2 units up. 12. Shift the graph 4 units right,
reflect across the x-axis, and shift 2 units up.
13. Reflect the graph across the x-axis and shift
1 unit down. 14. Reflect the graph across the
x-axis and shift 1 unit up. 15. Shift the graph
1 unit right and 5 units up.
1 unit left and 5 units up.
16. Shift the graph
17. Shift the graph 1 unit left and 2 units down.
18. Shift the graph 1 unit right and 2 units down.
19. y
20.
y
1
x ≥ 3, y ≥ 2 x ≥ 1, y ≥ 3
21. y 22.
x ≥ 1, y ≤ 3 x, y are all real
numbers.
23. y
24.
y
1
1
1
1
1
x
x
x
x, y are all real x, y are all real
numbers. numbers.
1
1
y
1
1
1
1
x
x
x
25. Domain: t ≥ 273, Range: v ≥ 0
26. y 27. 11.58C
250
75
x

LESSON
7.5
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice B
For use with pages 431–436
Match the function with its graph.
1. 2. 3.
4. 5. 6. f x
A. y
B. y
C.
y
3 f x x 2 1
3 f x x 2 1
3 f x x 1 1
f x x 1 1
f x x 1 1
x 2 1
D. y
E. y
F.
Describe how to obtain the graph of g from the graph of f x x.
7. gx x 4 3
8. gx x 4 2
9. gx x 4
10. gx x 4 3
11. gx x 4 2
12. gx x 4 2
Describe how to obtain the graph of g from the graph of f x 3 x.
13. 14. 15.
16. 17. 18. gx 3 gx x 1 2
3 gx x 1 2
3 gx
x 1 5
3 gx x 1 5
3 gx x 1
3 x 1
Graph the function. Then state the domain and range.
19. f x x 3 2
20. f x x 1 3
21.
22. 23. 24.
f x 3 x 1 3
Speed of Sound In Exercises 25–27, use the following information.
The speed of sound in feet per second through air of any temperature
measured in Celsius is given by
V
1
1087273 t
,
16.52
where t is the temperature.
1
1
25. Identify the domain and range of the function.
26. Sketch the graph of the function.
1
x
x
f x 3 x 4 2
27. What is the temperature of the air if the speed of sound is 1110 feet per
second?
1
1
1
2
x
x
f x x 1 3
f x 3 x 1 3
Algebra 2 69
Chapter 7 Resource Book
1
y
1
1
1
x
x
Lesson 7.5

Answer Key
Practice C
1. B 2. A 3. C
4. y
5.
1
x ≥ 3, y ≥ 0 x ≥ 4, y ≥ 0
6. y
7.
x ≥ 1, y ≥ 4 x ≥ 1, y ≤ 3
8. y
9.
x ≥ 1, y ≤ 2
10. y 11.
x, y are all real x, y are all real
numbers. numbers.
12. y
13. y
1
1
1
1
1
1
1
1
1
x
x
x
x
x
x ≥ 1
2, y ≥ 2
x, y are all real x, y are all real
numbers. numbers.
1
1
y
1
1
1
1
1
y
1
2
y
y
1
x
x
x
x
x
14. y 15.
16.
x, y are all real x, y are all real
numbers. numbers.
1, 1 and 0, 0
17. On the interval 0, 1, the larger the root, the
steeper the graph. On the interval 1, , the
larger the root the less steep the graph.
18. y
19.
1
1, 1, 0, 0, and
1, 1
20. On the interval 1, 1, the larger the root, the
steeper the graph. On the intervals , 1
and 1, ,
the larger the root, the less steep the
graph. 21.
y
22. 1994
Life expectancy
(years)
1
f(t)
80
75
70
65
60
0
0
1
1
(0.3, 62.7)
1
10 20 30 40 50 60 t
x
x
Years since 1940
1
x
1
y
2
x

Lesson 7.5
LESSON
7.5
Practice C
For use with pages 431–436
70 Algebra 2
Chapter 7 Resource Book
NAME _________________________________________________________ DATE ___________
Match the function with its graph.
1. f x x 2 1
2. f x x 2 1
3. f x x 2 1
A. y
B. y
C.
y
1
1
Sketch the graph of the function. Then state the domain and range.
4. 5. 6.
7. 8. 9.
10. 11. 12.
13. 14. f x 15.
4
5 3 f x x 1 2
3 f x
x 3 1
3
2 3 f x 4 x 2
3 f x
f x 23x
1 3
f x x 1 2
x 1
1
f x 2x 3
2x 4
Visual Thinking In Exercises 16–18, use the following information.
Graph the functions and on
the same coordinate plane. Use the window
and
16. What two points do all of the graphs have in common?
17. Describe how the graphs are related.
18. Using what you have learned in Exercises 16 and 17, sketch the graph of
f x 4 jx
xmin 1, xmax 2, xscl 1,
ymin 1, ymax 2, Yscl 1.
x 3 2.
8 hx x
6 gx x,
4 f x x, x,
Visual Thinking Graph the functions
and on the same coordinate plane. Use the window
and
19. What three points do all of the graphs have in common?
20. Describe how the graphs are related.
21. Using what you have learned in Exercises 19 and 20, sketch the graph of
f x
22. Life Expectancy From 1940 through 1996 in the United States, the age
to which a newborn can expect to live can be modeled by
5 jx xmin 2,
xmax 2, xscl 1, ymin 2, ymax 2, Yscl 1.
x 2 1.
9 h x
x
7 gx x,
5 f x x,
3 x,
f t 1.78t 0.3 62.7,
x
where t is the number of years since 1940. Graph the model. In what year
was the life expectancy at birth 75.7 years?
1
1
x
1
f x x 1 4
f x x 1
2 2
f x 3 x 3 2
f x 3 x 1 1
3
Copyright © McDougal Littell Inc.
All rights reserved.
2
x

Answer Key
Practice A
1. yes 2. yes 3. no 4. yes 5. no 6. yes
7. 16 8. 64 9. 64 10. 8 11. 4 12. 125
1
13. 16
14. 8 15. 81 16. 1 17. 27
18. 27 19. 3 20. no solution 21.
4
3
22. 10 23. 3 24. 2 25. 0.81 ft 26. 0.20 ft
27. 3.24 ft 28. 100 ft 29. 36 ft 30. 225 ft

Lesson 7.6
LESSON
7.6
Practice A
For use with pages 437–444
82 Algebra 2
Chapter 7 Resource Book
NAME _________________________________________________________ DATE ___________
Check whether the given x-value is a solution of the equation.
1. x 5 8; x 169
2. 2x 1 2 5; x 5
3. x 4 10; x 25
4. 1 x 3 5; x 3
5. 2x 5 12; x 20
6. 3x 1 3 2; x 0
Solve the equation. Check for extraneous solutions.
7. 8. 9.
10. 11. 12. 4x23 x 100
32 x 4 12
13 x
2 0
12 x 8
23 x 16
14 2
Solve the equation. Check for extraneous solutions.
13. 14. 15.
16. 17. 18. 5 3 2 x 15
3 4x
5x 3 4
x 6
3 x 3x 2
27
1
4
Solve the equation. Check for extraneous solutions.
19. 20. 21.
22. 23. 24. 35x 6 3 43x 1 4
4 3x 5 2x 2
3 x 3 6 2x 1 x 3x 2 2
5
Pendulums In Exercises 25–27, use the following information.
The period of a pendulum is the time T (in seconds) it takes for a pendulum of
length L (in feet) to go through one cycle. The period is given by
T 2 L
32 .
Given the period of a pendulum, find its length. Round your answers to two
decimal places.
25. T 1 second 26. T 0.5 second 27. T 2 seconds
Velocity of a Free-Falling Object
following information.
In Exercises 28–30, use the
The velocity of a free-falling object is given by where V is velocity
(in feet per second), g is acceleration due to gravity (in feet per second) and
h is the distance (in feet) the object has fallen. On Earth g 32 fts How far
did an object fall if it hits the ground with the given velocity?
28. 80 ft/s 29. 48 ft/s 30. 120 ft/s
2 V 2gh,
.
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice B
1. 8 2. 16 3. 8 4. 9 5. 8 6. 8
7. 12
8. 1 9. 10. 11. 3 12. no solution
7
5
3
1
3
13. 2 14. 12 15. 3 16. 4 17. 0 18.
19.
7
2 20. no solution 21. 5 22. 2, 1
23. 6 24. 3 25. 3, 4 26. 8 27. 5
28. 2.25 29. 3.24 30. 6.5 31. 3.85
32. 6.75 33. 1.10 34. 9.77 ft 35. 10.78 ft
36. 34,722.22 ft
3
2

LESSON
7.6
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice B
For use with pages 437–444
Solve the equation. Check for extraneous solutions.
1. 2. 3.
4. 5. 6.
7. 8. 9. 3x 412 2x 1 3 0
15 2x 3 2 3
13 2x
5 2
53 2x 1 64
32 x 1 54
23 2x
4
34 2x 8
34 x 7 23
43 5 11
Solve the equation. Check for extraneous solutions.
10. 11. 12.
13. 14. 15.
16. 17. 2 18. 5 2x 1 3
3 33x 1 5 3
53 x 4 3 1 3x 4 6
3 43x 5 6
3x 6 5 14 5x 1 8 2
32x 1 2 4 5x 4 1 3
Solve the equation. Check for extraneous solutions.
19. 20. 21. 42x 1
22. x 2 x 2
23. 2x 3 x 3
24. 12x 13 2x 1
25. 3x 13 x 5
26. 2x x 4
27. 2x 4 1 x
4 32x 1 3x 1 x 5
x 6
3 8
Use the Intersect feature on a graphing calculator to solve the
equation.
28. 29. 30.
31. 32. 33. 2x 323 2x 5
1.3x 11 4
343 5x 2.1
3
13 6x 3 2
35 2
3 18
x12 1
Velocity of a Free-Falling Object In Exercises 34–36, use the
following information.
The velocity of a free-falling object is given by where h is the
distance (in feet) the object has fallen and g is acceleration due to gravity (in
feet per second squared). The value of g depends on your altitude. If an object
hits the ground with a velocity of 25 feet per second, from what height was it
dropped in each of the following situations?
34. You are standing on the earth, so
35. You are on the space shuttle, so
36. You are on the moon, so g 0.009 fts2 g 29 fts
.
2 g 32 fts
.
2 V 2gh
.
Algebra 2 83
Chapter 7 Resource Book
Lesson 7.6

Answer Key
Practice C
1. 65 2. 516
5
3. 2
17
4. 3 5. no solution
6. 3 7. 18 8. no solution 9.
6751
4
10. 78, 78 11. 10, 10
12. 27, 27 13. 6 14. no solution
15. 7, 8 16. 3, 5 17. 1 18. 3, 6, –6
19. 5 20. 1, 2, 2 21. 4 22.
169
64
23. no solution 24. no solution 25.
16
45 26. 0
27. 1, 3 28. 4 in. 29. 24 in.

Lesson 7.6
LESSON
7.6
Practice C
For use with pages 437–444
84 Algebra 2
Chapter 7 Resource Book
NAME _________________________________________________________ DATE ___________
Solve the equation. Check for extraneous solutions.
1. 2. 3.
4. 5. 6.
1
32x 332 1
32x 3 2 7
32 1
23x 1 2 7
34 2x 3
3 1
23 2x 4 5 1
13 3x 1 7 9
23 4 52
Solve the equation. Check for extraneous solutions.
7. 8. 9.
10. 11. 12. 3 3 1 x2 2x 1 8
2 x 1 4 10
2 1 3
52x
3 5 4
1
4 3x 1 5
2 3 6
312
x 5 1 7
Solve the equation. Check for extraneous solutions.
13. 14. 15.
16. 17. 18.
19. 20. 54x 21. x 3 x 5
3 x2 32x 4 x
2 42x 39x 19 x 1
14 x 1
2 3x 1 x
2 x 7 x 7
12x 10 2x 5
2
53x 7
1
3 x 2x 3
5 2x 1
Solve the equation. Check for extraneous solutions.
22. x 3 4 x
23. x 5 2 x
24. x 5 2 x
25. 5x 1 3 5x
26. 2x 1 1 2x 27. 2x 3 1 x 1
28. Geometry The lateral surface area of a cone is given by
The surface area of the base of the cone is
given by B r The total surface area of a cone of radius
3 inches is square inches. What is the height of the cone?
2 S rr
.
2 h2 .
24
29. Geometry A container is to be made in the shape of a cylinder
with a conical top. The lateral surface areas of the cylinder and
cone are and The surface area of
the base of the container is B r The height of the cylinder
and cone are equal. The radius of the container is 5 inches and its
total surface area is square inches. Find the total height of
the container.
2 S2 2rr
.
2 h2 S1 2rh
.
275
h
h
h
5 in.
3 in.
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice A
1. 1, 1, 1, 2, 2, 3, 4, 5, 5, 6, 7, 7, 8, 8, 9; 4.6; 5; 1
2. 8, 10, 10, 10, 12, 12, 13, 15, 16, 19; 12.5; 12; 10
3. 24 4. 48 5. 3 6. 7 7. 149
8. 21 9. 7.5, 14 10. 136, 154.5 11. 1, 4.5
12. 35, 42
13.
14.
15.
16.
20 30 40 50 60
100
28 32 35 40 54
120 140 160 180 200
120
140 160 185 200
Interval Tally Frequency
1–2 7
3–4 4
5–6 4
7–8 7
9–10 3
Interval Tally Frequency
1–2 8
3–4 3
5–6 3
7–8 0
9–10 3
17. Exercise 16 18. Exercise 15

LESSON
7.7
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice A
For use with pages 445–452
Write the numbers in the data set in ascending order. Then find the
mean, median, and mode of the data set.
1. 2, 3, 7, 1, 8, 7, 4, 5, 1, 8, 2, 6, 5, 9, 1 2. 10, 15, 8, 19, 12, 13, 10, 16, 12, 10
Find the range of the data set.
3. 18, 24, 37, 29, 13, 22, 25, 30
4. 123, 100, 132, 112, 148, 129, 138, 118
5. 3, 2, 1, 2, 3, 3, 1, 4
6. 105, 110, 104, 109, 110, 111, 108, 106
7. 2, 7, 150, 125, 3, 2, 1, 20
8. 88, 72, 84, 71, 73, 85, 90, 92
Find the lower and upper quartiles of the data set.
9. 5, 10, 7, 13, 12, 8, 15, 20, 10
10. 153, 146, 128, 144, 156, 120, 148, 160
11. 0, 3, 2, 4, 1, 6, 3, 5, 1
12. 38, 43, 32, 33, 37, 41, 44, 40, 38
Use the given information to draw a box-and-whisker plot of the
data set.
13. minimum 28
14. minimum 120
maximum 54
maximum 200
median 35
median 160
lower quartile 32
lower quartile 140
upper quartile 40
upper quartile 185
Use the given intervals to make a frequency distribution of the
data set.
15. Use five intervals beginning with 1–2.
1, 1, 1, 1, 2, 2, 2, 3, 3, 4, 4, 5, 5, 5, 6, 7, 7, 8, 8, 8, 8, 8, 9, 9, 10
16. Use five intervals beginning with 1–2.
1, 1, 2, 2, 1, 3, 2, 10, 4, 1, 6, 5, 3, 1, 9, 10, 6
Match the histograms with the data sets from Exercise 15 and
Exercise 16.
17. 18.
10
8
6
4
2
0
1–2
3–4
5–6
7–8
9–10
10
8
6
4
2
0
1–2
3–4
5–6
7–8
9–10
Algebra 2 97
Chapter 7 Resource Book
Lesson 7.7

Answer Key
Practice B
1. 11.4; 9; 8 2. 20.4; 22; 22
3. 49.5;
48; 44 4. 127.2; 130; 100
5. 47, 16.7 6. 15.5, 5.01 7. 4.5
8. 25.2 oz 9. 25 oz 10. 28 oz 11. 6
12. 5; 7 13.
0 1 2 3 4 5 6 7 8 9
0 5 6 7

Lesson 7.7
LESSON
7.7
Practice B
For use with pages 445–452
98 Algebra 2
Chapter 7 Resource Book
NAME _________________________________________________________ DATE ___________
Find the mean, median, and mode of the data set.
1. 6, 22, 4, 15, 10, 8, 8, 7, 14, 20
2. 10, 15, 12, 20, 25, 22, 28, 24, 22, 26
3. 53, 51, 47, 44, 60, 48, 44, 55, 44
4. 100, 150, 100, 120, 130, 125, 135, 140, 145
Find the range and standard deviation of the data set.
5. 47, 18, 65, 28, 43, 18
6. 35.8, 29.4, 32.1, 24.9, 30.5, 20.3
7. Reading Levels The Pledge of Allegiance contains
31 words. The bar graph at the right shows the number
of words of different lengths in the pledge. Find the
mean word length of the set of 31 words.
Walking Shoes In Exercises 8–10, use the following information.
An important feature of walking shoes is their weight. The graph below shows
the weight of the top-10 rated men’s walking shoes.
8. Find the mean of the ten weights.
9. Find the median of the ten weights.
10. Find the mode of the ten weights.
World Series In Exercises 11–13, use the following information.
The World Series is a best-of-seven playoff between the National League
champion and the American League champion. The table shows the number
of games played in each World Series for 1981 through 1998.
11. Find the median of the number of games played.
12. Find the lower and upper quartiles of the number of games played.
13. Construct a box-and-whisker-plot of the number of games played.
Word Lengths in the Pledge of Allegiance
Frequency
12
10
Ranking Weight Ranking Weight
1 24 oz 6 28 oz
2 22 oz 7 22 oz
3 26 oz 8 28 oz
4 28 oz 9 22 oz
5 24 oz 10 28 oz
Year 1981 1982 1983 1984 1985 1986 1987 1988 1989
Games 6 7 5 5 7 7 7 5 4
Year 1990 1991 1992 1993 1994 1995 1996 1997 1998
Games 4 7 6 6 0 6 6 7 4
8
6
4
2
0
1
2 3 4 5 6 7 8 9 10 11
Word Length (number of letters)
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice C
1. 3; 1.05 2. 0.6; 0.208 3. 3; 0.957
4. 20; 6.54 5. b 6. a. 6.7, 2 b. 23.3, 25.5;
The median is a more accurate measure of central
tendency when a small number of data is much different
than the majority of the data.
7. 30 8. 107.4 9. 8.052
10. Machine #1: 1.0008; Machine #2: 0.9993
11. Machine #1: 0.00098; Machine #2: 0.0009
12. Machine #2
13. Children of U.S. Presidents
Interval Tally Frequency
0–2 16
14. 15. median
Number of
Presidents
3–5 16
6–8 7
9–11 1
12–14 1
Children of U.S. Presidents
20
16
12
8
4
0
0–2
3–5
6–8
9–11
12–14
Number of children

LESSON
7.7
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice C
For use with pages 445–452
Find the range and the standard deviation of the data set.
1. 1, 4, 3, 2, 1, 2, 1, 3, 1
2. 6.5, 7.1, 6.8, 6.6, 6.8, 7.0
3. 105, 106, 104, 105, 107, 106
4. 20, 18, 36, 16, 16, 17, 21
5. Test Scores The bar graphs below represent three collections of test
scores. Which collection has the smallest standard deviation?
A.
9
B.
9
C.
8
8
7
7
6
6
5
5
4
4
3
3
2
2
1
1
0
60 65 70 75 80 85 90 95
0
60 65 70 75 80 85 90 95
6. Critical Thinking Find the mean and median of the following data sets.
When is the median a more accurate measure of central tendency?
a. 1, 1, 2, 3, 3, 2, 1, 50, 1, 3
b. 20, 25, 30, 24, 26, 1, 28, 25, 26, 28
Breakfast Cereals In Exercises 7–9, use the following information.
The number of calories in a 1-ounce serving of ten popular breakfast cereals is
116, 113, 104, 110, 119, 101, 106, 110, 106, 89.
7. Find the range of this data. 8. Find the mean of this data.
9. Find the standard deviation of this data. Round to three decimal places.
Manufacturing Couplers In Exercises 10–12, use the following information.
A company that manufactures hydraulic couplers takes ten samples from one machine
and ten samples from another machine. The diameter of each sample is measured with a
micrometer caliper. The company’s goal is to produce couplers that have a diameter of
exactly 1 inch. The results of the measurements are shown below.
Machine #1: 1.000, 1.002, 1.001, 1.000, 1.002, 0.999, 1.000, 1.002, 1.001, 1.001
Machine #2: 0.998, 0.999, 0.999, 1.000, 0.998, 0.999, 1.000, 1.000, 1.001, 0.999
10. Find the mean diameter for each machine. 11. Find the standard deviation for each machine.
12. Which machine produces the more consistent diameter?
History In Exercises 13–15, use the following information.
The table at the right gives the number of
children of the Presidents of the United States.
13. Make a frequency distribution of the data set using five intervals beginning with 0–2.
14. Draw a histogram of the data set.
9
8
7
6
5
4
3
2
1
0
60 65 70 75 80 85 90 95
Number of Children of U.S. Presidents
0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3,
3, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 6, 6, 6, 6, 6, 7, 8, 10, 14
15. Based on the histogram, which is the better measure of central tendency, the mean or median?
Algebra 2 99
Chapter 7 Resource Book
Lesson 7.7

Answer Key
Test A
Graph 1–6 on graph paper
1. y
2.
Domain: Domain:
all real numbers all real numbers
Range: y > 0 Range: y > 1
3. y
4. y
Domain: Domain: x > 0
all real numbers Range: all real numbers
Range: y > 0
5. y
6.
y
1
1
2
1
1
1
x
x
x
Domain: Domain:
Range: all real numbers
all real numbers Range:
7. 8. 9. 4 10. 3 11. 12.
13. 14. 0 15. 1 16. 17. 5 18. 3
19. 4 is extraneous 20. exponential growth
21. 22. 23.
24. 25. 26. 1.431
27. 28.
29. y 20,000.90 $18,000 30. $1127.50
t y 2x
;
12
y 1
4 2x log 7x ln 3 ln x ln y
3
y 5 1.398 1.079
x
e
3
e
3 1
2
4
8
5
x > 1
y > 0
1
1
1
1
y
1
1
x
x
x

CHAPTER
8
NAME _________________________________________________________ DATE
Chapter Test A
For use after Chapter 8
____________
Graph the function. State the domain and range.
1. 2. y 2x1 y 2 1
x
3. y 4. y log x
1
1
3 ex
y
Copyright © McDougal Littell Inc.
All rights reserved.
1
1
1
Simplify the expression.
10. log3 27
11.
y
y
1
1
x
x
5. 6. y 2ex y ln x 1
x
7. 8. 3ee 9. log 10,000
2 e
3e2 e4 e3 3
e
Evaluate the expression without using a calculator.
12. 13. 14. 15. ln e1 log2 0.5 log12 4 log3 1
Solve the equation. Check for extraneous solutions.
16. 10 17. log32x 1 2
18. log54x 1 log52x 7 19. log2y 4 log2y 5
3x5 10x3 1
y
1
1
1
y
y
1
1
x
x
x
Answers
1. Use grid at left.
2. Use grid at left.
3. Use grid at left.
4. Use grid at left.
5. Use grid at left.
6. Use grid at left.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
Algebra 2 119
Chapter 8 Resource Book
Review and Assess

Review and Assess
CHAPTER
8
CONTINUED
NAME _________________________________________________________ DATE ____________
Chapter Test A
For use after Chapter 8
20. Tell whether the function f x 4 represents exponential
growth or exponential decay.
3
21. Find the inverse of the function y log5x. Use log 5 ≈ 0.699 and log 12 ≈ 1.079 to approximate the
value of the expression.
22. 23.
24. Condense the expression
25. Expand the expression
26. Use the change-of-base formula to evaluate the expression
27. Find an exponential function of the form y ab whose graph
passes through the points 2, 1 and 3, 2.
x
log 25
3 log x log 7.
ln 3xy.
log5 10.
28. Find a power function of the form y ax whose graph passes
through the points 4, 4 and 16, 8.
b
29. Car Depreciation The value of a new car purchased for $20,000
decreases by 10% per year. Write an exponential decay model for
the value of the car. Use the model to estimate the value after one
year.
30. Earning Interest You deposit $1000 in an account that pays 6%
annual interest compounded continuously. Find the balance at the
end of 2 years.
120 Algebra 2
Chapter 8 Resource Book
2 x
log 1
12
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Test B
Graph 1–6 on graph paper
1. y
2.
2
Domain: Domain: x > 0
all real numbers Range:
Range: y > 0
all real numbers
3. y
4.
y
2
Domain: Domain:
all real numbers all real numbers
Range: y > 1
Range: y > 0
5. y
6.
y
1
1
1
2
x
x
x
Domain: Domain:
all real numbers all real numbers
Range: Range:
7. 8. 9. 10. 5 11.
12. 13. 14. 0 15. 3 16. 16
17. 1 18. 19. 6 is extraneous
20. exponential growth 21.
22. 6.644 23. 24.
25. 26. 3.169
27. 28.
29. y 18,000.88 $13,939 30. $1161.83
t y 2.583x
;
0.6309
y 1001 2 x
log
ln 5 ln x ln 2
7
y 7
0.903
b
x
e
4 4
ln 5 2
7
2
8
y > 3
0 < y < 4
e
e
1
y
2
1
1
1
1
x
x
x

CHAPTER
8
NAME _________________________________________________________ DATE
Chapter Test B
For use after Chapter 8
____________
Graph the function. State the domain and range.
1. y 3 2. y 2 log x
x
Copyright © McDougal Littell Inc.
All rights reserved.
1
3. y 3 4.
x1 1
1
1
Simplify the expression.
7. 8. 2e4ee 9.
3 e
2e1 10. log5 3125
11.
y
y
y
1
1
1
x
x
4
5. 6. y
1 2ex y 3x 3
x
e 3 e 2 e
e 1
Evaluate the expression without using a calculator.
12. 13. 14. 15. ln e3 log2 0.0625 log12 16 log12 1
Solve the equation. Check for extraneous solutions.
16. 17.
18. 2e 19. 2 log5x log52 log52x 6
x 10
1 9
4x1 log4 x 2
1000
1
y
y 2
3 ex
1
1
1
y
y
1
1
log 1
100
x
x
x
Answers
1. Use grid at left.
2. Use grid at left.
3. Use grid at left.
4. Use grid at left.
5. Use grid at left.
6. Use grid at left.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
Algebra 2 121
Chapter 8 Resource Book
Review and Assess

Review and Assess
CHAPTER
8
CONTINUED
NAME _________________________________________________________ DATE ____________
Chapter Test B
For use after Chapter 8
20. Tell whether the function y represents exponential growth or
exponential decay.
1
4e2x 21. Find the inverse of the function y log7x. Use and to approximate the
value of the expression.
22. 23.
24. Condense the expression
25. Expand the expression
26. Use the change-of-base formula to evaluate the expression
27. Find an exponential function of the form y ab whose graph
passes through the points 1, 50 and 2, 25.
x
ln
log2 9.
5x
2 .
log
log 7 log b.
1
log210 ¯ 3.322 log 8 ¯ 0.903
log2 100
8
28. Find a power function of the form y ax whose graph passes
through the points 2, 4 and 6, 8.
b
29. Car Depreciation The value of a new car purchased for $18,000
decreases by 12% per year. Write an exponential model for the
value of the car. Use the model to estimate the value after two
years.
30. Earning interest You deposit 1000 in an account that pays 5%
annual interest compounded continuously. Find the balance at the
end of 3 years.
122 Algebra 2
Chapter 8 Resource Book
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Test C
Graph 1–6 on graph paper
1. y
2.
Domain: Domain: x > 0
all real numbers Range:
Range: y > 0 all real numbers
3. y
4.
y
Domain: Domain:
all real numbers all real numbers
Range: y > 0 Range: y > 0
5. y
6. y
1
1
2
1
1
1
x
x
x
Domain: Domain:
Range: all real numbers
all real numbers Range:
7. 8. 9. 10. 5 11.
12. 13. 14. 0 15. 2 16. 625
17. 2, 18. 8; is extraneous 19. 2
20. exponential decay 21. 22. 4.428
23. 1.176 24. 25.
26. 2.481 27. 28.
29. y 28,000.92 $18,454 30. $1053.22
t y 3.227x
;
0.631
y 3x y 8
log424 ln 2 ln y ln x
x
9e 3
2
2 3
2 4
2 e 4
x > 0
y > 0
1
10
y
1
2
2
1
x
x
x

CHAPTER
8
NAME _________________________________________________________ DATE
Chapter Test C
For use after Chapter 8
____________
Graph the function. State the domain and range.
y 3
1. 2.
y 1
3. 4.
1
2 x
y
Copyright © McDougal Littell Inc.
All rights reserved.
1
1
2 x1
1
Simplify the expression.
7. 8. 3e 9.
2
ee3 10. log2 32
11.
y
y
1
1
x
x
x
4e 4
e 5 e
2
y log 4 x
50
5. 6. y
1 125ex y lnx 2
log 1
1000
Evaluate the expression without using a calculator.
12. 13.
14. 15. ln e2 log2 0.25
log12 8
log2 1
Solve the equation. Check for extraneous solutions.
16. 17. 10x2 log5 x 4
1 100,000
1
y e x
10
y
y
1
2
1
y
1
x
x
x
Answers
1. Use grid at left.
2. Use grid at left.
3. Use grid at left.
4. Use grid at left.
5. Use grid at left.
6. Use grid at left.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
Algebra 2 123
Chapter 8 Resource Book
Review and Assess

Review and Assess
CHAPTER
8
CONTINUED
NAME _________________________________________________________ DATE ____________
Chapter Test C
For use after Chapter 8
18. 2 log3y log34 log3y 8
19. ln3x 1 lnx 5 0
20. Tell whether the function represents exponential
growth or exponential decay.
21. Find the inverse of the function y log8x. Use and 15 to approximate the
value of the expression.
log8100 2.214
24. Condense the expression
25. Expand the expression
26. Use the change-of-base formula to evaluate the expression
27. Find the exponential function of the form whose graph
passes through the points and
28. Find a power function of the form y ax whose graph passes
through the points 2, 5 and 8, 12.
29. Car Depreciation The value of a new car purchased for $28,000
decreases 8% per year. Write an exponential decay model for the
value of the car. Use the model to estimate the value after 5 years.
1
30. Earning Interest You deposit $800 in an account that pays 52%
annual interest compounded continuously. Find the balance at the
end of 5 years.
b
3, 0, 1.
1
y ab
27
x
ln
log7125. 2y
x .
log43 3 log42. 124 Algebra 2
Chapter 8 Resource Book
f x 31 2 2
log 1
≈ 1.176
22. log810,000 23. log 15
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Cumulative Review
13
1.
7
2.
1
3. 4. 20
13
5. 6. 2.25
4
7. 8.
1
9. 10.
1
11. 12.
1
y
y
y
4
1
1
1
3
x
x
x
13. 14.
15. 16. 17.
18. 19. 20.
21. 22. 23. 24.
25. 26. 27.
28. 29. 30.
31.
32.
33.
34.
35.
36.
37. 38. 39. 0, 2 40. 11, 8
41. 3, 3 42. 4, 1 43. 33 44. 102
2
y 2x
4, 1
3
2 y 5x
6x 5
2 y 9x
20x 22
2 y 2x
18x 4
2 y 2x
12x 19
2 y x
13x 15
2
7x 12
1
y y x 1 x 2
y 5 1, 5 2, 1
0, 5 2, 3 4, 1 2, 0
2, 1 5, 3 2, 0
6, 5 12, 2
1
2 , 3
3
y
5
4x 4
2
23
y 95
x 5
3x 60
14
1
1
1
y
y
y
1
1
1
x
x
x
45. 46. 47. 48.
49. 50. 51.
52. 53. 54. 1 i
55. 2 ±2 56.
5 ±i3
2
57. 3 ± 17
3
16 8
5 5 2 2i
i
52
1
3
25
5
14
8
3 4i 45 11i 5 12i
58.
2 ±6
2
59.
3 ±15
3
60.
5
, 1
2 2
61. 0; one real solution 62. 1; two real
solutions 63. 23;
two imaginary solutions 64.
160; two real solutions 65. 0; one real
solution 66. 81; two real solutions 67.
1
25
68.
1
69. 729 70. 27 71.
1
72.
216
73. 74. 75. 2x 1
5
x 2 x 2
3x 2
76. x 77. x 3 2 x 3
4
2x 1
78. x 79. 25 80. 32
2 2x 5
x2 5
17
3
729
81. 82. 125 83. 11 84. 8, 2
3x 1
x 2 3
85. $109,556.16 86. 1.9 years 87. $1176.43
9
4

Review and Assess
CHAPTER
8 Cumulative Review
NAME _________________________________________________________ DATE ____________
For use after Chapters 1–8
Solve the equation. (1.3)
1. 2. 3.
4. 5.
1
4x 6. x 0.05 2.3
1
5 3
5x 1
3a 5 7a 8
x 5 4 32 x
10b 5 5b
2
3 a 2 6 18
8
Use slope-intercept form to graph the equation. (2.3)
7. 8. y 9.
10. 4x 2y 8
11. 3x 6y 18
12.
1
y 3x 1
3x 2
Write an equation of the line from the given information. (2.3, 2.4)
13. The line passes through 2, 1 and 7, 8.
2
14. The line has a slope of and a y-intercept of 60.
15. The line passes through and is perpendicular to the line y
16. The line passes through 3, 4 and is parallel to the line that passes through 3, 8 and 5, 10.
4
1, 2
3x 3.
17. The line passes through 2, 6 and is parallel to x 8.
18. The line passes through 3, 5 and is perpendicular to x 10.
Graph the linear system and estimate the solution. Then check the
solution algebraically. (3.1)
19. 4x 2y 14
20. x 3y 5
21. 5x 2y 10
3x 5y 22
22. 3x 2y 12
23. 3x 5y 7
24. 5x 3y 10
2x y 1
Use an inverse matrix to solve the linear system. (4.5)
25. 4x 2y 10
26. x y 8
27. 4x 2y 8
3x y 7
28. 2x 3y 27
29. x 5y 2
30. 4x 9y 5
3x y 23
Write the quadratic function in standard form. (5.1)
31. 32. 33.
34. 35. 36. y 1
22x 32 1
y 5x 2 2
2 y 3x 2 2
2 y 2x 3
6x
2 y x 3x 4
y x 52x 3
1
Solve the quadratic equation. (5.2)
37. 38. 39.
40. 41.
42 3x2 5x 7 2x2 5a
2x 11
2 16 4a2 a 7
2 30x
19a 88 0
2 9a 60x 0
2 x 12a 4 0
2 5x 4 0
Simplify the expression. (5.3)
43. 27
44. 250
45. 5 10
130 Algebra 2
Chapter 8 Resource Book
3
2x 2y 6
2x y 7
2x 8y 14
2x 6y 12
y 5
y 4x
2
2x 3
3
4
4x 3y 15
4x 8y 8
8x 4y 16
6x 6y 5
Copyright © McDougal Littell Inc.
All rights reserved.

CHAPTER
8
CONTINUED
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ____________
Cumulative Review
For use after Chapters 1–8
Simplify the expression. (5.3)
46. 47.
2
5
48.
1
9
Write the expression as a complex number in standard form. (5.4)
49. 50. 51. 3 2i
52.
8
2 i
53.
4 3i
2i
54.
7 3i
2 5i
2
i4 3i
6 i7 3i
Solve the equation by completing the square. (5.5)
55. 56. 57.
58. 59. 60. 4r2 3x 9r r 5
2 2x 6x 2 0
2 u
4x 1
2 x 2u 4u 8
2 x 5x 7 0
2 4x 2
Find the discriminant of the quadratic equation and give the
number and type of solutions of the equation. (5.6)
61. 62. 63.
64. 65. 66. 4x2 64x 9x 0
2 4x 16x 1 0
2 3x
10 0
2 2x x 2 0
2 x 5x 3 0
2 4x 4 0
Evaluate the expression. (6.1)
5 4 5 2
67. 68. 69.
70. 71. 9 72.
3 90 1
3 3
Divide using polynomial long division. (6.5)
73. 74.
75. 76.
77. 78. x 4 2x3 5x2 10x 5 x2 x 5
3 3x2 6x 8 x2 2x
3
3 x2 6x 7x 7 2x 1
2 2x
x 3 3x 2
2 x 3x 2 2x 1
2 6x 8 x 4
Solve the equation. Check for extraneous solutions. (7.6)
79. 80. 81. 23x 1
82. x 25 10
83. x 8 x 2
84. x 5 20x 9
85. Land Value You purchased land for $50,000 in 1980. The value of the
land increased by approximately 4% per year. What is the approximate
value of the land in the year 2000? (8.1)
12 x 8
15 x 2 0
32 125
86. Depreciation You buy a new car for $21,000. It depreciates by 10.5%
each year. Estimate when the car will have a value of $17,000. (8.2)
87. Continuous Compounding You deposit $850 in an account that pays
6.5% annual interest compounded continuously. What is the balance after
5 years? (8.3)
62 65 7
32
3 3 2
2
3 2
Algebra 2 131
Chapter 8 Resource Book
Review and Assess

Answer Key
Practice A
1. F 2. B 3. A 4. E 5. C 6. D
7. Shift graph of f 2 units up. 8. Shift graph of f
5 units down. 9. Shift graph of f 1 unit left.
10. Shift graph of f 3 units right. 11. Reflect
graph of f across x-axis. 12. Shift graph of f
2 units up. 13. 1; x-axis 14. 1; x-axis
15. 2; x-axis 16. x-axis 17. 2;
x-axis
1
4 ;
18. x-axis 19. a. $2100 b. $2101.89
c. $2102.32
1
2 ;

Lesson 8.1
LESSON
8.1
Practice A
For use with pages 465–472
14 Algebra 2
Chapter 8 Resource Book
NAME _________________________________________________________ DATE ___________
Match the function with its graph.
1. 2. 3.
4. 5. 6.
A. B. C.
1
( 0, )
1
f x
y
y
(1, 6)
1
(0, 1)
1 x
2
2
(0, 2)
(1, 3)
1
2 3x f x
1
2 3x f x 23
x f x 3
x
f x 3x D. y
E. y
F.
1
(0, 2)
2
x
Explain how the graph of g can be obtained from the graph of f.
3 x
7. 8. f x 2 9.
x
f x 4
10. 11. f x 2 12.
x
f x 5x g x 2x g x 5
4
3 x
2
g x 5 x3
1
(1, 6)
x
g x 2 x
Identify the y-intercept and asymptote of the graph of the function.
13. 14. 15. y 24x y
6
y 3x 16. 17. 18. y
19. Account Balance You deposit $2000 in an account that earns 5% annual
interest. Find the balance after 1 year if the interest is compounded with
the given frequency.
a. annually b. quarterly c. monthly
1
4 4x y 24
x y
1
2 4x ( 0, )
1
2
5 x
1
1
( 1, )
3
2
x
f x 23 x
f x 5
3 x
g x 5
3 x1
f x 32 x
g x 32 x 2
y
1
(0, 1)
1
(1, 3)
Copyright © McDougal Littell Inc.
All rights reserved.
y
1
( 1, )
3
x
2
x

Answer Key
Practice B
1. B 2. A 3. C 4. E 5. F 6. D
7. Shift the graph of f 1 unit right and 2 units up.
8. Shift the graph of f 2 units left and reflect
across the x-axis. 9. Shift the graph of f 2 units
left and 4 units down. 10. 3; y 2
11.
1
x-axis 12. 1; y 2
27 ;
13. y 14.
15. y 16.
17. y 18.
19. y 20.
21. y 22. 25.2; 1.15; 15%
24. 88.7
1
2
1
1
1
1
1
1 x
x
1 x
2 x
x
23.
1
Number of computers
(per thousand people)
y
2
1
C
45
40
35
30
25
1
1
y
1
y
y
1
1
0
0 1 2 3 4 t
Years since 1991
x
x
x
x

LESSON
8.1
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice B
For use with pages 465–472
Match the function with its graph.
1. 2. f x 3.
4
f x 2
4
2
(1, 3)
3 x
D. y
E. y
F.
Explain how the graph of g can be obtained from the graph of f.
2 x
7. 8. f x 10 9.
x
f x 1
g x 1
2 x1
2
Identify the y-intercept and the asymptote of the graph of the function.
10. 11. 12. y 3x1 y 3 2
x3
y 3x 2
Graph the function.
13. 14. 15.
16. 17. 18. y 2x1 y 3 3
x1 y 2 2
x y 3
3
x y 2 1
x3
y 4x2 19. 20. y 3 21.
x2 y 2 1
x1 4
Computer Usage In Exercises 22–24, use the following information.
From 1991 through 1995, the number of computers C per 100 people worldwide can
be modeled by C 25.21.15 where t is the number of years since 1991.
t
22. Identify the initial amount, the growth factor, and the annual percent increase.
23. Graph the function.
1
(1, 1)
1
(0, 1)
( 0, 3 )
1
3
1
1
x
x
( 1, 2 )
3
4
( 0, )
1
3
3 x1
g x 10 x2
24. Estimate the number of computers per 1000 people worldwide in 2000.
1
1
(0, 3)
1
1
x
(2, 3)
x
f x 4
3 x2
1
4. 5. 6. f x 3
A. y
B. y
C.
y
x1 f x 3 2
x1
f x 3x1 1
( 0, )
1
3
f x 3 x
g x 3 x2 4
y 3
2 x2
1
Algebra 2 15
Chapter 8 Resource Book
y
1
(2, 0)
1
1
( 0, )
7
9
(2, 3)
x
x
Lesson 8.1

Answer Key
Practice C
1. 1; y 2
1
2. x-axis 3. 7; y 4
1
4. x-axis 5. 6; 6. 3.2 10
x-axis 7. domain: all real numbers; range: y > 3
5 75 y 7
;
;
8. domain: all real numbers; range: y > 2
9. domain: all real numbers; range: y > 4
10. domain: all real numbers; range: y > 2
11. domain: all real numbers; range: y > 4
12. domain: all real numbers; range: y < 3
13. y
14.
15. y 16.
17. y 18.
19. y 20.
21. y
2
1
1
1
1
1
1
1
1
1
x
x
x
x
x
5 ;
1
1
y
1
2
1
y
1
y
y
1
1
x
x
x
x
22. y All three graphs have a
23.
a. y
b.
c.
x
y 2
Cost of tuition
(dollars)
( )
4
3
y x
y 3x
2
2
2
C
30,000
25,000
20,000
15,000
y
0
0
y
28. 1994 29. $60,254.15
1
y 2x
1
1
y
( )
3
2
( )
4
3
x
x
x
y 2x
x
x
y-intercept of 1. The larger
a is, the steeper the graph.
Reflection across the
y-axis
24. a. $1077.80
b. $1077.88
c. $1077.88
25. yes; $1077.88
27.
26. C 15,0001.072t 1 2 3 4 5 6 7 8 9 t
Years since 1990
y 3x
3
y
1
y 3x
x

Lesson 8.1
LESSON
8.1
Practice C
For use with pages 465–472
16 Algebra 2
Chapter 8 Resource Book
NAME _________________________________________________________ DATE ___________
Identify the y-intercept and asymptote of the graph of the function.
1. 2. 3.
4. 5. 6. y 1
2 5x6 y 3
x y 7
1
3 5x2 y 35
x y 5 4
x1
y 5x 2
State the domain and range of the functions.
7. 8. 9.
10. 11. 12. y 23x1 y 32 3
x y 7 4
x5 y 6
2
x1 y 5 4
x3 y 8 2
x1 3
Graph the function.
13. 14. 15. y 22x1 y 4
3
y 4 2
x2 1
16. 17. 18. y 3x12 y 3 1
3x2
1
2
y 32x1 4
19. 20. y 21.
1
2 2x1 y 2 5
x32 1
3
22. Visual Thinking Sketch the graphs of on
the same coordinate plane. Explain how the value of a in the equation
affects the graph. Assume that
23. Visual Thinking Sketch the following pairs of graphs in the same
coordinate plane. Assuming explain the difference between
and y ax y a
.
x
y a a > 0.
a > 0,
x
y 2x , y 3x , and y 3
a. b. y 3 c.
x
y 2x y 2 x
24. Account Balance You deposit $1000 in an account that earns 2.5%
annual interest. Find the balance after 3 years if this interest is
compounded with the given frequency.
a. monthly b. daily c. hourly
25. Use your results from Exercise 24 to determine if there is a limit to how
much you can earn. If there is a limit, what is the maximum amount?
College Tuition In Exercises 26–29, use the following information.
In 1990, the tuition at a private college was $15,000. During the next 9 years,
tuition increased by about 7.2% each year.
26. Write a model giving the cost C of tuition at the college t years after 1990.
27. Graph the model.
28. Estimate the year when the tuition was $20,000.
29. Estimate the tuition in 2010.
y 3 x
2 x3
2 x
y 32 x13 1
2
y 4
3 x
y 4
3 x
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice A
1. exponential decay 2. exponential growth
3. exponential growth 4. exponential decay
5. exponential decay 6. exponential growth
7. A 8. E 9. D 10. F 11. C 12. B
13. 1; x-axis 14. 1; x-axis 15. 2; x-axis
1
4 ;
16. x-axis 17. x-axis 18. x-axis
5;
19. 8.78 grams
2
3 ;

LESSON
8.2
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice A
For use with pages 474–479
Tell whether the function represents exponential growth or
exponential decay.
1. 2. f x 3.
5
f x 2
4. 5. f x 6.
1
f x 0.7x Match the function with its graph.
3 x
7. 8. y 9.
1
y 1
10. 11. y 2 12.
A. y
B. y
C.
1
1
y 1
2 1
3 x
(0, 1)
D. y
E. y
F.
1
(0, 2)
1
Identify the y-intercept and asymptote of the graph of the function.
3 x
3 x
3
1
1
( 1, )
1
3
( 1, )
2
3
x
x
( 0, )
1
2
(0, 1)
13. 14. y 0.3 15.
x
y 2
16. 17. 18.
19. Radioactive Decay Ten grams of Carbon 14 is stored in a container. The
amount C (in grams) of Carbon 14 present after t years can be modeled by
C 100.99987 How much Carbon 14 is present after 1000 years?
t y 5
.
1
2 x
y 1
4 8
9 x
4 x
3 x
3 x
3 x
2
( 1, )
1
6
2
( 1, )
1
3
x
x
f x 6 x
f x 1
2 3x
y 2 1
3 x
y 1
2 1
3 x
( 0, )
1
2
y 2 1
3 x
y 2
3 1
5 x
Algebra 2 29
Chapter 8 Resource Book
2
1
y
y
1
( 1, )
1
6
3 x
2
3
(0, 2) ( 1, )
x
Lesson 8.2

Answer Key
Practice B
1. exponential decay 2. exponential growth
3. exponential decay 4. E 5. A 6. C
7. F 8. D 9. B
10. y
11.
12. y
13.
1
14. y 15.
16. $1.14 17.
18. 1995
1
1
1
1
1
Value of a dollar
x
x
x
V
1.24
1.18
1.12
1.06
1.00
.94
0
0
1 2 3 4 5 6 7 8 9 t
Years since 1990
1
y
1
1
1
y
1
y
x
1 x
x

Lesson 8.2
LESSON
8.2
Practice B
For use with pages 474–479
30 Algebra 2
Chapter 8 Resource Book
NAME _________________________________________________________ DATE ___________
Tell whether the function represents exponential growth or
exponential decay.
1. 2. f x 3.
1
3 7
5 x
f x 1
2 5
7 x
Match the function with its graph.
4. 5. 6.
7. 8. 9. y
A. y
B. y
1
C.
1
5 x
y 3 1
5 x2
y 2 1
1
5 x
y
3
1
5 x3
y 1
5 x2
y 1
5 x
(2, 1)
D. y
E. y
F.
(2, 2)
Graph the function.
2 x
1
1
( 0, 22
25 )
10. 11. y 2 12.
1
y 2 4
1
3
5 x3
( 0, 1
25)
1
1
x
x
(1, 5)
5 x1
13. 14. y 15.
3
y 2 3
1
Value of the Dollar In Exercises 16–18, use the following information.
From 1990 through 1998, the value of the dollar has been shrinking. That is,
you cannot buy as much with a dollar today as you could in 1990. The
shrinking value can be modeled by V 1.240.973 where t is the number of
years since 1990.
16. How much was a 1998 dollar worth in 1993?
17. Graph the model.
18. Estimate the year in which the 1998 dollar was worth $1.07.
t ,
1
3 x
2
(0, 1)
(1, 5)
(0, 1)
1
x
x
f x 34 x
25
(1, 13)
y
(0, 125)
1
2
y 3 1
4 x1
y 1
2 x2
1
y
(0, 5)
Copyright © McDougal Littell Inc.
All rights reserved.
1
(3, 1)
x
x

Answer Key
Practice C
1. exponential decay 2. exponential growth
3. exponential decay 4. exponential growth
5. exponential growth 6. exponential decay
7. 4; y 3 8. x-axis 9. x-axis
10. domain: all real numbers; range: y > 3
11. domain: all real numbers; range: y > 4
12. domain: all real numbers; range: y > 1
13. domain: all real numbers; range: y > 2
14. domain: all real numbers; range: y > 7
15. domain: all real numbers; range: y < 4
16. y
17.
18. y
19.
1
1
1
20. y 21.
2
1
22. y 23. y
1
1
1
8
27 ;
x
x
x
x
3
16 ;
1
1
1
y
1
1
y
y
1
1
1
x
x
x
x
24. 25. y 250,0000.88
26. $131,932.98
t
y
1
1
x
27. 28. 10 years
Value (dollars)
y
(0, 250,000)
250,000
200,000
150,000
100,000 (5, 131,932.98)
50,000
0
0
1 2 3 4 5 6 7 8 9 t
Years since purchase
29. y 30. $747.68
830,
8300.87t14 0 ≤ t ≤
,
1
4
t > 1
4

LESSON
8.2
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice C
For use with pages 474–479
Tell whether the function represents exponential growth or
exponential decay.
1. 2. f x 3.
3
f x 2
4. 5. f x 6.
3
f x 2
Identify the y-intercept and asymptote of the graph of the function.
2 x
3 x
3 x
7. 8. y 9.
2
y 1
3
State the domain and range of the function.
2 x1
10. 11. y 12.
1
y 4
1
3
5 x3
13. 14. 15. y 23x y 3 4
x y 7
3
2
Graph the function.
2 x1
16. 17. y 18.
1
y 2
1
3
3 x1
19. 20. y 2 21.
3
y 3 2
2
2
2 x32
3 x3
3 x2
3 x1
4 x1
3 x1
22. 23. y 2 24.
1
y 3
1
1
4
Equipment Depreciation In Exercises 25–28, use the following information.
A tool and die business purchases a piece of equipment for $250,000. The value
of the equipment depreciates at a rate of 12% each year.
25. Write an exponential decay model for the value of the equipment.
26. What is the value of the equipment after 5 years?
27. Graph the model.
28. Use the model to estimate when the equipment will have a value of
$70,000.
Stereo System In Exercises 29 and 30, use the following information.
You purchase a stereo system for $830. After a 3 month trial period, the value
of the stereo system decreases 13% each year.
29. Write an exponential decay model for the value of the stereo system in
terms of the number of years since the purchase.
30. What was the value of the system after 1 year?
2 x
2 x
f x 3
2 x
f x 2
3 x
y 1
4 3
4 x1
y 2
5 x4
1
y 2 1
2 x3
1
y 1
2 x13
2
y 3 2
3 x12
4
3
Algebra 2 31
Chapter 8 Resource Book
Lesson 8.2

Answer Key
Practice A
1. 54.598 2. 0.368 3. 1096.633 4. 1
5. 0.135 6. 1.948 7. 0.607 8. 9.974
9. exponential growth 10. exponential decay
11. exponential growth 12. exponential growth
13. exponential decay 14. exponential decay
e 8
e 6
e 10
15. 16. 17. 18. 19.
e 5 1
e 5
20. 8e 21. A 22. C 23. B 24. $829.79
25. 273,544
15
e 3

LESSON
8.3
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice A
For use with pages 480–485
Use a calculator to evaluate the expression. Round the result to
three decimal places.
1. 2. 3. 4.
5. 6. 7. e 8.
12
e23 e2 e7 e1 e4 Tell whether the function is an example of exponential growth or
exponential decay.
9. 10. 11.
12. 13. f x e 14.
2x
f x 1
f x e
x e x
f x e x
Simplify the expression.
15. 16. 17.
18. 19.
e
20.
3
e8 e2 e8 e3 e5 e 5
2
Match the function with its graph.
21. 22. f x 2e 23.
A. B. C.
x1
f x 2ex 1
3
y
1
x
24. Continuous Compounding You deposit $725 in an account that pays
4.5% annual interest compounded continuously. What is the balance after
3 years?
25. Population The population P of a city can be modeled by
P 250,000e where t is the number of years since 1990. What was
the population in 1999?
0.01t
e 2
1
y
1
x
f x 2e x
f x e 13x
e 2 5
2e 5 3
f x e 2x
e 0
e 2.3
Algebra 2 41
Chapter 8 Resource Book
1
y
1
x
Lesson 8.3

Answer Key
Practice B
1. 148.413 2. 0.717 3. 0.247 4. 4.113
5. exponential growth 6. exponential decay
7. exponential decay 8. exponential growth
9. exponential decay 10. exponential growth
11. 12. 13. 14. 16e 15. 6
2
3e
e
4 1
e8 16. 17. 18. e 19.
20.
21.
22.
23.
24. y 25.
y 0
26. y 27.
y 2
2e 2x3
2
1
1
1
8e 2x
x
x
y 0
y 1
1
2
y
y
1
e x
x 2 1.5 1 0
f(x) 0.27 0.45 0.74 2
x 1 1.5 2
f(x) 5.44 8.96 14.78
x 2 1.5 1 0
f(x) 14.78 8.96 5.44 2
x 1 1.5 2
f(x) 0.74 0.45 0.27
x 2 1.5 1 0
f(x) 3.02 3.05 3.14 4
x 1 1.5 2
f(x) 10.39 23.09 57.60
1
1
12e 3
x 2 1.5 1 0
f(x) 401.43 88.02 18.09 1
x 1 1.5 2
f(x) 1.95 1.99 2.00
x
x
28. y 29.
y 1
1
1
y 3
30. $1972.34 31. $1978.47
32. Continuous compounding
x
2
y
1
x

Lesson 8.3
LESSON
8.3
Practice B
For use with pages 480–485
42 Algebra 2
Chapter 8 Resource Book
NAME _________________________________________________________ DATE ___________
Use a calculator to evaluate the expression. Round the result to
three decimal places.
1. 2. 3. 4. e2 e1.4 e13 e5 Tell whether the function is an example of exponential growth or
exponential decay.
5. 6. f x e 7.
8. 9. 10.
3x
f x 2e3x f x 1
5 e5x
Simplify the expression.
e 4 2
11. 12. 13.
14. 15. 16. 2ex ex3 3e 4e2 4e32 e
64e 4x
f x 1
2 ex
e 2x e 12x
17. 18. 19.
Complete the table of values. Round to two decimal places.
20. 21. f x 2ex f x 2ex 22. f x e 23.
2x 3
Graph the function and identify the horizontal asymptote.
24. 25. 26.
27. 28. f x 29.
1
f x e3x f x 2e
1
x
f x 2ex 2 e2x 1
f x e 3x 2
Interest In Exercises 30–32, use the following information.
You deposit $1200 in an account that pays 5% annual interest. After 10 years,
you withdraw the money.
30. Find the balance in the account if the interest was compounded quarterly.
31. Find the balance in the account if the interest was compounded
continuously.
32. Which type of compounding yielded the greatest balance?
3e 5
x
f(x)
2 1.5 1 0 1 1.5 2
f x 2e 3x
f x 4e 5x
e
2 1
e
e x1
x
f(x)
2
1.5 1 0 1 1.5 2
x 2 1.5 1 0 1 1.5 2 x 2 1.5 1 0 1 1.5 2
f(x)
f(x)
f x e x 2
f x e 2.5x 3
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice C
1. 5.652 2. 0.074 3. 0.493 4. 15.154
8
5. 6. 7. 8.
8e 14
e 6x2
9. 10. 2e 11. y 1 12. y 4
13. y 0
4x
4
14. y Domain:
All real numbers;
3
Range: y > 1
15. y Domain:
All real numbers;
1
Range: y > 2
16. y
Domain:
All real numbers;
Range: y > 1
2
17.
1
y
1 x
Domain:
All real numbers;
Range: y > 5
Domain:
All real numbers;
Range: y > 1
1
81e 8
1
1
x
x
x
18.
e 6
2
y
1
1
4096e 3x
x
19.
1
y
1 x
Domain:
All real numbers;
Range: y > 3
20. exponential decay
21.
Ratio
(Carbon 14 to Carbon 12)
22. 10,000 years 23. exponential growth
24. 25. 13 units
y
30
26. 26 days
Units produced
25
20
15
10
5
0
0
R
1 1012 8 10 13
6 10 13
4 10 13
2 10 13
0
0
10 20 30 40
Days
2000 4000 6000 8000
Years
t
t

LESSON
8.3
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice C
For use with pages 480–485
Use a calculator to evaluate the expression. Round the result to
three decimal places.
1
1. 2. e 3. e 2
4.
2.6
e3 Simplify the expression.
5. 6. 7.
1
3 e2 4
e22e43 4e 0.5x 6
8. 9. 10.
Identify the horizontal asymptote of the function.
11. 12. 2 e 13.
3x1 f x 3e 4
2x 1
Graph the function. State the domain and range.
f x 2e 3x 1
14. 15. 16.
17. 18. 19.
f x 1
2 e2x1 5
Carbon Dating In Exercises 20–22, use the following information.
Carbon dating is a process to estimate the age of organic material. In carbon
dating the formula used is
R 1
et8233
1012 where R is the ratio of Carbon 14 to Carbon 12 and t is time in years.
20. Is the model an example of exponential growth or exponential decay?
21. Graph the function.
e3x
2e 2
f x 1
f x 2
3 e3x f x
1
1
4 ex 2
22. Use the graph to estimate the age of a fossil whose Carbon 14 to Carbon
12 ratio is 3 1013 .
Learning Curve In Exercises 23–26, use the following information.
The management at a factory has determined that a worker can produce a maximum
of 30 units per day. The model y 30 30e indicates the number
of units y that a new employee can produce per day after t days on
the job.
23. Is the model an example of exponential growth or exponential decay?
24. Graph the function.
25. How many units can be produced per day by an employee who has been
on the job 8 days?
26. Use the graph to estimate how many days of employment are required for
a worker to produce 25 units per day.
0.07t
e2
2 3
38e 12x
e e
f x 245e 0.023x
f x 2e x4 1
f x 5
4 e2x1 3
Algebra 2 43
Chapter 8 Resource Book
Lesson 8.3

Answer Key
Practice A
1. 2. 3.
4. 5. 6. 6 7. 2
8. 5 9. 2 10. 2 11. 0 12. 1 13. 0.778
14. 0.398 15. 0.571 16. 2.079
17. 1.470 18. 1.812 19. x 20. x 21. x
22. x 23. x 24. x 25. A 26. C 27. B
28. C 29. A 30. B 31. 110 decibels
1 2 6
4 7 16
2 3
49
3 5 27
2 2 25
3 8

Lesson 8.4
LESSON
8.4
Practice A
For use with pages 486–492
56 Algebra 2
Chapter 8 Resource Book
NAME _________________________________________________________ DATE ___________
Rewrite the equation in exponential form.
1. log2 8 3
2. log5 25 2
3. log3 27 3
4. log7 49 2
5. log2 16 4
6. log6 6 1
Evaluate the expression without using a calculator.
7. log2 4
8. log2 32
9. log8 64
10. log10 100
11. log7 1
12. log8 8
Use a calculator to evaluate the expression. Round the result to
three decimal places.
13. log 6
14. log 0.4
15. log 3.72
16. ln 8
17. ln 0.23
18. ln 6.12
Simplify the expression.
19. 20. 21.
22. 23. 24. log221221x log1515
x log33
x 13
log13 x
27log27 x
7log7 x
Match the function with its graph.
25. f x log3 x
26. f x log5 x
27.
A. B. C.
1
y
1
Match the function with the graph of its inverse.
28. f x log x
29. f x log13 x
30.
A. B. C.
1
y
1
31. Sound The level of sound V in decibels with an intensity I can be modeled by
I
V 10 log1016,
x
x
1
y
where I is intensity in watts per centimeter. Loud music can have an intensity of 10 watts per
centimeter. Find the level of sound of loud music.
5
1
2
y
1
x
x
f x log 12 x
1
y
1
f x ln x
y
1
Copyright © McDougal Littell Inc.
All rights reserved.
1
x
x

Answer Key
Practice B
1. 2. 3.
4. 5. 6.
7. 0.549 8. 1.061 9. 10. 3
11. 0 12. 13. 14. 15. undefined
16. 17.
18.
19.
20. 21. f
22. y
23. y
1 x 4x2 f 1 x 2x f
1
1 x 10
f
x
2
1 x 1
3 x
f 1 x ex f 1 x 3x 2
0.405
1
1
3
2
3
3 1
5 8
1 1
9 5
12 2
3
0 3 1
4 4 81
2 16
1
24. y
25.
26. y
27.
1
1
1
1
1
x
x
x
28. 127 strides 29. 267.4 miles per hour
1
1
1
y
1
y
1
1
x
x
x

LESSON
8.4
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice B
For use with pages 486–492
Rewrite the equation in exponential form.
1. 2. 3.
4. 5. 6. log2 1
8 3
log5 1
5 1
log log4 16 2
log3 81 4
log2 1 0
1
9 3 2
Use a calculator to evaluate the expression. Round the result to
three decimal places.
7. ln 3
8. log 11.5
9.
Evaluate the logarithm without using a calculator.
10. 11. 12.
13. 14. log5 5 15. log6 1
23
log3 27
log4 1
log8 2
Find the inverse of the function.
16. f x log3 x
17. f x ln x
18.
19. f x log 2x
20. f x log2 x 1
21.
Graph the function.
22. f x log6 x
23. f x 1 log6 x
24.
25. f x log6 x
26. f x log6 2x
27.
28. Galloping Speed Four-legged animals run with two different types of
motion: trotting and galloping. An animal that is trotting has at least one
foot on the ground at all times. An animal that is galloping has all four
feet off the ground at times. The number S of strides per minute at which
an animal breaks from a trot to a gallop is related to the animal’s weight w
(in pounds) by the model
S 256.2 47.9 log w.
Approximate the number of strides per minute for a 500 pound horse
when it breaks from a trot to a gallop.
29. Tornadoes The wind speed S (in miles per hour) near the center of
a tornado is related to the distance d (in miles) the tornado travels by
the model
S 93 log d 65.
Approximate the wind speed of a tornado that traveled 150 miles.
ln 2 3
log 2 1
2
f x log 13 x
f x log 4 16x
f x log 6 x 1
f x 1 log 6 x
Algebra 2 57
Chapter 8 Resource Book
Lesson 8.4

Answer Key
Practice C
1. 2. 3.
4. 5. 0.092 6. 7.
8. 9. 10. 11. 12.
2
8
2.099
1.199 5
3
2 3
13 5 2
3 125
13. f 14.
1 x 4x 15. 16.
17.
18. f
19. y
20.
y
1 x 4
x
2 or f 1 x 1
f
x 2
2 1 x ex1 f
2
1 x 10x 2
3
1
21. y
22.
1
1
1
23. y 24. y
1
3
1
x
x
x
4
3
f 1 x 2x
7
3 3 1
27
f 1 x e x3
1
1
1
3
2
y
1
1
1
x
x
x
25.
26. y 27. no 28. no
29. 41.9 seconds
30. 31. 41.2 seconds
70
65
60
55
50
45
40
35
x 1 1 1 1 1 1 1
y 0
1
1 2
1
2
1
0
1
2
20 40 60 80 100
x
2
2

Lesson 8.4
LESSON
8.4
Practice C
For use with pages 486–492
58 Algebra 2
Chapter 8 Resource Book
NAME _________________________________________________________ DATE ___________
Rewrite the equation in exponential form.
1. log5 125 3
2.
1
2 3.
Use a calculator to evaluate the expression. Round the result to three
decimal places.
ln 2.5
4. ln 3 1
5. 6.
10
Evaluate the expression without using a calculator.
7. 8. 9.
10. 11. log27 12.
1
32
1000
log8 4
log16 8
log 2 1
Find the inverse of the function.
13. f x log4 x
14. f x log2 7x
15.
16. f x ln x 3
17. f x ln x 2 1
18.
Graph the function.
19. f x log3 x
20. f x log3 x 2
21.
22. f x log3 x 2 1 23. f x log3 x 2
24.
Critical Thinking In Exercises 25–28, use the following information.
By definition of a logarithm, the base b of a logarithmic function must be a
positive number and b 1.
25. Assuming that b 1, the “logarithmic function’ would be written y log1 x.
Complete the table of values for this “logarithmic function.”
26. Use the data to sketch a graph.
27. Does the graph look like a typical logarithmic graph?
28. Is the relation a function?
log 1
400-Meter Relay In Exercises 29–31, use the following information.
The winning time (in seconds) in the women’s 400-meter relay at the
Olympic Games from 1928 to 1996 can be modeled by the function
f t 67.99 5.82 ln t, where t is the number of years since 1900.
29. In 1988 the United States team won the 400-meter relay. What was its
winning time?
30. Use a graphing calculator to graph the model.
31. Use the graph to approximate the winning time in the 2000 Olympic Games.
log 8
x
y 0
1
1 2
1
2
1
2
2
9
3
log 3 1
27 3
log 4 3
2
log 100 1
1000
f x log 3x 2
f x log 100 x2
f x log 3 x 1
f x log 3 x 2 1
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice A
1. 2.
3.
4.
5. 6.
7. 8.
9. 10. 11.
12. 13. 14.
15. 16. 17.
18. 19. 20. ln x
log 4
1 1
2 2
6 2 log3 x log 15 log2 7x
log3 14y
log2 x
2 log 2 0.602 log 7 log 2 1.146
log 7 log 2 0.544
log 2 log 7 0.544
3 log 7 2.535 2 log 7 1.69
log2 3 log2 x 2 log3 x
log x log 5 1 log6 x 5 log3 x
3 ln x
1
3 log x
21. 22.
23. 24. log 8x2 ln
log34x 20
2
x 1
log 6 x 2
25.
26.
27.
28.
29.
30.
log 5 ln 5
2.322
log 2 ln 2
log 10
log 7
log 17
log 3
log 200
log 6
log 1
2
log 1235
log 4
ln 10
ln 7
ln 17
ln 3
ln 200
ln 6
2
2.579
ln 1
0.431
log 5 ln 5
ln 1235
ln 4
x
1.183
ln I ln I0
31. t 32.
0.049
2.957
5.135
3
I 2000 3000 4000
t 14.1 22.4 28.3

Lesson 8.5
LESSON
8.5
Expand the expression.
Practice A
For use with pages 493–499
70 Algebra 2
Chapter 8 Resource Book
NAME _________________________________________________________ DATE ___________
Use the properties of logarithms to rewrite the expression in terms
of and Then use and to
approximate the expression.
1. 2. 3.
4. 5. log 7 6. log 49
3
log 2 log 7 log 2 log 7. log 2 ≈ 0.301 log 7 ≈ 0.845
log 4
log 14
2
7. log23x 8. log39x 9.
10. 11. 12. ln x3 log3 x5 6
log6 13. 14. 15. log327x2 log log22x 3 x
Condense the expression.
16. log 3 log 5
17. log2 x log2 7
18. log3 14 log3 y
19. log 4 log x
20. ln x ln 3
21. log x 1 log 6
22. ln 2 ln x 2
23. log3 x 5 log3 4
24. 2 log x log 8
Use the change-of-base formula to rewrite the expression. Then
use a calculator to evaluate the expression. Round your result to
three decimal places.
25. 26. 27.
28. 29. log5 30. log4 1235
1
log2 5
log7 10
log3 17
log6 200
Investments In Exercises 31 and 32, use the following information.
You want to invest in a stock whose value has been increasing by approximately
5% each year. The time required for an initial investment of I0 to grow to I can
be modeled by
t
I 0
7
x
ln I
I 0
0.049 ,
where and I are measured in dollars and t is measured in years.
31. Expand the expression for t.
32. Assume that you have $1000 to invest. Complete the table to show how
long your investment would take to double, triple, and quadruple.
I 2000 3000 4000
t
2
log x
5
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice B
1.
2. 3.
4. 5.
6.
7. 8.
9. 10.
11.
12. 13.
14.
16. 17.
15.
18.
19. 20.
4x
21. log3 2
log2 5
3 x2 y3 log x
log5 3x log4 5xy
4
2
log3 7 1
x
2 log2 x log2 y log2 z
1
log5 2 2 log x log 4
2 log x
1
2 log5 x
1
2 log3 x log3 y log3 z
log 3 log 4 0.125
log 3 log 4 1.079 2 log 3 0.954
2 log 4 1.204 log 4 0.602
log 4 3 log 3 0.829
log6 3 log6 x log2 x log2 5
log x 2 log y log4 x log4 y log4 3
22.
23.
24.
25.
26.
27.
log 6
log
28. pH 6.1 log B log C 29.
30. below normal
31. pH 7.48 log C 32. 1.2
1
ln 6
2 ln 1
log 2.8 ln 2.8
2.539
log 1.5 ln 1.5
2.585
2
pH
pH
9
8
7
6
5
4
3
0
log 12
log 3
log 2 ln 2
0.387
log 6 ln 6
log 0.5
log 4
ln 12
ln 3
log 12 ln 12
11.136
log 0.8 ln 0.8
0 1 2 3 4 5 6 7
Carbonic acid
ln 0.5
ln 4 0.5
C
2.262
7.2

LESSON
8.5
Expand the expression.
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice B
For use with pages 493–499
Use the properties of logarithms to rewrite the expression in terms
of and Then use and to
approximate the expression.
1. 2. 3.
4. 5. log 6.
1
log log 12
log 9
log 16
3
log 3 log 4. log 3 ≈ 0.477 log 4 ≈ 0.602
4
7. 8. 9. log xy2 log2 x
log6 3x
5
10. log4 11. log3 x y z
12. log5 2x
xy
3
13. 14. log 15.
10
log
x
x2
4
Condense the expression.
16. 17.
18. 19.
20.
2
3 21. log3 4 2 log3 x log3 5
log2 x 3 log2 y
1
2 log x log 4
log4 5 log4 x log4 y
log3 7 log3 x
2 log5 x log5 3
Use the change-of-base formula to rewrite the expression. Then
use a calculator to evaluate the expression. Round your result to
three decimal places if necessary.
22. log3 12
23. log6 2
24. log4 0.5
25. log0.8 12
26. log1.5 2.8
27. log12 6
Henderson-Hasselbach Formula In Exercises 28–32, use the following
information.
The pH of a patient’s blood can be calculated using the Henderson-Hasselbach
Formula, pH 6.1 log where B is the concentration of bicarbonate and C is
the concentration of carbonic acid. The normal pH of blood is approximately 7.4.
28. Expand the right side of the formula.
29. A patient has a bicarbonate concentration of 24 and a carbonic acid
concentration of 1.9. Find the pH of the patient’s blood.
30. Is the patient’s pH in Exercise 29 below normal or above normal?
31. A patient has a bicarbonate concentration of 24. Graph the model.
32. Use the graph to approximate the concentration of carbonic acid required
for the patient to have normal blood pH.
B
C ,
4
log 4
27
log 2 x2 y
z
Algebra 2 71
Chapter 8 Resource Book
Lesson 8.5

Answer Key
Practice C
1. 1.792
2. 1.203
3. 3.401
4. 2.485
5.
6.
7. 8.
9.
10.
11.
12. 13.
14.
15.
16. 17. 18. ln x3
y2z4 ln 3xz
log
y
3
ln 3 ln y
3log 3 log x log y 2 log z
4log2 x log2 y 2 log2 z
28
1
1
2 4 ln x
log5 x log5 y
1
2
ln x ln y ln z
1
2 log 3 log x log y
log4 x log4 y log4 z
ln 2 ln 3
ln 2 ln 5 ln 3
ln 2 ln 3 ln 5
2 ln 2 ln 3
ln 2 ln 5 0.916
ln 5 ln 3 ln 2 0.183
log 8 log x log3 x log3 y log3 z
19.
20.
21.
22.
23.
24.
log 2
log 2
x 2x 12
lnx 2x 153 y
y
y
x 4x 15
x 1 3
x 5
x 2
log x
log 3
logx 3
log 6
logx 1
log 2
ln y
or y ln x
ln 3
or y
3 or y lnx 1
ln 2
25.
lnSr Pn ln P ln n
t
nlnn r ln n
26. 19.7 years
lnx 3
ln 6
3

Lesson 8.5
LESSON
8.5
Expand the expression.
Practice C
For use with pages 493–499
72 Algebra 2
Chapter 8 Resource Book
NAME _________________________________________________________ DATE ___________
Use the properties of logarithms to rewrite the expression in terms
of and Then use and
to approximate the expression.
1. 2. 3.
4. 5. ln 6.
2
ln ln 30
ln 12
10
ln 2, ln 3, ln 5. ln 2 ≈ 0.693, ln 3 ≈ 1.099,
ln 5 ≈ 1.609
ln 6
3
7. log 8x
8. log3 xyz
9.
10. ln 11. log 3xy
12.
x
yz
13. 14. log3xyz 15.
23 ln 3y
4 x
Condense the expression.
16. log 3 log 4 log 7
17. ln x ln y ln z ln 3
18. 3 ln x 2 ln y 4 ln z
19. log2x 4 5 log2x 1 3 log2x 1
20.
1
logx 5 2 log x ln y
2
21. 3lnx 2 2 lnx 1 lnx 2 5 lnx 1
Use the change-of-base formula to rewrite the function in terms of
common (base 10) or natural (base ln) logarithms.
22. y log3 x
23. y log6x 3
24. y log2x 1 3
Annuities In Exercises 25 and 26, use the following information.
An ordinary annuity is an account in which you make a fixed deposit at the end
of each compounding period. You want to use an annuity to help you save money
for college. The formula
Sr Pn
ln Pn
t
n r
n ln n
gives the time t (in years) required to have S dollars in the annuity if your periodic
payments P (in dollars) are made n times a year and the annual interest rate is
r (in decimal form).
25. Expand the right side of the formula.
26. How long will it take you to save $20,000 in annuity that earns an annual
interest rate of 5% if you make monthly payments of $50?
5
ln5 6
log 4 2xy
z
log 5 x
y
log 2 xy4
z 2
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice A
1. yes 2. no 3. no 4. no 5. yes 6. no
7. no 8. yes 9. no 10. yes 11. no
12. yes 13. 1
14. 5 15. 2 16. 7
4
3
7
4
17. 18. 19. log29 20. log310 21. ln 5
ln 6
log510 22. 23. log27 24. 25. 7 26. 7
2
3
27. 3 28. 6 29. 30. 31. 32
e
32. 6562 33. 499,998.5 34. 35. 0
2 3
5
36. 25 37. 3.2 years 38. 13.5 years
39. 23.1 years
3
4
3
2

LESSON
8.6
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice A
For use with pages 501–508
Tell whether the x-value is a solution of the equation.
1. 2. 3. ln x 7, x 7e ln x 9, x e ln x 3, x 3e
9
4. 5. 6. ln 2x 14, x 2e14 ln 6x 4, x e4
ln 2x 8, x e
6
8
Tell whether the x-value is a solution of the equation.
7. 8. 9.
10. 11. 12. 5e x 3e 2 17, x ln 3
x 2e 1 11, x 4
x e
8, x ln 4
x e 3, x log 3
x e 7, x ln 7
x 5, x 5
Solve the equation.
13. 14. 15.
16. 17. 18. 10 x 1073x e2x1 e3x e3x e2x7 2 4x1 22x3 32x 3x5 4x 42x1 Solve the equation by taking the appropriate log of each side.
19. 20. 21.
22. 23. 24. 53x 2 2 8
x e 5 12
2x e
6
x 3 5
x 2 10
x 9
Use the following property to solve the equation. For positive
numbers b, x, and y where b 1, logb x logb y if and only if
x y.
25. log x log 7
26. logx 2 log 9
27. log24x log2 12
28. log3x 1 log32x 5 29. lnx 3 ln6 3x 30. log3x 2 logx 1
Solve the equation by exponentiating each side.
31. log2 x 5
32. log3x 1 8
33. log2x 3 6
34. ln5x 3 2
35. ln3x 1 0
36. log4x 1 3
Compound Interest You deposit $100 in an account that earns 3%
annual interest compounded continuously. How long does it take
the balance to reach the following amounts?
37. $110 38. $150 39. $200
Algebra 2 83
Chapter 8 Resource Book
Lesson 8.6

Answer Key
Practice B
1. 2.890 2. 2.544 3. 1.869 4. 1.609
5. 1.585 6. 0.646 7. 0.667 8. 0.805
9. 0.886 10. 0.462 11. 0.576
12. 2.322
13. 0.5 14. 0.973
15. 1.946 16. 1.609 17. 2 18. 1.792
19. 0.229 20. 0.308 21. 0 22. 0.347
23. 1.099 24. 25.850 25. 2.485
26. 1.445 27. 1.528 28. 148.413 29. 0.01
30. 2.828 31. 20.086 32. 100,000 33. 0.001
34. 2980.958 35. 20.086 36. 148.413
37. 10,000 38. 46.416 39. 3 40. 0.4
41. 0.002 42. 300,651.071 43. 21.333 44. 1
45. no solution 46. 1.5 47. no solution
48. 3 49. 11.185 years 50. 20.086

Lesson 8.6
LESSON
8.6
Practice B
For use with pages 501–508
84 Algebra 2
Chapter 8 Resource Book
NAME _________________________________________________________ DATE ___________
Solve the exponential equation. Round the result to three
decimal places if necessary.
1. 2. 3.
4. 5. 6.
7. 8. 9.
10. 11. 12.
13. 14. 15.
16. 17. 18.
19. 20. 21.
22. 23. 24.
25. 26.
2
3 27.
e2x 1
3 12
e x 2
1 5
0.1x 3e 6 12
x 4e 4 13
2x 22
3 5
3x 3e 2
5x 2e 14
4x 3e
5
x 42 18
x 2e 16
x e
10
x e 6 1
2x 4 5 12
2x 2
3 1
x e 1 6
4x e 3 7
3x 3
6 10
2x e 3 4
2x 2 5
3x 5
4
2x 2 8
x e 7 10
x e
3 8
2x 10 42
x e 350
x 18
Solve the logarithmic equation. Round the result to three
decimal places if necessary.
28. ln x 5
29. log10 x 2
30. log2 x 1.5
31. 7 ln x 21
32. 2 log10 x 10
33. 7 log10 x 4
34. 3 ln x 5
35. 4 ln x 1
36. 5 2 ln x 5
37. 3 log10 x 1 13
38. 9 log10 x 4 11
39. log3 3x 2
40. log2 5x 1
41. 2 log3 2x 3
42. ln 4x 6 8
43. 2 log2 3x 8
44. log2 x 2 log2 3x 45. log3 2x 1 log3 x 4
46. ln 5x 1 ln 3x 2 47. ln 2x 3 ln 2x 1 48. ln 4x 9 ln x
49. Compound Interest You deposit $2000 into an account that pays 2%
annual interest compounded quarterly. How long will it take for the
balance to reach $2500?
50. Rocket Velocity Disregarding the force of gravity, the maximum
velocity v of a rocket is given by v t ln M, where t is the velocity of
the exhaust and M is the ratio of the mass of the rocket with fuel to its
mass without fuel. A solid propellant rocket has an exhaust velocity of
2.5 kilometers per second. Its maximum velocity is 7.5 kilometers per
second. Find its mass ratio M.
3
82 3x 1 10
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice C
1. 2.197
2. 0.333 3. 3.386 4. 0.349
5. 1.436 6. 6.447 7. 0.376 8. 1.269
9. 0.258 10. 0 11. 1, 2 12. 1, 0.667
13. 4.5 14. 22,023.466 15. 11 16. 181.939
17. 2.414 18. 1 19. 3 20. 0.143 21. 3.333
22. no solution 23. 2, 3 24. 7 25. 4, 6
26. no solution 27. 0.461 28. 3.697
29. 8.266 30. no solution 31. 5.303
32. 7.193 33. 5.2 years 34. 30 years
35. $211,320 36. $131,320

LESSON
8.6
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice C
For use with pages 501–508
Solve the exponential equation. Round the result to three
decimal places if necessary.
1. 2. 3.
4. 5. 6.
7. 8. 9.
10. 11. 12. 23x1 22x e x2 e 1 x3 e x2
5
3
3 4
e1x 1 9
1
4 2 2
3x1 2
3 2 5
e4x 3
5 8
0.4x e 7 10
53x e 4 6
4x1 3
3 8
2x5 2 7
3x1 e 4
x 9
Solve the logarithmic equation. Round the result to three
decimal places if necessary.
13. 14. 15.
16. 17. 18.
19. 20.
21. 22.
23. logx 24. logx 2 logx 3 logx 29
25. log2 x log2x 2 log2x 3 3
26. log2x 3 log2x 1 log2x 3 1
2 log2x 1 1
lnx 3 2 8
log3x 2 5 7
ln6x 5 7
lnx 2 ln x 0
log2 x log2x 1 1
log3 x log3x 2 1 log2x 1 log2 x 3
log4x 2 log4x 3 2 log3x 2 log2x 1
1 logx 5
Solve the exponential equation. Round the result to three
decimal places.
27. 28. 29. 52x1 24x3 e x3 10 4x
2x1 32x Solve the logarithmic equation. Round the result to three
decimal places.
30. log2x 1 log42x 3 31. log3x 3 log9 x 32. logx 4 log100x 3
33. Compound Interest You deposit $2500 into an account that pays 3.5%
annual interest compounded daily. How long will it take for the
balance to reach $3000?
Loan Repayment In Exercises 34–36, use the following information.
r
1 n
The formula L P1
gives the amount of a loan L in terms
nt
r
n
of the amount of each payment P, the interest rate r, the number of payments
per year n, and the number of years t.
34. When purchasing a home, you need a loan for $80,000. The interest rate
of the loan is 8% and you are required to make monthly payments of
$587. How long will it take you to pay off the loan?
35. When the loan is paid off, how much money will you have paid the bank?
36. How much did you pay in interest?
Algebra 2 85
Chapter 8 Resource Book
Lesson 8.6

Answer Key
Practice A
1. 2. 3.
4. 5. 6.
7. yes 8. no 9. yes 10. yes
11. 12.
13.
14. 15.
16. 17. 18.
19. 20. no 21. yes 22.
23. 24. y x0.8 y x1.3 y x2.4 y x1.5 y 3x2 y 2x3 y 5.079.98t y 3459.922.81t y 3.1024.70t y 171.40186,278.85t y 1.523.33t y 4.961.38t y 2 3x y 2x y 1 24x y 2 5x y 3 2x y 3x

LESSON
8.7
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice A
For use with pages 509–516
Write an exponential function of the form y ab
passes through the given points.
whose graph
1. 0, 1), 3, 27
2. 1, 6, 2, 12
3. 1, 10, 2, 50
4. 1, 2, 2, 8
5. 4, 16, 6, 64
6. 2, 18, 3, 54
x
Use the table of values to determine whether or not an exponential
model is a good fit for the data t, y.
7.
8.
9.
10.
Solve for y.
11. ln y 0.324t 1.601 12. ln y 1.203t 0.418 13. ln y 12.135t 5.144
14. ln y 3.207t 1.132 15. ln y 1.032t 8.149 16. ln y 2.301t 1.624
Write a power function of the form y ax whose graph passes
through the given points.
17. 1, 2, 3, 54
18. 1, 3, 2, 12
19. (1, 1, 4, 8
b
Use the table of values to determine whether or not a power
function model is a good fit for the data x, y.
20.
21.
t 1 2 3 4 5 6 7 8
ln y 0.23 0.64 1.07 1.47 1.88 2.31 2.72 3.12
t 1 2 3 4 5 6 7 8
ln y 1.32 1.52 1.92 2.72 2.88 3.52 4.32 5.6
t 1 2 3 4 5 6 7 8
ln y 0.05 0.17 0.27 0.40 0.52 0.63 0.75 0.85
t 1 2 3 4 5 6 7 8
ln y 12.31 13.56 14.82 16.04 17.29 18.49 19.76 21.01
ln x 0 0.693 1.099 1.386 1.609
ln y 1.264 2.594 3.924 5.254 6.584
ln x 0 0.693 1.099 1.386 1.609
ln y 0.833 2.219 3.030 3.605 4.052
Solve for y.
22. ln y 2.4 ln x
23. ln y 1.3 ln x
24. ln y 0.8 ln x
Algebra 2 97
Chapter 8 Resource Book
Lesson 8.7

Answer Key
Practice B
1. 2. 3.
4. 5. 6. y
7. 8.
5
41 y 1 25x y 62 3 x
y 31 y 1
254x y 1 32x ln y
8
7
6
5
4
3
2
1
0
0 1 2 3 4 5 6 7 8 x
y 42 x
9. 10.
11.
12.
13.
14.
15. y 4.3x1.2 y 3x3.5 y 1.2x1.5 y 2x5 y 1
2x3 y 4x2 ln y
8
7
6
5
4
3
2
1
0
y 21.5 x
16. 17.
ln y
4
3
2
1
0
0 1 2 3 4 ln x
y 1.5x 2
0 1 2 3 4 5 6 7 8 x
ln y
8
y 1.52.4 x
ln y
y 2.4x 1.6
18. y 29.623x ; 3.313 million
0.809
7
6
5
4
3
2
1
0
0 1 2 3 4 5 6 7 8 x
4
3
2
1
3 x
2 x
0
0 1 2 3 4 ln x

Lesson 8.7
LESSON
8.7
Practice B
For use with pages 509–516
98 Algebra 2
Chapter 8 Resource Book
NAME _________________________________________________________ DATE ___________
Write an exponential function of the form
passes through the given points.
whose graph
1.
16
2. 2, 25 3.
, y ab
2 4
1, 2,
64
3, 25
x
8
5 25
4. 1, 4, 2, 5. 1, 2, 6.
Use the table of values to draw a scatter plot of ln y versus x. Then
find an exponential model for the data.
7.
8.
9.
Write a power function of the form y ax whose graph passes
through the given points.
10. 2, 16, 3, 36
11. 2, 4, 4, 32
12. 2, 64, 3, 486
13. 4, 9.6, 9, 32.4
14. 4, 384, 16, 49,152 15. 2, 9.879, 3, 16.070
b
Use the table of values to draw a scatter plot of ln y versus ln x.
Then find a power model for the data.
16.
17.
3 ,
3
3
2 ,
18. Consumer Magazines The table shows the circulation of the top 10 consumer
magazines in 1997 where x represents the magazine’s ranking. Use
a graphing calculator to find a power model for the data. Use the model to
estimate the circulation of the 15th ranked magazine.
2
3
2, 4 ,
3, 3
8
5
2, 36 , 5
3, 108
x 1 2 3 4 5 6 7 8
y 8 16 32 64 128 256 512 1024
x 1 2 3 4 5 6 7 8
y 3.6 8.64 20.736 49.766 119.439 286.654 687.971 1651.13
x 1 2 3 4 5 6 7 8
y 3 4.5 6.75 10.125 15.188 22.781 34.172 51.258
x 1 2 3 4 5 6 7 8
y 1.5 6 13.5 24 37.5 54 73.5 96
x 1 2 3 4 5 6 7 8
y 2.4 7.275 13.919 22.055 31.518 42.194 53.997 66.858
Rank Circulation Rank Circulation
(millions) (millions)
1 20.454 6 7.615
2 20.432 7 5.054
3 15.086 8 4.643
4 13.171 9 4.514
5 9.013 10 4.256
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice C
1. 2.
3. 4.
5.
6.
ln y lnabx y ab
x
y 1.52x y 43.5x y 5.32.8x y 4.50.2x y 2.31.6x ln y ln a ln b x
ln y ln a x ln b
constant
Thus, there is a linear relationship between x and ln
y. 7. 8.
9. 10. 11.
12.
constant
Thus, there is a linear relationship between ln x and
ln y. 13.
14. y 30.84x 15. The exponential model is
better because the relationship between x and ln y is
closer to linear than the relationship between ln x
and ln y.
0.33
y 28.381.14x ln y ln a ln x
ln y ln a b ln x
b
ln y ln axb y axb y 2.5x2.5 y 3x1.2 y 8.3x0.25 y 2.4x1.5 y 1.5x0.5

LESSON
8.7
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice C
For use with pages 509–516
Write an exponential function of the form y ab
passes through the given points.
whose graph
1. 2, 5.888, 3, 9.4208
2. 1, 0.9, 2, 0.18
3. 2, 41.552, 3, 116.3456
x
Find an exponential model for the data.
4.
5.
6. Critical Thinking To determine whether an exponential model fits the data, you
need to determine whether the data of the form is linear. To see that this test
works, start with y ab take the natural logarithm of both sides, and use the properties
of logarithms to verify that there is a linear relationship between x and ln y.
x x, ln y
,
Write a power function of the form y ax whose graph passes
through the given points.
7. 4, 3, 9, 4.5
8. 4, 19.2, 9, 64.8
9. 16, 16.6, 81, 24.9
b
Find a power model for the data.
10.
11.
x 1 2 3 4 5 6 7 8
y 14 49 171.5 600.25 2100.9 7353.1 25,736 90,075
x 1 2 3 4 5 6 7 8
y 3 6 12 24 48 96 192 384
x 1 2 3 4 5 6 7
y 3 6.8922 11.212 15.834 20.696 25.757 30.991
x 1 2 3 4 5 6 7
y 2.5 14.142 38.971 80 139.75 220.45 324.1
12. Critical Thinking To determine whether a power model fits the data, you need to
determine whether the data of the form is linear. To see that this test
works, start with y ax take the natural logarithm of both sides, and use the
properties of logarithms to verify that there is a linear relationship between ln x
and ln y.
Volunteer Work In Exercises 13–15, use the following information.
The table below shows the percent of the adult population P that participates in volunteer
work as a function of household income where t 1 represents a household income under
$10,000, t 2 represents a household income between $10,000 and $19,000, and so on.
b ln x, ln y
,
t 1 2 3 4 5 6
P 34.7 34.3 41.2 46.0 52.7 64.1
13. Use your graphing calculator to find an exponential model for the data.
14. Use your graphing calculator to find a power model for the data.
15. Which model is the better fitting model? Explain your answer.
Algebra 2 99
Chapter 8 Resource Book
Lesson 8.7

Answer Key
Practice A
1. about 1.4621
2. about 0.5379
3. about 1.9951 4. 1 5. about 1.2449
6. about 1.9354 7. about 0.9003
8. about 1.5546 9. C 10. A
11. B 12. y 0, y 1 13. y 0, y 5
14. y 0, y 6 15.
1
3 16. 2 17.
5
2
18. 0, 2 19. 1.1, 0.5 20. 0.23, 1
21. 89,963 units 22. No more than 100,000 units
will be sold each year.

Lesson 8.8
LESSON
8.8
Practice A
For use with pages 517–522
110 Algebra 2
Chapter 8 Resource Book
NAME _________________________________________________________ DATE ___________
2
Evaluate the function f x for the given value of x.
1 ex 1. 2. 3. 4.
5. f 6. f 3.4
7. f 0.2
8.
1
f 1
f 1
f 6
2
Match the function with its graph.
9. 10.
3
f x
1 e
11.
A. y
B. y
C.
2x
3
f x
1 ex Identify the horizontal asymptotes of the function.
12. 13.
5
f x
1 e
14.
2x
1
f x
1 4e2x Identify the y-intercept of the function.
5
15. 16. 17. y
1 e3x 4
y
1 ex 1
y
1 2ex Identify the point of maximum growth of the function.
1
18. 19. f x
20.
1 3ex 4
f x
1 e2x Advertising In Exercises 21 and 22, use the following information.
A company decides to stop advertising one of its products. The sales of the
product S can be modeled by
S 100,000
1 0.5e 0.3t
2
1
x
where t is the number of years since advertising stopped.
21. What are the sales 5 years after advertising stopped?
22. What can the company expect in terms of sales in the future?
1
1
x
f x
f x
f x
f 0
f 5 4
1
1 2e x
2
6
1 2e x
2
1 2e 3x
Copyright © McDougal Littell Inc.
All rights reserved.
y
1
x

Answer Key
Practice B
1. exponential decay 2. logarithmic
3. logistics growth 4. exponential decay
5. exponential growth 6. logarithmic
7. A 8. C 9. B 10. y 0, y 20
11. y 5, y 4 12. y 10, y 12
13. 14.
15. y
16. ln 2 0.693
17.
5
ln 3 0.511 18.
1
2 ln 5 0.805
19. P
20. y 0, y 500
500
400
21. 500
300
22. 451
Population
2
200
100
y
1
2
0
0 2 4 6 8 10 t
1
Year
x
x
2
y
1
x

LESSON
8.8
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice B
For use with pages 517–522
Tell whether the function is an example of exponential growth,
exponential decay, logarithmic, or logistics growth.
1. f x 2. f x ln 3x
3.
1
4. 5. f x 2.5 6.
x
f x e2x Match the function with its graph.
7. 8.
2
f x
1 2e
9.
A. y
B. y
C.
x
4
f x
1 2ex Identify the horizontal asymptotes of the function.
10. 11.
1
f x 5
1 e
12.
x
20
f x
1 0.4ex Sketch the graph of the function.
13. 14.
1
f x
1 5e
15.
x
3
f x
1 ex Solve the equation.
16.
4
1 2ex 2
17.
8
1 ex 5
18.
Wildlife Management In Exercises 19–22, use the following information.
A wildlife organization releases 100 deer into a wilderness area. The deer
population P can be modeled by
P
2 x
500
1 4e 0.36t
where t is the time in years.
2
19. Sketch the graph of the model.
1
20. Identify the horizontal asymptotes of the graph.
21. What is the maximum number of deer the wilderness area can support?
22. What is the deer population after 10 years?
x
2
1
x
f x
f x
1
f x 10
f x 1
1
1 3e x
f x log 6x
4
1 e 2x
12
1 5e2x 6
2
1 e x
5
1 e x
Algebra 2 111
Chapter 8 Resource Book
y
1
x
Lesson 8.8

Answer Key
Practice C
1. 2.667 2. 7.276 3. 0.194 4. 8
5. 0.0000012 6. 4.993 7. 0.400 8. 7.985
9. y 10.
3
11. y 12.
(0.549, 3.5)
2
13. y 14.
(1.24, 12.5)
5
(0, 1)
15. ln 2 0.693 16. 0 17. 0.661
5 136
ln 63
1
3
1
( 0, )
7
4
1
( 0, 25
13)
1
x
x
x
(0.277, 1.5)
1
2 81
5 ln 4
1 15
2 ln 4
18. ln 6 0.597 19. 0.702
20. 0.962 21.
22.
24.
years 23. 2000
25.
y c
c
y
1 ae
1 a
0
4 k 0.186
6.5
c
y
rx →
1 aer 0
26. 27. 28. 1 ae
29.
c
1 aerx → c
rx ae → 1
rx e → 0
rx → 0
2
2
y
( 0, 5
3)
2
y
y
(0.231, 2)
( 0, )
4
3
1
( 0, )
3
5
1
(3.2, 5)
x
x
x

Lesson 8.8
LESSON
8.8
Practice C
For use with pages 517–522
112 Algebra 2
Chapter 8 Resource Book
NAME _________________________________________________________ DATE ___________
8
Evaluate the function f x
for the given value of x.
1 2e3x 1. 2. 3. 4.
5. 6. 7. f 8.
3
f 2 f 0
f 1
f 1
f 5
Graph the function. Identify the asymptotes, y-intercept, and point
of maximum growth.
7
9. 10. 11. y
1 3e2x 4
y
1 2e3x 2
y
1 ex 10
12. 13. 14. y
1 5e12x 25
y
1 12e2x 3
y
1 4e5x Solve the equation. Round the answer to three decimal places.
10
12
15. 5
16. 3
17.
1 2ex 1 3e4x 28
32
18. 14
19. 18
20.
1 6e3x 1 4.5e2.5x Conservation In Exercises 21–23, use the following information.
A conservation organization believes that the growth of a population P of an
endangered species at its preserve can be modeled by the curve
where t is time in years.
21. After 1 year, the preserve’s population of endangered species is 215. Find k.
22. When will the population reach 500?
23. What is the maximum population the preserve can maintain?
24. Analyzing Models The graph of the logistic growth function
c
has a y-intercept of Verify this formula by
1 a
setting x equal to 0 and solving for y.
.
c
y
1 aerx P 2000
1 10ekt Analyzing Models In Exercises 25–29, use the function
25. As x →, what is the behavior of rx?
26. As what is the behavior of erx x →,
?
27. As what is the behavior of aerx x →,
?
28. As what is the behavior of 1 aerx x →,
?
c
29. As what is the behavior of
1 aerx x →,
5
4
y
c
1 ae rx.
f 5
f 7 3
13
5
1 6e2x 40
8.5
1 8e0.8x Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Test A
2
1. y ; 1
2. y 4;
2 3.
x x
4. z 5. z –xy; 8
6. y
7.
1
xy; 1
8
8. y
9.
1
1
10. y
11.
1
1
1
1
x
x
x
y 12
; 6
x
12. 13. 14. 2 15.
16. 17. 18. 19.
20. 21. 2 22.
23. (7 is extraneous) 24. z
25. 14,000 dozens of golf balls
xy
x 3 3
4
4
x 2
3
18x 4
63
32
xx 12
35x 1
3
x 5x
x 2
4x
x 3 4x
2 x
2 x 1
1
1
1
y
y
1
2
2
x
x
x

CHAPTER
9
NAME _________________________________________________________ DATE
Chapter Test A
For use after Chapter 9
____________
The variables x and y vary inversely. Use the given values to
write an equation relating x and y. Then find y when x 2.
1. x 1, y 2 2. x 4, y 1 3. x 6, y 2
The variable z varies jointly with x and y. Use the given
values to write an equation relating x, y, and z. Then find z
when x 2 and y 4.
4. x 2, y 4, z 1
5. x 2, y 1, z 2
Graph the function.
6. y 7.
1
x
8. y 9.
x
x 2
1
10. y x 11.
2
Copyright © McDougal Littell Inc.
All rights reserved.
y
1
1
1
y
y
1
1
x
x
x
y 2
x 1
y 1
x 2
1
1
y x2 1
x
1
y
y
y
1
1
1
x
x
x
Answers
1.
2.
3.
4.
5.
6. Use grid at left.
7. Use grid at left.
8. Use grid at left.
9. Use grid at left.
10. Use grid at left.
11. Use grid at left.
Algebra 2 93
Chapter 9 Resource Book
Review and Assess

Review and Assess
CHAPTER
9
CONTINUED
NAME _________________________________________________________ DATE ____________
Chapter Test A
For use after Chapter 9
Perform the indicated operation. Simplify the result.
x
12. 13.
3 2
4 x2 x 5 x 5
14. 15.
x 2x
5x
16. 17.
2 8x
x2 4x 9x2
9 x2 9
Simplify the complex fraction.
x
4
3
18. 19. 20.
5 1
5
x
1
4
2 2
3
Solve the equation using any method. Check each solution.
3x x 1
21. 22.
4 2
23.
2x 9
x 7
24. Geometry Connection The similar triangles below have congruent
angles and proportional sides. Express z in terms of x and y.
x 2
x 5
2 x 7
y z
25. Starting a Business You start a business manufacturing golf balls,
spending $42,000 for supplies and equipment. You figure it will
cost $12 per dozen to manufacture the golf balls. How many dozens
of golf balls must you produce before your average total cost per
dozen is $15?
94 Algebra 2
Chapter 9 Resource Book
x
x 1
x
3x 1
x 2
x 3
x 1 2
2x 1
x 2
9x3 2x 8
8x 32 3x4 10 10
6
x 3 3
x 3
3x 2
6x 2
x 3 2
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Test B
4
1. y 4;
1
2. y ; 1 3.
x x
4. z 1 xy; 1 5.
4
6. y
7.
8. y
9.
1
2
1
10. y
11.
1
11x
12. 13. 1 14. 2x 2 15.
2y
25
16. 2 17. 2x 18. 19.
x 2
10xy 15x
20. 21. 14
15y x2y 1
2
x y
x y
22. 1; (1 is extraneous) 23.
3 7
,
2 4
24.
yx 4
z
x
25. 160,000 hats
x
x
x
z 1
xy; 2
2
1
y 8
; 2
x
y
1
1
2
1
x 1
x 2
x
2
x
x

CHAPTER
9
NAME _________________________________________________________ DATE
Chapter Test B
For use after Chapter 9
____________
The variables x and y vary inversely. Use the given values to
write an equation relating x and y. Then find y when x 4.
1. 2. x 8, y 3.
1
x 2, y 2
The variable z varies jointly with x and y. Use the given
values to write an equation relating x, y, and z. Then find z
when x 1 and y 4.
4. x 2, y 4, z 2
5.
Graph the function.
6. xy 1
7.
8. y 9.
x
x 4
1
y
1
Copyright © McDougal Littell Inc.
All rights reserved.
1
10. y x 11.
2 1
1
y
y
1
1
x
x
x
2
y 3
x 1
y 1
2x 2
1
1
y x2
x 1
1
y
y
y
x 2
3, y 12
x 4, y 1
2 , z 1
1
1
1
x
x
x
Answers
1.
2.
3.
4.
5.
6. Use grid at left.
7. Use grid at left.
8. Use grid at left.
9. Use grid at left.
10. Use grid at left.
11. Use grid at left.
Algebra 2 95
Chapter 9 Resource Book
Review and Assess

Review and Assess
CHAPTER
9
CONTINUED
NAME _________________________________________________________ DATE ____________
Chapter Test B
For use after Chapter 9
Perform the indicated operation. Simplify the result.
x 5x
12. 13.
2y y
x 1
14. 15.
2 2x 2
x 1 x 1
6x 5 2x 7
16. 17.
2x 6 2x 6
Simplify the complex fraction.
x y
2 3
x y
x xy
18. 19.
x
20.
3 1
2
x 5
2 2xy y2 x2 2xy y2 5
x
x
5
Solve the equation using any method. Check each solution.
21. 22.
23.
7 2
4 3
24. Geometry Connection The similar triangles below have congruent
angles and proportional sides. Express z in terms of x and y.
y2 13y
x
6
2 3 2
x 1 x 4
2x 2 2x 3
x 1 x 1
x
x 4
y z
25. Starting a Business You start a business manufacturing hats,
spending $8,000 for supplies and equipment. You figure it will cost
$4.95 per hat to manufacture the hats. How many hats must you
produce before your average total cost per hat is $5?
96 Algebra 2
Chapter 9 Resource Book
y 3
y 3 y 3
x 2 5x 4
x 3
x 4
x
x 3 3x 2
3x 6 x3 8x 2 15x
6x 2 18x 60
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Test C
1. 2. y 3.
1 1
y ;
x 3
9
; 3
x
4. z 5. z 9xy; 54
1
xy; 34
8
6. y
7.
8. y
9.
2
10. y
11.
6
12.
5yz 3xz 2xy
xyz
13.
3
x 3
14.
7
10
15. 8xx 3x 2 16.
3x 1
2x 3
17. 1
2y 20
18. 19. 20.
x 7
2 20x2y 7xy2 15x2 21. 4, 4 22. 5 23. 3, 2 24. z
25. about 130 boxes
1
1
1
6
x
x
x
1
y
1
y 2
; 2
x 3
1
y
1
5
x
x 1
x
y
1
x
x
yx 3
x

CHAPTER
9
NAME _________________________________________________________ DATE
Chapter Test C
For use after Chapter 9
____________
The variables x and y vary inversely. Use the given values to
write an equation relating x and y. Then find y when x 3.
1. 2. x 3.
3
5, y 5
x 1, y 9
3
The variable z varies jointly with x and y. Use the given
values to write an equation relating x, y, and z. Then find z
when and
4. 5. x 1
x 2 y 3.
1 3
x 4, y 2, z 1
2 , y 3 , z 2
Graph the function.
6. xy 2
7.
8. y 9.
2x
x 4
2
10. y 11.
2x2
x 2
6
Copyright © McDougal Littell Inc.
All rights reserved.
y
y
1
2
1
y
1
x
x
x
y 2
x 2
1
y 4
x 2
y
1
1
y x2 3x 5
x 1
y
5
x 6, y 1
3
1
y
1
x
x
x
Answers
1.
2.
3.
4.
5.
6. Use grid at left.
7. Use grid at left.
8. Use grid at left.
9. Use grid at left.
10. Use grid at left.
11. Use grid at left.
Algebra 2 97
Chapter 9 Resource Book
Review and Assess

Review and Assess
CHAPTER
9
CONTINUED
NAME _________________________________________________________ DATE ____________
Chapter Test C
For use after Chapter 9
Perform the indicated operation. Simplify the result.
5 3 2
12. 13.
x y z
3y 5 4y 2
14. 15.
2y 6 5y 15
3x 3x 6
16. 17.
2x 3 2x2 x 6
Simplify the complex fraction.
18. 19. 20. 2
10
x 1
1
1 2
5x2 y
7 3
3
10x 2y 2 x 1
2
Solve the equation using any method. Check each solution.
21. 22.
3 4
x 2 x 3
23.
3 x 2 13
x 1 3 3x 3
24. Geometry Connection The similar triangles below have congruent
angles and proportional sides. Express z in terms of x and y.
6
x2 2 x
x x 5x 6
2 8
x 3
z y
25. Fund Raiser As a fund raiser, your junior class will make and sell
holiday greeting cards. You spend $750 as an initial startup cost. It
will cost you $4.25 per box to print, and you will sell the cards at
$10 per box. How many boxes must you sell to show a profit?
98 Algebra 2
Chapter 9 Resource Book
x
3x 5
x 2 9
7 x 1
9 x2 x 3
30x 3 6x 2 15x2 3x
4x 2 4x 24
6x2 x 2
6x2 7x 2 2x2 9x 4
4 7x 2x2 2
2 2
2 x
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Cumulative Review
Chapter 9
1. 3 or 2. or 3. 56 or 8
4. n > 2 or n < 1 5. 8 ≥ n ≥ 4
6. x ≥ 7 or x ≤ 29
7. 8.
17
2
7
2
7
3
9. 10.
11. 12.
13. C 14. A 15. B 16. infinite 17. none
18. one
19. 20.
1
y
1
1
y
1
1
y
y
1
1
1
x
x
x
x
1
1
y
y
1
1
1
y
1
1
y
1
x
x
x
x
21. y
22.
23. 24. x 1x 6
25. 3x 53x 10 26. 33x 1x 1
27. 7x 97x 9 28. 3y 83y 2
29. xx 32 30. 34 31. 3 32. 257
33. 5 34. 32 35. 17
36. 2 ± i14 37.
3 ± i7
2
38. 3, 1
9
13
5
15
3
15
39. 40. 41.
42.
43. 44. y x2 y 2x 1 3
2 y 3x 4
9
2 5 ± 37
2
2 ± 10
2
4, 2
6
45. 46. 47. 48. x3y14 16x4 x
3x
8y3 49. 50. x 51. 17 52. 281 53. 18
6
3
x 2
54. 25 55. f x 6x 13; first; linear; 6
f x 1
56. third; cubic;
57. no 58. 2x all real numbers
2 3
6x 9;
x3 2x 8;
59. 6x 9; all real numbers
60. 2x all real numbers
2 12x;
61. x all real numbers
4 6x3 9x2 54x;
62. x ; all real numbers
4 12x2 27
63. x ; all real numbers
4 18x2 72
64. 8 units left 65. 6 units left, reflected over xaxis
66. 1 unit left, 5 units up 67. 1 unit right
68. 1; y 0 69. 3; y 0 70. 4; y 3
71.
1
; y 0 72.
3
; y 0 73. 10; y 5
e2x 2
1
1
y 5
3e 3x
2
3e 3x1
74.
3
75. 76. 77. 2.398
78. 0.239 79. 1.375
x
y 6
14
8
2
7
12
16
1
3

Review and Assess
CHAPTER
9 Cumulative Review
NAME _________________________________________________________ DATE ____________
For use after Chapters 1–9
Solve the equation or inequality. (1.7)
Graph the equation. (2.3)
7. y 8. y 2x 6
9. 5x 3y 15
10. x 0
11. y 5
12. 3x 6y 18
3
4x 2
Match the equation with its graph. (2.8)
13. y x 3 3
14. y x 3
15. y x 3
A. B. C.
Tell how many solutions the system has. (3.1)
16. x 2y 6
17. 2x y 5
18. 3x 4y 5
3x 18 6y
Graph the system of inequalities. (3.3)
19. 2x y > 6
20. x y ≤ 0
21. 5x 3y ≤ 15
y < x
x > 4
1
Perform the indicated operations. (4.1, 4.2)
22. 23. 3
1
5
2
0
2
3
4
3
4 2
1
1
2
5
4
Factor the expression. (5.2)
24. 25. 26.
27. 28. 29. x2 9y 32x
2 49x 30y 16
2 9x
81
2 9x 12x 3
2 x 45x 50
2 7x 6
Find the absolute value of the complex number. (5.4)
30. 3 5i
31. 3i
32. 16 i
33. 2 i
34. 3 3i
35. 1 4i
104 Algebra 2
Chapter 9 Resource Book
y
1
x
2y 4x 20
x y ≥ 8
y ≤ 6
1
3
3
0 1
4
y
1 x
3
2
1 4x 6 8
1. 3x 1 8
2. 12 2x 5
3.
4. 4n 2 > 6
5. 6 3n ≤ 18
6. 11 x ≥ 18
x 2y 9
3x y ≤ 3
x ≤ 0
Copyright © McDougal Littell Inc.
All rights reserved.
1
y
1 x

CHAPTER
9
CONTINUED
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ____________
Cumulative Review
For use after Chapters 1–9
Use the quadratic formula to solve the equation. (5.6)
36. 37. 38.
39. 40. 41. x2 2c 1 6x 9 1
2 16x x 4 1
2 x
11x 3
2 x 2x 3
2 x 3x 4 0
2 4x 18
Write a quadratic function in vertex form whose graph has the
given vertex and passes through the given point. (5.8)
42. vertex: 4, 6
43. vertex: 1, 9
44. vertex: 0, 3
point: 2, 18
point: 2, 27
point: 5, 22
Simplify the expression. (6.1)
45. 46.
2x
47.
2y 6x3y4 x5y3 x3y0 xy 8
48. 49. 3x 50.
2y0 3x2 6x3y4 2x3y2 Use synthetic substitution to evaluate. (6.2)
51. 52.
53. f x x 54.
4 x2 f x 2x
5x 11, x 1
3 x2 2x 1, x 2
Decide whether the function is a polynomial function. If it is, write
the function in standard form and state the degree, type, and leading
coefficient. (6.2)
55. 56. f x 2x 57.
1
3 x3 f x 13 6x
8
Let and gx x Perform the indicated
operation and state the domain. (7.3)
58. f x gx
59. f x gx
60. f x f x
61. f x gx
62. f gx
63. ggx
2 f x x 9.
2 6x
Describe how to obtain the graph of g from the graph of f. (7.5)
64. gx x 8, f x x
65. gx x 6, f x x
66. gx x 1 5, f x x
67. gx 5x 1, f x 5x
Identify the y-intercept and the asymptote of the graph of the
function. (8.1)
68. 69. 70.
71. 72. 73. y 5x1 y 3 2 5
x1
y 2x1 y 2x y 3 5 3
x
y 6 x
Simplify the expression. (8.3)
74. 75. 327e9x 76.
3e 2x 1
4x 2 y 3 2
f x 4x 4 3x 2 5x 1, x 3
f x 3x 3 x 2 x 3, x 2
e x 3e 2x1
Use a calculator to evaluate the expression. Round the result to
three decimal places. (8.4)
77. ln 11
78. log 3
79. log 23.724
x 4
x 2
f x 6x 2 x 2
x
Algebra 2 105
Chapter 9 Resource Book
Review and Assess

Answer Key
Practice A
1. direct variation 2. inverse variation
3. neither 4. inverse variation
5. 6. y 9
y ; 9
x 4
8
; 2
x
7. y 36;
9 8.
x
y 12
; 3
x
9. 10. y 11. direct variation
5 5
y ;
x 4
4
; 1
x
12. neither 13. inverse variation 14. direct
variation 15. 16.
17. 18. z
19. k 0.055 20. I 0.055Pt 21. $220.00
1
z
z 2xy; 24
3xy; 4
2
z 3xy; 36
3xy; 8

Lesson 9.1
LESSON
9.1
Practice A
For use with pages 534–539
16 Algebra 2
Chapter 9 Resource Book
NAME _________________________________________________________ DATE ___________
Tell whether x and y show direct variation, inverse variation, or
neither.
1. 2. y 3. x y 7
4. xy 5
2
y 3x
x
The variables x and y vary inversely. Use the given values to write
an equation relating x and y. Then find y when x 4.
5. 6. 7.
8. 9. 10. x 10, y 1
x 16, y 2
1
x 2, y 4
x 3, y 3
x 4, y 9
x 3, y 4
4
Determine whether x and y show direct variation, inverse variation,
or neither.
11. x y
12.
3 12
8 32
11 44
0.5 2
13.
x y
14.
3 1
6 0.5
10 0.3
12 0.25
The variable z varies jointly with x and y. Use the given values to
write an equation relating x, y, and z. Then find z when x 3
and y 4.
15. x 1, y 2, z 6
16. x 2, y 3, z 4
17. x 4, y 3, z 24
18. x 8, y 54, z 144
Simple Interest In Exercises 19–21, use the following information.
The simple interest I (in dollars) for a savings account is jointly proportional to
the product of the time t (in years) and the principal P (in dollars). After six
months, the interest on a principal of $2000 is $55.
19. Find the constant of variation k.
20. Write an equation that relates I, t, and P.
21. What will the interest be after two years?
x y
1 6
2 5
4 3
5 2
x y
8 4
10 5
24 12
2 1
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice B
1. direct variation 2. direct variation
3. inverse variation 4. neither
5. direct variation 6. neither
7. 8. 9.
10. z 11. z 32xy; 192
12. z 3xy; 18 13. k 0.035
14. I 0.035Pt 15. $612.50 16. k 12.84
17. PV 12.84 18. 10.7 cubic liters
3
y
4xy; 92
3
y
4 4
y ;
x 3
; 1
x 54
; 18
x

LESSON
9.1
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice B
For use with pages 534–539
Tell whether x and y show direct variation, inverse variation, or
neither.
1. 2. y 3. xy 0.1
4. y x 5
5. 6.
1
2 x
y
x
9
x y
x y
5 15
3 5
8 24
5 21
1.5 4.5
4.5 16.25
0.5 1.5
7 45
The variables x and y vary inversely. Use the given values to write
an equation relating x and y. Then find y when x 3.
7. 8. x 72, y 9.
1
x 6, y 9
The variable z varies jointly with x and y. Use the given values to
write an equation relating x, y, and z. Then find z when x 2
and y 3.
10. 11. x 1, y 12.
1
x 2, y 4, z 6
8, z 4
Simple Interest In Exercises 13–15, use the following information.
The simple interest I (in dollars) for a savings account is jointly proportional to
the product of the time t (in years) and the principal P (in dollars). After nine
months, the interest on a principal of $3500 is $91.88.
13. Find the constant of variation k.
14. Write an equation that relates I, t, and P.
15. What will the interest be after five years?
Boyle’s Law In Exercises 16–18, use the following information.
Boyle’s Law states that for a constant temperature, the pressure P of a gas
varies inversely with its volume V. A sample of hydrogen gas has a volume of
8.56 cubic liters at a pressure of 1.5 atmospheres.
16. Find the constant of variation k.
17. Write an equation that relates P and V.
18. Find the volume of the hydrogen gas if the pressure changes to 1.2
atmospheres.
18
x 6, y 1
2
x 1
2, y 8, z 12
Algebra 2 17
Chapter 9 Resource Book
Lesson 9.1

Answer Key
Practice C
1. direct variation 2. inverse variation
3. direct variation 4. direct variation
5. inverse variation 6. neither
7. 8. 9.
10. 11.
12. z 13. k 150,000
14. dp 150,000 15. 12,500 units
16. k 0.22 17. H 0.22mT
18. 3.9424 kilocalories
11
y
z 12xy; 144 z 16xy; 192
6 xy; 22
1
y
1
;
5x 30
0.3
y
1
;
x 20
18
; 3
x

Lesson 9.1
LESSON
9.1
Practice C
For use with pages 534–539
18 Algebra 2
Chapter 9 Resource Book
NAME _________________________________________________________ DATE ___________
Tell whether x and y show direct variation, inverse variation, or
neither.
1. 2. 3. x 4.
5. 6.
y
x
3
5
x 4y
y
x y
x y
1 4
3 6
2 2
7 10
0.5 8
2.5 5.5
0.25 16
5.7 8.7
The variables x and y vary inversely. Use the given values to write
an equation relating x and y. Then find y when x 6.
7. x 8. x 3, y 0.1
9.
3
, y 12
2
The variable z varies jointly with x and y. Use the given values to
write an equation relating x, y, and z. Then find z when x 3
and y 4.
10. 11. x 12.
3
4, y 5
x 2, y 6, z 10
1
8, z 3
Product Demand In Exercises 13–15, use the following information.
A company has found that the monthly demand d for one of its products varies
inversely with the price p of the product. When the price is $12.50, the demand
is 12,000 units.
13. Find the constant of variation k.
14. Write an equation that relates d and p.
15. Find the demand if the price is reduced to $12.00.
Specific Heat In Exercises 16–18, use the following information.
The amount of heat H (in kilocalories) necessary to change the temperature of
an aluminum can is jointly proportional to the product mass m (in kilograms)
and the temperature change desired T (in degrees Celsius). It takes 1.54
kilocalories of heat to change the temperature of a 0.028 kilogram aluminum
can 250 C.
16. Find the constant of variation k.
17. Write an equation that relates H, m, and T.
18. How much heat is required to melt the can (at 660 C if its current
temperature is 20 C?
2 7
x y
x 1 2
2 , y 5
x 2
3, y 3
4, z 11
12
Copyright © McDougal Littell Inc.
All rights reserved.
Lesson 9.1

Answer Key
Practice A
1. all real numbers except 5 2. all real numbers
except 3. all real numbers except 0
4. 5. 6. 7. y
1
all real numbers except 2 8. y 1; all real
numbers except 1 9. y 6; all real numbers
except 6 10. B 11. C 12. A
13. 14.
1
2 ;
6
x 1 x 2 x 3
15. y 16. C 7x 250
18. y
y
2
1
10
10
1
x
1
x
x
17.
1
y
1
A
x
7x 250
x

LESSON
9.2
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice A
For use with pages 540–545
Find the domain of the function.
x 4
1. f x 2. f x 3.
x 6
3
x 5
Find the vertical asymptote of the graph of the function.
4. 5. f x 6.
6
x
f x 7
x 1
x 2
Find the horizontal asymptote of the graph of the function. Then
state the range.
x 3
7
7. f x 8. f x 1
9.
2x 1
x 2
Match the function with its graph.
10.
2x 1
f x
x 1
11.
x 1
f x
x 2
12.
A. y
B. y
C.
1 x
Graph the function.
13.
x 1
f x
x
14.
3
f x
x 2
15.
Sports Banquet In Exercises 16–18, use the following information.
You are organizing your high school’s sports banquet. The banquet hall rental is
$250. In addition to this one-time charge, the meal will cost $7 per plate. Let x
represent the number of people who attend.
16. Write an equation that represents the total cost C.
17. Write an equation that represents the average cost A per person.
18. Graph the model in Exercise 17.
2
1
2
x
f x 2
5
x
f x
f x 4
6
x
f x
2
y
x 7
x 3
x 1
x 2
1
f x 3
2
x 2
Algebra 2 29
Chapter 9 Resource Book
x
Lesson 9.2

Answer Key
Practice B
1. domain: all real numbers
except range: all real numbers except
2. domain: all real numbers
except ; range: all real numbers except
3.
domain: all real numbers except
2
3 range: all real numbers except 2
6. A
4. B 5. C
7. domain: all real 8. domain: all real
numbers except 0; numbers except 2;
range: all real numbers range: all real numbers
except 0 except 3
;
y 2; x 2
3 ;
3
4
1
y
4
3
4 ; x 14
;
y 5; x 4;
4;
5
9. domain: all real 10. domain: all real
numbers except 3;
numbers except 3;
range: all real numbers range: all real numbers
except 1
except 1
11. domain: all real
3
numbers except 2;
range: all real numbers
12. domain: all real
1
numbers except 2;
range: all real numbers
except except
3
2
1
y
1
1
y
1
1
y
x
1 x
x
1
1
y
1
y
1
2
1
y
1
1
x
x
x
13. r 14. y 2; the amount
4
of rain will be less than
2 inches
15. 0.8 inch
4
t

Lesson 9.2
LESSON
9.2
Practice B
For use with pages 540–545
30 Algebra 2
Chapter 9 Resource Book
NAME _________________________________________________________ DATE ___________
Identify the horizontal and vertical asymptotes of the graph of the
function. Then state the domain and range.
3x 4
2x 1
1. y 2. y 3. y 2
4x 1
3x 2 2
5
x 4
Match the function with its graph.
4. f x 5.
2x 3
f x
x 3
6.
x 3
y
x 2
A. y
B. y
C. y
2
1
x 3
2
1 x
Graph the function. State the domain and range.
7. y 2
x
8.
4
y 3
x 2
9.
10. 11. 12. y
x
x 1
3x 2
y y
x 3
2x 3
2x 1
Inches of Rain In Exercises 13–15, use the following information.
The total number of inches of rain during a storm in a certain geographic area
can be modeled by r where r is the amount of rain (in inches) and t is
the length of the storm (in hours).
2t
t 8
13. Graph the model.
14. What is an equation of the horizontal asymptote and what does the
asymptote represent?
15. Use the graph to find the approximate number of inches of rain during a
storm that lasts 5 hours.
2
1
x
2
1
y 2
1
x 3
Copyright © McDougal Littell Inc.
All rights reserved.
x

Answer Key
Practice C
1. domain: all real numbers except
range: all real numbers except 5
2. domain: all real numbers
except range: all real numbers except
3. y 10; x 7; domain: all real numbers
except 7; range: all real numbers except 10
4. C 5. A 6. B
7. domain: all real 8. domain: all real
numbers except 0; numbers except 3;
range: all real numbers range: all real numbers
except 1
except 4
3
1
8 4
;
y 3 1
4 ; x 8 ;
1
2 ;
y 5; x 1
2 ;
1
9. domain: all real
numbers except
range: all real numbers
10. domain: all real
3
numbers except 2
range: all real numbers
except 3
except 2
;
14
;
1
11. domain: all real
numbers except ;
range:all real numbers
except 1
3
2
3
y
y
1
1
x
x
1
y
1
1
y
1
1
y
1
x
x
x
12. domain: all real
numbers except 3;
range:all real numbers
except 5
13. c
14. 40 milligrams
100
80
60
15. y 100; the
child’s dose will be
40
20
less than 100
milligrams
Child's dosage
(milligrams)
0
0 2 4 6 8 10 12t
Age (years)
2
y
2
x

LESSON
9.2
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice C
For use with pages 540–545
Identify the horizontal and vertical asymptotes of the graph of the
function. Then state the domain and range.
6x 5
1. y 2. y 3.
8x 1
1
5
2x 1
Match the function with its graph.
4. 5. f x 6.
x 2
f x
x 1
A. y
B. y
C. y
1
1
f x 3
x 2
3
x 2
1
1
Graph the function. State the domain and range.
7. 8. 9. y
2
4
y 1
x
2
y 4
x 3
3
4x 1
4x 1
x 5
10. y 11. y 12.
2x 3
3x 2
Young’s Rule In Exercises 13–15, use the following information.
Young’s Rule is a formula that physicians use to determine the dosage levels of
medicine for young children based on adult dosage levels. The child’s dose can
be modeled by c where c is the child’s dose (in milligrams), a is the
adult’s dose (in milligrams), and t is the age of the child (in years).
ta
t 12
13. Graph the model for t > 0 and a 100.
x
14. Use the graph to find the approximate dose for an eight-year-old child.
15. What is an equation of the horizontal asymptote and what does the
asymptote represent?
2
2
x
y 12
10
x 7
1
y 5x
x 3
Algebra 2 31
Chapter 9 Resource Book
1
x
Lesson 9.2

Answer Key
Practice A
1. x-intercept: 0; vertical asymptotes: x 5,
x 5 2. x-intercept: 1; vertical asymptotes:
1
x 3, x 2 3. x-intercept: 2; vertical
asymptote: x 0 4. no x-intercepts; vertical
asymptote: x 5 5. x-intercepts: 9, 1; no
vertical asymptotes 6. x-intercepts: 6, 6;
vertical asymptote: x 0 7. B 8. A 9. C
10. 11.
12. 13.
14. 15.
16. 15 ft by 30 ft
1
1
y
y
1
1
1
y
1
x
x
x
2
y
1
1
2
y
y
1
2
x
x
x

LESSON
9.3
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice A
For use with pages 547–553
Identify the x-intercepts and vertical asymptotes of the graph of
the function.
x 1
1. 2. y 3. y
x2 x
y
x x 6
2 25
4. 5. y 6.
x2 8x 9
x2 y
2
2
x 5
Match the function with its graph.
7. 8. y 9.
A. y
B. y
C.
5x
x2 y
4
x2
x2 4
Graph the function.
1
1
x
10. 11. f x 12.
x2 1
x2 f x
4
x
x2 1
13. 14. f x 15.
16. Garden Fencing Suppose you want to make a rectangular garden with
an area of 450 square feet. You want to use the side of your house for one
side of the garden and use fencing for the other three sides. Find the
dimensions of the garden that minimize the length of fencing needed.
x2
x 1
f x
x x 1
2 4
1
2
x
y x2 6
x
y x2 4x 5
x 2
y
3
f x
f x
2x 1
x 2
1
x
x 1x 3
x
x 2 4x 12
Algebra 2 41
Chapter 9 Resource Book
x
Lesson 9.3

Answer Key
Practice B
1. x-intercepts: vertical asymptote:
x 5 2. no x-intercepts; vertical asymptotes:
x 1, x 1 3. x-intercepts: 0; vertical asymptotes:
x 4 4. B 5. C 6. A
7. 8.
1
2 , 4;
9. 10.
2
11. 12.
13. Answers may vary.
x 5
Sample answer: y
x
14. L
0.9
0.8
0.7
15. The oxygen level
dropped to 50% of
normal, then slowly
0.6
increased to 93%
0.5
of normal.
2 3x
Oxygen level
y
2
0.4
0.3
0.2
0.1
2
0
0
y
1
2
y
2
2 4 6 8 10 12 14t
x
x
x
Weeks
1
1
1
y
y
y
1
1
2
x
x
x

Lesson 9.3
LESSON
9.3
Practice B
For use with pages 547–553
42 Algebra 2
Chapter 9 Resource Book
NAME _________________________________________________________ DATE ___________
Identify the x-intercepts and vertical asymptotes of the graph of
the function.
1. 2. y 3.
x2 1
x2 y
1
2x2 7x 4
x 5
Match the function with its graph.
4. 5. y 6.
A. y
B. y
C.
x2 2
x2 4
y
x 16
2 5x 4
1
1
x
Graph the function.
7. 8.
5x 1
y
x
9.
2 2x 6
y
x 4
1
10. 11. y 12.
13. Critical Thinking Give an example of a rational function whose graph
has two vertical asymptotes: x 3 and x 0,
and one x-intercept: 5.
2x2 x 9
3x2 y
12
3x2
2x 6
Pollution In Exercises 14 and 15, use the following information.
Suppose organic waste has fallen into a pond. Part of the decomposition process
includes oxidation, whereby oxygen that is dissolved in the pond water is
combined with decomposing material. Let represent the normal oxygen
level in the pond and let t represent the number of weeks after the waste
is dumped. The oxygen level in the pond can be modeled by L
14. Graph the model for 0 ≤ t ≤ 15.
15. Explain how oxygen level changed during the 15 weeks after the waste
was dumped.
t 2 t 1
t 2 1 .
L 1
1
2
x
y 3x2 6x
x 2 6x 8
y x3
x 2
y 3x2 4x 4
x 2 5x 6
2
y 3x2 1
x 3
Copyright © McDougal Littell Inc.
All rights reserved.
y
4
x

Answer Key
Practice C
1. no x-intercepts; vertical asymptotes: x
x 3 2. x-intercept: 2; vertical asymptote
x 0 3. x-intercepts: 3, 5; no vertical
asymptotes 4. A 5. C 6. B
7. 8.
2
3 ,
9. 10.
11. 12.
13. Answers may vary.
2x
Sample answer: y
2
x2 x 12
14. h
15. S 2πr 2
16.
Surface area(cm )
2
1
y
S
500
400
300
200
100
1
1
y
1
300
πr 2
1
y
1 x
600
r
17. r 3.67 cm and h 8.42 cm
x
x
2 4 6 8 10 r
Radius (cm)
y
2
y
2
1
2
1
y
x
x
1 x

LESSON
9.3
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice C
For use with pages 547–553
Identify the x-intercepts and vertical asymptotes of the graph of
the function.
1. 2. y 3.
x3 8
x2 5
y
3x2 7x 6
Match the function with its graph.
4. 5. y 6.
A. y
B. y
C.
x3 1
x2 y
2
6
x2 9
Graph the function.
1
1
x
7. 8. y 9.
x2 10x 24
y
3x
2x2
x2 9
10. 11. y 12.
3
y
4x 10
13. Critical Thinking Give an example of a rational function whose graph
has two vertical asymptotes: x 4 and x 3, one x-intercept: 0, and
one horizontal asymptote: y 2.
3x3 1
4x3 y
32
x2 x 2
x 1
Manufacturing In Exercises 14–17, use the following information.
A manufacturer of canned soup wants the volume of its cylindrical cans to be
300 cubic centimeters.
14. Use the volume formula V πr 2 h to express the can’s height h as a
function only of the can’s radius r.
15. Use the surface area formula S 2πr2 2πrh and your answer to
Exercise 14 to express the can’s surface area as a function only of the
can’s radius.
16. Graph the function from Exercise 15 on the domain 0 < r < 10.
17. Find the dimensions of the can that has a volume of 300 cubic centimeters
and uses the least amount of material possible.
1
2
x
y x2 8x 15
x 2 4
y x2 2x 3
2x 2 x 3
y x2 6x 9
x 3 27
Algebra 2 43
Chapter 9 Resource Book
1
y
1
x
Lesson 9.3

Answer Key
Practice A
1. 2. 3. 4.
5. not possible 6. 7. 8.
9. 10. 11. 12.
13. 14. 15. 16.
1
2x
17. x 4x 3 18.
2x 2
x 6
4x 1
19.
3x 2
2
9x5 20x
3y
x
3x 1
x 11
x 8
y
2
3
x3 3
4x
x 2
x 1
xx 3
x 1 2
2
4x
2x 3
x 3
x 1
x 4
x 3
x 6
x 5
x 1
x 1
8x
5

LESSON
9.4
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice A
For use with pages 554–560
If possible, simplify the rational expression.
x
1. 2. 3.
2 2x 15
x2 4x
4x 5
2
2x2 3x
x
4. 5. 6.
2 2x 8
x2 x
3x 4
2 8x 12
x2 3x 10
Multiply the rational expressions. Simplify the result.
12x
7. 8.
2y 5y2 2xy
3x2 x
9. 10.
2 2x
x2 2x 1 x2 4x 3
x2 3x
Divide the rational expressions. Simplify the result.
5x 5
15x2
11. 12.
8 12
x
13. 14.
2
x2 3x
1 x 1
Perform the indicated operations. Simplify the result.
15. 16.
17. x 18.
19. CDs and Cassettes Use the diagrams below to find the ratio of the
volume of the compact disc storage crate to the volume of the cassette
storage crate.
2 x 30 x2 11x 30
x2 x 11
2x 10
x 6
7x 12 x 6
x2 8x 33 x 3
x 5 x2 5x2y 2xy 6x3y5 3x
10y y3 x
4x
x 1
CDs
x 2
x
3x
Cassettes
4y 2
9x
x 2 2x 3
x 2
48x 2
y
27
16xy 2
36xy2
5
x2 2x
x 2 1
x2 9x 22
x2 x 2
5x 24 x 3
x 2 16
x 2 x 12
x 2 2x 1
x 2 1
x2 5x 14
x2 6x 7 x2 4x 5 x2 x 30
2
Algebra 2 55
Chapter 9 Resource Book
Lesson 9.4

Answer Key
Practice B
1. 2. 3. not possible
4. 5. 6. 7. 8.
9. 10. 11.
12. 13. 14.
15.
y
16.
7
6xx 5
17.
x
3x 3
2
x 2x 6
5x
x 3
x 5x 4
2x 4
3x
8
x
2
9x 6x 2
x 3
3
10
8x
5
xx 2
5
6
4y5 1
5x5y2 x 9
x 1
1
x 2
18x 2

Lesson 9.4
LESSON
9.4
Practice B
For use with pages 554–560
56 Algebra 2
Chapter 9 Resource Book
NAME _________________________________________________________ DATE ___________
If possible, simplify the rational expression.
x 3
1. 2. 3.
x2 x
5x 6
2 8x 9
x2 1
Multiply the rational expressions. Simplify the result.
4.
4x
5.
2y3 x5y6 xy
20x3 x
6. 7.
2 4x 12
x 4 9x 3 18x 2 6x 2
Divide the rational expressions. Simplify the result.
12x
8. 9.
2y 3x2
2 5y 2xy
5x
10. 11.
2 20
25x2 x2 6x 8
x2 10x 24
Perform the indicated operations. Simplify the result.
12. x 13.
2 x 30 x2 2x 15
x2 x 5
7x 12 x 6
x
14. 15.
2 6x 7
3x2 6x x 1
x 7 4
Geometry Find the ratio of the area of the shaded region to the total area.
Write your result in simplified form.
16. 17.
x 2 5x
x 1
7
6(x 1)
81x 9
y 4
3x 2 12
5x 10
x 2 3x 2
25x
x 7 x2 9x 14
x 2 5x 6
x 2 x 20
x 1
3xy 3
x 3 y
x 2
36x 5 y
y 9y2
6x xy
x x
1
2x 4
x 1
5x 2
33x2 132x
16x 16
x
3
x 3
x 2 4
x 2 4
8x 40
11x 44
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice C
1. 2. not possible 3.
4. 5. 6. 7.
8. 9. 10.
11. 12. 13.
5x 5
4x3 xx
x 6
4x 2
6
5
2 3x
3x 2
7x 3
xx 5
2x 4
4x 1
11 x 5
x
x 6
x 2
x 1
3
10
y
25
2 3x 1
x 2
5x 25
14.
15.
1
x
16.
2 x 10x 2
x 8x 1
x 3x 3x 4
17. about 60,769 gallons
1

LESSON
9.4
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice C
For use with pages 554–560
If possible, simplify the rational expression.
2x 6
1. 2. 3.
x2 3x
6x 9
2 5x 2
x2 4
Multiply the rational expressions. Simplify the result.
x
4. x 5
5.
2 36
x2 11x 30
3x
6. 7.
2 12
5x 10
1
2x 4
Divide the rational expressions. Simplify the result.
8. x 9.
2 10x 24 x2 144
3x 36
x
10. 11.
3 8
64x x2 x 2
16x2 Perform the indicated operations. Simplify the result.
x
12. 13.
2 3x 2 3x 2x 4
x 2 x 2 5x2 5x
14. x 15.
2 7x 30 x2 5x 24 x 2
x 2 x2 3x 2
x2 2x
x2 2x 1 x2 4x 3
x2 3x
21x 10 y 5
5x 2
7x2 21x
x2 x2
2x 35 x 7
2x 3 12x 2
x 2 4x 12 8x3 24x 2
x 2 9x 18
x 2 100
4x 2
x3
35y 4
x3 5x 2 50x
x 4 10x 3
1
x3 10x2 x2 9
x 3
Swimming Pools In Exercises 16 and 17, use the following information.
You are considering buying a swimming pool and have narrowed the choices to
two—one that is circular and one that is rectangular. The width of the
rectangular pool is three times its depth. Its length is 6 feet more than its width.
The circular pool has a diameter that is twice the width of the rectangular pool,
and it is 2 feet deeper.
16. Find the ratio of the volume of the circular pool to the volume of the
rectangular pool.
17. The volume of the rectangular pool is 2592 cubic feet. How many gallons
of water are needed to fill the circular pool if 1 gallon is approximately
0.134 cubic foot?
x 2 25
x 3 125
x 102
5x
x 10
x 2 7x 12
Algebra 2 57
Chapter 9 Resource Book
Lesson 9.4

Answer Key
Practice A
1. 2. 3.
4. 5.
6. 7.
8. 9.
x2 4x 6
2x2 15x 2
3x2 2xx 12 4
x
5 x
x 1
2x 1
x 3
x 1x 1 x 4x 4
x 2x 1
10.
x 17
x 5x 1
11.
12.
x 6
x 2x 2
13.
2x 1 x 1
14. 15. 16.
x x 1
2
4
17. R 18. ohms
3
R1R2 R1 R2 x2 6x 13
x 3
4x
x 1x 1
3x x 2
x 1

LESSON
9.5
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice A
For use with pages 562–567
Perform the indicated operation and simplify.
7 9
5 x
1. 2. 3.
4x 4x
x 1 x 1
Find the least common denominator.
5
4. 5.
x 1 ,
6
x2 1
x
6. 7.
x2 1
,
x 2 x 2
Perform the indicated operation(s) and simplify.
5 2
8. 9.
x 3x2 3 4
10. 11.
x 5 x 1
4x
12. 13.
x2 3
4 x 2
Simplify the complex fraction.
1
2 x
14.
x
1
1 x
15.
1
1
16.
Electrical Resistors In Exercises 17 and 18, use the following information.
When two resistors with resistances R1 and R2 are connected in parallel, the
1
total resistance R is given by R
17. Simplify this complex fraction.
1
R1 1
R 2 .
18. Find the total resistance (in ohms) of a 4 ohm resistor and a 2 ohm resistor
that are connected in parallel.
x
3
x 4 ,
x
x2 16
5 1
,
2x 1 2x ,
1 2 3
2 x x2 6 5
x 3
x 3x
x 1 x2 1
3
2x 1 2
2x 1
x 3 x 3
6
3 x 1
3
x
Algebra 2 69
Chapter 9 Resource Book
Lesson 9.5

Answer Key
Practice B
1. 2x 12x 1
2. 4x 4
3. xx 1x 1 4.
7 x
x 2
2x 1
5. 6.
x 2x 1
7. 8.
9. 10.
11. 12.
3x 1
4x2 x2 9x 12
3x2 x 4x 7
x 3
2 24x x
x 1
3x 9
xx 3x 3
2 5x 3
x2x 3
11x 2
13. 14.
3x2 x 2
15.
6
x 6x 5
I 1374t2 20,461t 1,627,410
85 t55 2t
16. about 554,000 MDs; about 24,000 DOs
1
6

Lesson 9.5
LESSON
9.5
Practice B
For use with pages 562–567
70 Algebra 2
Chapter 9 Resource Book
NAME _________________________________________________________ DATE ___________
Find the least common denominator.
5
3 x 2
1. 2. , 3.
2x 1 x 4 4
,
6
4x2 1
Perform the indicated operation(s) and simplify.
7 x
4. 5.
x 2 x 2
x
6. 7.
x2 1
x 30 x 5
x 2 2
8. 9.
x 1 x 6
14
x2 5x 6
10. 4 11.
5
x 3
Simplify the complex fraction.
12. 13. 14.
1 4
3x x 2
x 1
x 2 1
x
1
2x 1
4x
2x
1
Doctors In Exercises 15 and 16, use the following information.
Over a twenty-year period the number of doctors of medicine M (in thousands)
in the United States can be approximated by where
represents 1980. The number of doctors of osteopathy B (in thousands) can be
776 12t
approximated by B
55 2t
15. Write an expression for the total number I of doctors of medicine (MD)
and doctors of osteopathy (DO). Simplify the result.
16. How many MDs and DOs did the United States have in 1995?
.
28,390 693t
M t 0
85 t
x
x
x2 1
x 2 x 2
4
x
2 4
2
x x 3
x
x2 9
3
xx 3
1 3 4
3 x x2 4
x2 1 ,
5
xx 1
2
4x 12
4 1
2x 6 x 3
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice C
1. 2.
3. 4.
5. 6.
7. 8. 9.
10. 11.
2x 12x 1
2xx 12 22x2 4x 3
x 32 x 5
x 2
x 3
2
5x
42x 5
x 2
2x 1
x
2 2
x3 2x2 xx 1x 1
xx 2x 6
1
x 1
8x 21
3x 4x 3
2
4x 4x 4
12. 13.
14.
x3x 4
4x3 x
9x 36
2 15x 14
10
15.
16.
R t
x 3
x
R 1 R 2 R 3 R 4
R 1 R 2 R 3 R 1 R 2 R 4 R 1 R 3 R 4 R 2 R 3 R 4
R 1 R 2 R 3 R 4 R 5
Rt
R1R2R3R4 R1R2R3R5 R1R2R4R5 R1R3R4R5 R2R3R4R5

LESSON
9.5
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice C
For use with pages 562–567
Find the least common denominator.
13
1. 2.
x2 2x 1 ,
4
x2 1 ,
3
5
x 4 xx 1
,
x
x2 x 2
,
16 4
3.
7
x 6 ,
5x
xx 2 ,
Perform the indicated operation(s) and simplify.
2x 1
4. 5.
x2 1
x 2 x 2
2 3x 1
6. 7.
x x2 x 2
x3 2x
8. 9.
x 2
8
x2 3
2x x
2x 5
10. 11.
x2 x
6x 9 x2 1
9 x 3
Simplify the complex fraction.
x 1
x 4 4
12. 13. 14.
9
4
x
x2
4x x 4
2 2
25 x 5
1
1
x 5 x 5
1 1
x 9 5
2
x2
10x 9
Electronics Pattern In Exercises 15 and 16, use the following
information.
The total resistance (in ohms) of three resistors in a parallel circuit is given
1
by the formula Rt
which can be simplified to
1
R1 1
R2 1
Rt ,
R3 R1R2R3 Rt
.
R1R2 R1R3 R2R3 3
x 2 8x 12
5 3x 1
3x 12 x2 2
x 12 3
3x 5x 40
x 2 x 2 x2 4
2x 1
x2 6x
4x 4 x2 3
4 x 2
5 1
2x 1 2x
15. Simplify the similar formula for four resistors in a parallel circuit given by
1
the formula Rt
1
R1 16. Following the pattern (without algebraically simplifying the complex
fraction), write the simplified formula for the total resistance Rt (in ohms)
of five resistors in a parallel circuit.
1
R2 1
R3 1
.
R4 3
2x 1 2
Algebra 2 71
Chapter 9 Resource Book
Lesson 9.5

Answer Key
Practice A
1. no 2. yes 3. no 4. no 5.
6. no solution 7. 8. 9.
10. 4 11. no solution 12.
13. 14. 15. 16.
17. 18. 3, 19. 3 20. 3 21. no solution
22. no solution 23. 4.5 miles, 8 miles
4
5, 1
6 2, 5 7, 4 5, 6
9
11
3
12
9
7
4 7
1
3

Lesson 9.6
LESSON
9.6
Practice A
For use with pages 568–574
82 Algebra 2
Chapter 9 Resource Book
NAME _________________________________________________________ DATE ___________
Determine whether the given x-value is a solution of the equation.
2 3
1. , x 1
2.
x 3 x 1
x
1
3. 4 , x 4
4.
x 5 x 3
Solve the equation by using the LCD. Check each solution.
3 2 4
x
4
5. 6. 1 7.
x x 1 x
x 4 x 4
4 1 2
8. 9.
x x 2 x
10.
Solve the equation by cross multiplying. Check each solution.
2x 3 3x
x 5
11. 12. 13.
x 3 x 4
2x 1 4 x
7 x
14. 15. 16.
x 3 4
2 x 8
x 1 x 1
Solve the equation using any method. Check each solution.
5x 14
17. 18. 2 19.
x 1 x2 3
5x
6
x 1 x 1
1
1 1 x 3
20. 21.
x 5 x 5 x2 25
22.
1 1 4
x 2 x 2 x2 4
1 1
x 2 x 3
5
x2 x 6
2x
3
5
x 3 x 3
2x 4
x 4
4
x 4
7
x 3
3x 1
x 2
23. Population Density The population density in a large city is related to
the distance from the center of the city. It can be modeled by
x
, x 4
4
D
where D is the population density (in people per square mile) and x is the
distance (in miles) from the center of the city. Find the areas where the
population density is 400 people per square mile.
5000x
x2 36
x
3 , x 2
x 2
15
x
6
4 3
x
x 6
x 3 x 3
x
x2 10
3
2x 1
5x 7
x 2
8
x 2
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice B
1. yes 2. no 3. no solution 4. 5. 0
6. no solution 7. 3 8. 9. 5 10. 11
11. 12. 3 13. 14. 15. no
solution 16. 17. 18.
19. 20. 1 21. 12,000 dozen cards
22. 30 miles per hour
1
7, 4
4, 4 5
0, 2 5, 2 2, 2
6
7
5
1
3

LESSON
9.6
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice B
For use with pages 568–574
Determine whether the given x-value is a solution of the equation.
1 1 10
1. 2.
x 3 x 3 x2 , x 5
9
Solve the equation by using the LCD. Check each solution.
3x
6
3. 1 4.
x 2 x 2
2
5. 6.
2x 5
3 5x 5
2x 5 4x2 25
7. 8.
15 6
4 3
x x
3x 1
x 2
Solve the equation by cross multiplying. Check each solution.
x 1
2 3
9. 2
10. 11.
x 3 x 3 x 1
x
12. 13. 14.
x2 6 5x 7
2
3x x
8 x
Solve the equation using any method. Check each solution.
x
4
1 , x 4
x 4 x 4
3x 1 4
x 2 x 2 x2 4
5
2x 3
4 14x 3
2x 3 4x2 9
3 x
x 2
5x 10
2x x2
15. 7 16. 17.
x 2 x 2
4 x x 4
18.
6 7x x
x 5 10
19.
3
4
12 2
x 3x
20.
21. Average Cost A greeting card manufacturer can produce a dozen cards
for $6.50. If the initial investment by the company was $60,000, how
many dozen cards must be produced before the average cost per dozen
falls to $11.50?
22. Brakes The braking distance of a car can be modeled by d s
where d is the distance (in feet) that the car travels before coming to a
stop, and s is the speed at which the car is traveling (in miles per hour).
Find the speed that results in a braking distance of 75 feet.
s2
20
7 x
x 3 4
2x
5 x2 5x
5x
3x 12
x 1 x2 2
1
x 2 2x 2
x 1
2x 3
x 1
Algebra 2 83
Chapter 9 Resource Book
Lesson 9.6

Answer Key
Practice C
1. 20 2. no solution 3. 10 4. 5.
6. 7. no solution 8. 9. 1, 3
10. 11. 2, 5 12. 13. 14. no
solution 15. 16.
1
2 17.
8
5 18. 4
19. 1.17 (Jan.), 12 (Dec.) 20. 50,000 baskets
1
2
2
1, 3
3
17
8
7
3 2
2

Lesson 9.6
LESSON
9.6
Practice C
For use with pages 568–574
84 Algebra 2
Chapter 9 Resource Book
NAME _________________________________________________________ DATE ___________
Solve the equation by using the LCD. Check each solution.
2 3
1. 2.
x 10 x 2
6
x2 12x 20
100 4x 5x 6
3. 6
4.
3 4
3 4
5. 6.
x 8 x 2
28
x2 10x 16
Solve the equation by cross multiplying. Check each solution.
3x 1 2x 5
5x 2 x 8
7. 8. 9.
6x 2 4x 13
10x 3 2x 3
2 2
x 2
10. 11. 12.
2x 3 x 5
3x 5 x 1
Solve the equation using any method. Check each solution.
x 2
13. 4
14.
3x 5
2x 5 18
15. 4 16.
x 3 x x2 3x
17. 18.
4
3 x 3
1
4x 1
4 x 3
2
x2 1 2
6x 8 x 4 x 2
4 3
x 2 x 1
8
x2 x 2
2x 4x 1 17x 4
x 2 3x 2 3x2 4x 4
4 1 5x 6
x 2 x 2 x2 4
1 1
x x 1
1
2
x 1
7 3
x 1 x 1
2
x2
1
19. Temperature The average monthly high temperature in Jackson,
191t 30
Mississippi can be modeled by T where T is
t
measured in degrees Fahrenheit and t 1, 2, . . . 12 represents the months
of the year. During which month is the average monthly high temperature
equal to 57.3 F?
20. Average Cost You invest $40,000 to start a nacho stand in a shopping
mall. You can make each basket of nachos for $0.70. How many baskets
must you sell before your average cost per basket is $1.50.
2 16.5t 114
3
x 3
2x 1 x 2
x 1
2
2x 3
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Test A
1. 72 8.49; 3, 3
2. 72 8.49; 3, 3 3.
4. 10; 0, 0
5. y
6.
7. y
8.
9. y 10.
11. 12.
13. 14.
15. 16.
17. circle;
18. parabola;
19. circle; x2 y2 y
16
2 x
2x
2 y2 x
16
2
x y2
1
1 3 2
x 1
y2
1
25 36 2 y 12 x 25
2 y2 x
16
2 y 24y
2 12x
20. hyperbola;
21. ellipse;
x 2
4
22. hyperbola;
4
4
2
x 2
4
(2, 16)
x 2
4
(2, 16)
2
x 2
4
y2
1
16
x 2
4
x
x
x
y2
1
25
y2
1
16
13; 4, 5
2
y x 2
4
y x 2
4
y x 2
4
23. hyperbola;
24. circle; x 6 25. none
2 y 62 x
36
2
y2
1
25 4
26. 2, 0 27. about 0.5 cm 28. parabolic
4
(2, 16)
4
(2, 16)
4
(2, 16)
x
x
x

CHAPTER
10
NAME _________________________________________________________ DATE
Chapter Test A
For use after Chapter 10
____________
Find the distance between the two points. Then find the
midpoint of the line segment connecting the two points.
1. 0, 0, 6, 6
2. 0, 0, 6, 6
3. 10, 5, 2, 0
4. 4, 3, 4, 3
Graph the equation.
5. 6. y2 x 4x
2 y2 16
Copyright © McDougal Littell Inc.
All rights reserved.
2
7. x 8.
2 y2 16
2
2
y
y
y
2
2
2
x
x
x 2
9. 10.
2
y2
1
4 1 4x2 9y2 100
x
1
2
y
y 2 x 2 16
y
1
2
1
y
x
x
1 x
Answers
1.
2.
3.
4.
5. Use grid at left.
6. Use grid at left.
7. Use grid at left.
8. Use grid at left.
9. Use grid at left.
10. Use grid at left.
Algebra 2 105
Chapter 10 Resource Book
Review and Assess

Review and Assess
CHAPTER
10
CONTINUED
NAME _________________________________________________________ DATE ____________
Chapter Test A
For use after Chapter 10
Write an equation for the conic section.
11. Parabola with vertex at 0, 0 and focus at 3, 0
12. Parabola with vertex at 0, 0 and directrix y 6
13. Circle with center at 0, 0 and radius 4
14. Circle with center 1, 1 and radius 5
15. Ellipse with center 0, 0, vertex at 0, 6, and co-vertex at 5, 0
16. Hyperbola with center 0, 0, foci at 2, 0 and 2, 0, and vertices
at 1, 0 and 1, 0
Classify the conic section and write its equation in standard
form.
17. 18.
19. 20.
21.
23.
24. x
22.
2 y2 4x
12x 12y 36 0
2 25y2 100
4x2 y2 4x 16
2 y2 25x
16 0
2 4y2 3x 100
2 3y2 y
48 0
2 x 2x 0
2 y2 16 0
Find the points of intersection, if any, of the graphs in the
system.
25. x2 y2 16
y 5
27. Telescope The equation of a mirror in a particular telescope is
y where x is the radius (in centimeters) and y is the depth
(in centimeters). If the mirror has a diameter of 32 centimeters,
x2
520 ,
what is the depth of the mirror?
28. Classify the mirror in Exercise 27 as parabolic, elliptical, or
hyperbolic.
106 Algebra 2
Chapter 10 Resource Book
26.
x2
4
y2
1
16
x 2
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Test B
1. 2.
3.
4. 41 6.40;
5. y
6.
y
15
82 9.06;
2 , 6
9
13 3.61;
2 , 12
3
7
13; 2, 2
2 , 1
7. y
8.
9. y 10.
11. 12. x2 y2 y 25
2 12x
13. 14.
x 12 y 22 16
x 2
15. 1 16.
16 9
y2
17. hyperbola;
18. ellipse;
19. circle; x2 y2 25
20. hyperbola;
21. ellipse;
2
1
2
x 2
9
2
1
2
x 2
9
y2
4
y2
5
1
x 2
4
1
y 2 x 2 1
y2
5
x 1 2 y 2 1
1
22. circle; x 4 2 y 1 2 25
x
x
x
2
y
2
2
2
y
2
x 2
9
x
x
6 x
y2
4
1
23. hyperbola;
24. parabola; x 25. 0, 0 26. none
2 y 2
12y
2 x 32
1
9 36
27. y 28. parabolic
0.1
2
x

CHAPTER
10
NAME _________________________________________________________ DATE
Chapter Test B
For use after Chapter 10
____________
Find the distance between the two points. Then find the
midpoint of the line segment connecting the two points.
1. 8, 6, 4, 1
2. 3, 2, 0, 0
3. 0, 0, 9, 1
4. 10, 8, 5, 4
Graph the equation.
5. 6. y2 x 25x
2 y2 30
Copyright © McDougal Littell Inc.
All rights reserved.
2
x
7. 8.
2
y2
1
9 16
1
y
y
9. x 2 10.
2 y 32 16
2
2
1
y
2
x
x
x
x 8 2
16
2
y
2
2
y 3 2 9
2x 2
2
y
y 52
1
4
y
2
2
x
x
x
Answers
1.
2.
3.
4.
5. Use grid at left.
6. Use grid at left.
7. Use grid at left.
8. Use grid at left.
9. Use grid at left.
10. Use grid at left.
Algebra 2 107
Chapter 10 Resource Book
Review and Assess

Review and Assess
CHAPTER
10
CONTINUED
NAME _________________________________________________________ DATE ____________
Chapter Test B
For use after Chapter 10
Write an equation for the conic section.
11. Parabola with vertex at 0, 0
and directrix x 3
12. Circle with center at (0, 0 and passing through 3, 4
13. Circle with center at 1, 2 and radius 4
14. Ellipse with center at 0, 0, x-intercepts
of 3, 0 and 3, 0, and
y-intercepts
0, 2 and 0, 2
15. Ellipse with center at 0, 0, vertex 4, 0, and co-vertex 0, 3
16. Hyperbola with foci at 3, 0 and 3, 0 and vertices at 2, 0 and
2, 0
Classify the conic section and write its equation in standard
form.
17. 18.
19. 20.
21.
23.
24. x
22.
2 y 32 y 32 x2 4y2 6x 16y 29 0
x2 y2 4x 8x 2y 8 0
2 8x 4y2 y
0
2 1 x2 x2 y2 4x
25 0
2 9y2 5x 36
2 9y2 45
Find the points of intersection, if any, of the graphs in the
system.
25. 26. y x2 x2 y2 2x 2y
x 2 y 2 2x 2y 0
27. Telescope The equation of a mirror in a particular telescope is
y where x is the radius (in centimeters) and y is the depth
(in centimeters). Graph the equation of the mirror.
x2
780 ,
28. Classify the mirror in Exercise 27 as parabolic, elliptical, or
hyperbolic.
108 Algebra 2
Chapter 10 Resource Book
y x 2
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Test C
1.
2. 162 12.7;
3. 116 10.8; 8, 3
4. 8 2.83; 6, 2
5. y
6.
1
80 8.94; 4, 2
1
2 , 2
7. y
8.
9. y 10.
11. 12.
13. 14.
x 32 x y 12
1
4 1
2
x 3
2 y
1
25 4 2 y 22 x 25
2 12y
x 3
15. 16.
2
x
9
2
y2
1
16 20
17. ellipse;
18. parabola; x 5
3y 11
x2 y2
1
16 9
19. hyperbola; x2
9
4
1
4
1
2
x
x
2 x
6 2 1
y2
1
16
y
4
12
y
6
2
1
2
y
1
x
x
x
y 22
16
1
20. parabola;
x 2 15
2 y
y 2
21. hyperbola;
2
1
x 62
9
22. circle; x 42 y 32 25
23. circle; x 22 y 32 16
24. ellipse;
25.
26. 27. 28. 1 feet
1
x2 0, 3,
0, 4 20y
23
, 11
2 4 , 23 x 8
, 11
2 4
2 y 52
1
16 4
4
1

CHAPTER
10
NAME _________________________________________________________ DATE
Chapter Test C
For use after Chapter 10
____________
Find the distance between the two points. Then find the
midpoint of the line segment connecting the two points.
1. 8, 4, 0, 0
2. 5, 4, 4, 5
3. 10, 8, 6, 2
4. 7, 3, 5, 1
Graph the equation.
5. 6. y2 x 9x
2 y2 121
Copyright © McDougal Littell Inc.
All rights reserved.
4
2
y
y
4
2
y 2
9. 10.
2
x 4
9
2 y 52
1
9 4
2
y
x
7. 8. x2 y2 3x 2x 4y 1
2 y2 12
x
2 x
2
y
1
2
y
1
1
y
1
x 32
36
x
x
1
x
Answers
1.
2.
3.
4.
5. Use grid at left.
6. Use grid at left.
7. Use grid at left.
8. Use grid at left.
9. Use grid at left.
10. Use grid at left.
Algebra 2 109
Chapter 10 Resource Book
Review and Assess

Review and Assess
CHAPTER
10
CONTINUED
NAME _________________________________________________________ DATE ____________
Chapter Test C
For use after Chapter 10
Write an equation for the conic section.
11. Parabola with vertex at 0, 0 and focus at 0, 3
12. Circle with center at (3, 2 and radius 5
13. Ellipse with vertices at 5, 0 and 5, 0, and co-vertices at 0, 2
and 0, 2
14. Ellipse with center at 3, 1, vertices at 1, 1 and 5, 1, and
co-vertices at 3, 0 and 3, 2
15. Hyperbola with vertices at 4, 0 and 4, 0 and foci at 6, 0
and 6, 0
16. Hyperbola with foci at 2, 2 and 8, 2 and asymptote with
slope
4
3
Classify the conic section and write its equation in standard
form.
17. 18.
19.
21.
20.
22.
23.
24. x2 4y2 x
16x 40y 148 0
2 y2 x
4x 6y 3 0
2 y2 x
8x 6y 0
2 9y2 12x 36y 9 0
2x2 16x 15y 0
2 9y2 y 3x
144 0
2 9x 5x 3
2 16y2 144 0
Find the points of intersection, if any, of the graphs in the
system.
25. x2 4y2 36
x 2 y 3
27. Communications The cross section of a television antenna dish is
a parabola. The receiver is located at the focus, 5 feet above the
vertex. Find an equation for the cross section of the dish. (Assume
the vertex is at the origin.)
28. If the television antenna dish in Exercise 27 is 10 feet wide, how
deep is it?
110 Algebra 2
Chapter 10 Resource Book
26.
16x2 y2 x
2y 8 0
2
y2
1
25 16
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Cumulative Review
1. 60 meters 2. 3744 hours 3. liters
4. yes; 18 5. yes; 6 6. yes;
7. no; 89 8. yes; 0 9. no; 52
10. 11.
y
1
1
12. 13.
14.
15.
16.
17.
18.
19.
20. 21. 22.
8 4
5 5 i
y 2x 5x 3;
9 18i 18 i
5
x 4; y 4 x 2; y 3
y x 3x 1; 3, 1
y x 5x 3; 5, 3
y xx 4; 0, 4
y 3x 2x 1; 2, 1
y x 3x 2; 3, 2
, 3 2
23. 24.
2
y
2
x
x
25.
26. A 27. C 28. B
29.
30.
31.
32. 33.
34. x 35. 8 36. 5 37. 7
2 x 5
3x 9
30
x 4
x 5
20
3x 7
x 4
7
x 5
x 1
2
6x 13
x 1
37
y
1
1
x
x 3
1
y
7 7
12
12
1
2
y
2
x
x
4 712
2 76
10 14
27 15
38. or 39. 40. 41. yes
42. no 43. yes 44. no 45. no 46. no
47. decay 48. growth 49. decay 50. growth
51. decay 52. growth 53. 5 54. 6
55. 56. 4 57. 58. 59.
60. 61. 62. 2.46 63. 1.03 64. 0.981
65. 66.
67. 68.
69. y 70. y 0; x 11
71. 3; $225
3
2
3 4
8
5
8
7
y 1; x 0 y 2; x 3
y 1; x 2 y 1; x 4
5 ; x 1
9
4

Review and Assess
CHAPTER
10 Cumulative Review
NAME _________________________________________________________ DATE ____________
For use after Chapters 1–10
Give the answer with the appropriate measure. (1.1)
1.
6 meters
10 minutes
1 minute 2.
72 hours
1 week 52 weeks
3.
Decide whether the function is linear. Then find the indicated value
of (2.1)
4. 5. 6.
7. 8. f x 2 5x; f 9.
2
f x 9x3 4x2 f x.
f x x 13; f 5
f x 6; f 7
x 1; f 2
Graph the step function. (2.7)
10.
2, if 0 < x ≤ 1
3, if 1 < x ≤ 2
f x 4, if 2 < x ≤ 3
5, if 3 < x ≤ 4
6, if 4 < x ≤ 5
11.
Solve the matrix equation for x and y. (4.1)
12. 13.
2x
1
3
4 8
1
3
y
Write the quadratic function in intercept form and give the
function’s zeros. (5.2)
14. 15. 16.
17. 18. 19. y 2x2 y x x 15
2 y 3x 5x 6
2 y x
9x 6
2 y x 4x
2 y x 2x 15
2 4x 3
Write the expression as a complex number in standard form. (5.4)
20. 21. 22.
Graph the system of inequalities. (5.7)
23. 24. 25. y > x2 y ≤ x 32 y ≥ x2 3i6 3i
3 2i4 3i
8
4 2i
6x
y ≤ x 2 8x 12
Use what you know about end behavior to match the polynomial
function with its graph. (6.2)
26. 27. 28. f x 3x
A. y
B. y
C. y
3 x2 f x x 1
4 4x2 f x 2x 3
3 6x2 8x 9
4
116 Algebra 2
Chapter 10 Resource Book
2
x
y ≥ x 2 5
1
1, if 10 < x ≤ 8
3, if 8 < x ≤ 6
f x 5, if 6 < x ≤ 4
7, if 4 < x ≤ 2
9, if 2 < x ≤ 0
3x
1
2
2y
3 3
8
x
5
15 1
3 liters 7 3
4 liters
1
1 9
9
f x x 5; f 7
f x 3
4 x2 4; f 8
7
4
y > x 2 4
2
1
Copyright © McDougal Littell Inc.
All rights reserved.
x

CHAPTER
10
CONTINUED
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ____________
Cumulative Review
For use after Chapters 1–10
Divide using synthetic division. (6.5)
29. 30. 31.
32. 33. 34. x3 x 27 x 3
2 x 5 x 5
2 3x
4 x 4
2 x 4x x 1
2 6x 4x 3 x 1
2 5x 2 x 3
Simplify the expression. (7.2)
35. 36. 37.
38. 34 39.
10
410
40.
4 45
4
4 16 125
4 16
Graph the function f. Then use the graph to determine whether the
inverse of f is a function. (7.4)
41. 42. f x x 43.
44. f x x 7
45. f x x 2x 3 46.
2 f x 3x 5
8
Tell whether the function represents exponential growth or
exponential decay. (8.2)
2 x
47. 48. 49.
50. 51. f x 4 52.
2
f x 52 f x 5 4x f x 31 3 x
Use a property of logarithms to evaluate the expression. (8.5)
53. 54. log2 4 55.
3
log39 27
1
56. log4 16 57. log
58.
1000
2
Solve the exponential equation. (8.6)
59. 60. 61.
62. 63. 64. 3 3ex 10 5
2x 3 5 120
x 8
15
3x 164x2 3x7 272x5 102x1 1003x4 Identify the horizontal and vertical asymptotes of the graph of the
function. (9.2)
x 1
65. 66. y 67. y
x 2
3
4
y 1
2
x x 3
68. 69. 70. y
4
3x 4
y y
5x 5
x 11
x
x 4
71. Breaking Even You start a business selling wooden carvings. You spend
$180 on supplies to get started; the wood for each carving costs $15. You
sell the carvings for $75. How many carvings must you sell for your
earnings to equal your expenses? What will your earnings and expenses
equal when you break even? (3.2)
5 x
47 4 7
53 5 81
59
f x 3x 3
f x 4x 4 2x 1
f x 4 3 x
f x 40.25 x
log 5 1
25
ln 1
e 4
Algebra 2 117
Chapter 10 Resource Book
Review and Assess

Answer Key
Practice A
1. 2.
3. 4.
5.
6.
7. 8.
9.
10.
11.
12. 13. isosceles
14. isosceles 15. scalene 16.
17. 18.
19. 20. y
21. y 2x 10 22. 4, 6 23. 0, 2
24. 1, 7 25. 0, 8 26. 16, 20
27. 0, 28 28. about 50.6 mi
3
y
11
4x 2
2
y
31
3x 6
3
52 7.07;
253 14.56; 3, 1
213 7.21; 1, 1
217 8.25; 1, 4
y x 7
y x 3
21
2x 4
5
82 9.06;
2 , 12
1
5; 2 , 12
5
13 3.61; 4,
2 , 1
1
52 7.07;
2
1
5;
1
2 , 2
11
5; 3,
11
37 6.08; 5, 2
2 , 4
5
5; 2, 2
3
2

LESSON
10.1
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice A
For use with pages 589–594
Find the distance between the two points. Then find the midpoint
of the line segment joining the two points.
1. 0, 0, 4, 3
2. 5, 4, 1, 1
3. 2, 5, 8, 6
4. 7, 6, 4, 2
5. 4, 0, 3, 1
6. 5, 1, 3, 2
7. 1, 1, 4, 3
8. 5, 1, 4, 0
9. 0, 3, 5, 2
10. 1, 8, 5, 6
11. 3, 2, 1, 4
12. 2, 0, 0, 8
The vertices of a triangle are given. Classify the triangle as scalene,
isosceles, or equilateral.
13. 0, 4, 8, 3, 8, 11 14. 0, 0, 3, 4, 4, 3
15. 1, 2, 1, 6, 0, 4
Write an equation for the perpendicular bisector of the line
segment joining the two points.
16. 0, 2, 5, 7
17. 2, 7, 4, 5
18. 0, 2, 3, 4
19. 2, 6, 0, 3
20. 1, 0, 5, 8
21. 2, 2, 6, 6
Use the given distance d between the two points to solve for x.
22. 3, 5, 0, x; d 10
23. 1, 4, x, 2; d 5
24. 6, x, 2, 3; d 42
25. x, 6, 4, 9; d 5
Rhode Island In Exercises 26–28, use the following information.
A coordinate plane is placed over the map of Rhode Island
shown at the right. Each unit represents four miles.
26. Approximate the coordinates of the point representing Westerly.
27. Approximate the coordinates of the point representing Woonsocket.
28. Use the distance formula to approximate the distance between
Westerly and Woonsocket.
Westerly
Algebra 2 13
Chapter 10 Resource Book
y
Woonsocket
Providence
RI
x
Lesson 10.1

Answer Key
Practice B
1.
2.
3.
4.
5.
6. 7. scalene
8. isosceles 9. scalene 10.
11. y 12. y x 4 13. 0, 4
14. 1, 15 15. about 166 miles 16. about 0.74
hours or 44 minutes
18. about 14.8 hours
17. about 74 miles
3
17 4.12;
y 3x 9
21
2x 4
1
13 3.61;
213 7.21; 2, 2
81.64 9.04; 0.4, 3
6 , 4
7
157 12.53; 1,
2 , 1
1
29 5.39; 5,
2
1
2

Lesson 10.1
LESSON
10.1
Practice B
For use with pages 589–594
14 Algebra 2
Chapter 10 Resource Book
NAME _________________________________________________________ DATE ___________
Find the distance between the two points. Then find the midpoint
of the line segment joining the two points.
1. 4, 3, 6, 2
2. 2, 5, 4, 6
3. 5, 0, 2, 2
4. 6, 1, 2, 5
5. 2.5, 1, 1.7, 7
6. , 6, 1,
2
The vertices of a triangle are given. Classify the triangle as scalene,
isosceles, or equilateral.
7. 1, 3, 6, 1, 2, 5
8. 9, 2, 3, 6, 3, 2 9. 8, 5, 1, 2, 3, 2
Write an equation for the perpendicular bisector of the line
segment joining the two points.
10. 9, 2, 3, 2
11. 2, 5, 1, 7
12. 0, 6, 2, 4
Use the given distance d between the two points to solve for x.
13. 3, 2, 10, x; d 53
14. 3, x, 5, 7; d 217
Wisconsin In Exercises 15–18, use the following information.
A coordinate plane is placed over the map of Wisconsin shown
at the right. Each unit represents 10.5 miles.
15. Approximate the distance in miles between LaCrosse and
Green Bay.
16. How long would a flight from LaCrosse to Green Bay take
traveling at 225 miles per hour?
17. Approximate the distance in miles between EauClaire and
LaCrosse.
18. What is the minimum time necessary to walk from EauClaire
to LaCrosse walking at a rate of five miles per hour?
2
3
WISCONSIN
EauClaire
y
LaCrosse
3
Green Bay
Copyright © McDougal Littell Inc.
All rights reserved.
x

Answer Key
Practice C
1. 2173 26.31; 8, 1
2. 61.61 7.85; 0.75, 1
3. 109.8 10.48; 3.9, 1.9
4.
493
9
1813
64
7.40; 17 6 , 1
1 19
5.32; 16 , 8
5.
6.
7. isosceles 8. scalene 9. isosceles
10. 11. y 12. x 3
13. 8.8, 1.2 14. 2, 8 15. about 169 miles
16. about 3.1 hours
18. 12:03 P.M.
17. 21, 31.5
9
y 2
4
37
5x 10
13,549
1 1
3600 1.94; 12 , 40

LESSON
10.1
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice C
For use with pages 589–594
Find the distance between the two points. Then find the midpoint
of the line segment joining the two points.
1. 2. 3.
4. 5, 2, 5. , 5, 3,
1
6.
2
10, 12, 6, 14
2.5, 3.2, 4, 1.2
5.1, 7, 2.7, 3.2
, 4
3
The vertices of a triangle are given. Classify the triangle as scalene,
isosceles, or equilateral.
7. 4, 2, 3, 1, 1, 4
8. 8, 3, 2, 1, 0, 4
9. 5, 8, 1, 6, 2, 1
Write an equation for the perpendicular bisector of the line
segment joining the two points.
10. 1, 7, 3, 2
11. 7, 3, 7, 12
12. 9, 2, 3, 2
Use the given distance d between the two points to solve for x.
13. 3.5, x, 6, 3.8; d 115.25
14. 5, 8, x, 11; d 32
Wisconsin In Exercises 15–18, use the following information.
A coordinate plane is placed over the map of Wisconsin shown
at the right. Each unit represents 10.5 miles.
15. Approximate the distance in miles between Green Bay and
EauClaire.
16. How long would a trip from Green Bay to EauClaire take
traveling at 55 miles per hour?
17. At the halfway point of your trip from Green Bay to EauClaire,
you need to pick up your friend. Approximate the coordinates
of the meeting point.
18. If you leave Green Bay at 10:30 A.M., at what time will you
meet your friend?
1 2
8
4
2
3, 45,
1 3
2 ,
WISCONSIN
EauClaire
Algebra 2 15
Chapter 10 Resource Book
y
LaCrosse
4
Green Bay
x
Lesson 10.1

Answer Key
Practice A
1. B 2. C 3. A 4. right 5. up 6. left
7. down
8. 9.
1
2, 0; x 2
10. 11.
1
y
y
1
1
x
x
0, 3; y 3
12. 13. 14.
15. 16. 17.
18. 19. 20. x2 x 80y
2 y 24y
2 y
16x
2 x 4x
2 x 12y
2 y
4y
2 y 12x
2 x 8x
2 0,
24y
1
2; y 1
4, 0; x 4
2
1
1
y
y
1
1
x
x

LESSON
10.2
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice A
For use with pages 595–600
Match the equation with its graph.
1. 2. 3. x
A. y
B. y
C.
2 x 2y
2 y 2y
2 2x
1
2
x
Tell whether the parabola opens up, down, left or right.
4. 5. 6. 7. y 4x2 y2 x 10x
2 2y 8y
2 x
Graph the equation. Identify the focus and directrix of the parabola.
8. 9. 10. 11. x2 y 2y
2 x 16x
2 y 12y
2 8x
Write the standard form of the equation of the parabola with the
given focus and vertex at (0, 0).
12. 0, 6
13. 2, 0
14. (3, 0
15. 0, 1
Write the standard form of the equation of the parabola with the
given directrix and vertex at (0, 0).
16. y 3
17. x 1
18. x 4
19. y 6
20. Sailboat Race The course for a sailboat race includes a
turnaround point marked by a stationary buoy. The sailboats
must pass between the buoy and the straight shoreline. The
boats follow a parabolic path past the buoy, which is 40 yards
from the shoreline. Find an equation to represent the parabolic
path, so that the boats remain equidistant from the buoy and
the straight shoreline.
2
1
x
40 yards
Shoreline
Algebra 2 27
Chapter 10 Resource Book
1
y
1
x
Lesson 10.2

Answer Key
Practice B
1. down 2. up 3. right 4. left
5. 6.
2; y 4, 0; x 4
7. 8.
1
2
0, 1
1
0, 3; y 3
9. 10.
1
1
4 , 0; x 4
0, 1, 0; x 1
11. 12.
1
16; y 1
16
3 2 , 0; x 32
2
1
1
y
y
y
y
1
1
1
1
x
x
x
x
1 8 , 0; x 18
13. 14. 15.
16. 17. 18.
19. 20. 21.
22. x2 x
5y
2 x 14y
2 y 2y
2 x
x
2 y 12y
2 x 4x
2 y
12y
2 x 2x
2 y 4y
2 8x
1
y
1
1
2
y
y
1
1
2
y
1
x
x
x
x

Lesson 10.2
LESSON
10.2
Practice B
For use with pages 595–600
28 Algebra 2
Chapter 10 Resource Book
NAME _________________________________________________________ DATE ___________
Tell whether the parabola opens up, down, left or right.
1. 2. 3. 4. y2 y 24x
2 x 16x
2 x 12y
2 8y
Graph the equation. Identify the focus and directrix of the parabola.
5. 6. 7. 8.
9. 10. 11. 12. x 2y2 y2 4x y 6x 0
2 4x 0
2 x
y 0
2 y 12y
2 y x
2 x 16x
2 2y
Write the standard form of the equation of the parabola with the
given focus and vertex at (0, 0).
13. 2, 0
14. 0, 1
15. , 0
16.
Write the standard form of the equation of the parabola with the
given directrix and vertex at (0, 0).
17. 18. 19. x 20.
1
x 1
y 3
21. Television Antenna Dish The cross section of a television antenna
dish is a parabola. For the dish at the right, the receiver is located at
the focus, 3.5 feet above the vertex. Find an equation for the cross
section of the dish. (Assume the vertex is at the origin.)
22. Sailboat Race The course for a sailboat race includes a
turnaround point marked by a stationary buoy. The sailboats
must pass between the buoy and the straight shoreline. Find
an equation to represent the parabolic path, so that the boats
remain equidistant from the buoy and the straight shoreline.
1 2
4
2.5 miles
Shoreline
(0, 3
y 1
2
3.5 feet
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice C
1. 2.
0, 1
0,
3. 4.
9
16; y 9
32; y 16
1
32
1
y
5. 6.
3, 0; x 3
1
5
3
16 , 0; x 3 16
1
7. 8.
1
y
y
y
9. 10. 11.
12. 13. 14.
15. 16. 17.
18. 19. 20.
21. 22. 23.
24. 25. 6.25 ft 26. about 13,741 ft3 y2 3
x2 1
3y x2 y y
2 x
2x
2 x 8y
2 y 24y
2 y
20x
2 y 4x
2 5
2x x2 y
y
2 x 3x
2 x 2y
2 y
64y
2 x 48x
2 y 8y
2
32x
1
0, 2; y 2
1
6 , 0; x 6
2 x
1
1
1
x
x
x
x
8, 0; x 8
0, 5; y 5
1
2
2
y
y
y
1
2
2
1
y
1
x
x
x
x

LESSON
10.2
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice C
For use with pages 595–600
Graph the equation. Identify the focus and directrix of the parabola.
1. 2. 3. 4.
5. 6. 7. 8. 2x 3y2 x 0
2 20y x 8y 0
2 y 0
2 y
12x 0
2 3x 4y 32x 0
2
x2 9
4y 8x2 y
Write the standard form of the equation of the parabola with the
given focus and vertex at (0, 0).
9. 10. 11. 12.
13. 14. 15.
1
0, 16.
3
8, 0
0, 2
12, 0
0, 16
0, 1
, 0
2
Write the standard form of the equation of the parabola with the
given directrix and vertex at (0, 0).
17. 18. 19. 20.
21. 22. 23. 24. x 3
y 8
1
y 12
1
x 4
1
x 1
x 5
y 6
y 2
2
25. Solar Energy Cross sections of parabolic mirrors at a solar-thermal
complex can be modeled by the equation
1
25 x2 y
where x and y are measured in feet. The oil-filled heating tube is
located at the focus of the parabola. How high above the vertex of the
mirror is the heating tube?
26. Storage Building A storage building for rock salt has the shape of
a paraboloid which has vertical cross sections that are parabolas. The
equation of a vertical cross section is If the building is
27 feet high, how much rock salt will it hold? (Hint: The volume of
a paraboloid is v where r is the radius of the base and h is
the height.)
1
2r 2 y
h,
1
12x2 .
4
4
5
Algebra 2 29
Chapter 10 Resource Book
r
5 8 , 0
y
y
heating
tube
27 ft
5
x
x
Lesson 10.2

Answer Key
Practice A
1. B 2. C 3. A
4. 5.
r 2
6. 7.
r 5
1
8. 9.
r 23 3.46
2
1
y
y
y
1
2
1
r 2 1.41
10. 11.
12. 13.
14. 15.
16. 17.
18. 19.
20. x2 y2 y
400
1
x
y 4x 17
10
3x 3
2 y2 x 29
2 y2 x
20
2 y2 x 25
2 y2 x
1
2 y2 x 2
2 y2 x
6
2 y2 x 64
2 y2 4
x
x
x
r 10
r 6 2.45
3
y
1
1
3
y
y
1
1
x
x
x

LESSON
10.3
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice A
For use with pages 601–607
Match the equation with its graph.
1. 2. 3. x
A y
B. y
C.
2 y2 x 3
2 y2 x 36
2 y2 16
1
1
x
Graph the equation. Give the radius of the circle.
4. 5. 6.
7. 8. 9. x2 y2 x 2
2 y2 x 12
2 y2 x
6
2 y2 x 25
2 y2 x 100
2 y2 4
Write the standard form of the equation of the circle with the given
radius and whose center is the origin.
10. 2 11. 8 12. 6
13. 2
Write the standard form of the equation of the circle that passes
through the given point and whose center is the origin.
14. 0, 1
15. 5, 0
16. 2, 4
17. 5, 2
The equation of a circle and a point on the circle is given. Write an
equation of the line that is tangent to the circle at that point.
18. 19. x2 y2 x 10; 1, 3
2 y2 17; 4, 1
20. Garden Irrigation A circular garden has an area of about 1257 square
feet. Write an equation that represents the boundary of the garden. Let
0, 0 represent the center of the garden.
2
2
x
Algebra 2 41
Chapter 10 Resource Book
2
y
2
x
Lesson 10.3

Answer Key
Practice B
1. 2.
r 4
3. 4.
r 210 6.32
5. 6.
r 7 2.65
1
2
1
7. 8.
1
y
y
y
y
1
2
1
2
x
x
x
x
r 13 3.61
r 11
r 3
1
3
1
1
y
y
y
y
1
3
1
1
x
x
x
x
9. 10.
11.
12.
13.
14.
15. x2 y2 x
40
2 y2 x
65
2 y2 x
490
2 y2 x
45
2 y2 x
42
2 y2 y
22
1
1
x
16. 17.
18. 19.
20. x2 y2 y
160,000
4
y
41
5x 5
2
x
13
3x 3
2 y2 x 41
2 y2 5

Lesson 10.3
LESSON
10.3
Practice B
For use with pages 601–607
42 Algebra 2
Chapter 10 Resource Book
NAME _________________________________________________________ DATE ___________
Graph the equation. Give the radius of the circle.
1. 2. 3.
4. 5. 6. 4x2 4y2 3x 36
2 3y2 x 21
2 y2 x
121
2 y2 x 40
2 y2 x 13
2 y2 16
The equations of both circles and parabolas are given. Graph the
equation.
7. 8. 9. x2 2x 12y 0
2 2y2 x 16
2 4y 0
Write the standard form of the equation of the circle with the given
radius and whose center is the origin.
10. 22
11. 42
12. 35
13. 710
Write the standard form of the equation of the circle that passes
through the given point and whose center is the origin.
14. 8, 1
15. 2, 6
16. 2, 1
17. 4, 5
The equation of a circle and a point on the circle is given. Write an
equation of the line that is tangent to the circle at that point.
18. 19. x2 y2 x 41; 4, 5
2 y2 13; 2, 3
20. Jacob’s Field Jacob’s Field is the home field of the
Cleveland Indians major league baseball team. The
stadium is approximately circular with a diameter of
800 feet. Suppose a coordinate plane was placed over
the base of the stadium with the origin at the center of
the stadium. Write an equation in standard form for the
outside boundary of the stadium.
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice C
1. 2.
r 7 2.65
3. 4.
r 4
5. 6.
r 6
1
1
2
7. 8.
1
y
y
y
y
1
1
2
1
x
x
x
x
r 6
r 26 4.90
r 25 4.47
2
2
2
1
y
y
y
y
2
2
2
1
x
x
x
x
9. 10.
11.
12.
13.
14.
15. x2 y2 257
x
4
2 y2 x
244
2 y2 x
54
2 y2 x
14
2 y2 x
32
2 y2 y
35
2
1
x
16. 17. x2 y2 x 10
2 y2 145
18. y 7x 50 19.
20. 17.05 cm
y 2
x 6
2

LESSON
10.3
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice C
For use with pages 601–607
Graph the equation. Give the radius of the circle.
1. 2. 3.
4. 5. 6. 20x2 20y2 7x 400
2 7y2 6x 252
2 6y2 3x
144
2 3y2 2 48
y 2 x 18
2 y2 7
The equations of both circles and parabolas are given. Graph the
equation.
7. 8. 9. 4x y2 4x 0
2 4x y 0
2 4y2 1
Write the standard form of the equation of the circle with the given
radius and whose center is the origin.
10. 35
11. 42
12. 14
13. 36
Write the standard form of the equation of the circle that passes
through the given point and whose center is the origin.
14. 10, 12
15. , 8
16. 12, 1
17. 1, 3
1 2
1
2x2 1
The equation of a circle and a point on the circle is given. Write an
equation of the line that is tangent to the circle at that point.
18. 19. x2 y2 x 24; 22, 4
2 y2 50; 7, 1
20. Water Lily In his novel Kavenaugh, Henry Wadsworth
Longfellow stated the following puzzle about the water lily.
When the stem of the water lily is vertical, the blossom is
10 centimeters about the surface of the lake. If you pull the lily
to one side, keeping the stem straight, the blossom touches the
water at a spot 21 centimeters from where the stem formerly
cut the surface. How deep is the water?
10 cm
x
21 cm
Algebra 2 43
Chapter 10 Resource Book
Lesson 10.3

Answer Key
Practice A
1. vertices: ±9, 0; co-vertices: 0, ±2;
foci: ±77, 0 2. vertices: 0, ±5;
co-vertices: ±4, 0; foci: 0, ±3
3. vertices: 0, ±4; co-vertices: ±23, 0;
foci: 0, ±2 4. 1; vertices:
1 4
0, ±2;
co-vertices: ±1, 0; foci: 0, ±3
x 2
5. 1; vertices:
169 1
±13, 0;
co-vertices: 0, ±1; foci:
y2
x2 y2
6. 1; vertices:
4 25
0, ±5;
co-vertices: ±2, 0; foci: 0, ±21
7. 8.
2
y
2
vertices: ±7, 0; vertices: 0, ±8;
co-vertices: 0, ±4; co-vertices: ±2, 0;
foci: foci: 0, ±215
±33, 0
9. y vertices: ±6, 0;
co-vertices: 0, ±2;
4
foci:
2
10. y vertices: 0, ±6;
co-vertices: ±3, 0;
2
foci: 0, ±33
2
x2 y2
x
x
x
±242, 0
2
y
4
±42, 0
x
11. 12.
vertices: vertices:
co-vertices: co-vertices:
foci: foci:
13. 14.
x2 x y2
1
25 9 2
0, ±4;
0, ±10;
±2, 0;
±1, 0;
0, ±23
0, ±311
y2
1
49 25
x2 y2
15. 1 16.
1 4
x 2
17. 1 18.
64 36
x 2
1
y
y2
19. 1 20.
32 36
y2
x2 y2
1
x2 y2
1
16 100
x 2
9
y2
8
1
x2 y2
1
25 16
21. 1 22. 3, 0, 3, 0
4 9
x
y
2
x

Lesson 10.4
LESSON
10.4
Practice A
For use with pages 609–614
54 Algebra 2
Chapter 10 Resource Book
NAME _________________________________________________________ DATE ___________
Write the equation in standard form (if not already). Then identify
the vertices, co-vertices, and foci of the ellipse.
1. 2. 3.
4. 5. 6. 25x2 4y2 x 100
2 169y2 144x 169
2 36y2 x
144
2
x y2
1
12 16 2
x y2
1
16 25 2
y2
1
81 4
Graph the equation. Then identify the vertices, co-vertices, and foci
of the ellipse.
x 2
7. 1
8. 1
9.
49 16 4 64
y2
x2 y2
x2 y2
x2 y2
10. 1
11. 1
12.
9 36 4 16
Write an equation of the ellipse with the given characteristics and
center at (0, 0).
13. Vertex: 7, 0
14. Vertex: 5, 0
15. Vertex: 0, 2
Co-vertex: 0, 5
Co-vertex: 0, 3
Co-vertex: 1, 0
16. Vertex: 0, 10
17. Vertex: 8, 0
18. Vertex: 3, 0
Co-vertex: 4, 0
Co-vertex: 0, 6
Focus: 1, 0
19. Vertex: 0, 6
20. Co-vertex: 0, 4
21. Co-vertex: 2, 0
Focus: 0, 2
Focus: 3, 0
Focus: 0, 5
22. Archway A semi-elliptical archway is to be formed over
the entrance to an estate. The arch is to be set on pillars
that are 10 feet apart. The arch has a height of 4 feet above
the pillars. Where should the foci be placed in order to
sketch the plans for the semi-elliptical archway?
x2 y2
1
36 4
x 2
1
(0, 0)
y2
1
100
y
10 ft
4 ft
Copyright © McDougal Littell Inc.
All rights reserved.
x

Answer Key
Practice B
1. 2.
vertices: 0, ±9; vertices: 0, ±7;
co-vertices: ±8, 0; co-vertices: ±1, 0;
foci: 0, ±17 foci: 0, ±43
3. y vertices: ±11, 0;
co-vertices: 0, ±10;
3
foci:
x
4. 5.
2
x y2
1;
25 4 2
y2
1;
16 9
vertices: ±4, 0; vertices: ±5, 0;
co-vertices: 0, ±3; co-vertices: 0, ±2;
foci: foci:
6.
x 2
1
2
1
y
±7, 0
y2
1;
169
y
2
1
3
3
x
x
x
x
y
8
±21, 0
±21, 0
vertices: 0, ±13;
co-vertices: ±1, 0;
foci: 0, ±242
4
y
2
2
x
x
7. 8.
9. 10.
11. 12.
13. 1 14.
9 36
15. 1 16.
49 16
17. 1 18.
9 36
19.
20.
x 2
5
1
1
y
y
y
x2 y2
y2
x2 y2
x2 2
57.95 y2
2 1
56.71
x2 y2
1;
16 36
5
1
1
x
x
x
x 2
4
x 2
1
y2
1
16
y2
4
x2 y2
1
36 4
2
y
2
2
1
2
y
y
y
1
2
1
2
x
x
x
x

LESSON
10.4
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice B
For use with pages 609–614
Write the equation in standard form (if not already) and graph the
equation. Then identify the vertices, co-vertices, and foci of the
ellipse.
1. 2. 3.
4. 5. 6. 169x2 y2 4x 169
2 25y2 9x 100
2 16y2 x
144
2
x y2
1
121 100 2
x y2
1
1 49 2
y2
1
64 81
In Exercises 7–12, the equation of parabolas, circles, and ellipses
are given. Graph the equation.
7. 8. 9.
10. 11. 12. x2 y2 82 4y2 18y x 8x
2 6x
0
2 3y2 1
49 9
24
x2 y2 152 Write an equation of the ellipse with the given characteristics and
center at (0, 0).
13. Vertex: 0, 6
14. Vertex: 0, 4
15. Vertex: 7, 0
Co-vertex: 3, 0
Co-vertex: 2, 0
Focus: 33, 0
16. Vertex: 0, 2
17. Co-vertex: 3, 0
18. Co-vertex: 0, 2
Focus: 0, 3
Focus: 0, 33
Focus:
19. Astronomy In its orbit, Mercury ranges between 46.04 million
kilometers and 69.86 million kilometers from the sun. Use this
information and the diagram shown at the right to write an equation
for the orbit of Mercury.
20. Swimming Pool An elliptical pool is 12 feet long and 8 feet wide.
Write an equation for the swimming pool. Then graph the equation.
(Assume that the major axis of the pool is vertical.)
x 2
y2
42, 0
a y a
20
20
69.86 46.04
Algebra 2 55
Chapter 10 Resource Book
c
x
Lesson 10.4

Answer Key
Practice C
1.
2.
3.
4.
x 2
4
x 2
25
9
y2
1;
16
1
1
x2 y2
1;
324 225
5
x2 y2
1;
15 10
1
y
y
y
y
1
y2
49 1;
9
1
5
1
x
x
x
x
vertices: 0, ±4;
co-vertices: ±2, 0;
foci: 0, ±23
vertices:
co-vertices:
foci:
vertices:
0, ± 7
± 5
3
26
0, 3
3;
, 0;
±18, 0;
co-vertices: 0, ±15;
foci:
±311, 0
vertices: ±15, 0;
co-vertices: 0, ±10;
foci: ±5, 0
5.
6.
x 2
4
y2
1;
20
1
x2 y2
1;
24 64
2
vertices: 0, ±25;
co-vertices: ±2, 0;
foci: 0, ±4
vertices:
7. 8.
1
9. 10.
2
1
2
1
x
x
x
8 x
0, ±8;
co-vertices: ±26, 0;
foci: 0, ±210
1
2
1
1
x
x

Answer Key
11. 12.
x 2
13. 1 14.
64 81
x 2
15. 1 16.
121 100
x 2
2
17. 1 18.
25 4
y2
x2 y2
2
15 4
19. or
4 2 1
20. 15 in. 2
2
y2
y2
x
x2 y2
1
16 9
x 2
1
x 2
1
2
y2
1
169
x2 15 4 2 y2
4
2
y2
1
49
2 1
x

Lesson 10.4
LESSON
10.4
Practice C
For use with pages 609–614
56 Algebra 2
Chapter 10 Resource Book
NAME _________________________________________________________ DATE ___________
Write the equation in standard form (if not already) and graph the
equation. Then identify the vertices, co-vertices, and foci of the
ellipse.
1. 2. 3.
4. 5. 6. 64x2 24y2 100x 1536
2 20y2 2x 400
2 3y2 x
30
2
9x y2
3
108 75 2
x 9y2
1
25 49 2
y2 1
8 32 2
In Exercises 7–12, the equation of parabolas, circles, and ellipses
are given. Graph the equation.
7. 8. x 9.
2 y2 2 2
12x2 24y
10. 11. 12. x2 y2 42 2
16x 0
4 x2 15y2 15
Write an equation of the ellipse with the given characteristics and
center at (0, 0).
13. Vertex: 0, 9
14. Vertex: 4, 0
15. Vertex: 11, 0
Co-vertex: 8, 0
Co-vertex: 0, 3
Focus: 21, 0
16. Vertex: 0, 7
17. Co-vertex: 0, 2
18. Co-vertex: 1, 0
Focus: Focus: Focus: 0, 242
0, 43
21, 0
Bicycle Chainwheel In Exercises 19 and 20, use the following information.
The pedals of a bicycle drive a chainwheel, which drives a smaller
sprocket wheel on the rear axle. Many chainwheels are circular.
However, some are slightly elliptical, which tends to make
pedaling easier. The front chainwheel on the bicycle shown at
the right is 8 inches at its widest and 7 inches at its narrowest.
19. Find an equation for the outline of this elliptical chainwheel.
20. What is the area of the chainwheel?
1
2
y2
x 2
49 y2 1
Front Chainwheel
1
7 in.
2
8 in.
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice A
1. A 2. C 3. B
5. 6.
4.
x
7. vertices: ±12, 0; foci: ±65, 0
8. vertices: 0, ±3; foci: 0, ±109
9. vertices: 0, ±11; foci: 0, ±221
10. 11.
2
y y2
1
4 49 2
x2
1
4 9
x2 y2
1
1 36
2
foci: foci:
asymptotes:
4
y ± 5 asymptotes:
12. 13.
x
±41, 0;
0, ±58;
2
y
y
2
2
foci:
foci:
asymptotes: asymptotes: y ±
14. y foci: ±26, 0;
6
asymptotes: y ±5x
8
7x 5
y ± 6x ±61, 0
0, ±113;
2
x
x
x
3
3
y
y
3
3
x
y ± 7
3 x
x
15. y foci:
asymptotes:
16. 1 17.
4 5
18. 1 19.
1 35
20. y2
9
x2 y2
y2 x2
x2
9
4
2
2
1
x
x2 y2
1
16 9
x 2
1
y2
1
15
y ± 5
4x ±41, 0;

LESSON
10.5
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice A
For use with pages 615–621
Match the equation with its graph.
x 2
1. 1
36 4
2. 1
4 36
3.
A.
y
B.
y
C.
Identify the vertices and foci of the hyperbola.
x 2
7. 1
8. 1
9.
144 36 9 100
Graph the equation. Identify the foci and asymptotes.
x 2
10. 1
11. 1
12.
25 16 49 9
y 2
y2
Write the equation of the hyperbola in standard form.
4. 5. 6. 49x2 4y2 9y 196
2 4x2 36x 36
2 y2 36
y2
y2
x2 y2
13. 1
14. 1
15.
64 49 1 25
x2
3
3
x
y2 x2
y2 x2
Write an equation of the hyperbola with the given foci and
vertices.
16. Foci: 3, 0, 3, 0
17. Foci: 5, 0, 5, 0
Vertices: 2, 0, 2, 0
Vertices: 4, 0, 4, 0
18. Foci: 0, 6, 0, 6
19. Foci: 4, 0, 4, 0
Vertices: 0, 1, 0, 1
Vertices: 1, 0, 1, 0
20. Write an equation for the hyperbola having vertices at 0, 3 and 0, 3
and with asymptotes y 2x and y 2x.
y 2
x2
1
1
x
x 2
4
y2
1
36
y2 x2
1
121 100
x2 y2
1
36 25
x2 y2
1
16 25
Algebra 2 67
Chapter 10 Resource Book
1
y
1
x
Lesson 10.5

Answer Key
Practice B
1. 2.
3.
x
4. vertices: ±9, 0; foci: ±313, 0
5. vertices: ±6, 0; foci: ±210, 0
6. vertices: 0, ±3; foci: 0, ±109
7. 8.
2
y
y2
1
16 9 2
x x2
1
64 4 2
y2
1
25 4
1
y
1
foci: foci:
asymptotes: asymptotes:
9. foci:
asymptotes: y ± 5
3x y ±
y
0, ±34;
3
2x 3
y ± 4x (0, ±5;
±13, 0;
2
2
x
10. foci:
asymptotes:
y ± 2
2 x
y
±3, 0;
1
1
x
x
1
y
1
x
11. 12.
foci: ±37, 0; foci: 0, ±53;
asymptotes: y ±6x asymptotes:
13. 14.
15. y
16.
x 2
y
8
1
y
2
1
1
19. 20. R2
16
64 y2 1
1
x
x
x
17.
18.
r2
8
x 2
9
x 2
9
1
y
4
1
y2
1
72
y2
1
40
y 2
9 x2 1
1
y
2
y ± 2
7 x
x
x

Lesson 10.5
LESSON
10.5
Practice B
For use with pages 615–621
68 Algebra 2
Chapter 10 Resource Book
NAME _________________________________________________________ DATE ___________
Write the equation of the hyperbola in standard form.
1. 2. 3. 9x2 16y2 y 144 0
2 16x2 4x 64
2 25y2 100
Identify the vertices and foci of the hyperbola.
x 2
4. 1
5. 1
6.
81 36 36 4
y2
Graph the equation. Identify the foci and asymptotes.
7. 8. 9.
10. 11. 12. 49y2 4x2 36x 196
2 y2 x 36
2 2y2 y
2
2
x x2
1
25 9 2
y y2
1
4 9 2
x2
1
9 16
In Exercises 13–15, the equations of parabolas, circles, ellipses, and
hyperbolas are given. Graph the equation.
13. 14. 15. 9x2 4y2 9x 36
2 9x 4y 0
2 4y2 36
Write an equation of the hyperbola with the given foci and
vertices.
16. Foci: 9, 0, 9, 0
17. Foci: 7, 0, 7, 0
Vertices: 3, 0, 3, 0
Vertices: 3, 0, 3, 0
18. Foci: 0, 10, 0, 10
19. Foci: 65, 0, 65, 0
Vertices: 0, 3, 0, 3
Vertices: 8, 0, 8, 0
20. Machine Shop A machine shop needs to make a small engine part by
drilling two holes of radius r from a flat circular piece of radius R. The
area of the resulting part is 16 square inches. Write an equation that relates
r and R.
x 2
y2
y 2
9
x2
1
100
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice C
y 2
1. 1 2.
100 4
x2
3.
x
4. vertices: ±4, 0; foci: ±25, 0
5. vertices: 0, ±2; foci: 0, ±6
6. vertices: ±53, 0; foci:
7. y foci: (0, ±9;
asymptotes:
2
y2
1
4 9
8. foci:
asymptotes:
y ± 3
3 x
y
±8, 0;
4
4
x
9. y foci: ±7, 0;
10. 11.
1
y
1
2
4
2
4
asymptotes:
y ± 310
20 x
foci: ±6.1, 0; foci: ±4, 0
x
x
x 2
4
x
y2
1
49
±57, 0
y ± 817
17 x
asymptotes: y ± asymptotes: y ±15x
5
6x 1
y
2
x
12. y foci:
13. 14.
15. y
16.
19.
4
x 2
2 y2 1
y
4
x2 y2
4
2
asymptotes:
17.
18.
20. 1; about 15.8 m
50 225
2
x
6
x
x
x 2
4
y2 x2
1
48
y 2
1
16
109
0, ±
2 ;
4
y
4
y2
1
21
x2
15 1
16
y ± 3
10 x
x

LESSON
10.5
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice C
For use with pages 615–621
Write the equation of the hyperbola in standard form.
1. 2. 3. 4y2 9x2 49x 36 0
2 4y2 y 196 0
2 25x2 100
Identify the vertices and foci of the hyperbola.
y
4. 5. 6.
2
x x2
1
4 2 2
y2
1
16 4
Graph the equation. Identify the foci and asymptotes.
x
7. 8. 9.
2
y y2
1
48 16 2
x2
1
64 17
10. 11. 12.
15x2 y2 2.5x 15
2 3.6y2 9
In Exercises 13–15, the equations of parabolas, circles, ellipses, and
hyperbolas are given. Graph the equation.
13. 14. 15. 4x2 4y2 y
100
2
y x2
1
169 225 2
x2
1
169 225
Write an equation of the hyperbola with the given foci and
vertices.
16. Foci: 17. Foci:
Vertices: Vertices:
18. Foci: 19. Foci:
Vertices: 0, Vertices: 2, 0, 2, 0
1
4, 0, 1
5, 0, 5, 0
0, 7, 0, 7
2, 0, 2, 0
0, 1, 0, 1
0, 1, 0, 1
3, 0, 3, 0
4
20. Modeling a Hyperbolic Lobby The diagram at the right shows the
hyperbolic overview of a building’s lobby. Write an equation that models
the curved sides of the lobby. Then find the width of the lobby halfway
between the main entrance and the front desk. (Note: x and y are measured
in meters.)
x2 y2
1
75 100
y 2
9
4y 2
9
x2
1
40
x2
1
25
5
Algebra 2 69
Chapter 10 Resource Book
y
5
Front desk
x
Main entrance
Lesson 10.5

Answer Key
Practice A
1.
2.
3.
y 42 x 2
x 12
1
9 4
2 x 4
12y 2
2 y 62 49
x 2
4. 5. B 6. E 7. A
8. D 9. C 10. F
11. circle;
center: radius
12. parabola;
vertex: focus:
13.
x 3
ellipse;
vertices: 5, 1, 1, 1;
foci: 3 3, 1, 3 3, 1
2
x 5
5, 6; 5, 5
y 12
1;
4 1
2 x 6
6, 9; 11
4y 6;
2 y 92 y 52
1
25 24
121;
y 2
14. hyperbola;
vertices: foci:
15. x 452 405
x 12
1;
4 3
1, 2, 1, 2;
1, 7, 1, 7
y 20
4

LESSON
10.6
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice A
For use with pages 623–631
Write an equation for the conic section.
1. Circle with center at 4, 6
and radius 7
2. Parabola with vertex at 2, 2 and focus at 2, 5
3. Ellipse with vertices at 1, 7 and 1, 1 and co-vertices at 3, 4 and
1, 4
4. Hyperbola with vertices at 5, 5 and 5, 5 and foci at 7, 5 and 7, 5
Match the equation with its graph.
5. 6.
y 4
7.
2
x 5 x 52
1
16 25
2 y 42
1
25 16
8. 9.
y 4
10.
A. y
2
B. y
C.
2
x 5 x 52
1
25 16
2 y 42
1
16 25
8
x
D. y
E. y
F.
2
2 x
Classify the conic section and write its equation in standard form.
For circles, identify the radius and center. For parabolas, identify the
vertex and focus. For ellipses and hyperbolas, identify the vertices
and foci.
11. 12.
13. 14. 4x
15. Sprinkler System A sprinkler system shoots a stream of water that follows
a parabolic path. The nozzle is fastened at ground level and water reaches a
maximum height of 20 feet at a horizontal distance of 45 feet from the
nozzle. Find the equation that describes the path of the water.
2 3y2 x 8x 16 0
2 4y2 x
6x 8y 9 0
2 x 10x 4y 1 0
2 y2 12x 18y 4 0
2
2
2
2
x
x
y 5 2
16
x 4 2
16
4
2
y
Algebra 2 81
Chapter 10 Resource Book
y
2
x 42
1
25
y 52
1
25
4
x
x
Lesson 10.6

Answer Key
Practice B
1.
2.
3.
4.
y
5. 6.
2
x 3
x 82
1
16 20
2
y 2
y 12
1
4 1
2 x 3
8x 3
2 y 12 4
vertex: 1, 4; center: 1, 2;
focus: 3, 4
radius 1
7. y
center: 10, 2;
vertices: 7, 2,
13, 2;
2
2
x foci: 10 5, 2,
10 5, 2
8.
2
y
2
center:
vertices:
foci:
9. hyperbola 10. parabola 11. parabola
12. ellipse 13. circle 14. hyperbola
15. x 32 y 22 1, 1;
1, 1 30, 1, 1 30;
1, 1 55, 1, 1 55
1;
1
y
2
1
y
2
x
x
x
1
y
1
x
16. y 12 16x 2;
17.
18.
19.
2
y
2
x 12
4
y 32
2
2
1
y
y
2
y 20 2
200
4
x
y 22
16
x
x 12
18
x
x2
1;
32
1;
1;
10
y
5
x

Lesson 10.6
LESSON
10.6
Practice B
For use with pages 623–631
82 Algebra 2
Chapter 10 Resource Book
NAME _________________________________________________________ DATE ___________
Write an equation for the conic section.
1. Circle with center at 3, 1 and radius 2
2. Parabola with vertex at 3, 2 and focus at 5, 2
3. Ellipse with vertices at 5, 1 and 1, 1 and co-vertices at 3, 2 and
3, 0
4. Hyperbola with vertices at 8, 4 and 8, 4 and foci at 8, 6 and
8, 6
Graph the equation. Identify the important characteristics of the
graph, such as the center, vertices, and foci.
5. 6. x 12 y 22 y 4 1
2 8x 1
7.
x 102
9
y 22
4
1
Classify the conic section.
9. 10.
11. 12.
13. 14. 5x2 3y2 3x 2x 3y 4 0
2 3y2 x
3x 3y 1 0
2 3y2 x x 2y 4 0
2 3y
2x 3y 5 0
2 4x 2x 3y 1 0
2 4y2 2x 4y 5 0
Write the equation of the conic section in standard form. Then
graph the equation.
15. 16.
17. 18.
19. Designing a Menu You are opening a restaurant called
the Treetop Restaurant. You are using a computer program to
design the menu cover as shown at the right. The equation
for the tree trunk is 25x Write
this equation in standard form and then sketch its graph.
2 4y2 9y
160y 800 0.
The TREETOP
2 x2 4x 2x 54y 62 0
2 y2 y
8x 4y 8 0
2 x 2y 16x 31 0
2 y2 6x 4y 12 0
8.
y 1 2
30
x 12
1
25
Restaurant
and lounge
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice C
1.
2.
3.
4.
x 3
5. 6.
2
x 2
y 32
1
1 9
2
x 4
y 22
1
4 9
2 x 5
8y 1
2 y 32 2
4
y
4
vertex: 4, 1; center: 5, 2;
focus: 4, 3 radius: 3
7. y center: 0, 3;
4
vertices: 0, 1, 0, 7;
2
x
foci: 0, 3 32,
0, 3 32
8. y center: 3, 4;
vertices: 8, 4, 2, 4;
4
foci: 3 7, 4,
3 7, 4
2
x
9. hyperbola 10. ellipse 11. ellipse
12. circle 13. hyperbola 14. parabola
15. y 1 y
2 4x 2
x
1
1
1
y
1 x
x
16.
17.
18.
1
y 22
9
y
1
x 1 2
x 2
x 32
16
x 1 2 y 3 2 4;
y 22
4
1;
19. 8500 yd2 y 852
1002
852 1;
x
1;
1
1
y
y
1
1
x
x

LESSON
10.6
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice C
For use with pages 623–631
Write an equation for the conic section.
1. Circle with center at 5, 3
and radius 2
2. Parabola with vertex at 4, 1 and directrix y 1
3. Ellipse with vertices at 2, 1 and 2, 5 and foci at 2, 2 5 and
2, 2 5
4. Hyperbola with vertices at 4, 3 and 2, 3 and foci at 3 10, 3 and
3 10, 3
Graph the equation. Identify the important characteristics of the
graph, such as the center, vertices, and foci.
5. 6. x 52 y 22 x 4 3
2 16y 1
7.
y 3 2
16
x2
1
2
Classify the conic section.
9. 10.
11. 12.
13. 14. x2 x 6x 2y 13 0
2 y2 x
2x 12y 31 0
2 y2 x 2x 6y 9 0
2 36y2 25x
16x 72y 64 0
2 y2 x 100x 2y 76 0
2 25y2 14x 100y 76 0
Write the equation of the conic section in standard form. Then
graph the equation.
15. 16.
17. 18. 4x
19. Aussie Football In Australia, football (or rugby) is played on elliptical
fields. The field can be a maximum of 170 yards wide and a maximum of
200 yards long. Let the center of the field of maximum size be represented
by the point 0, 85. Write an equation of the ellipse that represents this
field. Find the area of the field.
2 y2 x 8x 4y 4 0
2 y2 9x
2x 6y 6 0
2 16y2 y 54x 64y 161 0
2 2y 4x 7 0
8.
x 3 2
25
y 42
1
18
Algebra 2 83
Chapter 10 Resource Book
Lesson 10.6

Answer Key
Practice A
1. no 2. yes 3. yes 4. yes 5. no 6. no
7. 5, 4, 4, 5
8. 4, 3, 4, 3
9. 3, 6, 3, 6 10. (4, 3, 3, 4
11. none 12. 2, 1, 2, 1
13. 3, 3, 3, 5 14. 2, 0 15. 2, 3
16. none 17. 220 ft by 1980 ft or
990 ft by 440 ft

Lesson 10.7
LESSON
10.7
Practice A
For use with pages 632–638
96 Algebra 2
Chapter 10 Resource Book
NAME _________________________________________________________ DATE ___________
Determine whether the given point is a point of intersection of the
graphs in the system.
1. 2. 3.
Point: Point: Point:
4. 5. 6. 6x
y x
3x y 6
y x 2
Point: 6, 6
Point: 0, 2
Point: 0, 2
2 3y2 4x 12
2 5y2 x 16
2 x
y 4
y x 1
x y 0
1, 2
2, 3
3, 3
6y
2 y2 x 18
2 y2 x 13
2 y2 5
Find the points of intersection, if any, of the graphs in the system.
7. 8. 9. x2 y2 x 45
2 y2 x 25
2 y2 41
y x 1
10. 11. 12. x2 y2 x 3
2 y2 x 36
2 y2 25
y x 1
13. 14. x2 8y2 x 4x 16y 4 0
2 y2 x 2y 21 0
x 2 y 2 5x 2y 9 0
Find the points, if any, that the graphs of all three equations have
in common.
15. 16. x2 y2 y x 1
4
4x y 11
x 2 4x y 2 5
y 3
x y 12
x 2 4x 16y 4 0
x 2y 5
17. Farming A farmer has 2420 feet of fence to enclose a
rectangular area that borders a river as shown in the figure
at the right. Notice that no fence is needed along the river.
Find the possible dimensions to enclose 10 acres.
1 acre 43,560 ft 2
x 2 y 2 14
y 2x
2y x 2
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice B
1. yes 2. yes 3. no
4.
5.
6.
7.
9.
8.
10.
11. ,
12.
13. 14. 3, 3
15. none
1127 ft
16. 563.5 ft by 773 ft or 386.5 ft by
3
3
,
2 2 , 3
1, 1, 3, 7
3
,
2 2
10
6 214
,
3 3
10
6 214
,
3 3 ,
1, 0, 1, 0, 1, 4, 1,
4, 1 0, 0, 0, 4
1
2, 9, 3
2, 2, 4, 8
2
12
22, 1, 22, 1, 22, 1,
22, 1 2, 2, 2, 2
16
5 , 5 , 4, 0
14 214
,
7 7 , 14, 214
7 7

LESSON
10.7
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice B
For use with pages 632–638
Determine whether the given point is a point of intersection of the
graphs in the system.
1. 2. 3. 3x
3x y 7
y 3x 5
y 2x 1
Point: 2, 1
Point: 2, 1
Point: 1, 3
2 y2 x 6
2 y2 x 5
2 y 5
Find the points, if any, that the graphs of all the equations in the
system have in common.
4. 5. 6. x2 y2 2x 4
2 3y2 2x 19
2 3y2 4
y 2x
7. 8. 9. 4y2 x x
2 x 2y
2 y2 16
x 2y 4
10. 11. x2 y2 2x 4x 4y 0
2 2y2 8x 2 0
x 2 5y 2 4x 5 0
12. 13. x2 y2 x 3 0
2 y 2 0
2x 2 y 6x 7 0
14. 15. x2 y2 x 16
2 y2 x 2y 21 0
x 2 y 2 5x 2y 9 0
9y 4x 15
x 2 y 2 9
x y 4
16. Farming A farmer has 1900 feet of fence to enclose a
rectangular area that borders a river as shown in the figure
at the right. No fence is needed along the river. Is it possible
for the farmer to enclose 10 acres? If
1 acre 43,560 ft 2
2x 2 y 0
x 2 5y 5
x 2 y 2 27 0
possible, find the dimensions of the enclosure. If not possible,
justify your answer.
2x 2 y 2 6x 4y 0
x y
x 4y 3
Algebra 2 97
Chapter 10 Resource Book
Lesson 10.7

Answer Key
Practice C
1. no 2. yes 3. yes
4.
5.
6. 7.
8. 9.
10. 0, 2 11. 0, 1, 5, 6, 5, 6
12. 2, 4, 2, 2 13. 10, 12 14. none
15. 2, 0
16. yes; about 3.12 ft by 3.12 ft by 1.64 ft or 2 ft
by 2 ft by 4 ft
8
5, 3
4, 5, 0, 1
4
3, 2, 1
5,
0, 0, 2, 1 3, 4, 5, 0
3
25
2 , 1, 1
2 21, 7 221,
2 21, 7 221
2

Lesson 10.7
LESSON
10.7
Practice C
For use with pages 632–638
98 Algebra 2
Chapter 10 Resource Book
NAME _________________________________________________________ DATE ___________
Determine whether the given point is a point of intersection of the
graphs in the system.
1. 2. 3. 5x
x 8y 0
y 2x
x y 1
Point: 8, 1
Point: Point:
2 3y2 y 17
2 2x2 x 2y 6
2 6
Find the points, if any, that the graphs of all the equations in the
system have in common.
4. 5. 6.
x2 2x 2y
2 4y 22
y 2x 3
7. 8. 9. x2 4y2 y 4
1
x2 y2 25
y 10 2x
10. 11. x2 y2 x 8y 7 0
2 y2 4x 4y 4 0
x 2 y 2 4x 4y 4 0
12. 13. 4x2 y2 x 32x 24y 64 0
2 y2 4x 6y 4 0
x 2 y 2 4x 6y 12 0
14. 15. x2 4y2 x 4x 8y 4 0
2 2x 4 y2 10 0
y 3x 5
2y 2 x 3 0
12 x2
3, 23
4x 2y 5
y 1 2
6x 3
x 2 y 1 0
4x 2 y 2 56x 24y 304 0
x 2 4y 4 0
7x 5y 14
16. Aquarium You want to construct an aquarium with a glass top and
two square ends. The aquarium must hold 16 cubic feet of water and you
only have 40 square feet of glass to work with. Is it possible to construct
such an aquarium? If possible, find the approximate dimensions of the
aquarium. If not possible, justify your answer.
y 2 1
2 x
7 3
4 , 4
x 2y 0
y x 1
x
x
Copyright © McDougal Littell Inc.
All rights reserved.
y

Answer Key
Test A
1. arithmetic; 2. neither; no constant or
3. geometric; 4. arithmetic;
5. 6.
7. 8. 9.
10. 11. 12.
13. 14.
15.
16. a1 36; an 17. 1275 18. 1000
19. 5 20. 62 21. 2800 22.
121
23. 650
1
1 1
;
32 2
a1 5; an 0.4an1 a1 1; an an1 5
2an1 n
243; 3 1; 6 n
n
d 2
d
r
r 2
d 5
3, 4, 5, 6, 7, 8 2, 6, 12, 20, 30, 42
3, 6, 9, 12, 15, 18 25; 5n 19; 4n 1
21; 3n 2
4
n1
24. 16 25. 6n 26. 27. 610
28. about $87,900
5
9
243

CHAPTER
11
NAME _________________________________________________________ DATE
Chapter Test A
For use after Chapter 11
____________
Tell whether the sequence is arithmetic, geometric, or
neither. Explain your answer.
1. 1, 1, 3, 5, . . .
2. 3, 8, 9, 12, . . .
3. 2, 4, 8, 16, . . .
4. 6, 1, 4, 9, . . .
Write the first six terms of the sequence.
5. an n 2 6. an nn 1 7. an 3n
Write the next term of the sequence, and then write the rule
for the nth term.
8. 9. 10.
11. 12. 13.
1
2, 1
4, 1
8, 1
5, 10, 15, 20, . . . 3, 7, 11, 15, . . . 9, 12, 15, 18, . . .
3, 9, 27, 81, . . . 5, 4, 3, 2, . . .
16, . . .
Write a recursive rule for the sequence. (Recall that d is the
common difference of an arithmetic sequence and r is the
common ratio of a geometric sequence.)
14. r 0.4, a1 5 15. d 5, a1 1 16. 36, 18, 9, . . .
Find the sum of the series.
50
17. i
18. 3n 1 19.
i1
5
20. 21. 22. 5
7n 2i i1
Copyright © McDougal Littell Inc.
All rights reserved.
25
n1
4
n1
10
5 n
n1
i1
1 3 i
Answers
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
Algebra 2 81
Chapter 11 Resource Book
Review and Assess

Review and Assess
CHAPTER
11
CONTINUED
NAME _________________________________________________________ DATE ____________
Chapter Test A
For use after Chapter 11
23. Find the sum of the first 25 terms of the arithmetic sequence
2, 4, 6, 8, . . . .
24. Find the sum of the infinite geometric series
8 4 2 1 . . . .
25. Write the series 6 12 18 24 with summation notation.
26. Write the repeating decimal 0.5 as a fraction.
27. Stacking Containers Containers are stacked in 20 rows, with 2 in
the top row, 5 in the second row, 8 in the third row, and so on. How
many containers are in the stack?
28. Land If a parcel of land originally worth $25,000 increases in value
15% per year, what will the land be worth in the tenth year?
82 Algebra 2
Chapter 11 Resource Book
23.
24.
25.
26.
27.
28.
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Test B
1. arithmetic; d 3
2. geometric; r 2
3. neither; no common d or r
4. geometric; 5.
6. 7.
8. 3125; 5 9. 28; 6n 2 10. 5; n
n
r 3 0, 3, 8, 15, 24, 35
2, 5, 8, 11, 14, 17 10, 17, 26, 37, 50, 65
11. 30; nn 1 12.
13.
14 n 9
;
3 3
14. a1 10; an 0.5an1 15. a1 1; an an1 10
16. a1 22; an 17. 15 18. 1890
19. 420 20. 1364 21. 31 22.
61
23. 620
an1 2
2
3
5
n1
24. 25. 3n 7 26. 27. $46.50
28. about $412,000
1 1
;
25 n2 5
11
27

CHAPTER
11
NAME _________________________________________________________ DATE
Chapter Test B
For use after Chapter 11
____________
Tell whether the sequence is arithmetic, geometric, or
neither. Explain your answer.
1. 7, 10, 13, 16, . . .
2. 3, 6, 12, 24, . . .
3. 0, 1, 3, 8, 15, . . .
4. 4, 12, 36, 108, . . .
Write the first six terms of the sequence.
5. an n 6. an 3n 1
7. a1 10 , an an1 2n 3
2 1
Write the next term of the sequence, and then write the rule
for the nth term.
8. 5, 25, 125, 625, . . .
9. 4, 10, 16, 22, . . .
10. 1, 2, 3, 4, . . . 11. 2, 6, 12, 20, . . .
12.
1 1 1
1, , , , . . .
13.
11 13
, , 4, , . . .
4
Write a recursive rule for the sequence. (Recall that d is the
common difference of an arithmetic sequence and r is the
common ratio of a geometric sequence.)
14. r 0.5, a1 10 15. d 10, a1 1 16.
Find the sum of the series.
5
a1
17. a
18. 90 2n 19.
5
n1
9
16
20. 21. 22. 5
2i1 4n Copyright © McDougal Littell Inc.
All rights reserved.
35
n1
5
i1
10
3
3
3
22, 11, 11
2 , 11
4 , . . .
15
3i 4
i1
3
n1
1
3 n1
Answers
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
Algebra 2 83
Chapter 11 Resource Book
Review and Assess

Review and Assess
CHAPTER
11
CONTINUED
NAME _________________________________________________________ DATE ____________
Chapter Test B
For use after Chapter 11
23. Find the sum of the first 10 terms of the arithmetic sequence
8, 20, 32, 44, . . . .
24. Find the sum of the infinite geometric series
1
25. Write the series 10 13 16 19 22 with summation notation.
1
2 1
4 18
. . . .
26. Write the repeating decimal 0.45 as a fraction.
27. Saving Dimes Your little sister decides to save dimes. She saved
one dime the first day, two dimes the second day, and so on. How
much money did she save in 30 days?
28. Value of a Home Suppose the average value of a home increases
5% per year. How much would a house costing $100,000 be worth
in the 30th year?
84 Algebra 2
Chapter 11 Resource Book
23.
24.
25.
26.
27.
28.
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Test C
1. arithmetic;
2. neither; no common or
3. arithmetic; 4. geometric;
5.
6. 7.
8. 9. 10. 1024; 4n 0, 6, 0, 6, 12, 18, 24
4; n 1
7 n 2
;
8 n 3
3
r
0, 2, 4, 6, 8, 10
8 15 24 35
2 , 3 , 4 , 5 , 6
2
d 6
d r
d 1.5
3
11. 12. 13.
14.
15. a1 1; an an1 4
120; n!
a1 10; an 2an1 3
6
125; n
n 1
;
5 n
3
16. a1 55; an 17. 63 18. 134
19. 195 20.
31
21.
1360
22. about 6.67
an1 10
23. 500 24. 4 25.
11
90
32
13
81
4 3n
n1
26. 27. 0.25 meters 28. 120

CHAPTER
11
NAME _________________________________________________________ DATE
Chapter Test C
For use after Chapter 11
____________
Tell whether the sequence is arithmetic, geometric, or
neither. Explain your answer.
1. 2.
3. 4. 6, 4, 8
2, 4, 10, 16, . . .
0, 4, 9, 15, 22, . . .
2, 0.5, 1, 2.5, . . .
16
3 , 9 , . . .
Write the first six terms of the sequence.
5. 6. an n 7. a1 6
an an1 6
1
an 2 2n
n
Write the next term of the sequence, and then write the rule
for the nth term.
8. 9.
10. 11.
12. 2, 13. 1, 2, 6, 24, . . .
3
0, 1, 2, 3, . . .
5 6 7 , . . .
4, 16, 64, 256, . . .
1, 8, 27, 64, . . .
, 4,
5,
. . .
Write a recursive rule for the sequence. (Recall that d is the
common difference of an arithmetic sequence and r is the
common ratio of a geometric sequence.)
14. a1 10, r 2
15.
16. 55, 5.5, 0.55, 0.055, . . .
Find the sum of the series.
6
17. 3n
18. 8 n 19.
n1
5
20. 21. 22. 10
n1
2
1 2 n
Copyright © McDougal Littell Inc.
All rights reserved.
3
4
43
n40
4
i1
5 3 i
3 4 5 6
4 , , ,
a 1 1, d 4
3
30 n 4
n1 3
2 i
10
i0
1
Answers
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
Algebra 2 85
Chapter 11 Resource Book
Review and Assess

Review and Assess
CHAPTER
11
CONTINUED
NAME _________________________________________________________ DATE ____________
Chapter Test C
For use after Chapter 11
23. Find the sum of the first 25 terms of the arithmetic sequence
4, 2, 0, 2, . . . .
24. Find the sum of the infinite geometric series
2 1
25. Write the series 7, 10, 13, . . . , 43 with summation
notation.
1 1
2 4 . . . .
26. Write the repeating decimal 0.12 as a fraction.
27. Ball Bounce You drop a ball from a height of 128 meters. Each
time it hits the ground, it bounces 50% of its previous height. How
high does the ball go after the ninth time it hits the ground?
28. Invitations You ask your friends to help you spread the word about
your upcoming picnic that you are hosting at your house. You give
an invitation to each of your three best friends. They in turn each
give invitations to three more friends. How many friends will have
received an invitation after the fourth level of friends has been
invited?
86 Algebra 2
Chapter 11 Resource Book
23.
24.
25.
26.
27.
28.
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Cumulative Review
1.
2.
3.
if 2 ≤ x < 1
5, if 1 ≤ x < 3
f x 3,
7, if 3 ≤ x < 7
9, if 7 ≤ x < 9
if 0 ≤ x < 1
4, if 1 ≤ x < 2
f x 2,
6, if 2 ≤ x < 3
8, if 3 ≤ x < 4
if 8 ≤ x < 6
3, if 6 ≤ x < 4
f x 1,
5, if 4 ≤ x < 2
7, if 2 ≤ x < 0
4.
5.
6.
7.
8.
9.
10. 11. 12. not defined
13. not defined 14. 15. not defined
16. 17. 18. 19.
20. 21. 22. 5
2, 1 0, 7
33
±
4 4
2
z x
2 4 2 5
3 3
3, 1 6, 1
1
2 , 3
5
3 , 2
2
z
z 2x 2y 8; 2
z 2x 2y 7; 13
z 4x 2y 8; 8
3y 3; 10 3
1
z
1 13
2x 2y 5; 2
3 2 8
5x 5y 3; 5
23. 24. 25.
26.
1 5
±
3 3
27. 4 ± 21
28. 29.
i
32
±
2
2, 8
1
2 ± i
1
30. 31.
2
y
y
1
1
x
x
1
1
y
y
2
2
x
x
32. 33.
1
34.
35.
36.
37.
38.
39.
40. 5 41. 2 42. 43. 44. 64 45.
46. 47. 27 48. 17 49. 50.
51. 5 52. 5 53. 0 54. 3 55. 2
56. does not exist 57. 3 58. 5 units left
59. 3 units left 60. 5 units down
61. reflected over x-axis 62. 5 units down
7
x 1x 1x
1
6561
1
9
1
9
35
3
4
2 x
2x5x 15x 1
x 1
2 x
9x 3x 3
2 3x
5x 5
3x2 6x 536x
4x 2x 2
2 30x 25
63. 5 units left, one unit down, reflects over x-axis
64.
67.
65.
68.
66.
69.
70. 2 71. 3.457 72. 0.932 73. 5.457
74. 2.711 75. 5.548 76. 3 77.
78. 79. 80. 81.
82. circle; x 32 y 12 12
4
5 , 5
7, 8
1
3 , 3 7, 8 10, 9
25
2 1
6 144
1 6
1
3 2 9
70 4 5 1
2 16
83. ellipse;
84. hyperbola;
y
1
x 12
4
x
25 12 1
x 1 2
y 1 2 4x
y 22
9
y 12
4
1
1
1
64
85. parabola;
86. circle;
87. parabola; 88.
89. 90.
91. 92.
93. 94.
95. 96.
97. 98.
99. 5, 5
2, 5
3, 5
4, 1, 5
0, 0, 2, 5, 4, 3, 0
1, 3, 1, 3 3, 4, 5, 0
4, 4, 0, 0 4, 5, 6, 7, 8, 9
4, 3, 2, 1, 0, 1 1, 0, 1, 4, 9, 16
1, 8, 27, 64, 125, 216
4 5 2 7 8 1
3 , 6 , 3 , 12 , 15 , 2
6
1
x 2 3, 0, 0, 3
2
2 x
8y
2 y 32 9
2
y
1
x

Review and Assess
CHAPTER
11 Cumulative Review
NAME _________________________________________________________ DATE ____________
For use after Chapters 1–11
Write equations for the piecewise function whose graph is shown. (2.7)
1. y
2. y
3.
2
2
2
Write the linear equation as a function of x and y. Then evaluate
the function when x 1 and y 2. (3.5)
4. 3x 2y 5z 15
5. x y 2z 10
6. 2x 2y z 8
7. 2x 2y z 7
8. 4x 2y z 8
9. 3x 2y 3z 9
State whether the product of AB is defined. If so, give the dimensions
of AB. (4.2)
10. A: 2 3, B: 3 4
11. A: 2 4, B: 4 5
12. A: 3 4, B: 3 5
13. A: 2 4, B: 2 4
14. A: 3 4, B: 4 3
15. A: 2 5, B: 2 5
Solve the quadratic equation by factoring. (5.2)
16. 17. 18.
19. 20. 21. 3x2 4x 21x 0
2 6w 12x 8 0
2 2x
11w 10 0
2 a 7x 3 0
2 x 5a 6 0
2 4x 3 0
Solve the quadratic equation. (5.2, 5.5, 5.6)
22. 23. 24.
25. 26. 27. x2 3x 8x 5
2 2x 1 2x 2 0
2 x 3
4 0
2 4x 25
2 2x 16 2
2 5x 1 0
Graph the polynomial function. (6.2)
28. 29. 30.
31. 32. f x x 33.
3 f x x x x
4
f x x4 f x x3 Factor the polynomial. (6.4)
34. 35. 36.
37. 38. 39. x 4 x3 50x x 1
3 x 2x
4 x
81
3 5x2 3x 5x 25
7 48x3 216x3 125
Evaluate the expression without using a calculator. (7.1)
40. 41. 42.
43. 44. 32 45.
65
2723 812 664
3125
Solve the equation. Check for extraneous solutions. (7.6)
46. 47. 48.
49. 50. x 51. 2x 6 x 1
2 x 3x 2 5 x 8 5
23x 1 1 11
2 x 4
1
3
92 Algebra 2
Chapter 11 Resource Book
x
2
x
f x x 5 1
f x x 3 x 2 1
16 32
Copyright © McDougal Littell Inc.
All rights reserved.
2
y
2 x

CHAPTER
11
CONTINUED
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ____________
Cumulative Review
For use after Chapters 1–11
Find the indicated real nth root(s) of a. (7.1)
52. n 2, a 25
53. n 5, a 0
54. n 3, a 27
55. n 6, a 64
56. n 4, a 1
57. n 5, a 243
Describe how to obtain the graph of g from the graph of f. (7.5)
58. gx x 5, f x x
59. gx 4x 3, f x 4x
60. gx x 5, f x x
61. gx 2x 3, f x 2x 3
62. gx 3x 5, f x 3x
63. gx 4x 5 1, f x 4x
Rewrite the equation in exponential form. (8.4)
64. 65. 66.
67. 68. 69. log12 1
log25 log7 1 0
log13 9 2
log6 6 1
144 2
1
5 1
log 4 16 2
2
6
Evaluate the function f x for the given value of x. (8.8)
1 2ex 70. 71. 72.
73. 74. f 75.
1
f 0
f 1
f 3
Solve the equation by using the LCD. Check each solution. (9.6)
76.
2 2 16
5 x 15
77.
4 29
x
x 5
3x 4 50
78. 79.
8 x 1 2x 2
5 x
80. 81.
x 3 4 3
Classify the conic section and write its equation in standard form (10.6)
82. 83.
84. 85.
86. 87. x2 x 4x 8y 4 0
2 y2 y
6y 0
2 4x 4x 2y 1 0
2 y2 9x
8x 2y 1 0
2 4y2 x 18x 16y 11 0
2 y2 6x 2y 15 0
Find the points of intersection, if any, of the graphs in the system. (10.7)
88. 89. 90. x2 y2 x 9
2 x 8y
2 y2 9
y x 3
91. 92. 93. y2 x 4x
2 y2 2x 25
2 2y2 20
y 3x
y 1
4 x
y 2x 10
Write the first six terms of the sequence. (11.1)
2
6x 1 8 5x 2
2x 1 x 2x2 x
x x 9
2x 10 x 7
f 1
f 3.2
2x y 6
x y 0
94. 95. 96.
97. 98. 99. an 5
an n
n 3
an
3n
n
3
an n 22 an n 3
an 5 n
Algebra 2 93
Chapter 11 Resource Book
Review and Assess

Answer Key
Practice A
1. 2.
3. 4.
5. 6.
7. 8.
9. 16; an 2 10. 10; an 2n
11. 12.
n1
25; an n 6; an n 1
2
1, 3, 5, 7, 9, 11
3, 2, 1, 0, 1, 2
2, 8, 18, 32, 50, 72 1, 1, 1, 1, 1, 1
1 1 1 1 1 1
2 , 4 , 6 , 8 , 10 , 12
1 1 3 2 5 3
3 , 2 , 5 , 3 , 7 , 4
13. 14.
50
5
n1
15. 3n 1 16. 2n 17.
18. 19. 15 20. 60 21. 60
4 n
3n 1
n1
5
a n
a n
1
1
22. 110 23. 35 24. 45 25. 78 26. 2870
27. 36 28. 20 diagonals
n
n
6
n1
5
2
a n
a n
1
1
n
n
6
2
n1
n

Lesson 11.1
LESSON
11.1
Practice A
For use with pages 651–657
14 Algebra 2
Chapter 11 Resource Book
NAME _________________________________________________________ DATE ___________
Write the first six terms of the sequence.
1. 2. 3.
4. 5. 6. an n
an
n 2
1
an 1
2n
n
an 2n2 an 2n 1
an 4 n
Write the next term in the sequence. Then write a rule for the nth
term.
7. 1, 4, 9, 16, . . . 8. 2, 3, 4, 5, . . .
9. 1, 2, 4, 8, . . . 10. 2, 4, 6, 8, . . .
Graph the sequence.
11. 1, 3, 6, 10, 15, 21 12. 1, 5, 9, 13, 17, 21
13. 1, 3, 9, 27, 64, 243 14. 5, 3, 1, 1, 3, 5
Write the series with summation notation.
15. 2 5 8 11 14
16. 2 4 6 8 10 12
17. 2 4 8 16 32 64
1 2 3 4
18. 4 7 10 13
Find the sum of the series.
6
n2
19. n 1
20. 4i
21.
6
k2
22. 23. n 24.
2 kk 1
1
Use one of the formulas for special series to find the sum of the
series.
12
i1
4
n0
5
i1
25. 26. i 27.
2
i
20
i1
28. Geometry Connection A diagonal is an edge that joins two nonadjacent
vertices in a polygon. The number of diagonals in the first four polygons
is shown. Following the pattern, determine how many diagonals could be
drawn in a polygon having eight sides (octagon). Make sure you only
count each diagonal once.
4
2n
n1
2
5
2n 3
n1
36
1
i1
0 diagonals
2 diagonals
5 diagonals
9 diagonals
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice B
1. 2.
3. 4.
5. 6.
7. 8.
9. 36; an n 1
10. 11.
2
5
2
13; an 3n 2 0; an 5 n
13; an 2n 3 19; an 4n 1
; a 5, 3,
1 4 9 16 25 36
2 , 3 , 4 , 5 , 6 , 7
8, 27, 64, 125, 216, 343
n
n 2
7 9 5
3 , 2, 5 , 3
5
n1
12. 2n 13. 2n 1 14.
5
a n
1
1n1
n1
n
5
1
n1
n n3 15.
n1 n
16.
n1
17.
18. 100 19. 77 20. 11 21. 18 22. 24
23. 22140 24. 5050 25. 50
26. 55 members 27. 54 diagonals
n 2
0.2
a n
1
4
n1
n
n
3n 1

LESSON
11.1
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice B
For use with pages 651–657
Write the first six terms of the sequence.
1. 2. 3. an n 13 an n2
n 4
an
n
n 1
Write the next term in the sequence. Then write a rule for the nth
term.
1 3
4. 2 , 1, 2 , 2, . . .
5. 1, 4, 7, 10, . . . 6. 4, 3, 2, 1, . . .
7. 5, 7, 9, 11, . . . 8. 3, 7, 11, 15, . . . 9. 4, 9, 16, 25, . . .
Graph the sequence.
10. 3, 7, 11, 15, 19, 23 11.
Write the series with summation notation.
12. 13. 14.
15. 1 16. 1 4 9 16 . . . 17. 1 8 27 64 125
1
2 4 6 8 10
1 3 5 7 . . .
1 2 3 4
2 5 8 11
1 1
. . .
Find the sum of the series.
7
j3
18. 19. 20. 2 21.
n
6j 10
2n 5
Use one of the formulas for special series to find the sum of the
series.
24
i1
2
3
4
6
n0
40
i1
1 3 5 7 9 11
2 , 5 , 8 , 11 , 14 , 17
22. 23. i 24. i
25.
2
1
4
n0
26. Marching Band To begin the half-time performance, a high school band
marches onto the football field in a pyramid formation. The drum major
leads the band alone in the first row. There are two band members in the
second row, three in the third row, four in the fourth row, and so on. The
pyramid formation has 10 rows. How many members does the band have?
27. Geometry Connection A diagonal is an edge that joins two nonadjacent
vertices in a polygon. The number of diagonals in the first four polygons is
shown. Following the pattern, determine how many diagonals could be
drawn in a polygon having twelve sides (dodecagon).
100
i1
5
3 1
n0
n 50
1
i1
0 diagonals
2 diagonals
5 diagonals
9 diagonals
Algebra 2 15
Chapter 11 Resource Book
Lesson 11.1

Answer Key
Practice C
1. 2.
3.
4. 5.
1
5 ; a 1
30
18; an 3n 3
1n
n
n
; an
1
nn 1
5
6
n1
a n
2
6. 2n 7.
2 1
n
6
2
n1
n1
8. 9. 10.
11. 12. 13. 6 14. 322
15. 9.407 16. 42925 17. 29 18. 5050
19. 9455 20. 15 rows 21. 1440
22. 128 people
3
19 10
3
12 8
1
2
5
n1
1n1
n 12 5
2n 1
n1 3n 1
0.5
a n
1
7 17
60
n

Lesson 11.1
LESSON
11.1
Practice C
For use with pages 651–657
16 Algebra 2
Chapter 11 Resource Book
NAME _________________________________________________________ DATE ___________
Write the next term in the sequence. Then write a rule for the nth
term.
1 1 1 1
1. , , , , . . .
2. 6, 9, 12, 15, . . . 3.
2
6
Graph the sequence.
4. 2, 4, 6, 8, . . ., 20
5.
Write the series with summation notation.
6. 3 9 19 33 51 73 7. 1 2 4 8 16 32
8.
1 3 5 7 9
2 5 8 11 14
1 1 1 1 1
9. 4 9 16 25 36
Find the sum of the series.
10. 11. 12.
6
i
6 2n
2n 1
n2
13. 14. 15.
8
n2n 1
6 1
10 2n1
n1
Use one of the formulas for special series to find the sum of the
series.
50
i1
12
20
29
i1
1 2 4 8 16 32
7 , 9 , 11 , 13 , 15 , 17
4
i1
16. i 17. 1
18. i
19.
2
100
i1
20. Marching Band You are the choreographer of a marching band
consisting of 120 members. You plan to have them march onto the field in
a pyramid formation. The drum major leads the band alone in the first
row, then there are two members in the second row, three in the third row,
and so on. How many rows will there be in the pyramid formation?
21. Geometry Connection The sum of the measures of the angles in a
triangle is 180. A quadrilateral can be divided into two triangles, so the
sum of the measures of the four angles in a quadrilateral is
2180 360. Following this pattern, what is the sum of the ten angles
in a decagon?
22. Spreading a Rumor Your best friend tells you a rumor. Every hour a
person who was told the rumor tells someone new. After a 6 hour period,
how many people will have heard the rumor?
n5
1, 1
2
, 1
1
3 , 4
4
10
n0
1
2 n
3
80.15
n0
n
, . . .
30
i
i1
2
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice A
1. yes; constant difference is 3
2. no; difference is not constant
3. yes; constant difference is 3
4. no; difference is not constant
5. yes; constant difference is 7
6. yes; constant difference is 2
7. an 3 4n; 37
8. an 4 5n; 46
9. an 1 4n; 39 10. an 6 5n; 44
11. an 4 n; 14 12. an 6 3n; 24
13. an 7 4n 14. an 4 2n
15. an 10 5n 16. an 4 4n
17. an 3 2n 18. an 4 3n
19. 20.
1
21. 22. a. 290 b. 24
1
a n
a n
1
1
28. 2800 29. 2379 bales
n
n
5
a n
23. a. 490 b. 32
24. a. 483 b. 15
1
25. a. 1328 b. 12
26. 1325 27. 4060
n

Lesson 11.2
LESSON
11.2
Practice A
For use with pages 659–665
26 Algebra 2
Chapter 11 Resource Book
NAME _________________________________________________________ DATE ___________
Decide whether the sequence is arithmetic. Explain why or why not.
1. 4, 7, 10, 13, 16, . . . 2. 3, 6, 12, 24, 48, . . . 3. 2, 5, 8, 11, 14, . . .
4. 1, 2, 4, 7, 11, . . . 5. 2, 9, 16, 23, 30, . . . 6. 5, 3, 1, 1, 3, . . .
Write a rule for the nth term of the arithmetic sequence. Then
find
a 10.
7. 1, 5, 9, 13, 17, . . . 8. 1, 6, 11, 16, 21, . . . 9. 3, 7, 11, 15, 19, . . .
10. 1, 4, 9, 14, 19, . . . 11. 5, 6, 7, 8, 9, . . . 12. 3, 0, 3, 6, 9, . . .
Write a rule for the nth term of the arithmetic sequence.
13. d 4, a1 3
14. d 2, a1 2
15. d 5, a1 15
16. d 4, a8 36
17. d 2, a6 15
18. a5 11, a11 29
Graph the arithmetic sequence.
19. an 4 n
20. an 3 2n
21. an 5 n
For part (a), find the sum of the first n terms of the arithmetic
series. For part (b), find n for the given sum Sn .
22. 2 8 14 20 26 . . . 23. 9 13 17 21 25 . . .
a. n 10 b. Sn 1704
a. n 14 b. Sn 2272
24. 7 4 1 2 5 . . . 25. 5 2 1 4 7 . . .
a. n 21 b. Sn 210
a. n 32 b. Sn 138
Find the sum of the series.
25
i1
26. 4i 1
27. 5i 1
28.
40
i1
29. Baling Hay As a farmer bales a field of hay, each trip around the field
gets shorter. On the first trip around the field, there were 267 bales of hay.
On the second trip, there were 253. The number of bales on each succeeding
trip decreases arithmetically. The total number of trips is 13. How
many bales of hay does the farmer get from the field?
50
2i 5
i1
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice B
1. yes; constant difference is 5
2. no; difference is not constant
3. yes; constant difference is 0.2
4.
5.
6. 7.
8. an 4 9. an 6 2n; 34
10. an 11 4n 11. an 14 5n
12. an 6 2n 13. an 29 3n
14. an 2 5n 15. an 1 3n
16. 17.
1
an 5 6n; 115
an 12 7n; 128
an 1 3n; 59 an 5 7n; 135
2n; 14
1
a n
1
18. 19. a. 230 b. 100
an 2
1
20. a. 1425 b. 23
21. a. 712.5 b. 60
22. a. 2520 b. 20
23.
2225
24. 2178 25. 837.5 26. 1805 bales
27. $2737.50
n
n
5
a n
1
n

LESSON
11.2
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice B
For use with pages 659–665
Decide whether the sequence is arithmetic. Explain why or why not.
1. 7, 12, 17, 22, 27, . . . 2. , . . .
3. 0.8, 1, 1.2, 1.4, 1.6, . . .
Write a rule for the nth term of the arithmetic sequence. Then
find
a 20.
4. 1, 7, 13, 19, 25, . . . 5. 5, 2, 9, 16, 23, . . . 6. 2, 5, 8, 11, 14, . . .
7. 2, 9, 16, 23, 30, . . . 8.
9 11 13
, 5, , 6, , . . .
9. 4, 2, 0, 2, 4, . . .
Write a rule for the nth term of the arithmetic sequence.
10. d 4, a1 7
11. d 5, a1 9
12. d 2, a12 18
13. d 3, a8 5
14. a4 18, a10 48
15. a7 22, a11 34
Graph the arithmetic sequence.
16. an 2 17. an 1 3n
18. an 3 2n
1
For part (a), find the sum of the first n terms of the arithmetic
series. For part (b), find n for the given sum Sn .
19. 2 3 4 5 6 . . .
20. 25 35 45 55 . . .
a. n 20 b. Sn 5150
a. n 15 b. Sn 3105
21. 2 22. 32, 24, 16, 8, 0, . . .
a. n 50 b. Sn 1005
a. n 30 b. Sn 880
5 7
2 3 2 4 . . .
Find the sum of the series.
25
i1
2 n
1 3 9 27 81
2 , 2 , 2 , 2 , 2
23. 2 7i
24. 5 3i
25.
36
i1
26. Baling Hay As a farmer bales a field of hay, each trip around the field
gets shorter. On the first trip around the field, there were 230 bales of hay.
On the second trip, there were 219. The number of bales on each succeeding
trip decreases arithmetically. The total number of trips is 10. How
many bales of hay does the farmer get from the field?
27. Well-drilling A well-drilling company charges $15 for drilling the first
foot of a well, $15.25 for drilling the second foot, $15.50 for drilling the
third foot, and so on. How much would it cost to have this company drill a
100-foot well?
2
2
2
50
4
i1
1
2i
Algebra 2 27
Chapter 11 Resource Book
Lesson 11.2

Answer Key
Practice C
1.
2.
3.
4.
5. 6.
7. 8.
9. 10.
11. an 24 12. an 4 2.6n
13. 14.
1
3n an
an 42 4n an 12.8 2.4n
34 2
3 3n a an
n 15.8 0.2n
7
an 2
2 53
3 3n; 3
1
an 5 4n; 115
an 12 5n; 138
an 2.8 0.3n; 6.2
an 1.6 3.4n; 103.6
4n; 9.5
an 0.5
15. 16. a. 23 b. 30
1
a n
1
3
n
n
17. a. 230 b. 32
18. a. 17.25 b. 30
19. a. 1344 b. 17
20. 525 21. 5
22. 4077.5
25. 16 cans
23. 13,530 24. 114 chimes
1
a n
1
n

Lesson 11.2
LESSON
11.2
Practice C
For use with pages 659–665
28 Algebra 2
Chapter 11 Resource Book
NAME _________________________________________________________ DATE ___________
Write a rule for the nth term of the arithmetic sequence. Then
find
a 30.
1. 1, 3, 7, 11, 15, . . . 2. 7, 2, 3, 8, 13, . . .
3. 2.5, 2.2, 1.9, 1.6, . . .
9 5 11 13
4. 5, 8.4, 11.8, 15.2, . . . 5. , , , 3, , . . .
6.
Write a rule for the nth term of the arithmetic sequence.
7. 8. d 9. d 4, a10 2
10. a6 27.2, a13 44
11. a15 19, a24 16 12. a8 24.8, a18 50.8
2
3 , a1 12
d 0.2, a1 16
Graph the arithmetic sequence.
13. 0.25 0.35n
14.
1
4 15.
a n
For part (a), find the sum of the first n terms of the arithmetic series.
For part (b), find n for the given sum Sn .
16. 0.5 0.9 1.3 1.7 . . . 17. 40 37 34 31 . . .
a. n 10 b. Sn 189
a. n 20 b. Sn 208
18. 1.50 1.45 1.40 1.35 . . . 19. 6 2 2 6 . . .
a. n 15 b. Sn 23.25
a. n 28 b. Sn 442
Find the sum of the series.
30
i1
40
i1
20. 21. 5 22. 2.5 3.1i 23.
1
2 i
24. Clock Chimes A clock chimes once at 1:00, twice at 2:00, three times at
3:00, and so on. The clock also chimes once at 15-minute intervals that are
not on the hour. How many times does the clock chime in a 12-hour period?
25. Soup cans You are stacking soup cans for a display in a grocery store.
Your manager wants you to stack 136 cans in layers, with each layer after
the first having one less can than the layer before it. One can should be in
the top layer. If you must use all 136 soup cans, how many cans should be in
the first layer?
4
a n
4i
2
4
4
3 n
50
i1
5
3
, 1, 1
1
3 , 3
a n 3 1
2 n
, 1
60
12 7i
i1
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice A
1. geometric; common ratio of 4
2. neither; no common ratio or difference
3. neither; no common ratio or difference
4. arithmetic; common difference of 3
5. arithmetic; common difference of 9
6. geometric; common ratio of 7.
8. 9. 10.
11. 12.
13.
14.
15.
16. 17.
18. 19.
20. 21. an 56
22. 23.
n1
an 23n1 an 152 3 n1
an 73n1 an 13 5 n1
an 61 2n1 an 100 1
20 n1 ; 3.125 105 an 44n1 an 1
; 4096
2
3 n1 ; 32
an 53
243
n1 an 52
; 1215
n1 2
4
1
2
; 160
20
24. 25. a. 349,525 b. 8
0.5
a n
a n
1
1
n
n
an 43 2 n1 ; 243
8
26. a. 43,690 b. 7
27. about 8.00
28. 6,046,617.5
29. about 12.00
30. $10.23 for 10 days; $10,485.75 for 20 days;
$10,737,418.23 for 30 days
1
500
a n
1
4
3
n

LESSON
11.3
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice A
For use with pages 666–673
Decide whether the sequence is arithmetic, geometric, or neither.
Explain your answer.
1. 1, 4, 16, 64,
. . . 2. 2, 5, 10, 13 . . . 3. 5, 5, 7, 7, . . .
4. 3, 6, 9, 12, . . . 5. 3, 12, 21, 30, . . . 6.
Find the common ratio of the geometric sequence.
7. 6, 8, . . . 8. 2, 8, 32, 128, . . . 9. 24, 12, 6, 3, . . .
Write a rule for the nth term of the geometric sequence. Then find a 6 .
10. 5, 10, 20, 40, . . .
11. 5, 15, 45, 135, . . . 12.
13.
2 4 8
1, , , , . . .
14. 4, 16, 64, 256, . . . 15.
3
Write a rule for the nth term of the geometric sequence.
16. 17. 18.
19. a1 15, r 20. a3 18, a6 486
21. a3 180, a6 38,880
2
a1 1, r a1 7, r 3
3
a1 6, r 5
1
2
Graph the geometric sequence.
22. 23. an 24 24.
n1
an 32n1 For part (a), find the sum of the first n terms of the geometric
series. For part (b), find n for the given sum S n .
25. 1 4 16 64 . . .
26. 2 4 8 16 . . .
a. n 10 b. Sn 21,845
a. n 16 b. Sn 86
Find the sum of the series.
15
i1
32 128
3 , 9 ,
9
4 1
27
2 i1
3
27. 28. 26 29.
i1
10
i1
30. Salary Plan Suppose you go to work at a company that pays $.01 for
the first day, $.02 for the second day, $.04 for the third day, and so on. So,
each day your wage doubles. What would your total income be if you
worked 10 days? 20 days? 30 days?
1
5, 5 5 5
2 , 4 , 8
100, 5, 1
4, 6, 9,
1
4 , 80 , . . .
27
2 , . . .
an 21 3 n1
11
6
i0
1
2 i
, . . .
Algebra 2 41
Chapter 11 Resource Book
Lesson 11.3

Answer Key
Practice B
1. arithmetic; common difference of 3
2. geometric; common ratio of
3. neither; no common ratio or difference
4. 3 5. 6. 7.
8.
9. 10.
11. 12. an 22
13. 14.
n1
an 41 8 n1
an 81 an 24n1 an 1
; 32,768
4
9 n1 ; 16,384
an 4
4,782,968
1
2 n1 ; 1
4
2
3
32
100
a n
1
n
1
4
15. an 16. a. 13,107
b. 6
17. a. about 232.74
2
1
n
18.
b. 9
1640
19. about 45.33 20. about 14.00
21.
22. 126 in. 2
an 50001.15n1 ; about 23,262 bacteria
0.5
a n
1
2 n1
n

Lesson 11.3
LESSON
11.3
Practice B
For use with pages 666–673
42 Algebra 2
Chapter 11 Resource Book
NAME _________________________________________________________ DATE ___________
Decide whether the sequence is arithmetic, geometric, or neither.
Explain your answer.
3 3 3
1. 1, 2, 5, 8,
. . . 2. 3, , , , . . .
3.
Find the common ratio of the geometric sequence.
4. 5, 15, 45, 135, . . . 5. 6, 24, 96, 384, . . . 6.
Write a rule for the nth term of the geometric sequence. Then find a 8 .
7. 8. 1, 9. 2, 8, 32, 128, . . .
4
1
16 64
4, 2, 1, , . . .
, , , . . .
2
Write a rule for the nth term of the geometric sequence.
10. 11. a1 4, r 12. a3 8, a6 64
1
a1 8, r 1
Graph the geometric sequence.
13. 14. 15. an 51.1n1 an 21 an 23n1 For part (a), find the sum of the first n terms of the geometric
series. For part (b), find n for the given sum S n .
16. 17. 2 3
a. n 8 b. Sn 819
a. n 14 b. Sn 31.55
9
1 4 16 64 . . .
4 . . .
Find the sum of the series.
8
3
i1
i1
2
18. 19. 20.
21. Bacteria A certain bacteria culture initially contains 5000 bacteria and
increases by 15% every hour. Write a rule for the number of bacteria
present at the beginning of the nth hour. How many bacteria are present at
the beginning of the 12th hour?
22. Geometry A square has 16-inch sides. It is partitioned to form a new
square by connecting the midpoints of the sides of the original square.
Then two of the corner triangles are shaded. This process is repeated five
more times. Each time, two of the corner triangles are shaded. The portion
1
of the original square that is shaded on the nth partitioning is 4 Find
the total shaded area.
1
2n1 an .
9
10
i1
4
81
16
729
2 n1
2 3
64
2 i1
8
2 27
2, 9
2
1 2 4 8
3 , 9 , 27 , 81
11
7
i0
1
2 i
19
, 7, , . . .
2
, . . .
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice C
1.
4.
2. 3.
5.
6.
8. 9.
7.
an
10. 11.
1
19,6833n1 an 10241 4 n1
an 51.1n1 an 74n1 an 20.4
; 114,688
n1 an 3
; 0.0033
1
4 n1 3
4
3
; 16,384
1
3
4
1
12. an 13. a. about 5.79
b. 2
5
a n
1
1
n
n
14. a. about
b. 4
15. about
8.93
3.33
16. about
17. about
18.
19. about 324 in. 2
an 25,0000.75n1 7.50
62.34
; about 3.55 years
20
a n
1
n

LESSON
11.3
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice C
For use with pages 666–673
Find the common ratio of the geometric sequence.
1. 1, 3, 9, 27,
. . . 2. , 1 , . . .
3.
Write a rule for the nth term of the geometric sequence. Then find a 8 .
4. 3, 5. 2, 0.8, 0.32, 0.128, . . . 6. 7, 28, 112, 448, . . .
3 3 3
, , , . . .
Write a rule for the nth term of the geometric sequence.
7. 8. 9.
a3 64, a7 1
a1 5, r 1.1
Graph the geometric sequence.
10. 11. 12. an 201.05n1 an 103 an 41 For part (a), find the sum of the first n terms of the geometric
series. For part (b), find n for the given sum S n .
13. 14. 5
a. n 20 b. Sn 5.5
a. n 11 b. Sn 3.13
5
2 5
9 2 4
2 1 9 81 . . .
4 58
. . .
Find the sum of the series.
10
i1
4
16
64
2 n1
1
2, 2
15. 20.8 16. 17.
i1
12
i1
5 1
1
8 , 32
2 n1
3 i1
18. Depreciation The yearly depreciation rate of a certain automobile is
25% of its value at the beginning of the year. The original cost of the
automobile was $25,000. Write a rule for the value of the automobile at
the beginning of the nth year. After how many years will the automobile
be worth $12,000?
19. Geometry A 27-inch by 27-inch square is partitioned into nine squares
and the center square is shaded. Each of the unshaded squares is then
partitioned into nine squares and their center squares are shaded. The
process is repeated three more times. The portion of the original square
1
that is shaded on the nth partitioning is 9 Find the total shaded area.
8
9 n1 an .
4
7, 21
4
63 189
, 16 , 64
a8 1
9 , a15 243
5
3
i0
3
2 i
, . . .
Algebra 2 43
Chapter 11 Resource Book
Lesson 11.3

Answer Key
Practice A
1. no;
3. no;
5. yes;
7. no;
2.
4. yes;
6. no;
8. no;
9. 6 10. 16 11. 9 12. no sum 13.
14. 15. no sum 16. 17. 18.
19. 20. 21. 22. 23.
5
9
24.
1
9 25.
8
9 26.
4
33 27.
3
11 28.
31
99
29. 8 revolutions
2
5
2
9
1
3
2
1
4
1
10
1
2
2
50
7 7
r 2 , 2 > 1
r 1, 1 1
4 4
r 5 , 5 < 1
r 4, 4 > 1
1 1
yes; r 6 , 6 < 1
2 2
r 5 , 5 < 1
8 8
r 7 , 7 > 1
r 2, 2 > 1
20
3
9

LESSON
11.4
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice A
For use with pages 675–680
Decide whether the infinite geometric series has a sum. Explain
why or why not.
1. 2. 3. 101 4.
n1
4 1
3 7
5. 6. 7. 8.
24 n
8
3 4
n1
n1
n1
n0
Find the sum of the infinite geometric series if it has one.
9. 10. 11. 12.
13. 14. 15. 16.
4 3
50.1n
101
n1
1
8 8n1
5 n1
4
9 n1
12
n0
1
4 n
2 n1
2
3 n1
n1
2 n1
5 n
2 n1
n1
n0
7 n1
6 n1
Find the common ratio of the infinite geometric series with the
given sum and first term.
17. 18. 19.
20. 21. 22. S 5
7 , a1 1
S 9, a1 11
S 10, a S 4, a1 3
S 20, a1 18
S 6, a1 3
1 15
Write the repeating decimal as a fraction.
23. 0.555. . .
24. 0.111. . .
25. 0.888. . .
26. 0.1212. . .
27. 0.2727. . .
28. 0.3131. . .
29. Compact Disc In coming to a rest, suppose that a compact disc makes
one half as many revolutions in a second as in the previous second. How
many revolutions does the compact disc make in coming to a rest if it
makes 4 revolutions in the first second after the stop function is activated?
n0
n0
2 n
5 n1
2 5 n1
n1
1
4 2n1
n0
1
3 n
Algebra 2 57
Chapter 11 Resource Book
Lesson 11.4

Answer Key
Practice B
1. yes;
3. no;
2. no;
4.
5. 6 6. no sum 7. 8. 9. 4 10. 10
11. 12. 13. 14. 15. 16.
17.
23.
4 7 2 2 35 74
9 18. 8 19. 3 20. 9 21. 99 22. 99
181 400
9 9
333 24. 11 25. finite; r 10 , 10 < 1;
200 in. 26. 300 ft
2
5
1
1 1
r 4 , 4 < 1
r 2, 2 > 1
4 4
r 3 , 3 > 1
2 2
yes; r 9 , 9 < 1
4
3
50
9
5
7
20
9
4
5
1
4
3

Lesson 11.4
LESSON
11.4
Practice B
For use with pages 675–680
58 Algebra 2
Chapter 11 Resource Book
NAME _________________________________________________________ DATE ___________
Decide whether the infinite geometric series has a sum. Explain
why or why not.
1. 2. 3. 4.
62
n0
n
n1
2
3 4
3 n1
4
n0
1
4 n
Find the sum of the infinite geometric series if it has one.
5. 6. 7. 2 8.
1
3 4
3 1
n0
9. 10. 11. 12.
0.4n
0.9n
n1
Find the common ratio of the infinite geometric series with the
given sum and first term.
13. 14. 15.
16. S 17. S 9, a1 5
18.
25
7 , a1 5
S 16, a1 12
S 15, a1 3
Write the repeating decimal as a fraction.
19. 0.666. . .
20. 0.222. . .
21. 0.3535. . .
22. 0.7474. . .
23. 0.543543. . .
24. 36.3636. . .
25. Length of a Spring The length of the first loop of a spring is 20 inches.
9
The length of the second loop is 10 the length of the first. The length of
9
the third loop is 10 the length of the second, and so on. Suppose the spring
had infinitely many loops. Does it have a finite or infinite length? Explain.
If it has a finite length, find the length.
26. Ball Bounce A ball is dropped from a height of 60 feet. Each time it
hits the ground, it bounces two-thirds of its previous height. Find the total
distance the ball has traveled before coming to rest.
60 ft
73 4 n1
2 n
40 ft
40 ft 26.7 ft
26.7 ft 17.8 ft
17.8 ft
n0
n0
3 n
n0
n0
2 n
2 0.1
n0
n
S 2, a1 1
S
4
3
4 , a1 1
n1
2 9 n1
5 n1
1
10 n1
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice C
1. 3 2. no sum 3.
2
4.
1
5. 6. 10
7. no sum 8. 9. no sum 10. 2
5
11. 6 12. 9 13. 4 14. 4 15.
1
1 8 40
16. 17. 18. 19. 20. 21.
10
109
1
24
5
4
11
653
21
2
3
2
50,000
300
11
22. 333 23. 999 24. 333 25. 120 cm 1.2 m;
after 6 swings 26. $3,000,000
9
3
1
3
99
1
2

LESSON
11.4
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice C
For use with pages 675–680
Find the sum of the infinite geometric series if it has one.
1. 2. 3. 4.
5. 6. 7. 8.
3 7
40.6n
0.3 1
10 n1
0.60.1
n0
n
7
n0
1
3 n
2 n0
5
4 n
4 n1
1 3 n1
9. 10. 11.
n1
1
4 7
8 n1
24
n0
n
12.
n1
n1
1
6 1 2 n1
n0
Find the common ratio of the infinite geometric series with the
given sum and first term.
13. 14. 15.
16. 17. S 18. S 200, a1 100
44
15 , a1 4
10
S 9 , a S
1 1
16
3 , a 8
S 9 1 8
, a S 4, a1 7
2
1 3
Write the repeating decimal as a fraction.
n0
1
2 2
5 n
19. 0.888. . .
20. 0.4040. . .
21. 27.2727. . .
22. 0.327327. . .
23. 0.653653. . .
24. 150.150150. . .
25. Pendulum A pendulum is released to swing freely. On the first swing, the
pendulum travels a distance of 24 centimeters. On each successive swing,
the pendulum travels four fifths of the distance of the previous swing. What
is the total distance the pendulum swings? After how many swings has the
pendulum traveled 70% of its total distance?
26. Economy A manufacturing company has opened in a small community.
The company will pay two million dollars per year in employees’ salaries.
It has been estimated that 60% of these salaries will be spent in the community,
and 60% of this money will again be spent in the community. This
process will continue indefinitely. Find the total amount of spending that
will be generated by the company’s salaries.
n1
2 n1
n1
4 1
6 n1
Algebra 2 59
Chapter 11 Resource Book
Lesson 11.4

Answer Key
Practice A
1. 4, 2, 0, 2. 3, 15, 75, 375, 1875
3. 4.
5.
6. 7. 2, 4, 16, 256, 65,536
8. 9.
10. ;
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21. a1 1, an an1 22. a1 50, an 1.01an1 56; $766.56
23. a1 60, an an1 16; $112
2 a1 48, an
a1 1, a2 3, an an1 an2 1
1
2a an 8
an 6 10n; a1 4, an an1 10
an 2 2n; a1 0, an an1 2
an 4 3n; a1 7, an an1 3
a1 3, an an1 5
a1 2, an 4an1 a1 12, an an1 9
n1
1
2 n1 ; a1 8, an 1 an 23 a1 2, an 3an1 2an1 n1 an 65 a1 6, an 5an1 ;
n1
10, 5,
2, 5, 14, 41, 122
7, 9, 12, 16, 21
5, 4, 8, 1, 15 1, 4, 19, 364, 132,499
5
2, 4
1, 7, 13, 19, 25
5 5
2 , 4 , 8

Lesson 11.5
LESSON
11.5
Practice A
For use with pages 681–687
70 Algebra 2
Chapter 11 Resource Book
NAME _________________________________________________________ DATE ___________
Write the first five terms of the sequence.
1. a0 4
2. a0 3
3. a0 1
a n a n1 2
a n 1
2 a n1
7. a0 2
8. a0 5
9. a1 1
a n a n1 2
Write an explicit rule and a recursive rule for the sequence. (Recall
that d is the common difference of an arithmetic sequence and r is
the common ratio of a geometric sequence.)
10. a1 6
11. a1 2
12. a1 8
r 5
13. a1 4
14. a1 0
15. a1 7
d 10
a n 5a n1
4. a1 10
5. a1 2
6. a1 7
a n 3a n1 1
a n n 2 a n1
r 3
d 2
Write a recursive rule for the sequence. The sequence may be
arithmetic, geometric, or neither.
16. 3, 8, 13, 18, . . .
17. 2, 8, 32, 128, . . .
18. 12, 3, 6, 15, . . .
19. 48, 24, 12, 6, . . .
20. 1, 3, 4, 7, 11, . . .
21. 1, 2, 5, 26, . . .
22. Savings Account On January 1, 2000, you have $50 in a savings
account that earns interest at a rate of 1% per month. On the last day of
every month you deposit $56 in the account. Write a recursive rule for the
account balance at the beginning of the nth month. Assuming you do not
withdraw any money from the account, what will your balance be on
January 1, 2001?
23. Layaway Suppose you buy a $300 television set on layaway by making
a down payment of $60 and then paying $16 per month. Write a recursive
rule for the total amount of money paid on the television set in the nth
month. How much will you have left to pay on the television set in the
ninth month?
a n a n1 6
a n n a n1
a n a n1 2 3
r 1
2
d 3
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice B
1. 3, 8, 13, 18, 23
2.
3.
4. 2, 2, 5, 7, 12
5. 1, 5, 29, 845, 714,029 6. 5, 9, 14, 23, 37
7. ;
8.
9.
10.
11.
12.
13.
14.
15.
16. a1 1, an an1 17. a1 7500, an 0.88an1 600;
6022 trees
18. a1 200, an 1.005an1 70; $704.52
19. a1 50, an 0.4an1 50; about 83.3 mg
2 a1 36, an
a1 4, an an1 2
3
1
3a an
a1 1, an an1 6
n1
11 1
2 2n; a1 6, an a an
1
n1 2
14
3 5n; a 1
1 3 , an a an 16
an 2 3n; a1 1, an an1 3
n1 5
1
4 n1 ; a1 16, an 1
an 105
4an1 n1 an 42 a1 4, an 2an1 ; a1 10, an 5an1 n1
32, 20, 14, 11, 19
2, 8, 32, 128, 512
2

LESSON
11.5
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice B
For use with pages 681–687
Write the first five terms of the sequence.
1. a0 3
2. a1 2
3. a1 32
a n a n1 5
a n n 2 a n1 3
Write an explicit rule and a recursive rule for the sequence. (Recall
that d is the common difference of an arithmetic sequence and r is
the common ratio of a geometric sequence.)
7. a1 4
8. a1 10
9. a1 16
10. 11. a1 12. a1 6
1
r
a1 1
1
r 2
r 5
4
d 3
a n 4a n1
4. a0 2
5. a0 1
6. a1 5, a2 9
a n a n1 2 4
d 5
Write a recursive rule for the sequence. The sequence may be
arithmetic, geometric, or neither.
13. 14. 36, 12, 4,
15. 4, 2, 0, 2, . . .
16. 1, 4, 19, 364, . . .
4
1, 7, 13, 19, . . .
3 , . . .
17. Tree Farm Suppose a tree farm initially has 7500 trees. Each year 12%
of the trees are harvested and 600 seedlings are planted. Write a recursive
rule for the number of trees on the tree farm at the beginning of the nth
year. How many trees remain at the beginning of the eighth year?
18. Savings Account On January 1, 2000, you have $200 in a savings
1
account which earns interest at a rate of 2%
per month. On the last day
of every month you deposit $70 in the account. Write a recursive rule for
the account balance at the beginning of the nth month. Assuming you do
not withdraw any money from the account, what will your balance be on
August 1, 2001?
19. Dosage A person takes 50 milligrams of a prescribed drug every day.
Suppose that 60% of the drug is removed from the bloodstream every day.
Write a recursive rule for the amount of the drug in the bloodstream after
n doses. What value does the drug level in the person’s body approach
after an extended period of time?
3
an 1
2an1 4
a n a n1 a n2
d 1
2
Algebra 2 71
Chapter 11 Resource Book
Lesson 11.5

Answer Key
Practice C
1. 8, 10, 14, 22, 38 2. 81, 33, 17,
3. 2, 2, 4, 10, 22 4.
5. 6. 2, 6, 4,
7. ;
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18. an 2 19. 4.25 minutes;
18.20 hours; 136.19 years
n an 10
an 3.5 1.5n; a1 2, an an1 1.5
a1 3, an 3an1 a1 4.3, an an1 0.6
a1 2, a2 3, an an1 an2 a1 24, a2 13, an an2 an1 a1 1, an 2an1 1
1
3
4n1 ; a1 10, an 3 an 60.2
4an1 n1 an
; a1 6, an 0.2an1 5 1
6 3n; a 1
1 2 , an a a1
an 3 4n; a1 7, an an1 4
1
n1 3
2
3 , an 2a an n1
2
32n1 1, 2, 6, 15, 31
1, 4, 4, 16, 64
2, 6
20. a 1 1, a n a n1 3 n1
35 89
3 , 9

Lesson 11.5
LESSON
11.5
Practice C
For use with pages 681–687
72 Algebra 2
Chapter 11 Resource Book
NAME _________________________________________________________ DATE ___________
Write the first five terms of the sequence.
1. a1 8
2. a1 81
3. a0 2
an 2an1 6
4. a0 1
5. a1 1, a2 4
6. a0 2, a1 6
a n a n1 n 2
Write an explicit rule and a recursive rule for the sequence. (Recall
that d is the common difference of an arithmetic sequence and r is
the common ratio of a geometric sequence.)
7. a1 8. a1 7
9.
2
3
r 2
10. a1 6
11. a1 10
12. a1 2
r 0.2
Write a recursive rule for the sequence. The sequence may be
arithmetic, geometric, or neither.
13. 3, 33, 9, 93, . . .
14. 4.3, 4.9, 5.5, 6.1, . . .
15. 2, 3, 6, 18, . . .
16. 24, 13, 11, 2, . . .
Tower of Hanoi In Exercises 17–20, use the following information.
This popular puzzle has three pegs and a number of discs of different
diameters, each with a hole in the center. The initial position of the
discs is shown in the figure. The objective is to move the tower to one
of the other pegs by moving the discs to any peg one at a time in such
a way that no disc is ever placed upon a smaller one.
17. Write a recursive rule for an , the number of moves required to transfer
n discs from one peg to another.
18. Find an explicit rule for an .
an 1
3an1 6
a n a n1 a n2
d 4
r 3
4
19. Suppose you can move one disc per second. Estimate the time required
to transfer the discs if n 8, n 16, and n 32.
20. Suppose the traditional rules for the Tower of Hanoi are modified. Now
you are required to move discs only to an adjacent peg. Write a recursive
rule for an .
a n n 2 n a n1
a n a n1 a n2
d 1
a1
3
1
2
d 1.5
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Test A
1. 120 2. 210 3. 5 4. 35 5. 12
6.
7.
8.
9. 10.
13
52 0.25
11.
4
52 0.0769 12.
4
52 0.0769
13.
1
52 0.0192 14.
2
52 0.0385 15.
1
2
16. 0% 17. 0.5 18. 0.30 19. 0.10 20.
21. 68%; 68 students 22. 0.95 23. 0.475
24. 8; 2.19 25. 455
8x3 12x2y 6xy2 y3 x5 5x 4y 10x3y2 10x2y3 5xy4 y5 x 4 12x3 54x2 x
108x 81
3 3x2y 3xy2 y3 1
1000

Review and Assess
CHAPTER
12
NAME _________________________________________________________ DATE
Chapter Test A
For use after Chapter 12
____________
Find the number of permutations or combinations.
1. 2. 3. 4.
5 P 4
7 P 3
5. Find the number of distinguishable permutations of the letters in
ERIE.
Expand the power of the binomial.
6. 7. 8. 9. 2x y3 x y5 x 34 x y3 A card is drawn randomly from a standard 52-card deck.
Find the probability of drawing the given card.
10. a diamond 11. a queen 12. an ace
13. the ten of spades 14. any black ace
Find the indicated probability.
15. PA 16. PA 60% 17. PA ?
PA ?
PB 40% PB 0.8
PA or B 100% PA or B 0.7
PA and B ? PA and B 0.6
1
2
108 Algebra 2
Chapter 12 Resource Book
5 C 4
7C 3
Answers
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
Copyright © McDougal Littell Inc.
All rights reserved.

CHAPTER
12
CONTINUED
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ____________
Chapter Test A
For use after Chapter 12
Find the indicated probability.
18. A
and B are independent events.
PA 0.5
PB 0.6
PA and B ?
19. A and B are dependent events.
PA ?
PBA 0.6
PA and B 0.06
20. Suppose you play the three digit number 917 in your state’s lottery.
If you assume that digits can be repeated what is the probability you
will win? (You must “hit” the number in the exact order.)
21. ACT Test One hundred students in your school took the ACT test.
Assuming that a normal distribution existed after the results, how
many of the students scored within one standard deviation of the
mean? (Give the percent and the number.)
22. A normal distribution has a mean of 8 and a standard deviation of 1.
Find the probability that a randomly selected x-value
is in the interval
between 6 and 10.
23. In Exercise 22, what is the probability that the randomly selected
x- value is between 8 and 10?
24. Find the mean and standard deviation of a normal distribution that
approximates a binomial distribution of 20 trials with a probability
of success of 0.40.
25. Find the number of possible twelve member juries that can be
selected from fifteen qualified people.
18.
19.
20.
21.
22.
23.
24.
25.
Algebra 2 109
Chapter 12 Resource Book
Review and Assess

Answer Key
Test B
1. 12 2. 181,440 3. 6 4. 36 5. 180
6.
7.
8.
9. 8x
10.
13.
26
2
52 0.5 11. 52 0.0385
1
52 0.0192
4
14. 52 0.0769
13
12. 52 0.25
1
15. 4
16. 0% 17. 0.6 18. 0.24 19. 0.8 20.
1
1000
21. 95%; 475 students 22. 0.68 23. 0.475
24. 13.5; 2.72 25. 362,880
3 12x2y 6xy2 y3 x8 4x6 6x 4 4x2 x
192x 64
1
6 12x5 60x 4 160x3 240x2 x
5 5x 4y 10x3y2 10x2y3 5xy4 y5

Review and Assess
CHAPTER
12
NAME _________________________________________________________ DATE
Chapter Test B
For use after Chapter 12
____________
Find the number of permutations or combinations.
1. 2. 3. 4.
4 P 2
9 P 7
5. Find the number of distinguishable permutations of the letters in
DALLAS.
Expand the power of the binomial.
6. 7. 8. 9. 2x y3 x2 14 x 26 x y5 A card is drawn randomly from a standard 52-card deck.
Find the probability of drawing the given card.
10. a red card 11. a red ace 12. a spade
13. the queen of diamonds 14. a jack
Find the indicated probability.
15. PA 16. PA 30% 17. PA 0.5
PA ?
PB 70% PB 0.3
PA or B 100% PA or B ?
PA and B ? PA and B 0.2
3
4
110 Algebra 2
Chapter 12 Resource Book
4 C 2
9C 7
Answers
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
Copyright © McDougal Littell Inc.
All rights reserved.

CHAPTER
12
CONTINUED
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ____________
Chapter Test B
For use after Chapter 12
Find the indicated probability.
18. A
and B are independent events.
PA 0.40
PB 0.60
PA and B ?
19. A and B are dependent events.
PA ?
PBA 0.7
PA and B 0.56
20. Suppose you play a three digit number of your choice in the lottery.
If you assume that digits can be repeated calculate the probability of
winning. (You must “hit” the number in the exact order.)
21. SAT Test Five hundred students in your school took the SAT test.
Assuming that a normal curve existed for your school, how many of
those students scored within 2 standard deviations of the mean?
(Give the percent and the number.)
22. A normal distribution has a mean of 10 and a standard deviation of
2. Find the probability that a randomly selected x-value
is in the
interval between 8 and 12.
23. In Exercise 22, what is the probability that the randomly selected
x- value is between 6 and 10?
24. Find the mean and standard deviation of a normal distribution that
approximates a binomial distribution of 30 trials with a probability
of success of 0.45.
25. Batting Orders Find the number of possible batting orders for the
nine starting players on a girls high school softball team.
18.
19.
20.
21.
22.
23.
24.
25.
Algebra 2 111
Chapter 12 Resource Book
Review and Assess

Answer Key
Test C
1. 2520 2. 3,991,680 3. 21 4. 792
5. 90,720
6.
7.
8. x6 12x5 60x 4 160x3 240x2 8x
3 12x2y 6xy2 y3 x5 5x 4y 10x3y2 10x2y3 5xy4 y5 192x 64
9. 1 5x
10.
8
48 0.167 11.
4
48 0.0833
12.
14.
12
48 0.25 13.
2
48 0.0417
16
48 0.333
15.
0
48 0 16.
2
5 17. 100% 18.
3
4 19. 0.65
20.
2
9 21. 84%; 16,800 22. 0.95 23. 0.135
24. 25.5; 4.10 25.
59
0.413
143 2 10x 4 10x6 5x8 x10

Review and Assess
CHAPTER
12
NAME _________________________________________________________ DATE
Chapter Test C
For use after Chapter 12
____________
Find the number of permutations or combinations.
1. 2. 3. 4.
7 P 5
5. Find the number of distinguishable permutations of the letters in
CLEVELAND.
Expand the power of the binomial.
6. 7. 8. x 2 9.
6
2x y3 x y5 A card is drawn randomly from a standard 48-card pinochle
deck. Find the probability of drawing the given card. (Note
that a pinochle deck consists of all four suits. The cards 9,
10, jack, queen, king, ace appear twice in each suit. There
are no 2, 3, 4, 5, 6, 7, or 8s.)
10. any ace 11. any black queen 12. any heart
13. any 9 or 10 14. any ace of hearts 15. any 7
Find the indicated probability.
16. PA 17. PA 50% 18. PA ?
3
5
PA ?
12 P 7
PB 50%
112 Algebra 2
Chapter 12 Resource Book
7 C 5
PA or B ?
PA and B 0%
12C 7
1 x 2 5
PA and B 1
PA or B
4
5
PB
6
1
3
Answers
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
Copyright © McDougal Littell Inc.
All rights reserved.

CHAPTER
12
CONTINUED
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ____________
Chapter Test C
For use after Chapter 12
Find the indicated probability.
19. A
and B are independent events.
PA 0.35
PB ?
PA and B 0.2275
20. A and B are dependent events.
PA
2 PBA 3
PA and B ?
1
3
21. ACT Test Twenty thousand students in your state took the ACT
test. On the math portion the mean was 21 and the standard
deviation was 5. If the scores resulted in a normal distribution,
how many students scored at least 16? (Give the percent and the
number.)
22. A normal distribution has a mean of 200 and a standard deviation of
25. Find the probability that a randomly selected x-value
is in the
interval between 150 and 250.
23. In Exercise 22, what is the probability that the randomly selected
x- value is between 225 and 250?
24. Find the mean and standard deviation of a normal distribution that
approximates a binomial distribution of 75 trials with a probability
of success of 0.34.
25. Committee Selection A committee of 5 people is to be selected
from student council. Council has 6 boys and 7 girls. What is the
probability that the committee will have at least 3 boys?
19.
20.
21.
22.
23.
24.
25.
Algebra 2 113
Chapter 12 Resource Book
Review and Assess

Answer Key
Cumulative Review
1. 2. 3.
4. y 5. y 3x 4
6. y 4x 11
7. 8.
5
y y 2x 9
4x 4
2
y 3x 4
3
3x 5
x
9. 10.
x
11. 12.
x
z
z
z
y
y
y
x
x
x
z
z
z
y
y
y
13. 14. 15.
16. 17. 18. no solution
19. 20.
21.
23.
22.
24.
25. 1, 2 26. 1, 2 27. 2
28. 2, 1 29. 2, 2 30. 1 31. 2
32. ±3 33. 2 34. 5.62 35. 0, – 4
5
x < 0 or x > 2
2 ≤ x ≤ 3
3
3
4 < x < 4
2
1 ≤ x ≤
3
< x < 3 2
5
x ≥ 3 or x ≤ 1
2
1
5,
1, 6
1
2 , 3
1
(0, 3
4, 1
36. 1.97 37. 38. 39.
40. 41. 42. 43. 8; 3.02
44. 13; 4.06 45. 8; 2.77 46. 23; 6.82
47. 22; 6.54 48. 1.1; 0.368 49. B 50. C
51. A 52. 54.598 53. 0.513 54. 9.974
55. 56. 0.025 57.
58. 0.845 59. 2.398 60. 0.349 61. 0.766
62. 1.668 63. 2.303 64. 65. 1
66. no solution 67. 3.81 68. 0.42 69. 3.07
70. 3.457 71. 5.457 72. 0.380 73. 4.820
74. 2.860 75. 1.101 76. 25 4.47
77. 42 5.66 78. 213 7.21
79. 229 10.77 80. 31.33 5.60
81.
10
0.79
4
82. down 83. up 84. right
85. down 86. left 87. right 88. 165
89. 276
93. 120
90. 2500 91. 143 92. 625
3
3
0.149
0.034
4
5 2
33
3
2
2
5 12
2
4 53 22 2
2

CHAPTER
12 Cumulative Review
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ____________
For use after Chapters 1–12
Write an equation of the line using the given information. (2.4)
1. 2.
3. passes through 4. passes through and
5. passes through and is perpendicular to y
6. passes through (2, 3 and is parallel to y 4x 1
1
m
m 2,
(4, 1
(0, 4 4, 1
(1, 1
3x 8
2
3, b 3
m 3, b 4
5
Plot the ordered triple in a three-dimensional coordinate system.
(3.5)
7. 3, 2, 1
8 2, 1, 0
9. 4, 1, 2
10. 2, 0, 0
11. 1, 2, 3
12. 4, 0, 3
Use Cramer’s rule to solve the linear system. (4.3)
13. 2x y 3
14. x y 5
15. x 4y 7
5x 2y 6
16. 5x y 1
17. 4x 3y 1
18. 4x 3y 8
3x y 3
Solve the inequality algebraically. (5.7)
x 2 2x 3 ≥ 0
19. 20. 21.
22. 23. 24.
16x 2 9 < 0
2x 3y 11
6x 3y 4
2x 2 7x 5 ≤ 0
2x 2 4x > 0
Use synthetic division to decide which of the following are zeros of
the function: (6.6)
25. 26.
27. 28.
29. 30. f x x 4 5x3 f x x x 5
5 4x3 8x2 f x x
32
4 3x3 7x2 f x x 15x 18
4 8x3 21x2 f x x
18x
3 7x2 f x x 14x 8
3 2x2 1, 1, 2, 2.
5x 6
Solve the equation. Round your answer to two decimal places when
appropriate. (7.1)
31. 32. 33.
34. 35. 36. x 4 x 2 3 12
4 x 3 1 15
3 4x
18
3 3x 32
4 x 243
5 32
Write the expression in simplest form. (7.2)
37. 38. 39.
40. 41.
3
42.
1
44
564
9
4 75
16
2x 6y 7
8x 6y 4
3 4 8 2 4 4
3
516
Find the range and standard deviation of the data set. (7.7)
43. 1, 1, 3, 5, 6, 7, 9, 9
44. 12, 18, 15, 15, 16, 10, 19, 22, 23
45. 2, 3, 5, 9, 7, 7, 8, 8, 2, 10
46. 75, 77, 78, 84, 80, 80, 61
47. 19, 19, 18, 1, 14, 15, 23
48. 0.1, 0.8, 0.7, 1.2, 0.5, 1.1
6x 2 5x 6 < 0
2x 2 x 15 ≤ 0
Algebra 2 119
Chapter 12 Resource Book
Review and Assess

Review and Assess
CHAPTER
12
CONTINUED
NAME _________________________________________________________ DATE ____________
Cumulative Review
For use after Chapters 1–12
Match the function with the graph. (8.1)
49. 50. 51. y 3
A. y
B. y
C.
y
x y 3 4 3
x3
y 4x Use a calculator to evaluate the expression. Round the result to
three decimal places. (8.3 and 8.4)
e 4
1
52. 53. 54.
55. 56. 57. 5e
58. log 7
59. ln 11
60. log5
61. log 5.83
62. ln 5.3
63. ln 10
5
0.03e0.2 3e3 Solve the equation. Round your answer to two decimal places
when appropriate. (8.6)
64. 65. 66.
67. 68. 69. 3x 10 2 27
3x 2 2 20
x 81
14
x8 92x 253x 125x1 102x1 1003x1 6
Evaluate the function f x for the given value of x.
1 2e
Round the result to three decimal places. (8.8)
x
70. 71. 72.
73. 74. f 75.
3
f 1
f 3
f 2.1
Find the distance between the two points. (10.1)
76. 5, 4, 7, 8
77. 6, 1, 2, 3
78. 3, 4, 3, 0
79. 8, 3, 2,1
80. 6.3, 9.2, 2.1, 5.5
81. , 1
Tell whether the parabola opens up, down, left, or right. (10.2)
82. 83. 84.
85. 86. 87. x 2
3y2 x 7y2 5y 2x2 2x 3y2 3y 8x2 y 4x2 Find the sum of the first n terms of the arithmetic series. (11.2)
88. 3 6 9 12 15 . . . ; n 10 89. 1 5 9 13 17 . . . ; n 12
90. 1 3 5 7 9 . . . ; n 50 91. 7 4 1 2 5 . . . ; n 13
92. 40 45 50 55 60 . . . ; n 10 93. 22 20 18 16 14 . . . ; n 15
120 Algebra 2
Chapter 12 Resource Book
2
x
e 23
5
1
1
x
e 2.3
f 2
1
f 0.8
1 1
2 , 4, 3 4
1
2
Copyright © McDougal Littell Inc.
All rights reserved.
x

Answer Key
Practice A
1. 8 2. 6 3. 21 4. 30 5. a. 6,760,000
b. 3,276,000 6. a. 2,600,000 b. 786,240
7. a. 45,697,600 b. 32,292,000
8. a. 118,813,760 b. 78,936,000 9. 720
10. 24 11. 6 12. 39,916,800 13. 24 14. 5
15. 20,160 16. 42 17. 6 18. 120 19. 24
20. 720 21. 3 22. 12 23. 2520 24. 180
25. 1920 26. 12

Lesson 12.1
LESSON
12.1
Practice A
For use with pages 701–707
16 Algebra 2
Chapter 12 Resource Book
NAME _________________________________________________________ DATE ___________
Each event can occur in the given number of ways. Find the number
of ways all of the events can occur.
1. Event 1: 2 ways, Event 2: 4 ways 2. Event 1: 6 ways, Event 2: 1 way
3. Event 1: 7 ways, Event 2: 3 ways 4. Event 1: 2 ways, Event 2: 5 ways,
Event 3: 3 ways
For the given configuration, determine how many different
computer passwords are possible if (a) digits and letters can be
repeated, and (b) digits and letters cannot be repeated.
5. 4 digits followed by 2 letters 6. 5 digits followed by 1 letter
7. 4 letters followed by 2 digits 8. 5 letters followed by 1 digit
Evaluate the factorial.
9. 6!
10. 4!
11. 3!
12. 11!
Find the number of permutations.
13. 14. 15. 8 16.
P 4 6
P4 5P 1
Find the number of distinguishable permutations of the letters in
the word.
17. CAT 18. MONEY 19. UTAH 20. FAMILY
21. MOM 22. TENT 23. PHYSICS 24. FOLLOW
25. Home Decor You are choosing curtains, paint, and carpet for your
room. You have 12 choices of curtains, 8 choices of paint, and 20 choices
of carpeting. How many different ways can you choose curtains, paint,
and carpeting for your room?
26. Naming a Dog You are choosing a name for your registered beagle.
Your dog’s grandparent’s names were Willow-Sutton, Carolina-Downing,
Hollybrook-Loner, and Starfire-Wolf. You want your dog’s first name to
be the same as one of its grandparents’ first names, and its second name to
be the same as one of its grandparents’ second names. However, your dog
cannot have exactly the same name as one of its grandparents. How many
names are possible?
7 P 2
Copyright © McDougal Littell Inc.
All rights reserved.
Lesson 11.3

Answer Key
Practice B
1. 12 2. 5 3. 48 4. 90 5. a. 6,760,000
b. 3,276,000 6. a. 2,600,000 b. 786,240
7. a. 17,576,000 b. 11,232,000
8. a. 118,813,760 b. 78,936,000 9. 720
1.31 10 12
10. 6,227,020,800 11. 1 12.
13. 1,814,400 14. 1 15. 6 16. 720
17. 5040 18. 120 19. 24 20. 12 21. 3
22. 20,160 23. 10,080 24. 907,200 25. 72
26. 120 27. 201,600 28. 5040

LESSON
12.1
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice B
For use with pages 701–707
Each event can occur in the given number of ways. Find the number
of ways all of the events can occur.
1. Event 1: 3 ways, Event 2: 4 ways 2. Event 1: 1 way, Event 2: 5 ways
3. Event 1: 4 ways, Event 2: 6 ways 4. Event 1: 2 ways, Event 2: 9 ways,
Event 3: 2 ways Event 3: 5 ways
For the given configuration, determine how many different
computer passwords are possible if (a) digits and letters can be
repeated, and (b) digits and letters cannot be repeated.
5. 2 letters followed by 4 digits 6. 1 letter followed by 5 digits
7. 3 digits followed by 3 letters 8. 1 digit followed by 5 letters
Evaluate the factorial.
9. 6!
10. 13!
11. 0!
12. 15!
Find the number of permutations.
13. 14. 15. 16.
10 P 8
5 P 0
Find the number of distinguishable permutations of the letters in
the word.
17. ENGLISH 18. NORTH 19. MATH 20. BELL
21. EYE 22. ALPHABET 23. OKLAHOMA 24. CALIFORNIA
25. School Lunch Your school cafeteria offers three salads, four main
courses, two vegetables, and three desserts. How many different lunches
consisting of a salad, main course, a vegetable, and dessert are possible?
26. Stacking Books Five books are taken from a shelf and laid in a stack
on a table. In how many different orders can the books be stacked?
27. Batting Order A baseball coach is determining the batting order for the
team. The team has nine members, but the coach does not want the pitcher
to be one of the first four to bat. How many batting orders are possible?
28. Scheduling Classes Next year you are taking math, English, history,
keyboarding, chemistry, physics, and physical education. Each class is
offered during each of the seven periods in the day. In how many different
orders can you schedule your classes?
6 P 1
6 P 6
Algebra 2 17
Chapter 12 Resource Book
Lesson 12.1

Answer Key
Practice C
1. 360 2. 120 3. a. 10,000 b. 3024
4. a. 3125 b. 120 5. a. 50,000 b. 15,120
6. a. 20,000 b. 6048 7. 24 8. 1
about 8.72 10 10
about 2.43 10 18
9. 10.
11. 1 12. 40,320 13. 120 14. 10
15. 362,880 16. 60 17. 3 18. 120 19. 420
20. 19,958,400 21. 4,989,600 22. 39,916,800
23. 85,765,680; 4080 24. 64,000 25. 40,320

Lesson 12.1 12.1
LESSON
12.1
Practice C
For use with pages 701–707
18 Algebra 2
Chapter 12 Resource Book
NAME _________________________________________________________ DATE ___________
Each event can occur in the given number of ways. Find the number
of ways all of the events can occur.
1. Event 1: 6 ways, Event 2: 5 ways 2. Event 1: 2 ways, Event 2: 4 ways,
Event 3: 12 ways Event 3: 5 ways, Event 4: 3 ways
For the given configuration, determine how many different 5-digit
postal zip codes are possible if (a) digits can be repeated, and
(b) digits cannot be repeated.
3. Begins with a 4. 4. Has all even digits.
5. Is divisible by 2. 6. Begins with a 3 or a 1.
Evaluate the factorial.
7. 4!
8. 0!
9. 14!
10. 20!
Find the number of permutations.
11. 12. 13. 14.
12 P 0
8 P 8
Find the number of distinguishable permutations of the letters in
the word.
15. CHEMISTRY 16. PAPER 17. EEL 18. ALASKA
19. SUCCESS
22. BILLIONAIRES
20. PERMUTATION 21. MATHEMATICS
23. Dog Show In a dog show, how many ways can four Pomeranians, five
golden retrievers, two Great Pyrenees, and six English terriers line up in
front of the judges if the dogs of the same breed are considered identical?
In how many different ways can three dogs win first, second, and third
place?
24. Combination Lock You have forgotten the combination of the lock on
your school locker. There are 40 numbers on the lock, and the correct
combination is “R
are there?
-L -R .” How many possible combinations
25. Circular Permutations In how many different ways can nine
people be seated around a circular table?
E
6 P 3
A
D C
B
B
A
This is the same permutation.
C
10 P 1
D
E
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice A
1. 20 2. 21 3. 3 4. 5 5. 1 6. 6 7. 1
8. 7 9. 2600 10. 4 11. 220 12. 286
13. 52 14.
15.
16.
17.
18.
19.
20.
21. 8x 22. 560
23. 61,236 24. 220 25. 126
3 12x2y 6xy2 y3 x4 12x3y 54x2y2 108xy3 81y4 x4 8x3y 24x2y2 32xy3 16y4 x5 5x4y 10x3y2 10x2y3 5xy4 y5 x4 20x3 150x2 x
500x 625
3 6x2 x
12x 8
3 12x2 x
48x 64
4 12x3 54x2 108x 81

LESSON
12.2
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice A
For use with pages 708–715
Find the number of combinations.
1. 2. 3. 3 4.
5. 6. 7. 8.
C 7 1
C 6 5
C3 2 C 2
In Exercises 9–13, find the number of possible 3-card hands that
contain the cards specified.
9. 3 red cards
10. 3 aces
11. 3 face cards
12. 3 hearts
4 C 2
13. 3 of one kind (kings, queens, and so on)
Expand the power of the binomial.
14. 15. 16. 17.
18. 19. 20. 21.
22. Find the coefficient of in the expansion of
23. Find the coefficient of in the expansion of x 3y
24. Pizza Toppings A pizza shop offers twelve different toppings. How
many different three-topping pizzas can be formed with the twelve
toppings? (Assume no topping is used twice.)
10 x .
5
2x 17 x .
4
x 3y4 x 2y4 x y5 x 54 x 23 x 43 x 34 25. Bowling Team Nine people in your class want to be on a 5-person
bowling team to represent the class. How many different teams can be
chosen?
5C 5
5 C 4
7C 1
2x y 3
Algebra 2 31
Chapter 12 Resource Book
Lesson 12.2

Answer Key
Practice B
1. 56 2. 120 3. 1 4. 792 5. 65,780
6. 3744 7. 658,008 8. 5148
9. x7 7x6 21x5 35x4 35x3
21x 2 7x 1
10.
11.
12. x
13. 60,555,264 14. 2,449,440 15. 1287
16. 300 17. 90
4 16x3y 96x2y2 256xy3 256y4 8x3 36x2 x
54x 27
6 12x5 60x4 160x3 240x2 192x 64

Lesson 12.2
LESSON
12.2
Practice B
For use with pages 708–715
32 Algebra 2
Chapter 12 Resource Book
NAME _________________________________________________________ DATE ___________
Find the number of combinations.
1. 2. 3. 4.
8 C 5
In Exercises 5–8, find the number of possible 5-card hands that
contain the cards specified.
5. 5 black cards
10 C 3
6. 3 of one kind (kings, queens, and so on) and 2 of a different kind
7. 5 cards, none of which are face cards (either kings, queens, or jacks)
8. 5 cards of the same suit
Expand the power of the binomial.
9. 10. 11. 12.
13. Find the coefficient of in the expansion of
14. Find the coefficient of in the expansion of 3x 2
15. Basketball Starters A basketball team has five starting players. There
are 13 girls on the team. In how many ways can the coach select players
to start the game? (Assume each player can play each position.)
10 x .
6
2x 411 x .
5
x 4y4 2x 33 x 26 x 17 10 C 10
16. School Faculty A high school needs four additional faculty members:
two math teachers, a chemistry teacher, and a Spanish teacher. In how
many ways can these positions be filled if there are six applicants for
mathematicians, two for chemistry, and ten applicants for Spanish?
17. Geometry How many different rectangles occur in the grid shown
below? (Hint: A rectangle is formed by choosing two of the vertical lines
in the grid and two of the horizontal lines in the grid.)
12C 5
Copyright © McDougal Littell Inc.
All rights reserved.
Lesson 12.1

Answer Key
Practice C
1. 210 2. 462 3. 1 4. 495 5. 4
6. 3744 7. 123,552 8. 3120
9.
10. 64x6 192x5y2 240x4y4 160x3y6 32x
5 80x4 80x3 40x2 10x 1
60x 2 y 8 12xy 10 y 12
11.
12. x21 7x18y 21x15y2 35x12y3 256x
4 256x3y3 96x2y6 16xy9 y12 35x 9 y 4 21x 6 y 5 7x 3 y 6 y 7
13. 69,672,960 14. 316,800,000 15. 302,400
16. 386 17. 126

Lesson 12.1
LESSON
12.2
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice C
For use with pages 708–715
Find the number of combinations.
1. 2. 3. 4.
10 C 6
In Exercises 5–8, find the number of possible 5-card hands that
contain the cards specified.
5. 4 aces and 1 king
11 C 5
6. 3 of one kind (kings, queens, and so on) and 2 of a different kind
7. 2 of one kind, 2 of a second kind, and 1 other card
8. 3 face cards (kings, queens, or jacks) of the same suit and 2 other cards
(none of which are face cards)
Expand the power of the binomial.
9. 10. 11. 12.
13. Find the coefficient of in the expansion of
14. Find the coefficient of in the expansion of 2x 5
15. Football Starters A high school football team has 2 centers, 9 linemen
(who can play either guard or tackle), 2 quarterbacks, 5 halfbacks, 5 ends,
and 6 fullbacks. The coach uses 1 center, 4 linemen, 2 ends, 2 halfbacks, 1
quarterback, and 1 fullback to form an offensive unit. In how many ways
can the offensive unit be selected?
12 x .
7
4x 310 x .
6
x3 y7 4x y34 2x y26 2x 15 14 C 14
16. Ice Cream Sundaes An ice cream shop has a choice of ten toppings.
Suppose you can afford at most four toppings. How many different types
of ice cream sundaes can you order?
17. Geometry How many different rectangles occur in the grid shown
below? (Hint: A rectangle is formed by choosing two of the vertical lines
in the grid and two of the horizontal lines in the grid.)
12C 8
Algebra 2 33
Chapter 12 Resource Book
Lesson 12.2

Answer Key
Practice A
1. 0.5 2. 0.25 3. 1 4. 0.75 5. 0.5 6. 0
7. 0.182 8. 0.091 9. 0.455 10. 0.636
11. 0.306 12. 0.660 13. 0.665 14. 0.125
15. 0.0425 16. 0.01

LESSON
12.3
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice A
For use with pages 716–722
Spinning a Spinner You have an equally likely chance of spinning
any value on the spinner. Find the probability of spinning the given
event.
1. a shaded region 2. a factor of 27
3. a number less than 6 or a shaded region
4. an even number or perfect square
5. a prime number 6. a two-digit number
Choosing Marbles A jar contains 5 red marbles, 3 green marbles, 2 yellow
marbles, and 1 blue marble. Find the probability of randomly drawing the given
type of marble.
7. a yellow marble 8. a blue marble
9. a green or yellow marble 10. a red or yellow marble
School Mascot In order to choose a mascot for a new school, 2755 students
were surveyed: 896 chose a falcon, 937 chose a ram, and 842 chose a panther.
The remaining students did not vote. A student is chosen at random.
11. What is the probability that the student’s choice was a panther?
12. What is the probability that the student’s choice was not a ram?
13. What is the probability that the student’s choice was either a falcon or a
ram?
Hitting a Star In Exercises 14–16, use the following information.
You are throwing a dart at the square shown at the right. Assume that
the dart is equally likely to land at any point in the square. The square
is 2 inches by 2 inches. Each star has an area of 0.01 square inch.
14. The dart has landed inside the square. What is the probability that
it hit a star?
15. The dart has landed inside the square. What is the probability that
it hit a star in the top three rows?
16. The dart has landed inside the square. What is the probability that
it hit one of the four corner stars?
4
9
2
5
Algebra 2 45
Chapter 12 Resource Book
Lesson 12.3

Answer Key
Practice B
1. 0.5 2. 0.417 3. 0.333 4. 0.25 5. 0.222
6. 0.667 7. 0.444 8. 0.518 9. 0.852
10. 0.019 11. about 2.48 10 12. 0.624
5

Lesson 12.3
LESSON
12.3
Practice B
For use with pages 716–722
46 Algebra 2
Chapter 12 Resource Book
NAME _________________________________________________________ DATE ___________
Choosing Numbers You have an equally likely chance of choosing any integer
from the set 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12.
Find the probability of the
given event.
1. An even number is chosen. 2. A prime number is chosen.
3. A multiple of 3 is chosen. 4. A two-digit number is chosen.
Farm Animals Your cousin lives on a small farm. She is a member of the
4-H Club and is showing nine animals at the county fair. Two of her animals
won a blue ribbon (1st place), one won a red ribbon (2nd place), and three won
white ribbons (3rd place). You do not know which animals won which prizes.
You choose one of your cousin’s animals at random.
5. What is the probability that the animal won a 1st place ribbon?
6. What is the probability that the animal won a ribbon?
7. What is the probability that the animal won a red or white ribbon?
Live Births In Exercises 8–10, use the following information.
Of all live births in the United States in 1996, 12.9% of the mothers were
teenagers, 51.8% were in their twenties, 33.4% were in their thirties, and the
rest were in their forties. Suppose a mother is chosen at random.
8. What is the probability that the mother gave birth in her twenties?
9. What is the probability that the mother gave birth in her twenties or
thirties?
10. What is the probability that the mother gave birth in her forties?
11. Choosing Coins You have 8 pennies in your pocket dated 1972, 1978,
1979, 1985, 1989, 1991, 1993, and 1999. You take the coins out of your
pocket one at a time. What is the probability that they are taken out in
order by date?
12. Geometry Find the probability that a dart thrown at the given target will
hit the shaded region. Assume the dart is equally likely to hit any point
inside the target.
5
7
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice C
1. 0.278 2. 0.722 3. 0.278 4. 0.167
5. 0.563 6. 0.813 7. 0.25 8. 0.188
9. 0.0218 10. 0.0654 11. 0.153 12. 0.455
13. 0.771 14. 0.033

LESSON
12.3
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice C
For use with pages 716–722
Rolling Dice You have an equally likely chance of rolling any value on each
of two dice. Find the probability of the given event.
1. rolling a sum of either 7 or 9 2. rolling a sum greater than 5
3. rolling a 6 on exactly one die 4. rolling doubles
Genetics Common parakeets have genes that can produce
four feather colors: green (BBCC, BBCc, BbCC, or BbCc),
blue (BBcc, or Bbcc), yellow (bbCC or bbCc), or white (bbcc).
Complete the Punnett square to the right to find the possible
feather colors of the offspring of two green parents (both with
BcCc feather genes). Then find the probability of the given
event.
5. green feathers 6. not blue feathers
7. yellow or white feathers 8. yellow feathers
Geometry A marble is dropped into a large box whose base
is painted different colors, as shown at the right. The marble
has an equal likelihood of coming to a rest at any point on the
base. Find the probability of the given event.
9. the center circle 10. the first ring
11. the third ring 12. the border
Test Scores Thirty-five students in an Algebra 2 class took a test: 9 received
A’s, 18 received B’s, and 8 received C’s. Find the probability of the given event.
13. If a student from the class is chosen at random, what is the probability that
the student did not receive a C?
14. If the teacher randomly chooses 3 test papers, what is the probability that
the teacher chose tests with grades A, B, and C in that order?
BC
Bc
bC
bc
BC
Bc
Ring 1
Ring 2
Ring 3
Ring 4
24 in.
bC
bc
2 2 2 2 2 24 in.
Algebra 2 47
Chapter 12 Resource Book
Lesson 12.3

Answer Key
Practice A
1. 0.15; no 2. 0.35; yes 3. 0.45; no
4. 0.80; no 5. 0.70; no 6. 0; yes 7. 0.75
1
3
8. 9. 0.36 10. 1 11. 0.0833 12. 0.0556
13. 0.417 14. 0.923 15. 0.769 16. 0.692
17. 0.692 18. 0.60

Lesson 12.4
LESSON
12.4
Find
P A.
Practice A
For use with pages 724–729
58 Algebra 2
Chapter 12 Resource Book
NAME _________________________________________________________ DATE ___________
Find the indicated probability. State whether A and B are mutually
exclusive.
1. PA 0.2
2. PA 0.45
3. PA 0.25
PB 0.55
PA or B 0.6
PA and B ?
PB 0.40
PA or B ?
PA and B 0.10
PB ?
PA or B 0.80
PA and B 0
4. PA 0.50
5. PA ?
6. PA 0.45
PB 0.40
PA or B 0.80
PA and B 0.30
7. PA 0.25
8. 9. PA 0.64
PA 2
3
PB 0.32
PA or B ?
PA and B 0.12
PB 0.15
PA or B 0.60
PA and B ?
Rolling Dice
given event.
Two six-sided dice are rolled. Find the probability of the
10. The sum is even or odd. 11. The sum is 3 or 12.
12. The sum is greater than 8 and prime. 13. The sum is 10 or a multiple of 3.
Using Complements A card is randomly drawn from a standard 52-card
deck. Find the probability of the given event.
14. not an ace 15. not a face card
16. less than 10 (an ace is one) 17. not a diamond or a five
18. Snow The probability that it will snow today is 0.30, and the probability
that it will snow tomorrow is 0.50. The probability that it will snow both
days is 0.20. What is the probability that it will snow today or tomorrow?
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice B
6
11 ;
13
24 ;
1. no 2. 0%; yes 3. no 4. 0.3 5.
6. 37% 7. 0.308 8. 0.0577 9. 0.923
10. 0.308
13. 50%
11. 0.743 12. 0.917; 0.083
1
4

LESSON
12.4
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice B
For use with pages 724–729
Find the indicated probability. State whether A and B are mutually
exclusive.
1. PA 2. PA 28%
3.
4
Find
P A.
11
PB ?
PA and B 2
PA or B
11
8
11
PB 14%
PA or B 42%
PA and B ?
4. 5. 6.
Choosing Cards A card is randomly drawn from a standard 52-card deck.
Find the probability of the given event.
7. an ace or a club 8. a face card and a diamond
9. not an ace 10. less than or equal to four (an ace is one)
11. Honors Banquet Of the 148 students honored at an academic banquet,
40 won awards for mathematics and 82 for English. Twelve of these
students won awards for both mathematics and English. One of the 148
students is chosen at random to be interviewed for a newspaper article.
What is the probability that the student won an award in mathematics or
English?
12. Hockey or Swimming The probability that you will make the hockey
team is The probability that you will make the swimming team is If
1
the probability that you make both teams is 2 what is the probability that
you at least make one of the teams? that you make neither team?
13. Weather Forecast The probability that it will snow today is 40%, and
the probability that it will snow tomorrow is 20%. The probability that it
will snow both days is 10%. What is the probability that it will snow
today or tomorrow?
,
3
4 .
2
3 .
PA 0.7
4
PA 63%
PA 3
PB 1
PA
2
2
3
PA or B ?
PA and B 5
8
Algebra 2 59
Chapter 12 Resource Book
Lesson 12.4

Answer Key
Practice C
1. 10%; no 2. 92%; yes
1
3. no 4. 0.98
7
5. 63% 6. 7. 0.167 8. 0.944 9. 0.75
10. 0.0278 11. 5 to 3 12. 9 13. 0.31 14. 3
12
5
3 ;

Lesson 12.4
LESSON
12.4
Practice C
For use with pages 724–729
60 Algebra 2
Chapter 12 Resource Book
NAME _________________________________________________________ DATE ___________
Find the indicated probability. State whether A and B are mutually
exclusive.
1. PA 12%
2. PA 85%
3.
PB 48%
PA or B 50%
PA and B ?
PB 7%
PA or B ?
PA and B 0%
Find P A.
4. PA 0.02
5. PA 37%
6.
Rolling Dice
event.
Two six-sided dice are rolled. Find the probability of the given
7. The sum is even and a multiple of 3. 8. The sum is not 2 or 12.
9. The sum is greater than 7 or odd. 10. The sum is prime and even.
Odds In Exercises 11 and 12, use the following information.
The odds in favor of an event occurring are the ratio of the probability that the
event will occur to the probability that the event will not occur.
11. A jar contains three red marbles and five green marbles. What are the
odds that a randomly chosen marble is green?
12. A jar contains three red marbles and some green marbles. The odds are 3
to 1 that a randomly chosen marble is green. How many green marbles are
in the jar?
13. Science Class Students at Northwestern High School have three
choices for a required science in their junior year: physics, chemistry, or
biology. Experience has shown that the probability of a student selecting
physics is 0.12 and the probability of a student selecting chemistry is 0.57.
If each student can select only one science course, what is the probability
that a randomly chosen student will select biology?
14. Cars A parking lot has 25 cars. Eight are red and 13 have four doors.
Six are both red and have four doors. Find the probability that a randomly
chosen car will be red or have four doors.
PA 3
4
PB ?
PA and B 2
PA or B
3
5
12
PA 5
12
Copyright © McDougal Littell Inc.
All rights reserved.
Lesson 12.3

Answer Key
Practice A
1. independent 2. dependent 3. independent
1
3
4. independent 5. 6. 0.08 7. 0.80
8. 0.80 9. 0.06 10. 0.50 11. 0.216
12. 0.0234 13. 0.784

Lesson 12.5
LESSON
12.5
Practice A
For use with pages 730–737
70 Algebra 2
Chapter 12 Resource Book
NAME _________________________________________________________ DATE ___________
State whether A and B are independent or dependent.
1. A single coin is tossed twice. Event A is having the coin land heads up on
the first toss. Event B is having the coin land tails up on the second toss.
2. Two cards are drawn from a standard 52-card deck. The first card is not
placed back in the deck before the second card is drawn. Event A is
drawing a queen for the first card. Event B is drawing a king for the
second card.
3. Two cards are drawn from a standard 52-card deck. The first card is
placed back in the deck before the second card is drawn. Event A is
drawing a queen for the first card. Event B is drawing a king for the
second card.
4. You buy one state lottery ticket this week and one next week. Event A is
winning the lottery this week. Event B is winning the lottery next week.
Events A and B are independent. Find the indicated probability.
5. 6. PA 0.40
7. PA 0.80
PB 2
PA
3
1
2
PA and B ?
PB 0.20
PA and B ?
Events A and B are dependent. Find the indicated probability.
8. PA 0.50
9. PA 0.60
10. PA ?
PBA ?
PBA 0.10
PBA 0.70
PA and B 0.40
PA and B ?
PA and B 0.35
Marbles in a Jar In Exercises 11–13, use the following information.
A jar contains 12 red marbles, 16 blue marbles, and 18 white marbles.
11. Three marbles are chosen from the jar without replacement. What is the
probability that none are white?
12. Four marbles are chosen from the jar with replacement. What is the
probability that all are white?
13. Three marbles are chosen from the jar without replacement. What is the
probability that at least one is white?
PB ?
PA and B 0.64
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice B
3
1. 2. 0.2 3. 1 4. 0.06 5. 0.75
4
6. 0.9 7. 0.25 8. 0.998 9. 0.985
10. 0.681 11. a. 0.0178 b. 0.0181
12. a. 0.00592 b. 0.00603 13. a. 0.00137
b. 0.00145 14. a. 0.000455 b. 0.000181

LESSON
12.5
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice B
For use with pages 730–737
Events A and B are independent. Find the indicated probability.
1. PA ?
2. PA ?
3. PA 0.6
PA and B 1
PB
2
2
3
PB 0.4
PA and B 0.08
Events A and B are dependent. Find the indicated probability.
4. PA 0.2
5. PA ?
6. PA 0.3
PBA 0.3
PBA 0.2
PBA ?
PA and B ?
PA and B 0.15
PA and B 0.27
File Cabinet In Exercises 7–9, use the following information.
Each drawer in a file cabinet that has 4 drawers has 100 folders. You are
searching for some information that is in one of the folders, but you do not
know which folder has the information.
7. What is the probability that the information is in the first drawer you
choose?
8. What is the probability that the information is not in the first folder you
choose?
9. What is the probability that the information is not in the first six folders
you choose?
10. Apples The probability of selecting a rotten apple from a basket is 12%.
What is the probability of selecting three good apples when selecting one
from each of three different baskets?
Drawing Cards Find the probability of drawing the given cards from a standard
52-card deck (a) with replacement and (b) without replacement.
11. a face card, then an ace 12. a 2, then a 10
PB ?
PA and B 0.6
13. an ace, then a face card, then a 7 14. a king, then another king, then a third king
Algebra 2 71
Chapter 12 Resource Book
Lesson 12.5

Answer Key
Practice C
7
3
1. 12
2. 4 3. 0.29 4. 0.01 5. 12 6.
7. a. 0.097 b. 0.0928 8. a. 0.153 b. 0.148
9. a. 0.0355 b. 0.0379 10. a. 0.0266
b. 0.0261 11. 0.509 12. 458 sets
13. 503,159 tickets
7
5
6

Lesson 12.5
LESSON
12.5
Practice C
For use with pages 730–737
72 Algebra 2
Chapter 12 Resource Book
NAME _________________________________________________________ DATE ___________
Events A and B are independent. Find the indicated probability.
PB 7
PA
8
2
3
1. 2. 3.
PA and B ?
Events A and B are dependent. Find the indicated probability.
4. PA 0.1
5. 3
6. PA ?
PBA 0.1
A ?
PA and B ?
PA 1
2
PB ?
PA and B 3
8
PA 2
PB
PA and B 7
18
PA ?
Marbles in a Jar In Exercises 7–10, use the following information.
A jar contains 12 red marbles, 16 blue marbles, and 18 white marbles. Find the
probability of choosing the given marbles from the jar (a) with replacement and
(b) without replacement.
7. red, then blue 8. white, then white
9. red, then white, then blue 10. red, then red, then white
11. Table Tennis Tim has 4 table tennis balls with small cracks. His friend
accidentally mixed them in with 16 good balls. If Tim randomly picks 3
table tennis balls, what is the probability that at least 1 is cracked?
12. Television Sets An electronics manufacturer has found that only 1 out
of 500 of its television sets is defective. You are ordering a shipment of
television sets for the electronics store where you work. How many
television sets can you order before the probability that at least one
defective set reaches 60%?
13. Lottery To win a state lottery, a player must correctly match six
different numbers from 1 to 60. If a computer randomly assigns six
numbers per ticket, how many tickets would a person have to buy to
have a 1% chance of winning?
PB 0.80
PA and B 0.232
PA and B 5
3 PBA 4
8
Copyright © McDougal Littell Inc.
All rights reserved.
Lesson 12.3

Answer Key
Practice A
1. 0.0417 2. 0.196 3. 0.0916 4. 0.00320
5. 0.202 6. 0.00992 7. 0.00000343
8. 9.09 10 9. 0.0705 10. 0.913
13
11. 0.472 12. 0.633
13. 14.
k 2
15. 16.
0.5
0.4
0.3
0.2
0.1
0
k 1
17. 18.
k 0
0.5
0.4
0.3
0.2
0.1
0
0.6
0.5
0.4
0.3
0.2
0.1
0
0 1 2 3
0 1 2 3 4 5
0 1 2 3 4
k 2
k 4
k 1
0 1 2 3 4 5 6
0 1 2 3 4 5
19. 0.00856 20. Do not reject the claim because
the probability of these findings is 0.158 which is
greater than 0.1.
0.4
0.3
0.2
0.1
0
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0.5
0.4
0.3
0.2
0.1
0
0 1 2

Lesson 12.6
LESSON
12.6
Practice A
For use with pages 739–744
86 Algebra 2
Chapter 12 Resource Book
NAME _________________________________________________________ DATE ___________
Calculate the probability of tossing a coin 15 times and getting the
given number of tails.
1. 4 2. 7 3. 10 4. 2
Calculate the probability of randomly guessing the given number
of correct answers on a 20-question multiple-choice exam that has
choices A, B, C, and D for each question.
5. 5 6. 10 7. 15 8. 20
Calculate the probability of k successes for a binomial experiment
consisting of n trials with probability p of success on each trial.
9. k ≥ 4, n 6, p 0.3
10. k ≥ 2, n 5, p 0.6
11. k ≤ 3, n 5, p 0.7
12. k ≤ 4, n 10, p 0.4
A binomial experiment consists of n trials with probability p of
success on each trial. Draw a histogram of the binomial
distribution that shows the probability of exactly k successes. Then
find the most likely number of successes.
13. n 3, p 0.6
14. n 2, p 0.8
15. n 5, p 0.3
16. n 6, p 0.7
17. n 4, p 0.15
18. n 5, p 0.25
19. Automobile Accidents An automobile-safety researcher claims that
1 in 10 automobile accidents is caused by driver fatigue. What is the
probability that at least three of five automobile accidents are caused by
driver fatigue?
20. College Enrollment A guidance counselor claims that only 60% of
high school seniors capable of doing college-level work actually go to
college. The recruitment office polls a random sample of 12 high school
seniors capable of doing college-level work. Five of the seniors said they
had plans to attend collge. Would you reject the guidance counselor’s
claim? Explain.
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice B
1. 0.00000894 2. 0.0974 3. 0.0143
4. 0.00000003 5. 0.00992 6. 0.0609
7. 0.000000002 8. 0.202 9. 0.294
10. 0.496
11. 12.
k 2
13. 14. 5 or 6
k 5
0.5
0.4
0.3
0.2
0.1
0
0.5
0.4
0.3
0.2
0.1
0
0 1 2 3 4
0 1 2 3 4 5 6
k 4
15. 0.274
0 1 2 3 4 5
16. 0.00301
17. Reject the claim because the probability of
these findings is 0.02, which is less than 0.1.
0.5
0.4
0.3
0.2
0.1
0

LESSON
12.6
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice B
For use with pages 739–744
Calculate the probability of tossing a coin 25 times and getting the
given number of heads.
1. 2 2. 10 3. 18 4. 25
Calculate the probability of randomly guessing the given number
of correct answers on a 20-question multiple choice exam that has
choices A, B, C, and D for each question.
5. 10 6. 8 7. 18 8. 5
Calculate the probability of k successes for a binomial experiment
consisting of n trials with probability p of success on each trial.
9. k ≥ 4, n 8, p 0.35
10. k ≤ 5, n 10, p 0.55
A binomial experiment consists of n trials with probability p of
success on each trial. Draw a histogram of the binomial
distribution that shows the probability of exactly k successes. Then
find the most likely number of successes.
11. n 4, p 0.45
12. n 5, p 0.75
13. n 6, p 0.83
Puppies In Exercises 14 and 15, use the following information.
A registered golden retriever gives birth to a litter of 11 puppies. Assume that
the probability of a puppy being male is 0.5.
14. Because the owner of the dog can expect to get more money for a male
puppy, what is the most likely number of males in the litter?
15. What is the probability at least 7 of the puppies will be male?
Automobile Theft In Exercises 16 and 17, use the following information.
The probability is 0.58 that a car stolen in a city in the United States will be
returned to its lawful owner. Suppose that in one day 30 cars were stolen.
16. What is the probability that at least 25 of these stolen cars will be returned
to their lawful owners?
17. The police department claims that 75% of stolen cars are returned to their
lawful owners. You decide to test this claim by polling a random sample
of 10 stolen cars. Four of the stolen cars were returned. Would you reject
the police’s claim? Explain.
Algebra 2 87
Chapter 12 Resource Book
Lesson 12.6

Answer Key
Practice C
1. 0.00545 2. 0.144 3. 0.0280
4. 0.0000255 5. 0.0355 6. 0.00000003
7. 8. 1.07 10 9. 0.937
21
1.57 1013 10. 0.115
11. 12.
0.5
0.4
0.3
0.2
0.1
0
k 5
13.
0 1 2 3 4 5 6
0.6
0.5
0.4
0.3
0.2
0.1
0
k 2
0 1 2 3 4 5 6 7 8 9 10
0 1 2 3 4 5 6 7 8
k 0
14. 6 15. no 16. Do not reject the claim
because the probability of this finding is 0.608,
which is much greater than 0.1.
0.5
0.4
0.3
0.2
0.1
0

Lesson 12.6
LESSON
12.6
Practice C
For use with pages 739–744
88 Algebra 2
Chapter 12 Resource Book
NAME _________________________________________________________ DATE ___________
Calculate the probability of tossing a coin 30 times and getting the
given number of tails.
1. 8 2. 15 3. 20 4. 26
Calculate the probability of randomly guessing the given number
of correct answers on a 30-question multiple-choice exam that has
choices A, B, C, D, and “none of these” for each question.
5. 10 6. 20 7. 25 8. 30
Calculate the probability of k successes for a binomial experiment
consisting of n trials with probability p of failure on each trial.
9. k ≥ 3, n 8, p 0.42
10. k ≤ 4, n 7, p 0.18
A binomial experiment consists of n trials with probability p of
success on each trial. Draw a histogram of the binomial
distribution that shows the probability of exactly k successes. Then
find the most likely number of successes.
11. n 6, p 0.76
12. n 8, p 0.245
13. n 10, p 0.066
Side Effects In Exercises 14 and 15, use the following information.
According to a medical study, 40% of the people will experience an adverse
side effect within one hour after taking an experimental drug to reduce cholesterol.
Fifteen people participated in the study.
14. What is the most likely number of people experiencing an adverse effect
in the study?
15. If seven of the people experience an adverse effect, would you reject the
study’s claim?
16. Class President You read an article in your school newspaper in which
a candidate claims that 30% of the class will vote for her. To test this
claim, you survey 20 randomly selected students in the class and find that
6 are planning on voting for her. Would you reject the claim? Explain.
Copyright © McDougal Littell Inc.
All rights reserved.
Lesson 12.3

Answer Key
Practice A
1. 68% 2. 97.5% 3. 47.5% 4. 4.7%
5. 0.815 6. 0.0235 7. 0.34 8. 0.5
9. 0.025 10. 0.84 11. 0.593 12. 0.951
13. 16, 1.79 14. 10.5, 2.71 15. 8.4, 2.59
16. 0.025 17. 0.8385

Lesson 12.7
LESSON
12.7
Practice A
For use with pages 746–752
98 Algebra 2
Chapter 12 Resource Book
NAME _________________________________________________________ DATE ___________
Give the percent of the area under a normal curve represented by
the shaded region.
1. 2.
x σ
3. 4.
x
x σ
x 2σ
A normal distribution has a mean of 56 and a standard deviation
of 8. Find the probability that a randomly selected x-value is in the
given interval.
5. between 40 and 64 6. between 32 and 40 7. between 56 and 64
8. at most 56 9. at least 72 10. at most 64
A normal distribution has a mean of 100 and a standard deviation
of 16. Find the given probability.
11. three randomly selected x-values are all 84 or greater
12. two randomly selected x-values are both 132 or less
Find the mean and standard deviation of a normal distribution that
approximates a binomial distribution consisting of n trials with
probability p of success on each trial.
13. n 20, p 0.8
14. n 35, p 0.3
15. n 42, p 0.2
Photography In Exercises 16 and 17, use the following information.
The developing times of photographic prints are normally distributed with a
mean of 15.4 seconds and a standard deviation of 0.48 second.
16. What is the probability that the developing time of a print will be at least
16.36 seconds?
17. What is the probability that the developing time of a print will be between
13.96 seconds and 15.88 seconds?
x 3σ
x 2σ
x 2σ
x 2σ
x 3σ
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice B
1. 0.3% 2. 49.85% 3. 0.815 4. 0.4985
5. 0.68 6. 0.975 7. 0.84 8. 0.025
9. 0.000625 10. 0.000332 11. 35, 3.24
12. 31.2, 4.805 13. 15.48, 3.75 14. 0.16
15. 0.025 16. 0.000000391

LESSON
12.7
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice B
For use with pages 746–752
Give the percent of the area under a normal curve represented by
the shaded region.
1. 2.
x 3σ
A normal distribution has a mean of 31 and a standard deviation
of 3. Find the probability that a randomly selected x-value is in the
given interval.
3. between 25 and 34 4. between 22 and 31 5. between 28 and 34
6. at least 25 7. at most 34 8. at least 37
A normal distribution has a mean of 85 and a standard deviation of
15. Find the given probability.
9. two randomly selected x-values are both 55 or less
10. four randomly selected x-values are all between 55 and 70
Find the mean and standard deviation of a normal distribution that
approximates a binomial distribution consisting of n trials with
probability p of success on each trial.
x 3σ
11. n 50, p 0.7
12. n 120, p 0.26
13. n 172, p 0.09
Bank Loans In Exercises 14 and 15, use the following information.
A loan officer at a bank may reject a loan application if the borrower does not
have enough assets or has too many debts based on their income. At a certain
bank, 20% of the loan applications are rejected. Assume there were 225
applications.
14. What is the probability that at most 39 will be rejected?
15. What is the probability at least 57 will be rejected?
16. Great Danes The heights of adult great danes are normally distributed
with a mean of 31 inches and a standard deviation of 1 inch. If you
randomly choose 4 adult great danes, what is the probability that all four
are 33 inches or taller?
x 2σ
x σ
x
x 1σ
x 2σ
x 3σ
Algebra 2 99
Chapter 12 Resource Book
Lesson 12.7

Answer Key
Practice C
1. 50% 2. 5% 3. 0.16 4. 0.84 5. 0.1585
6. 0.975 7. 0.4985 8. 0.0015
9. 0.0000156 10. 0.494 11. 38, 4.85
12. 2.1, 1.44 13. 115.5, 5.15 14. 0.0256
15. 0.16

Lesson 12.7
LESSON
12.7
Practice C
For use with pages 746–752
100 Algebra 2
Chapter 12 Resource Book
NAME _________________________________________________________ DATE ___________
Give the percent of the area under a normal curve represented by
the shaded region.
1. 2.
x 3σ
x 2σ
x σ
x
x 1σ
x 2σ
A normal distribution has a mean of 47.3 and a standard deviation
of 2.7. Find the probability that a randomly selected x-value is in
the given interval.
3. at most 44.6 4. at most 50 5. between 39.2 and 44.6
6. at most 52.7 7. between 47.3 and 55.4 8. at least 55.4
A normal distribution has a mean of 24.5 and a standard deviation
of 3.5. Find the given probability.
9. three randomly selected x-values are all 31.5 or greater
x 3σ
10. four randomly selected x-values are all between 14 and 28
Find the mean and standard deviation of a normal distribution that
approximates a binomial distribution consisting of n trials with
probability p of success on each trial.
11. n 100, p 0.38
12. n 210, p 0.01
13. n 150, p 0.77
14. Saint Bernards The weights of adult Saint Bernards are normally
distributed with a mean of 70.5 kilograms and a standard deviation of
20.5 kilograms. If you randomly choose 2 adult Saint Bernards, what
is the probability that both are at least 91 kilograms?
15. Medicine According to a medical study, 23% of all patients with high
blood pressure have adverse side effects from a certain kind of medicine.
What is the probability that out of the 120 patients with high blood
pressure treated with this medicine, more than 33 will have adverse side
effects?
x 3σ
x 2σ
x 2σ
x 3σ
Copyright © McDougal Littell Inc.
All rights reserved.
Lesson 12.3

Answer Key
Test A
1.
2.
3.
3
cos 5 ,
4
sin 5 ,
3
cot 4 ,
2
sin
2 ,
cot 1, sec 2, csc 2
4. 5. 6. 180 7. 720 8. 270
2 4
9.
in.;
2 2
10. 11. 0
12. 1 13.
2
2
14. 0 15. 0, 0
in.2
16. , 45
4
17. , 45
4
18. , 180
19. B 60, a 5.77, c 11.5
20. C 145, a 4.51, b 5.96
21. A 73.9, B 46.1, c 7.21
22. A 20, C 40, b 24.6 23. 30
24. 34.6 25. 159
26. y 27.
y
28. 25 m 29. 200 m
1
1
sec 5
3 ,
sec 13
5 ,
5
cot 12 ,
5
cos 13 ,
12
sin 13 ,
cos 2
2 ,
x
tan 4
3 ,
csc 5
4
tan 12
5 ,
csc 13
12
tan 1,
6 ft; 27 ft 2
1
1
y
Domain:
x
2
2
2 ≤ 0 ≤ 4
x

Review and Assess
CHAPTER
13
NAME _________________________________________________________ DATE
Chapter Test A
For use after Chapter 13
____________
Evaluate the six trigonometric functions of .
1.
θ
2. 3.
3
5
12
Rewrite each degree measure in radians and each radian
measure in degrees.
4. 90
5. 45
6.
4
7. 8.
Find the arc length and area of a sector with the given
radius r and central angle .
Evaluate the function without using a calculator.
11. 12.
13. sin 14. tan
3
sin 180
tan 135
4
Evaluate the expression without using a calculator. Give
your answer in both radians and degrees.
15. 16.
17. 18. cos1 sin 1
1 2
tan
2
1 sin 1
1 0
Solve ABC.
19. B
20.
C
10
30
21. C 60, a 8, b 6
22. B 120, a 10, c 18
104 Algebra 2
Chapter 13 Resource Book
A
θ
5
3
2
9. r 2 in., 45
10. r 9 ft, 120
A
15
C
10
θ
7
20
B
7
Answers
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
Copyright © McDougal Littell Inc.
All rights reserved.

CHAPTER
13
CONTINUED
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ____________
Chapter Test A
For use after Chapter 13
Find the area of ABC.
23. B
24.
25.
13
23
5
A 12 C
Graph the parametric equations. Then write an xy-equation
and state the domain.
26. x t 2 and y t
27. x 2t 2 and y t 3
for 0 ≤ t ≤ 4
for 0 ≤ t ≤ 3
1
y
40
A 32 C
1
28. Measuring Lake Width You want to
measure the width across a lake before you
swim across it. To measure the width, you
plant a stake on one side of the lake,
directly across from the dock. You then
walk 25 meters to the right of the dock and
measure a 45 angle between the stake and
the dock. What is the width w of the lake?
x
12
B
25 m
29. Ski Lift From the base of a ski lift, the angle of elevation of the
summit is 30. If the ride on the ski lift is 400 meters to the summit,
what is the vertical distance between the base of the lift and the
summit?
B
C
1
10
60
8
y
1
w
A
x
45
23.
24.
25.
26. Use grid at left.
27. Use grid at left.
28.
29.
Algebra 2 105
Chapter 13 Resource Book
Review and Assess

Answer Key
Test B
1.
2.
3.
5
sin 13 ,
12
cot 5 ,
529
sin
29 ,
2
cot
5 ,
1
sin
2 ,
cot 3,
4.
4
5. 6. 360 7. 180 8. 150
9. 10.
12 cm; 72 cm 2
11. 0 12. 1 13. 14. 0 15.
16. 17. 18.
19. B 20, a 13.2, b 4.79
20. C 80, a 13.1, b 17.6
21. A 27.5, B 112.5, c 13.9
22. A 15.5, B 14.5, c 28
23. 72.4 24. 56.9 25. 20.8
26. y 27. y
, 45
4
0, 0 , 180 , 60
3 2
2
50,000
1
12
cos 13 ,
sec 13
12 ,
sec 29
2 ,
3
cos
2 ,
1
sec 23
3 ,
x
tan 5
12 ,
csc 13
5
229
cos
29 ,
csc 29
5
tan 3
3 ,
csc 2
12 ft; 96 ft 2
y
Domain:
x 1
2 2
1 ≤ x ≤ 5
28. 52,360 mi 29. 102 km
3
2
2
1
tan 5
2 ,
x

Review and Assess
CHAPTER
13
NAME _________________________________________________________ DATE
Chapter Test B
For use after Chapter 13
____________
Evaluate the six trigonometric functions of .
1. 2. 3.
13
Rewrite each degree measure in radians and each radian
measure in degrees.
4. 45
5. 180
6.
7. 8.
Find the arc length and area of a sector with the given
radius r and central angle .
Evaluate the function without using a calculator.
11. ° 12. °
13. 14. cot 3
sin 2
cos 90
tan 225
Evaluate the expression without using a calculator. Give
your answer in both radians and degrees.
15. 16.
17. cos 18.
1 tan
1
1 sin 0
1 2
2
Solve ABC.
19. A
20.
C
70
θ
12
4
14
21. C 40, a 10, b 20
22. C 150, a 15, b 14
106 Algebra 2
Chapter 13 Resource Book
B
θ
2
5
6
9. r 12 cm, 180
10. r 16 ft, 135
5
C
A
40
6
tan 1 3
60
20
2
B
12
θ
Answers
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
Copyright © McDougal Littell Inc.
All rights reserved.

CHAPTER
13
CONTINUED
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ____________
Chapter Test B
For use after Chapter 13
Find the area of ABC.
23. B
24.
25.
105
A 15 C
A 8 B
60
6
C
Graph the parametric equations. Then write an xy-equation
and state the domain.
26. x t and y t 1 27. x 2t 1 and y t
for 0 ≤ t ≤ 3
for 1 ≤ t ≤ 2
1
y
1
10
28. Radar A radar system has been set up to track approaching weather
storms. The radar is set to reach 200 miles and cover an arc of 150.
Find the area of the sector that the radar covers.
29. Ships Two ships leave Boston Harbor
at the same time. What is the distance
between ships A and C after they have
traveled 80 kilometers and
70 kilometers respectively?
x
A
A
1
14
y
9
1
80 km
B
13
C
d
85
Boston
x
70 km
C
23.
24.
25.
26. Use grid at left.
27. Use grid at left.
28.
29.
Algebra 2 107
Chapter 13 Resource Book
Review and Assess

Answer Key
Test C
1.
2.
3.
5
sin 13 ,
12
cot 5 ,
26
sin
26 ,
cot 5,
3
sin
4 ,
7
cot
3 ,
4.
10
5. 6. 150 7. 270 8. 110
9. 10.
11. 0 12. 1 13. 1 14. 2
27 cm; 243 cm 2
15. , 45
4
16. , 30
6
17. , 150
6
18. 0, 0 19. B 70, b 1.92, c 2.05
20. C 74, b 8.89, c 10.2
21. B 19.9, C 25.1, a 25
22. A 81, B 36, C 63 23. 30.8
24. 53.4 25. 45
26. y 27.
y
2
4
2
12
cos 13 ,
sec 13
12 ,
sec 26
5 ,
7
cos
4 ,
47
sec
7 ,
x
tan 5
12 ,
csc 13
5
526
cos
26 ,
tan 1
5 ,
csc 26
tan 37
7 ,
csc 4
3
0.2 ft; 0.08 ft 2
5
Domain:
28. 36.8 m 29.
16t2 y 16t
50.3t 3
2 y
6 ≤ x ≤ 6
x 95 cos 32t 80.6t
95 sin 32t 3
x
1
3
1
1
x

Review and Assess
CHAPTER
13
NAME _________________________________________________________ DATE
Chapter Test C
For use after Chapter 13
____________
Evaluate the six trigonometric functions of .
1.
5
13
θ
2.
θ
3.
10
Rewrite each degree measure in radians and each radian
measure in degrees.
4. 18
5. 720
6.
3
7. 8.
2
Find the arc length and area of a sector with the given
radius r and central angle .
9. r 18 cm, 270
10. r 0.8 ft, 45
Evaluate the function without using a calculator.
11. 12.
13. 14. sec 5
tan
4
7
sin 720
cos180
4
Evaluate the expression without using a calculator. Give
your answer in both radians and degrees.
15. 16.
17. cos 18.
13 tan
2
11 Solve ABC.
19. B
20.
0.7
C
20
21. A 135, b 12, c 15
22. a 10, b 6, c 9
108 Algebra 2
Chapter 13 Resource Book
A
2
11
18
sin11 2
sin 1 0
C
A
49
8
θ
5
6
57
12
B
9
Answers
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
Copyright © McDougal Littell Inc.
All rights reserved.

CHAPTER
13
CONTINUED
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ____________
Chapter Test C
For use after Chapter 13
Find the area of ABC.
23. A
24.
25.
10
12
C
Graph the parametric equations. Then write an xy-equation
and state the domain.
26. x 3t and y t 1 27. x 2t 4 and y 2t
for 2 ≤ x ≤ 2
for 0 ≤ x ≤ 3
2
140
C 8 B
60 58
A B
y
2
28. Ravine Width Use the diagram to
find the distance across the ravine.
x
29. Baseball A baseball is hit at a speed of 95 feet per second during a
high school baseball game. The baseball was hit from a height of
3 feet and at an angle of 32. Write a set of parametric equations for
the path of the baseball.
C
C
10 11
A 13 B
1
a ?
y
1
110
B
x
31
A
45 m
23.
24.
25.
26. Use grid at left.
27. Use grid at left.
28.
29.
Algebra 2 109
Chapter 13 Resource Book
Review and Assess

Answer Key
Cumulative Review
1. 2. 3.
4. 5.
6. 7. 8.
9.
11. 12.
10.
13. none
14. infinite 15. 16. 17. none
18. infinite 19. 20. 21.
22. 23. 24.
25. 26.
27. 28.
29. 30.
31. quartic;
32. not a polynomial function 33. not a
polynomial function 34. constant; 5
35. linear; 3
36. f x x quadratic; 1
37. x 2x 3x 1
38. x 3x 5x 4
39. x 1x 5x 6
40. x 3x 5x 1
41. 2x 32x 3x 1
2 f x 4x 4
f x 5; 0;
f x 3x 2; 1;
0.6x 3; 2;
4 1
3x2 y 4x
7; 4;
2 y 12x
3
4x2 3
y
4x 15
1
3x2 x 10
y 3x 3
2 y x
15x 18
2 y x 3x 10
2 1,
8x 15
1
12
y 23
2, 7 4, 2
2, 1 2, 1 0, 4
1, 5 3, 3
3
23
2 x;
36 y 5
5
6x; y 48
1
8x; 24
1
y 4x; 4
y 3
2x; 15
2
y 5x; 1
x >
12 < x < 6 x ≥ 6 or x ≤ 1
3 ≤ x ≤ 1
3
x ≥ 3 x ≥ 4
4
42. 2x 1x 5x 6 43.
44. 45.
46. 47. all reals; all reals
48. 49.
50. 51.
52. 53. 54. y x
y 2
1
y 8x 12
1; x 0
x
12x 4
; x 0
x
x ≥ 14; y ≥ 0
x ≥ 3; y ≥ 0 x ≥ 5; y ≥ 4
x ≥ 4; y ≤ 5 x ≥ 3; y ≥ 0
55. 56. 57. y e
58. 59.
x y e 5
x y 2
ex
5
1
y
1
x
3 x
4 1
; x
3x 1 3
domain: all real numbers domain: all real
except 0; range all real numbers except 4;
numbers except 0 range: all real numbers
1
y
1 x
except 1
60. 61.
4
y
domain: all real numbers domain: all real
except 8; range: all real numbers except 2;
numbers except 2 range: all real numbers
except 1
62. 63.
1
2
domain: all reals numbers domain: all real
except 2; range: all real
numbers except
numbers except 0;
range: all real numbers
except 2
64. 65.
66.
67.
x2
±4, 0; 0, ±3; ±5, 0 ±6, 0; 0, ±5;
±11, 0 0, ±25; ±23, 0; 0, ±22
y2
1; 0, ±10; ±2, 0; 0, ±46
4 100 3
4
x 2
y
2
68.
69.
x
70.
3
2 71.
2
3 72.
9
2 73. none 74.
3
10
75. none 76. a.
1
16 b.
13
204 77. a.
1
169 b.
4
663
78. a.
3
b.
2
y2
1; 0, ±4; ±3, 0; 0, ±7
9 16
y2
1; 0, ±5; ±10, 0; 0, ±15
10 25
169
1
4
221
8
x
x
13
850
79. a. b. 80. a. b.
81. a. b. 82. 0.00977
83. 0.205 84. 0.0439 85. 0.117 86. 0.00097
87. 0.117 88. 89. 90.
91. 92. 93. 3
1
2
3
2
3
3
2
2197 16,575
64
3
169
4
221
1
2 2
1
y
1
1
1
y
1
x
x

CHAPTER
13 Cumulative Review
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ____________
For use after Chapters 1–13
Solve the inequality. (1.6, 1.7)
1. 3x 5 ≥ 14
2. 2x 1 ≤ 7
3.
4. x 3 < 9
5. 2x 5 ≥ 7
6.
The variables x and y vary directly. Write an equation that relates
the variables. Then find x when y 6. (2.4)
7. 8. 9.
10. 11. x 12. x 0.2, y 2.3
3
2, y 5
x 5, y 2
x 8, y 12
x 4, y 1
x 16, y 2
4
Graph the linear system and tell how many solutions it has. If there
is exactly one solution, estimate the solution and check it algebraically.
(3.1)
13. 4x 2y 8
14. x y 10
15. y 3x 1
6x 3y 9
1
16. 17. 18.
x 0.5x 2y 8
10y 3x 12
1
2x 2y 6
x 4y 0
1.2x 4y 4.8
2y 3
Use an inverse matrix to solve the linear system. (4.5)
19. 4x 3y 11
20. 3x 5y 1
21. 5x 2y 8
5x 2y 12
22. 3x y 8
23. 2x 6y 12
24. 7x 3y 6
4x 2x 6
2x 20 2y
4x 5y 13
7x 2y 15
Write the quadratic function in standard form. (5.1)
25. 26. 27.
28. 29. y 30. y 4xx 3
3
y 4x 5x 4
1
y x 3x 5
y x 5x 2
y 3x 1x 6
3x 2x 5
Decide whether the function is a polynomial function. If it is, write the
function in standard form and state the degree, type, and leading
coefficient. (6.2)
31. 32. 33.
34. 35. 36. f x 0.6x x2 f x 5x
f x 5
f x 3x 2
3
2 4x2 f x x x
3 3x f x 1
3x2 4x4 7
Factor the polynomial given that (6.5)
37. 38.
39. 40.
41. f x 4x 42.
3 4x2 f x x
9x 9; k 1
3 2x2 f x x
29x 30; k 1
3 6x2 f k 0.
11x 6; k 2
Let f x 4x and g x 3x 1. Perform the indicated operation
and state the domain. (7.3)
1
42x 2 < 14
43x 1 2 ≤ 10
4x 2y 6
9x 3y 12
4x 6y 2
f x x 3 4x 2 17x 60; k 3
f x x 3 x 2 17x 15; k 5
f x 2x 3 3x 2 59x 30; k 6
43. f gx
44. g f x
45. f x g x
Algebra 2 115
Chapter 13 Resource Book
Review and Assess

Review and Assess
CHAPTER
13
CONTINUED
NAME _________________________________________________________ DATE ____________
Cumulative Review
For use after Chapters 1–13
Find the domain and range of the function without graphing. (7.5)
46. 47. y 2 48. y x 3
49. y x 5 4
50. y x 4 5
51. y 3x 3
3 y x 14
x 2
Find the inverse of the function. (8.4)
52. 53. 54. y log 8 64
55. y ln 5x
56. y ln x 2
57. y ln x 5
x
y log 8 x
y log 13 x
Graph the function. State the domain and range. (9.2)
5
4
58. y 59. y 1
60.
x
x 4
x 3
3x 5
61. y 62. y 63. y
x 2
4x 8
Write the equation in standard form (if not already). Then identify
the vertices, co-vertices, and foci for the ellipse. (10.4)
64. 65. 66.
67. 68. 69. 25x2 10y2 16x 250
2 9y2 25x 144
2 y2 x
100
2
x y2
1
12 20 2
x y2
1
36 25 2
y2
1
16 9
Find the sum of the infinite geometric series if it has one. (11.4)
n013 n
70. 71. 72.
73. 74. 75.
n1
1
22 3 n1
2 n0
5
3 n
Find the probability of drawing the given cards from a standard 52-card
deck (a) with replacement and (b) without replacement. (12.5)
76. a diamond, then a spade 77. a king, then a queen
78. a 3, then a face card (K, Q, or J) 79. an ace, then a 3, then a 5
80. a diamond, then a spade, then another diamond 81. a face card (K, Q, or J), then a 10
Find the probability of getting the given number of heads in 10
tosses of a coin. (12.6)
82. 1 83. 4 84. 8 85. 3 86. 10 87. 7
Evaluate the function without using a calculator. (13.3)
88. sin 89. 90.
91. 92. 93. tan 5 sin
3
11
cos 6
5
750
cos 225
tan 210
6
116 Algebra 2
Chapter 13 Resource Book
n012 n
y 1
2
x 8
4x 3
2x
3 n0
1
3 n
n0
1
2 3n
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice A
1.
tan 6 7 85
; cot ; sec
7 6 7 ;
sin 685 785
; cos
85 85 ;
2.
tan 3 2 13
; cot ; sec
2 3 2 ;
sin 313 213
; cos
13 13 ;
3. sin 3 4 3
; cos ; tan
5 5 4 ;
cot 4 5 5
; sec ; csc
3 4 3
4.
sin 26 526
; cos
26 26 ;
5. sin 1 35 35
; cos ; tan
6 6 35 ;
tan csc 26
1 26
; cot 5; sec
5 5 ;
cot 35; sec 635
; csc 6
35
6.
cot 3
sin
34 34
; sec ; csc
5 3 5
534 334 5
; cos ; tan
34 34 3 ;
7. x 8; y 43 8. x 43; y 4
9. x 22; y 22 10. 0.2588
11. 0.6820 12. 2.1445 13. 3.2361
14. 1.1034 15. 0.5317 16. 0.9848
csc 85
6
csc 13
3
17. 0.9848 18. A 78; b 0.9; c 4.1
19. B 16; a 19.2; b 5.5
20. B 40; a 9.5; c 12.4
21. A 52; a 5.5; b 4.3
22. B 18; a 55.4; c 58.2
23. A 68; b 2.0; c 5.4 24. about 346 ft

LESSON
13.1
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice A
For use with pages 769–775
Evaluate the six trigonometric functions of the angle .
1. 2. 3.
6
4.
2
θ
5. 6.
10
θ
Find the missing side lengths x and y.
7. 8. 9.
30
x
y
7
θ
4
60
y
Use a calculator to evaluate the trigonometric function. Round the
result to four decimal places.
10. sin 15
11. cos 47
12. tan 65
13. csc 18
14. sec 25
15. cot 62
16. sin 80
17. cos 10
Solve ABC using the diagram and the given measurements.
18. B 12, a 4 19. A 74, c 20
20. A 50, b 8 21. B 38, c 7
22. A 72, b 18 23. B 22, a 5
24. Redwood Trees You are standing 200 feet from
the base of a redwood tree. You estimate the angle of
elevation to the top of the tree is 60. What is the
approximate height of the tree?
θ
18
3
8
8
x
12
60
200 ft
A
b
4
10
θ
45
C a B
Not drawn to scale.
Algebra 2 15
Chapter 13 Resource Book
4
6
y
c
5
θ
x
Lesson 13.1

Answer Key
Practice B
1. sin 8 15 8
; cos ; tan
17 17 15 ;
cot 15
8
2.
cot 21
sin
521 5
; sec ; csc
2 21 2
2 21 221
; cos ; tan
5 5 21 ;
3.
17 17
; sec ; csc
15 8
sin 22
3
1
; cos ; tan 22;
3
cot 2
32
; sec 3; csc
4 4
4. x 72; y 7 5. x 5; y 53
6. x 23; y 3 7. 0.8910
8. 0.0875 9. 0.7431 10. 0.1584
11. 2.5593
14. 0.5299
12. 2.4586 13. 4.3315
15. B 44; a 8.3; c 11.5
16. A 66; a 11.9; b 5.3
17. A 72; a 9.5; b 3.1
18. B 35; b 14.0; c 24.4
19. A 20; b 16.5; c 17.5
20. B 83; a 2.2; c 18.1
21. about 14.4 ft 22. about 21,477 ft or 4.1 mi

Lesson 13.1
LESSON
13.1
Practice B
For use with pages 769–775
16 Algebra 2
Chapter 13 Resource Book
NAME _________________________________________________________ DATE ___________
Evaluate the six trigonometric functions of the angle .
1. 2. 3.
θ
8
5
θ
2
15
Find the missing side lengths x and y.
4. 5. 6.
10
x
x
7
30
y
45
y
Use a calculator to evaluate the trigonometric function. Round the
result to four decimal places.
7. cos 27
8. tan 5
9. sin 48
10. cot 81
11. csc 23
12. sec 66
13. cot 13
14. sin 32
Solve ABC using the diagram and the given measurements.
15. A 46, b 8 16. B 24, c 13
17. B 18, c 10 18. A 55, a 20
19. B 70, a 6 20. A 7, b 18
C a B
21. Flagpole You are standing 25 feet from the base of a flagpole. The
angle of elevation to the top of the flagpole is 30. What is the height of
the flagpole to the nearest tenth?
22. Mount Fuji Mt. Fuji in Japan is approximately 12,400 feet high.
Standing several miles away, you estimate the angle of elevation to the top
of the mountain is 30. Approximately how far way are you from the base
of the mountain?
A
b
c
x
60
y
3
3
Copyright © McDougal Littell Inc.
All rights reserved.
θ
1

Answer Key
Practice C
1.
cot 69 1369
; sec ; csc
10 69
13
sin
10
10 69 1069
; cos ; tan ;
13 13 69
2. sin 3 4 3
; cos ; tan
5 5 4 ;
cot 4 5 5
; sec ; csc
3 4 3
3. sin 1 3 3
; cos ; tan
2 2 3 ;
cot 3; sec 23
; csc 2
3
4. x 10; y 53 5. x 42; y 42
6. x 163; y 32 7. 0.1763
8. 1.5557 9. 0.7771 10. 0.0175
11. 1.1434 12. 0.9986 13. 1.2799
14. 2.5593 15. B 76; b 24.1; c 24.8
16. B 33; a 18.5; c 22.0
17. A 58; a 17.3; b 10.8
18. B 26; a 11.5; b 5.6
19. A 17; b 55.6; c 58.1
20. A 80; a 79.4; c 80.6
21. about 66.78 ft or 66 ft 9 in.

LESSON
13.1
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice C
For use with pages 769–775
Evaluate the six trigonometric functions of the angle .
1. 2. 3.
10
13
θ
Find the missing side lengths x and y.
4. 5. 6.
5
x
30
x
8
y
Use a calculator to evaluate the trigonometric function. Round the
result to four decimal places.
7. tan 10
8. csc 40
9. sin 51
10. cos 89
11. sec 29
12. cos 3
13. cot 38
14. sec 67
Solve ABC using the diagram and the given measurements.
15. A 14, a 6 16. A 57, b 12
17. B 32, c 20.4 18. A 64, c 12.8
19. B 73, a 17 20. B 10, b 14
21. Baseball Diamond A baseball diamond is laid out
so that the bases are 90 feet apart and at right angles as
shown at the right. The distance from home plate to the
pitcher’s mound is 60 feet 6 inches. Find the distance
from the pitcher’s mound to second base. (Hint: The
pitcher’s mound is not exactly halfway between home
plate and second base.)
θ
12
y
45
9
c
A b C
Pitcher
B
a
9
θ
y
60
16
90 ft
6 3
Home Plate
Algebra 2 17
Chapter 13 Resource Book
x
Lesson 13.1

Answer Key
Practice A
1. B 2. A 3. C
4. y 5.
6. y 7.
8–11. Sample angles are given.
8. 585; 135 9. 420; 300 10.
6
11. ; 4 12. 13. 14.
5 5 4 9
43
100
8 π
9
15. 16. 105 17. 150 18. 120
36
2
19. 20. 21.
25
m;
12 24
22. 23.
1
2 24. 1
25. 0.9511 26. 0.9239 27. about 4.19 ft
m2
4
in.;
3 3 in.2
30
14 cm; 84 cm 2
x
x
3
2
y
y
5
45 x
12 π
5
3
;
2 2
13
9
x

LESSON
13.2
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice A
For use with pages 776–783
Match the angle measure with the angle.
1. 320
2.
5
3.
A. y
B. y
C.
Draw an angle with the given measure in standard position.
4. 100
5. 45
6. 7.
9
Find one positive angle and one negative angle coterminal with the
given angle.
8. 225
9. 60
10. 11.
2
Rewrite each degree measure in radians and each radian measure
in degrees.
12. 13. 14. 15.
16. 17. 18.
3
19.
6
5
135
40
260
215
12
6
7
x
Find the arc length and area of a sector with the given radius r and
central angle .
20. 21. r 5 m, 22. r 12 cm, 210
r 4 in.,
12
6
Evaluate the trigonometric function using a calculator if necessary.
If possible, give an exact answer.
23. 24. 25. sin 26.
2
tan
5
cos
4
3
15
27. Pendulum The pendulum of a grandfather clock is 4 feet long and
swings back and forth creating a 60 angle. Find the length of the arc of
the pendulum, after one swing.
6
x
8
2
7
4
12
5
16
cos
8
Algebra 2 29
Chapter 13 Resource Book
5
y
x
Lesson 13.2

Answer Key
Practice B
1. y 2.
3. y 4.
5–8. Sample angles are given.
5. 700; 20 6. 180; 180
2
215
7 π
12
7. 8. 9.
10. 11. 12. 13.
14. 15. 16.
17. 18.
3
in.;
2 2
19. 20.
3
2
21. 0.4142
in.2
12 9
585
480 120 15
17
; 4
3 3
; 8
5 5 6
9
11
18 ft; 108 ft 2
20 m; 200 m 2
x
x
2
3
5
7
22. 1 23. 0.9010 24.
23
3
25. 2
26. 0.1045 27. 0.4142 28. about 2.75 in.
29. 1080; 6
y
y
135
5 π
6
x
x

Lesson 13.2
LESSON
13.2
Practice B
For use with pages 776–783
30 Algebra 2
Chapter 13 Resource Book
NAME _________________________________________________________ DATE ___________
Draw an angle with the given measure in standard position.
1. 215
2. 135
3. 4.
12
Find one positive angle and one negative angle coterminal with the
given angle.
5. 340
6. 540
7. 8.
3
Rewrite each degree measure in radians and each radian measure
in degrees.
9. 10. 11. 12.
13. 14. 15. 16.
12
2
210
340
165
100
4
3
3
13
8
Find the arc length and area of a sector with the given radius r and
central angle .
17. 18. r 2 in., 19. r 20 m, 180
3
r 12 ft,
4
3
2
Evaluate the trigonometric function using a calculator if necessary.
If possible, give an exact answer.
20. 21. 22. 23.
24. 25. 26. cos 27.
28. Fire Truck Ladder For the ladder on a fire truck to
operate properly, the base of the ladder must be almost
7 in.
level. The diagram at the right shows part of a leveling Allowable
device that is used to determine whether the level of the range
ladder’s base is within the allowable range. Find the
π
length of the arc that describes the allowable range.
8
29. Snowboarding During a competition, a snowboarder performs a trick
involving three revolutions. Find the measure of the angle generated as the
snowboarder performs the trick. Give the answer in both degrees and
radians.
7
csc
15
sec
4
sin
6
tan
2
sin
8
3
7
20
5
6
12
5
cos
7
cot 3
8
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice C
1.
2.
3. y 4.
5–8. Sample angles are given.
10
7. ; 2 8. ; 9 9.
3 3 4 4
10. 11. 12. 13.
14. 15. 16. about
17. 18.
19.
112
m;
3 3
20.
3
3
21. 3
22. 2.6131 23. 0.3090 24. 0.9945
25. 2.6131 26. 3 27. 2 28. 540; 3
29. about 4190 mi
m2
169
cm;
3 3
735
in.;
4 16 cm2
90 180
150
135 40
172
5
12
26
28
y
7 π
15
290
5. 465; 255 6. 285; 435
x
x
7
37
35
y
y
7
4
15 π
4
x
500
x
in.2

LESSON
13.2
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice C
For use with pages 776–783
Draw an angle with the given measure in standard position.
7
1. 2. 3. 290
4. 500
15
15
4
Find one positive angle and one negative angle coterminal with the
given angle.
5. 105
6. 75
7. 8.
3
Rewrite each degree measure in radians and each radian measure
in degrees.
9. 10. 11. 12.
13. 14. 15.
9
16. 3
3
315
75
2
37
6
4
5
Find the arc length and area of a sector with the given radius r and
central angle .
17. r 13 cm, 18. r 10.5 in., 150 19. r 8 m, 210
2
3
Evaluate the trigonometric function using a calculator if necessary.
If possible, give an exact answer.
20. 21. 22. 23.
24. 25. 26. 27. csc
28. Bicycles A bicycle’s gear ratio is the
number of times the freewheel turns for every
one turn of the chainwheel. The table shows
the number of teeth in the freewheel and
chainwheel for the first 5 gears on an 18-speed
bicycle. In first gear, if the chainwheel
completes 2 rotations, through what angle
does the freewheel turn? Give your answer in
both degrees and radians.
29. Earth Assuming that Earth is a sphere of diameter 8000 miles,
what is the distance between city A and city B in the figure shown
if the central angle is 60?
cot
4
sec
6
3
sin
8
7
cos
15
2
csc
5
tan
8
cot
3
3
Gear Number of teeth Number of teeth
Number in freewheel in chainwheel
1
2
3
4
32
26
22
32
24
24
24
40
5 19 24
4
2
60
B
4
Algebra 2 31
Chapter 13 Resource Book
A
Lesson 13.2

Answer Key
Practice A
1. sin 3
3
; cos 4;
tan
5 5 4 ;
2.
cot 2; sec 5
sin
; csc 5
2 5 25
; cos ; tan 1
5 5 2 ;
cot 4
; sec 5;
csc 5
3 4 3
3.
tan 5
9 ;
csc 106
5
4.
cot 5
sin
89 89
; sec ; csc
8 5 8
889 589 8
; cos ; tan
89 89 5 ;
5. sin
cot 1; sec 2; csc 2
2
; cos 2;
tan 1;
2 2
6.
sin 5106
; cos 9106
106 106 ;
sin 758
58
cot 3 58 58
; sec ; csc
7 3 7
7.
cot 5; sec
sin 0; cos 1; tan 0;
8.
26
sin
; csc 26
5 26
1
; cos 526;
tan
26 26 5 ;
cot undefined; sec 1;
sec undefined
cot 9
5
; sec 106;
9
358 7
; cos ; tan
58 3 ;
9. sin 1; cos 0; tan undefined;
cot 0; sec undefined; csc 1
10. sin 0; cos 1; tan 0;
cot undefined; sec 1; csc undefined
11.
θ
30
13. y 14.
θ
7 π
4
y
x
π
θ
4
12.
15. 16. 17. 18. 1
19. 20. 2 21. 2 22. 3
23. 0.9659 24. 0.1736 25. 2.4751
26. undefined 27. 0.8391 28. 1.0101
29. 0.5774 30.
1
31. no
3
2
3
2
2
3
2
2
x
θ 150
π
θ
4
θ 315
y
y
θ
x
θ 45
13 π
4
x

Lesson 13.3
LESSON
13.3
Practice A
For use with pages 784–790
42 Algebra 2
Chapter 13 Resource Book
NAME _________________________________________________________ DATE ___________
Use the given point on the terminal side of an angle in standard
position. Evaluate the six trigonometric functions of .
1. y
2. y
3.
Evaluate the six trigonometric functions of the quadrantal angle .
180
3
(8, 6)
3
θ
x
4. 5, 8
5. 4, 4
6. 3, 7
7. 10, 2
90
8. 9. 10.
Sketch the angle. Then find its reference angle.
11. 150
12. 315
13. 14.
4
Evaluate the function without using a calculator.
15. 16. 17. 18.
19. 20. 21. 22. tan 17
sec
3
5
csc
4
11
sin 4
2
sin 300
csc 225
cos 750
tan 405
3
Use a calculator to evaluate the function. Round the result to four
decimal places.
23. 24. 25. 26.
27. 28. 29. 30. cos
31. Baseball You are at bat and hit a baseball so that it has an initial
velocity of 80 feet per second and an angle of elevation of 40. Assuming
the ball is not caught and the fence is 305 feet away, did you hit a
homerun?
7
cot
3
11
tan sec 3
3
2
sin 435
cos 100
tan 112
sec 450
9
θ
3
6
(10, 5)
x
7
(9, 5)
360
3
13
4
y
Copyright © McDougal Littell Inc.
All rights reserved.
3
θ
x
Lesson 13.2

Answer Key
Practice B
1.
tan 9
4 ;
csc 97
9
2.
tan 5
4 ;
csc 41
5
3. sin 3 4 3
; cos ; tan
5 5 4 ;
cot 4 5 5
; sec ; csc
3 4 3
4.
8
tan
5 ;
csc 89
8
5.
cot 0; sec undefined; csc 1
6.
cot 0; sec undefined; csc 1
7.
sin 997 497
; cos
97 97 ;
sin 541
; cos 441
41 41 ;
sin 889
; cos 589
89 89 ;
sin 1; cos 0; tan undefined;
sin 1; cos 0; tan undefined;
sin 0; cos 1; tan 0;
cot undefined;
sec 1; csc undefined
y
8. 9. y
θ 45
cot 4 97
; sec
9 4 ;
cot 4
; sec 41
5 4 ;
cot 5
; sec 89
8 5 ;
x
θ 225
θ θ
65
x
10. y
11.
θ 40
12. y
13.
π
θ
3
14. y
15.
π
θ
3
θ 220
x
2 π
θ
3
x
8 π
θ
3
x
θ 25
θ
θ
16. 17. 18. 19.
20. 21. 22. 23.
24. 0.3090 25. 1.1434 26. 0.5
27. 1.0515 28. The terminal side of a 10
angle would be in the first quadrant where the sine
function is positive. Your friend’s calculator was in
radian mode. 29. 307.75 ft; 312.5 ft; 307.75 ft
2
2
3
23
3
3
2
3
2
3
1
2
7 π
3
12 π
5
y
y
y
π
θ
3
θ
x
2 π
5
x
x
θ 155

Lesson 13.2
LESSON
13.3
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice B
For use with pages 784–790
Use the given point on the terminal side of an angle
position. Evaluate the six trigonometric functions of .
in standard
1. 4, 9
2. 4, 5
3. 8, 6
4. 5, 8
Evaluate the six trigonometric functions of the quadrantal angle .
270
5. 6. 7.
Sketch the angle. Then find its reference angle.
8. 9. 10. 11.
12. 13. 14. 15.
5
8
3
3
2
225
65
220
155
3
7
90
Evaluate the function without using a calculator.
16. 17. 18. 19.
20. 21. 22. 23. sin 3 tan
4
7
csc
3
2
cot
3
7
tan 135
sin 60
cos 210
sec 315
6
Use a calculator to evaluate the function. Round the result to four
decimal places.
180
24. 25. 26. cos 27.
28. Critical Thinking Your friend used a calculator to evaluate sin 10 and
obtained 0.544. How can you tell this is incorrect? What did your friend
do wrong?
29. Baseball You are at bat and hit the baseball so that it has an initial
velocity of 100 feet per second. Approximately how far will the ball travel
horizontally if the angle of elevation is 40? 45? 50?
10
sin 18
sec 29
3
12
csc 18
5
Algebra 2 43
Chapter 13 Resource Book
Lesson 13.3

Answer Key
Practice C
1.
tan 2
3 ;
csc 13
2
2. sin 1
; cos 3;
tan 3
2 2 3 ;
3. sin 2
cot 3; sec
; cos 2;
tan 1;
2 2 23
; csc 2
3
4. sin 15 8 15
; cos ; tan
17 17 8 ;
cot 1; sec 2; csc 2
cot 8 17 17
; sec ; csc
15 8 15
5.
sin 213 313
; cos
13 13 ;
sin 1; cos 0; tan undefined;
cot 0; sec undefined; csc 1
6. sin 0; cos 1; tan 0;
cot undefined; sec 1; csc undefined
7. sin 0; cos 1; tan 0;
cot undefined; sec 1; csc undefined
8. y
9.
θ 30
10. y 11. y
θ 20
cot 3 13
; sec
2 3 ;
x
θ 510
θ 200
x
θ 345
θ 60
y
x
θ 15
x
θ 240
12. y
13.
π
θ
4
14. y
15.
12 π
θ
5
θ
21 π
4
x
x
2 π
θ 5
π
θ
3
π
θ
3
16. 17. 18. 19. 3
20.
2
2
21. 2 22. 3 23. 2
24. 0.0402 25. 0.5774 26. undefined
27. 0.9511 28. about 152 ft/sec; about 722 ft
29. about 6.70 ft
23
3
2
2
2
y
y
θ
θ
20 π
3
2 π
3
x
x

Lesson 13.3
LESSON
13.3
Practice C
For use with pages 784–790
44 Algebra 2
Chapter 13 Resource Book
NAME _________________________________________________________ DATE ___________
Use the given point on the terminal side of an angle
position. Evaluate the six trigonometric functions of .
in standard
1. 3, 2
2. 3, 1
3. 2, 2
4. 8, 15
Evaluate the six trigonometric functions of the quadrantal angle .
90
5. 6. 7.
Sketch the angle. Then find its reference angle.
8. 9. 10. 11.
12. 13. 14. 15.
3
12
510
345
200
240
4
3
5
21
20
180
Evaluate the function without using a calculator.
16. 17. 18. 19.
20. 21. 22. cot 23.
11
csc
6
5
cos
6
15
sec 225
cos 225
csc 120
tan 240
4
Use a calculator to evaluate the function. Round the result to four
decimal places.
360
24. 25. 26. sec 27.
28. Driving Golf Balls You and a friend are driving golf balls at a driving
range. If the angle of elevation is 30 and the ball travels 625 feet
horizontally, what is the initial velocity of the ball? Suppose you use the
same initial velocity and hit the ball at an angle of 45. How far would the
ball travel?
29. Fishing You and a friend are fishing. Each of you casts with an initial
velocity of 40 feet per second. Your cast was projected at an angle of 45
and your friend’s at an angle of 60. About how much further will your
fishing tackle go than your friend’s?
9
tan 2.3
cot 420
2
2
sec 4
3
sin 18
5
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice A
1. ; 180
2. ; 30 3. ; 30 4.
6 6
5. 6. 7. 8.
9. 33.7 10. 36.9 11. 39.8 12. 36.9
13. 18.4 14. 71.6 15. 0.644; 36.9
16. 2.42; 139 17. 1.35; 77.5 18. 1.82; 104
19. 1.47; 84.3 20. 1.19; 68.2
21. 1.12; 64.2 22. 0.412; 23.6 23. 166
24. 214 25. 68.2 26. 320
27. 35.8; 0.625
0; 0 ; 45
4
; 60
3
; 45
4
; 30
6

LESSON
13.4
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice A
For use with pages 792–798
Evaluate the expression without using a calculator. Give your answer
in both radians and degrees.
1. 2. sin 3. tan 4.
3
11
cos
2
11 5. 6. 7. 8. tan1 1 1
tan sin cos 1
2
2
1 0
Find the measure of the angle . Round to three significant digits.
9. 10. 11.
θ
3
5
3
2
12. 13. 14.
10
2
θ
6
Use a calculator to evaluate the expression in both radians and
degrees. Round to three significant digits.
15. 16. 17. 18.
19. 20. 21. 22. sin1 sin 0.4
1 tan 0.9
1 cos 2.5
1 cos
0.1
1 tan 0.25
1 cos 4.5
1 sin 0.75
1 0.6
Solve the equation for . Round to three significant digits.
23. 24. cos 0.83; 180 < < 270
25. tan 2.5; 0 < < 90
26. sin 0.64; 270 < < 360
sin 0.25; 90 < < 180
27. Basketball The height of an outdoor basketball backboard is feet,
and the backboard casts a shadow 17 feet long, as shown below. Find the
angle of elevation of the sun. Give your answer in both radians and
degrees.
1
2
3
1
12 ft
2
8
θ
1
17 ft
3
θ
1 2
θ
1 3
12 1
6
θ
3 θ
Algebra 2 55
Chapter 13 Resource Book
5
3
cos1 2
9
Lesson 13.4

Answer Key
Practice B
2
1. ; 120
2. ; 45 3.
3 4
; 30
6
4. ; 60
3
5. 36.9 6. 25.4 7. 18.4
8. 1.43; 82.0 9. 0.222; 12.7
10. 0.644; 36.9 11. 0.381; 21.8
12. 259 13. 297 14. 127 15. 56.8
16. about 127 17. about 11.5

Lesson 13.4
LESSON
13.4
Practice B
For use with pages 792–798
56 Algebra 2
Chapter 13 Resource Book
NAME _________________________________________________________ DATE ___________
Evaluate the expression without using a calculator. Give your answer
in both radians and degrees.
1. 2. sin 3. tan13 4.
3
1 2 cos
2
1 1 Find the measure of the angle . Round to three significant digits.
5. 6. 7.
θ
Use a calculator to evaluate the expression in both radians and
degrees. Round to three significant digits.
8. 9. 10. 11. tan1 sin 0.4
1 sin 0.6
1 cos 0.22
1 0.14
Solve the equation for . Round to three significant digits.
12. tan 5.3; 180 < < 270
13. sin 0.89; 270 < < 360
14. cos 0.6; 90 < < 180
15. tan 1.53; 0 < < 90
16. Geometry Find the measure of angle in the diagram below. Round the
result to three significant digits.
17. Video Games In a video game, a target appears on the left side of the
television screen and moves at the rate of 2 inches per second across the
screen. You fire a laser beam that travels 10 inches per second. If the
player tries to hit the target as soon as it appears, at what angle should the
laser beam be aimed?
θ
5
4
2
θ
3 1
3
1
3
7
θ
tan 1 3
6
2 2
θ
6
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice C
5
1. 2. 3.
4. 5. 17.4 6. 45 7. 44.4
8. 0.694; 39.8 9. undefined
10. 0.955; 54.7 11. 1.48; 84.6
12. 281 13. 164 14. 215 15. 221
16. about 12 17. about 51.3
; 150
6
; 60
3
; 45
4
; 90
2

LESSON
13.4
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice C
For use with pages 792–798
Evaluate the expression without using a calculator. Give your answer
in both radians and degrees.
2 1 1. 2. tan 3. cos 4.
2
1 cos 3
1 3 2
Find the measure of the angle . Round to three significant digits.
5. 6. 7.
θ
2.5
θ
8
2
2
Use a calculator to evaluate the expression in both radians and
degrees. Round to three significant digits.
8. 9. 10. tan 11.
1 cos 2
1 sin 1.3
1 0.64
Solve the equation for Round to three significant digits.
12. 13.
14. 15. tan1 cos 0.88; 180 < < 270
1 sin
0.82; 180 < < 270
1 tan 0.28; 90 < < 180
1 .
5.3; 270 < < 360
16. Ramp Construction A builder needs to construct a wheelchair ramp
24 feet long that rises to a height of 5 feet above level ground.
Approximate the angle that the ramp should make with the ground.
17. Casting Shadows At a certain time of the day a child five feet tall casts
a four foot long shadow as shown below. Approximate the angle of
elevation of the sun.
5 ft
θ
4 ft
5
sin 1 1
tan 1 10.5
Algebra 2 57
Chapter 13 Resource Book
θ
7
5
Lesson 13.4

Answer Key
Practice A
1. one triangle 2. one triangle 3. no triangle
4. one triangle 5. two triangles
6. one triangle
7. C 105, b 14.1, c 19.3
8. C 78, b 5.82, c 6.58
9. B 55.2, C 87.8, c 18.3; or
B 124.8, C 18.2, c 5.71
10. B 21.6, C 122.4, c 11.5
11. no solution
12. B 10, b 69.5, c 137
13. B 70.4, C 51.6, c 4.16; or
B 109.6, C 12.4, c 1.14
units 2
14. 408 15. 120
units 2
16. 12.0 17. 2.6 18. 23.8
units 2
19. 361 20. 24.3
21. about 9.58 ft
units 2
units 2
units 2
units 2

Lesson 13.5
LESSON
13.5
Practice A
For use with pages 799–806
70 Algebra 2
Chapter 13 Resource Book
NAME _________________________________________________________ DATE ___________
Decide whether the given measurements can form exactly one
triangle, exactly two triangles, or no triangle.
1. B 110, C 30, a 15
2. B 35, a 12, b 26
3. B 130, a 10, b 8
4. B 60, b 30, c 20
5. C 16, b 92, c 32
6. A 10, C 130, b 5
Solve ABC. (Hint: Some of the “triangles” have no solution and
some have two solutions.)
7. C
8. C
9.
10
12.
30 45
A B
10. A 36, a 8, b 5
11. C 160, c 12, b 15
A 150, C 20, a 200
Find the area of the triangle with the given side lengths and included
angle.
14. A 70, b 28, c 31
15. B 35, a 12, c 35
16. C 95, a 8, b 3
17. A 10, b 5, c 6
Find the area of
18.
6
C
82
8
19.
A
45
34
30
C
20.
A
ABC.
21. Surveying A surveyor wants to find the width of a narrow, deep gorge
from a point on the edge. To do this, the surveyor takes measurements as
shown in the figure. How wide is the gorge?
105
10
50 ft
B
42 60
A B
13.
A 58, a 4.5, b 5
B
4.5
37
A B
A C
5 10
76
B
15
C
11
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice B
1. no triangle
4. one triangle
2. one triangle 3. two triangles
5. C 110, b 22.4, c 24.4
6. B 21.4, C 116.6, c 29.4
7. C 35, b 18.5, c 10.8
8. A 38, a 22.0, c 34.0
9. no solution
10. A 40.9, C 84.1, c 30.4
11. B 71.8, C 78.2, c 39.2; or
B 108.2, C 41.8, c 26.7
units 2
12. 2290 13. 10.4
units 2
14. 24.3 15. 23.8
units 2
16. 361 17. 24.3
units 2
18. 1680 19. about $5,680
20. about 550 feet
units 2
units 2
units 2

LESSON
13.5
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice B
For use with pages 799–806
Decide whether the given measurements can form exactly one
triangle, exactly two triangles, or no triangle.
1. A 63, a 42, b 120
2. B 47, A 60, a 45
3. B 30, b 40, a 60
4. A 60, B 40, c 6
Solve ABC. (Hint: Some of the “triangles” have no solution and
some have two solutions.)
5. C
6. C
7.
10
4.5
12 22
60
A B
42
A B
8. B 34, C 108, b 20
9. A 42, a 10, b 21
10.
B 55, a 20, b 25
Find the area of
12. A
13. A
14.
52
102
C 90 B
15. C 82, a 8, b 6
16. A 45, b 30, c 34
17. B 76, a 10, c 5
18. A 43.75, b 57, c 85
19. Real Estate You are buying the triangular piece of land shown. The price
of the land is $2500 per acre (1 acre 4840 square yards). How much does
the land cost?
100 yd
C
95
A 250 yd B
20. Measuring an Island What is the width w of the island in the figure
shown below?
1200 ft
ABC.
27
39
w
6
11.
120
C 4
A 30, a 20, b 38
B
B
80
65
A
A C
75
5 10
B
17
Algebra 2 71
Chapter 13 Resource Book
C
Lesson 13.5

Answer Key
Practice C
1. no triangle 2. two triangles
3. two triangles 4. one triangle
5.
6.
7. C
8. C 100, a 4.76, b 10.2
9. C 100, b 25.8, c 30.2
10. B 55.2, C 87.8, c 18.3; or
B 124.8, C 18.2, c 5.7
5
B 51.4, C 53.6, b 4.85
A 29.3, C 132.7, c 28.5; or
A 150.7, C 11.3, c 7.61
, a 32.2, b 39.4
12
11. no solution 12. 1680
units 2
13. 366 14. 110 15. 7
units 2
16. 1.41 17. 46.8 18. 98.3
19. about 2.67 miles
units 2
units 2
units 2
units 2
units 2

Lesson 13.5
LESSON
13.5
Practice C
For use with pages 799–806
72 Algebra 2
Chapter 13 Resource Book
NAME _________________________________________________________ DATE ___________
Decide whether the given measurements can form exactly one
triangle, exactly two triangles, or no triangle.
1. A 76.4, a 176, b 189
2. A 48.2, a 15, b 20
3. A 20, a 10, c 11
4. C 95, a 8, c 9
Solve ABC. (Hint: Some of the “triangles” have no solution and
some have two solutions.)
5. C
6. C
7.
12
19
8. A 23, B 57, c 12
9. A 23, B 57, a 12
10. A 37, a 11, b 15
11. B 130, a 10, b 8
Find the area of
12. B
13. A C
14.
45
43.75
A
57
C
15. B 150, a 7, c 4
16.
17. A 60, b 9, c 12
18. B 25, a 15, c 31
19. Hot Air Balloon You and a friend live 8.4 miles apart. A hot air balloon is
floating between your houses as shown in the figure. Given the angles of
elevation, approximate the height of the balloon. (Hint: The height of the
balloon is the altitude of the triangle.)
Your
house
85
6
75
A 5 B
24
8.4 mi
ABC.
48
Friend's
house
A B
18
34
60
B
B
, a 4, c 1
4
π
π
A
4
44
3
B
C
10 95
C
A 25 B
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice A
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13. 16.2 14. 41.2 15. 96.8
16. 54 17. 1350 18. 713
19. 56.9 20. 10.4 units 21. 6
22. B 52.6 E of S; C 25.3 W of S
2
units2 units2 units2 units2 units2 A 26.7, C 33.3, b 141
A 95.3, B 24.7, c 27.0
A 76.7, B 38.7, C 64.6
A 54.3, B 79.7, c 100
A 57.5, B 71.5, c 283
A 44.4, B 44.4, C 91.2
B 74.5, C 43.5, a 51.3
A 142.0, B 12.8, C 25.2
A 62.9, B 79.6, C 37.5
A 48.8, B 65.6, C 65.6
A 122.2, B 19.8, c 29.1
B 104.9, C 15.1, b 33.5
units 2
units 2
units 2

Lesson 13.6
LESSON
13.6
Solve ABC.
Practice A
For use with pages 807–812
82 Algebra 2
Chapter 13 Resource Book
NAME _________________________________________________________ DATE ___________
1. A
2. A
3.
89
120
B
Use the Law of Sines, Law of Cosines, or the Pythagorean theorem to solve
10. C
11.
C
38
40
B
12.
40 33
16
A
A 40 B
Find the area of
13. B
14. B
15.
10
A 5 C
73
4. C 46, a 113, b 137 5. C 51, a 307, b 345 6. a 7, b 7, c 10
7. A 62, b 56, c 40 8. a 39, b 14, c 27 9. a 19, b 21, c 13
ABC.
7
C
13
60
C 31 B
15
A 7 C
A 10 C
16. a 9, b 12, c 15
17. a 75.4, b 52, c 52 18. a 47, b 36, c 41
19. a 13, b 14, c 9
20. a 2.5, b 10.2, c 9 21. a 3, b 4, c 5
22. Boat Race A boat race occurs along a triangular course marked by
buoys A, B, and C. The race starts with the boats going 8000 feet due
north. The other two sides of the course lie to the east of the first side, and
their lengths are 3500 feet and 6500 feet as shown at the right. Find the
bearings for the last two legs of the course.
B
8000
W
3500
C
N
S
E
12
A 9 C
A
60
9 B
A
B
13 14
B
20 20
ABC.
C
30
6500
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice B
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14. 2813 15. 10.4
16. 56.9 17. 1.62
18. 0.468 19. 43.3
20. 9.92 units 21. about 110 ft 22. about 4 ft
2
units2 units2 units2 units2 units2 units2 B 37.5, C 84.5, a 15.3
A 82.1, B 58.8, C 39.1
A 51.6, B 27.3, C 101.1
A 38.0, C 42, b 19.2
A 38.3, B 99.7, c 23.8
A 102.2, B 38.4, c 81.8
A 153.5, B 15.5, C 11.0
B 12, a 17.9, c 20.8
A 30, a 29.0, c 41.0
C 105, b 18.4, c 35.5
A 48.5, C 69.5, b 4.71
B 79, a 102, c 17.7
A 55.8, B 8.6, C 115.6

LESSON
13.6
Solve ABC.
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice B
For use with pages 807–812
1. B
2. B
3.
18
A
58
11
C
4. B 100, a 12, c 13
5. C 42, a 22, b 35
6. C 39.4, a 126, b 80.1
7. a 21.46, b 12.85, c 9.179
Use the Law of Sines, Law of Cosines, or the Pythagorean theorem
to solve ABC.
8. A 48, C 120, b 5
9. B 15, C 135, b 15
10. A 45, B 30, a 26
11. B 62, a 4, c 5
12. A 91, C 10, b 100
13. a 11, b 2, c 12
Find the area of
14. B
15. B
2.5
10.2
16.
A 9 C
89
120
A
ABC.
73
17. a 4.25, b 1.55, c 3
18. a 1.42, b 0.75, c 1.25
19. a 10, b 10, c 10
20. a 11, b 2, c 12
21. Measuring a Pond How wide is the pond shown in the figure below?
152 ft
C
45
131 ft
22. Softball The pitcher’s mound on a softball field is 46 feet from
home plate. The distance between the bases is 60 feet. How much
closer is the pitcher’s mound to second base than it is to first base?
14
22
A 19 C
60 ft
15
A 7 C
B
13 14
A 9 C
60 ft
46 ft
60 ft
45
60 ft
Algebra 2 83
Chapter 13 Resource Book
B
12
Lesson 13.6

Answer Key
Practice C
1. A 48.0, B 82.0, c 15.5
2. A 117.9, B 29.4, C 32.7
3. A 62.5, C 77.5, b 72.4
4. A 52.4, B 82.6, c 16.4
5. B 42.1, C 20.4, a 9.92
6. A 27.3, B 33.7, C 119
7. A 40.9, B 82.2, C 56.9
8. B 17.4, C 109.6, c 9.4
9. A 50.5, C 89.5, c 15.6; or
10.
11.
12.
13.
14. 0.496 15. 159 16. 116
17. 43.2 18. 20.4 19. 62.0
20. 0.959 units
22. about 92 ft
21. about 2.01 acres
2
units2 units2 units2 units2 A 129.5, C 10.5, c 2.83
A 34.0, B 122.9, C 23.1
A 15, a 3.7, c 12.2
C 98, a 9.68, c 18.1
A 70.5, B 86.6, C 22.9
units 2
units 2

Lesson 13.6
LESSON
13.6
Solve ABC.
Practice C
For use with pages 807–812
84 Algebra 2
Chapter 13 Resource Book
NAME _________________________________________________________ DATE ___________
1. B
2. B
3.
Use the Law of Sines, Law of Cosines, or the Pythagorean theorem
to solve ABC.
8. A 53, a 8, b 3
9. B 40, a 12, b 10
10. a 10, b 15, c 7
11. B 45, C 120, b 10
12. A 32, B 50, b 14
13. a 17, b 18, c 7
Find the area of
14. B
15.
12
B
34
32
16.
A 40 C
2 2
A 1
2
C
15
50
A 20 C
4. C 45, a 132, b 23
5. A 117.5, b 7.5, c 3.9
6. a 4.3, b 5.2, c 8.2
7. a 20.1, b 30.4, c 25.7
ABC.
17. a 4, b 24, c 26
18. a 12, b 9, c 5
19. a 21.5, b 14.3, c 10.2
20. a 2.32, b 5.76, c 3.48
21. Farming A farmer has a triangular field with sides of lengths
125 yards, 160 yards, and 225 yards. Find the number of acres in
the field. (1 acre 4840 square yards)
125 yd 160 yd
22. Guy Wire A vertical telephone pole 40 feet tall stands on the
side of a hill as shown in the figure to the right. Find the length of
the wire that will reach from the top of the pole to a point 72 feet
downhill from the pole.
55
A
90
50
C
A
A
34
16 C
225 yd
72 ft
17
110
26
40
B
C
100
40 ft
B
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice A
1. 2.
(1, 2)
3. 4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
4
y
(29, 3)
2
y 1
3
y 1
2
y 1
2
(11, 2)
(9, 1)
y 1
y 2x; 0 ≤ x ≤ 12
2x; 0 ≤ x ≤ 8
x 8.06 cos 65.6t or x 3.33t;
y 8.06 sin 65.6t or y 7.33t
x 9.13 cos 61.2t 2 or x 4.40t 2;
y 9.13 sin 61.2t 5 or y 8.00t 5
x 8.72 cos 83.4t 9 or x 1.00t 9;
y 8.72 sin 83.4t 24 or y 8.67t 24
x 18 cos 15t or x 17.4t;
y 4.9t 2 18 sin 15t 2 or
y 4.9t 2 4.66t 2
15. about 22.1 m
y
2 (0, 2)
2
4
y
x
4 x
(8, 14)
x 4; 6 ≤ x ≤ 18
x 1; 4 ≤ x ≤ 4
x 1; 2 ≤ x ≤ 6
x
2
y
2
2
y
2
(6, 4)
(3, 4)
(11, 0)
x
(10, 0) x

LESSON
13.7
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice A
For use with pages 813–819
Graph the parametric equations.
1. x 3t 1 and y t 2 for 0 ≤ t ≤ 4
2. x 2t 3 and y t 4 for 0 ≤ t ≤ 4
3. x 1 5t and y t 3 for 2 ≤ t ≤ 6
4. x t 5 and y 5 t for 1 ≤ t ≤ 5
5. x 2t and y 3t 2 for 0 ≤ t ≤ 4
Write an xy-equation for the parametric equations. State the
domain.
6. x 3t and y 6t for 0 ≤ t ≤ 4
7. x 2t and y t for 0 ≤ t ≤ 4
8. x 3t 3 and y t 3 for 1 ≤ t ≤ 5
9. x 2t 8 and y t 3 for 2 ≤ t ≤ 6
10. x 2t 2 and y t 2 for 0 ≤ t ≤ 4
Use the given information to write parametric equations describing
the linear motion.
11. An object is at 0, 0 at time t 0 and then at 10, 22 at time t 3.
12. An object is at 2, 5 at time t 0 and then at 24, 45 at time t 5.
13. An object is at 12, 2 at time t 3 and then at 15, 28 at time t 6.
Snowboarding In Exercises 14 and 15, use the following information.
A snowboarder jumps off a ramp at a speed of 18 meters per second. The
ramp’s angle of elevation is 15, and the height of the end of the ramp
above level ground is 2 meters.
14. Write a set of parametric equations for the snowboarder’s jump.
15. Use the equation to determine how far from the ramp the snowboarder
landed.
15
2 m
Algebra 2 95
Chapter 13 Resource Book
Lesson 13.7

Answer Key
Practice B
1. 2.
3. 4.
5.
6.
7. y
8. y 2x 13; 6 ≤ x ≤ 46
9. x 19.5 cos 62.6t or x 9.00t;
y 19.5 sin 62.6t or y 17.3t
1
y
y x 10; 7 ≤ x ≤ 11
5x 2; 20 ≤ x ≤ 0
3
2x 1; 0 ≤ x ≤ 8
10. x 21.4 cos 46.1t 6 or x 14.8t 6;
y 21.4 sin 46.1t 15 or y 15.4t 15
11. x 7.35 cos 54.7t 1 or x 4.25t 1;
y 7.35 sin 54.7t 7 or y 6.00t 7
12.
y 6.43 sin 66.2t 6 or y 5.88t 6
13.
y
2
(0, 0)
4
(2, 3)
2
y
2
x
(12, 8)
(10, 1)
x
x 6.43 cos 66.2t 5 or x 2.60t 5;
x 140 cos 22.5t or x 129t;
y 16t
14. about 456 ft 15. about 3.53 seconds
2 y 16t
53.6t 10
2 140 cos 22.5t 10 or
25
y
2
y
2
(0, 2)
(5, 10) 100
(4, 10)
(85, 190)
x
x

Lesson 13.7
LESSON
13.7
Practice B
For use with pages 813–819
96 Algebra 2
Chapter 13 Resource Book
NAME _________________________________________________________ DATE ___________
Graph the parametric equations.
1. x 3t and y 2t for 0 ≤ t ≤ 4
2. x t and y 3t 2 for 0 ≤ t ≤ 4
3. x 3t 1 and y t 2 for 1 ≤ t ≤ 3
4. x 20t 5 and y 50t 10 for 0 ≤ t ≤ 4
Write an xy-equation for the parametric equations. State the
domain.
5. x 2t and y 3t 1 for 0 ≤ t ≤ 4
6. x t 5 and y 5 t for 2 ≤ t ≤ 6
7. x 5 5t and y t 3 for 1 ≤ t ≤ 5
8. x 2t 6 and y 4t 1 for 0 ≤ t ≤ 20
Use the given information to write parametric equations describing
the linear motion.
9. An object is at 0, 0 at time t 0 and then at 27, 52 at time t 3.
10. An object is at 6, 15 at time t 0 and then at 80, 92 at time t 5.
11. An object is at 1, 7 at time t 2 and then at 18, 31 at time t 6.
12. An object is at 5, 6 at time t 4 and then at 20.6, 41.3 at time t 10.
Snow Skiing In Exercises 13–15, use the following information.
A snow skier jumps off a ramp at a speed of 140 feet per second. The
ramp’s angle of elevation is 22.5, and the height of the end of the ramp
above level ground is 10 feet.
13. Write a set of parametric equations for the snow skier’s jump.
14. Use the equation to determine how far from the ramp the skier landed.
15. Determine how many seconds the snow skier is in the air.
22.5
10 ft
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice C
1. 2.
3. 4.
5. y x 19; 7 ≤ x ≤ 12
6. y 3x 10; 4 ≤ x ≤ 20
7. y 1.04x; 0 ≤ x ≤ 148
8. y 2.20x; 0 ≤ x ≤ 50
9. x 29.2 cos 69.3t or x 10.3t;
y 29.2 sin 69.3t or y 27.3t
10.
y 4.75 sin 14.6t 1 or y 1.20t 1
11.
y 2.49 sin 23.6t or y 1.00t
12.
25
y
2 (0, 1)
y
2
(110, 180)
(30, 20)
25
(8, 13)
x
x
x 4.75 cos 14.6t 4 or x 4.60t 4;
x 2.49 cos 23.6t 2 or x 2.29t 2;
x 10.0 cos 39.8t 2 or x 7.71t 2;
y 10.0 sin 39.8t 3 or y 6.43t 3
13. about 29.7 ft 14. x 6.1 cos 125t 3.5 or
x 3.5t 3.5; y 6.1 sin 125t or y 5.0t
6
y
4
(0, 0)
y
4
18
(10, 7)
(18, 23)
x
(49, 28)
x

LESSON
13.7
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice C
For use with pages 813–819
Graph the parametric equations.
1. x 2t and y 3t 1 for 0 ≤ t ≤ 4
2. x 2t 6 and y 4t 1 for 2 ≤ t ≤ 6
3. x 20t 10 and y 40t 20 for 1 ≤ t ≤ 5
4. x 14.1 cos 30t and y 14.1 sin 30t for 0 ≤ t ≤ 4
Write an xy-equation for the parametric equations. State the
domain.
5. x t 7 and y 12 t for 0 ≤ t ≤ 5
6. x 2t 4 and y 6t 2 for 0 ≤ t ≤ 8
7. x 21.4 cos 46.1t and y 21.4 sin 46.1t for 0 ≤ t ≤ 10
8. x 8.1 cos 65.6t and y 8.1 sin 65.6t for 0 ≤ t ≤ 15
Use the given information to write parametric equations describing
the linear motion.
9. An object is at 0, 0 at time t 0 and then at 31, 82 at time t 3.
10. An object is at 4, 1 at time t 0 and then at 27, 7 at time t 5.
11. An object is at 2, 0 at time t 1 and then at 14, 7 at time t 8.
12. An object is at 2, 3 at time t 5 and then at 56, 42 at time t 12.
13. Soccer You are a goalie in a soccer game. You save the ball and then
drop kick it as far as you can down the field. Your kick has an initial speed
of 30 feet per second and starts at a height of 2.5 feet. If you kick the ball
at an angle of 50, how far down the field does the ball hit the ground?
14. Bike Path A bike trail connects State and Peach Streets as
y
shown. You enter the trail 3.5 miles from the intersection of the
streets and pedal at a speed of 12 miles per hour. You reach
Peach Street 5 miles from the intersection. Write a set of
parametric equations to describe your path.
5 mi
Peach Street
3.5 mi
State Street
Algebra 2 97
Chapter 13 Resource Book
x
Lesson 13.7

Answer Key
Test A
1. y
2.
3. y 4.
5. y
6.
7. cos x 8. cos x 9. 2 sin x
10.
1
sin x 1
sin x
1
11. sin x 1
sin x
12. 2 tan 13.
2 x 1 1 tan2 x
1
2
14. 15.
16. 17. 18.
19. 20.
21.
22.
23. 24. a: 5, P:
25. 5
1
a: 60
1
11
,
6 6
5
2n, 2n
6 6
2 3
6 2
4
2 3
2 6
4
a: 2, P: 2, y 2 sin x
a: 3, P: , y 3 cos 2x
1
2 , P: 2, y 2 cos x
2n
π
2
π
2
1
π
x
x
x
1
1
y
y
2π
2
π
y
π
2
2
x
x
x
4
,
3 3

CHAPTER
14
NAME _________________________________________________________ DATE
Chapter Test A
For use after Chapter 14
____________
Draw one cycle of the function’s graph.
1. y sin x
2. y cos x
1
3. y tan x
4.
5. y 4 sin x
6.
2
y
y
π
2
π
2
Simplify the expression.
7. sin 8.
9. sin x cos x tan x
x 2
Verify the identity.
10. sin x csc x 1
11.
12. 2 sec 2 x 1 tan 2 x
Copyright © McDougal Littell Inc.
All rights reserved.
1
y
π
x
x
x
1
1
y
y
cotx
cscx
2
π
y 2 cos 1
2 x
2π
y 3 tan 1
2 x
y
π
2
cos
xcsc x 1
2
x
x
x
Answers
1. Use grid at left.
2. Use grid at left.
3. Use grid at left.
4. Use grid at left.
5. Use grid at left.
6. Use grid at left.
7.
8.
9.
10.
11.
12.
Algebra 2 103
Chapter 14 Resource Book
Review and Assess

Review and Assess
CHAPTER
14
CONTINUED
NAME _________________________________________________________ DATE ____________
Chapter Test A
For use after Chapter 14
Solve the equation in the interval 0 ≤ x < 2.
Check your
solutions.
13. 2 cos 1 0
14. 5 cos x 3 3 cos x
Find the general solution of the equation.
15. 2 sin x 1 0
16. 5 sec x 5 0
Find the exact value of the expression.
17. 18.
19. 20. sin 7
tan
12
tan 15
sin 15
12
Find the amplitude and period of the graph. Then write a
trigonometric function for the graph.
21. 22. 23.
1
y
π
2
24. The voltage E in an electrical circuit is given by E 5 cos 120t.
Find the amplitude and the period.
25. In Exercise 24, find E when t 0.
104 Algebra 2
Chapter 14 Resource Book
x
1
y
π
2
x
1
y
2
x
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Test B
1. y
2.
3. y 4.
5. y
6.
7. 8. 1 9. 10. sin2 cot x
x
11.
12.
7
11
13. , , 14.
6 6 2
1
1
1
π
π
2
2π
sec 2 x 1 4 sec 2 x 3
1 cos 2x 1 cos 2x
sin 2x sin 2x sin 2x
x
x
x
1 cos2 x sin 2 x
sin 2x
1 cos2 x sin 2 x
sin 2x
sin2 x sin 2 x
sin 2x
2 sin2 x
2 sin x cos x
sin x
tan x
cos x
7
11
,
6 6
15. 16.
17. 18. 19.
20. 21.
22.
23. 24. a: 3.8, P:
25. 3.8
1
a: 25
1
a:
3 , P: 2, y 13
sin x
1
a: 1, P: 4, y cos
1
2 , P: , y 2 sin 2x
1
2x 5
2n, 2n
6 6
n
4 2
6 2
4
2 3
2 6
4
2 1
1
1
y
y
π
2
3
π
y
π
tan y 1
1
tan y
x
x
x

CHAPTER
14
NAME _________________________________________________________ DATE
Chapter Test B
For use after Chapter 14
____________
Draw one cycle of the function’s graph.
1. y sin 2x
2. y 2 cos x
3. y tan 4. y 1 sin 2x
1
5. y sinx 6. y 2 tan x
Simplify the expression.
7. tan 8.
x 2
9.
1
1
y
y
cos 2 x
cot 2 x
2 x
Verify the identity.
10.
12. csc 2x cot 2x tan x
11. tan2 x 4 sec2 tan y cot y 1
x 3
Copyright © McDougal Littell Inc.
All rights reserved.
1
π
π
y
π
2
2
x
x
x
1
1
y
y
1
π
π
2
1
sin x 2
1
tan x 2
y
π
x
x
x
Answers
1. Use grid at left.
2. Use grid at left.
3. Use grid at left.
4. Use grid at left.
5. Use grid at left.
6. Use grid at left.
7.
8.
9.
10.
11.
12.
Algebra 2 105
Chapter 14 Resource Book
Review and Assess

Review and Assess
CHAPTER
14
CONTINUED
NAME _________________________________________________________ DATE ____________
Chapter Test B
For use after Chapter 14
Solve the equation in the interval 0 ≤ x < 2.
Check your
solutions.
13. 2 sin 14. 4 csc 6 csc
2 x sin x 1
Find the general solution of the equation.
15. 16. tan2 3 sin x sin x 1
x 1 0
Find the exact value of the expression.
17. 18.
19. 20. tan
cos
8
7
sin 75
tan 105
12
Find the amplitude and period of the graph. Then write a
trigonometric function for the graph.
21. 22. 23.
2
y
2π
24. The voltage E in an electrical circuit is given by E 3.8 cos 50t.
Find the amplitude and the period.
25. In Exercise 24, find E when t 0.
106 Algebra 2
Chapter 14 Resource Book
x
1
y
π
2
x
y
1
1
x
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Test C
1. y
2.
3. y
4.
5. y
6.
7. sec x 8. sec x 9. 1
10. 11.
sin2 x cos2 x 1
12.
7 2 4 5
13. , 14. , , , 15.
4 4 3 3 3 3
16.
17. 18. 19.
20. 21.
22.
23. a: 24. P 3 sin 660 πt
1
a:
1
, P: 2, y sin x
2
a: 3, P: 4, y 3 sin
2
3 , P: , y 3 cos 2x
1
2x 5
2n, 2n, 2n
3 3
6 2
4
6 2
4
2 3
6 2
4
25.
1 sec x
sin x tan x
3
1
1
2
1
330
π
π
2
1
π
2
x
x
x
2
2
1
cos x
cot x
sin x
1 1
cos x
sin x
sin x
cos x
cos x 1
sin x cos x sin x
1
cos x 1
sin xcos x 1
csc x
sin x
y
y
π
π
2
1
y
π
2
cos x
cos x
n
x
x
x

CHAPTER
14
NAME _________________________________________________________ DATE
Chapter Test C
For use after Chapter 14
____________
Draw one cycle of the function’s graph.
1. y 2 sin 2. y 4 cos 2x
1
2 x
3. y 2 cosx 4. y 2 tan x
5. y tan2x 6.
Simplify the expression.
7. csc x
8.
2
9.
1
1
y
y
1
sin x cos x tan x
tanx sin 2 x
Copyright © McDougal Littell Inc.
All rights reserved.
π
π
2
y
π
2
2
2
x
x
x
2
y 4 sin 1
2 x
1
y
y
π
cos x
tan x
1 sin x
1
π
2
y
π
2
x
x
x
Answers
1. Use grid at left.
2. Use grid at left.
3. Use grid at left.
4. Use grid at left.
5. Use grid at left.
6. Use grid at left.
7.
8.
9.
Algebra 2 107
Chapter 14 Resource Book
Review and Assess

Review and Assess
CHAPTER
14
CONTINUED
12.
NAME _________________________________________________________ DATE ____________
Chapter Test C
For use after Chapter 14
Verify the identity.
10. 11.
sin
sin
2
sin x
2 x 1
sec2 1
x
1 secx
csc x
sinx tanx
Solve the equation in the interval Check your
solutions.
13. 14. 4sin 2 sin
3
cos 1
0 ≤ x < 2.
Find the general solution of the equation.
15. 16. 2 sin2 sin x sin x cos x 0
x cos x 1 0
Find the exact value of the expression.
17. 18.
19. 20. sin 5
tan
12
cos 75
sin 255
12
Find the amplitude and period of the graph. Then write a
trigonometric function for the graph.
21. 22. 23.
y
3
π
24. Music A tuning fork vibrates with a frequency of 330 hertz (cycles
per second). You strike the tuning fork with a force that produces a
maximum pressure of 3 Pascals. Write the sine model that gives the
pressure P as a function of time (in seconds).
25. In Exercise 24, what is the period of the sound wave?
108 Algebra 2
Chapter 14 Resource Book
x
1
y
π
2
x
x
1
cot x
y
1
x
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Cumulative Review
1. 2. 3.
4. 5. 6. 7. 6
8. 28 9. 0 10. 11. 10 12. 36
13. 14. 15.
16.
17.
18.
19.
20.
21.
22. maximums,
minimum; 4th degree
23. maximum, minimum;
3rd degree 24. maximum,
minimum; 3rd degree 25. 7.67, 7, 6
26. 85.4, 85, 85 27. 0.267, 0.25, 0
28. 242, 242.5, 230 29. 30.
31. 32. 33.
34. 35. 36.
x 3
9x2 x
15x 18
2 y 3
8x
6x 6
x
y 1
54x y 253x y 31.5x y 2x y 1
24x y
1.1, 3.1 1.1, 3.1
0, 1 1.8, 1.8;
2.3, 11 0, 2 4.1;
0, 3 1.1, 4.1
2.5;
2
3x 9
2 2 29
y 2x 1
2 ; 92
, 29 2
2 y x 3
1; 1, 1
2 y x
1; 3, 1
7
2 2 53
y x 4
4 ; 72
, 53 4
2 y x 3
2; 4, 2
2
53
1
4
311
14
4
2; 3, 2
3
y y 5x 19
1, 3, 3 5, 5
2, 0
1
3
y 2 2x 3
x
37. 38.
39.
40.
41.
x 5
42. geometric 43. arithmetic 44. geometric
45. arithmetic 46. neither 47. arithmetic
48. 12 49. 2520 50. 20,160 51. 15,120
52. 1 53. 2
54. sin 5 cos 5
tan 3 cot 4
sec csc
2
x 6
y2
1
64 36 2
y 6
4
2 x 2
1
2 x 2
16 y 3
2 y 32 x 2
2x
25
2 8x 24
4
4
5
3
2
55. sin
2
cos
2
tan cot
sec csc 2
1
2
3
3
5
4
2
1
9117
56. sin cos
117
3
tan cot
2
117
sec csc
6
3
57. sin cos
2
3
tan cot
2
sec csc
4
58. sin 5 cos
tan 3 cot
sec csc
4
5
10149
59. sin cos
149
3
10
tan cot
7
149
6117
2
117
1
3
23
3
3
5
7149
149
7
10
149
sec csc
60. 61. 2 62. 64. 4
3
637
7
10
358
58
37
2
4
3
3
9
3
5
4
117

Review and Assess
CHAPTER
14
NAME _________________________________________________________ DATE
Cumulative Review
For use after Chapters 1–14
____________
Write an equation of the line described. (2.4)
1. passes through and is perpendicular to the line
2. passes through and is parallel to the line y
3. passes through 3, 4 and 4, 1
1
y
4, 5
2x 6
2
2, 3
3x 5
Solve the system using the linear combination method or the
substitution method. (3.6)
4. a 3b 3c 1
5. 4x 5y 45
6. 2x 3y 3
2a 3b 4c 1
b c 0
Evaluate the determinant of the matrix. (4.3)
7. 8. 9.
1
2
1
4
1
3
5
3
2
5
0
3
Simplify the expression. (5.3)
10. 75
11. 25 5
12. 43 27
1
16
13. 14. 11 9
15.
Write the quadratic function in vertex form and identify the vertex. (5.5)
16. 17. 18.
19. 20. 21. y 2
3x2 y 2x 6x 1
2 y x 4x 3
2 y x
6x 10
2 y x 7x 1
2 y x 8x 14
2 6x 11
Estimate the coordinates of each turning point and state whether
each corresponds to a local maximum or a local minimum. Then
list all the real zeros and determine the least degree that the
function can have. (6.8)
22. y
23. y
24.
1
Find the mean, median, and mode of the data set. (7.7)
25. 5, 6, 6, 8, 10, 11 26. 87, 85, 85, 86, 87, 85, 83, 81, 90
27. 0, 0, 0.2, 0.3, 0.4, 0.7 28. 230, 230, 240, 245, 247, 260
114 Algebra 2
Chapter 14 Resource Book
1
x
x y
2
2
2
x
4x 6y 6
1
3
3
7
8
0
2
2
4
1
1
Copyright © McDougal Littell Inc.
All rights reserved.
1
y
1
x

CHAPTER
14
CONTINUED
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ____________
Cumulative Review
For use after Chapters 1–14
Write an exponential function of the form y ab whose graph
passes through the given points. (8.7)
x
29. 1, 2, 3, 32
30. 2, 4, 1, 0.5
31. 1, 4.5, 2, 6.75
32. 33. 1, 34. 3, 27, 5, 243
4
5, 3, 64
2, 225, 3, 675
Simplify the complex fraction. (9.5)
35. 36.
1
3x
37.
2 3
2
x 1
x
x2 x
4
2
3
2x 3
3
x
Write an equation for the conic section. (10.6)
38. Circle the center at 2, 3 and radius 5
39. Parabola with vertex at 2, 3 and focus at 2, 7
40. Ellipse with vertices at 4, 6 and 8, 6 and co-vertices at 6, 7 and 6, 5
41. Hyperbola with vertices at 5, 8 and 5, 8 and foci at 5, 10 and
5, 10
Decide whether the sequence is arithmetic, geometric, or neither.
(11.3)
1
42. 1, 3, 9, 27, . . . 43. 1, 3, 5, 7, 9, . . . 44. 1, 3, 9, . . .
1
2 ,
45. 1, 2, . . . 46. 1, 4, 9, 16, 25, . . . 47.
Find the number of permutations. (12.1)
48. 4P2 49. 7P5 50.
51. 52. 53.
9 P 5
3
2 ,
Use the given point on the terminal side of an angle in standard
position. Evaluate the six trigonometric functions of . (13.3)
54. 3, 4
55. 1, 1
56. 6, 9
57. 1, 3
58. 6, 8
59. 7, 10
Find the value of the indicated trigonometric function of (14.3)
60. tan find sin 61. sec 0 < < find tan
2 ;
, 0 < <
7 2 ;
.
3
6,
8 P 0
5,
3
< < 3
62. cot find cos 63. sin find cot
2 ;
5 ,
< 0 < ;
2
5
1
x3 8
4
x2 4
2
x2 2x 4
3 ,
9, 5, 1, 3, . . .
8P 6
2 P 1
Algebra 2 115
Chapter 14 Resource Book
Review and Assess

Answer Key
Practice A
1. C 2. B 3. A 4. amplitude: 4, period:
5. amplitude: 2 period: 6. amplitude: 2,
2
,
4
period: 7. amplitude: 1, period:
4
1
8. amplitude: 3, period:
9. amplitude: 10, period:
10. y
11. y
2
12. y
13.
1
π
2
4π
1
x
x
4
14. 15. y
16. y 4 sin 4x 17. y 2 sin 528 x
1 1
sin
8 4 x
y 2 sin
2 x
1
1
π
y
π
4
x
x
4

Lesson 14.1
LESSON
14.1
Practice A
For use with pages 831–837
14 Algebra 2
Chapter 14 Resource Book
NAME _________________________________________________________ DATE ___________
Match the function with its graph.
1. 2. y 4 sin 3. y 4 sin 4x
1
y 4 cos 4x
A. y
B. y
C.
Find the amplitude and period of the graph of the function.
4. 5. 6.
7. 8. y 9.
1
y sin 8x
cos 2x
Graph the function.
10. 11. 12. y sin 13. y 2 tan x
1
1
y 6 sin x
y cos x
Write an equation of the form y a sin bx, where a > 0 and
b > 0, with the given amplitude and period.
14. Amplitude: 2 15. Amplitude: 8
16. Amplitude: 4
Period: 4 Period:
Period:
2
17. Sound Waves Plucking or striking a stretched string, such as a guitar
string, causes sound waves. Sound waves can be modeled by sine
functions of the form y a sin bx, where x is measured in seconds. Write
an equation of a sound wave whose amplitude is 2 and whose period is
second.
1
264
2
2
y
π
8
π
x
x
2
2
1
3
y
2π
π
8
8
4 x
1
x
x
8 x
1
2
y
y
π
y 10 sin 1
2x
π
4
Copyright © McDougal Littell Inc.
All rights reserved.
x
x

Answer Key
Practice B
1. A 2. C 3. B 4. amplitude: 5, period:
5. amplitude: 1, period: 6. amplitude:
period: 7. amplitude: 4, period:
8. amplitude: 2, period: 2
1
9. amplitude: 4 period: 4
10. y
11. y
,
3
1
12. y 13.
14. y
15.
1
16. y
17.
1
1
18. y 3 sin 19.
2 x
20. y 12 sin 21. 4 sec 22. 15
2x
7
23. y
1
π
4
π
4
1
1
π
π
16
x
x
x
x
x
1
2
1
1
y 1
sin 6x
3
y
y
π
2
8
2π
π
3
y
1
8
1
3 ,
x
x
x
x
2

LESSON
14.1
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice B
For use with pages 831–837
Match the function with its graph.
1. 2. y 2 cos 3. y 2 tan 2x
1
y 2 sin 2x
A. y
B. y
C.
1
Find the amplitude and period of the graph of the function.
4. 5. 6.
7. y 4 cos 8. y 2 cos x
9.
1
y 5 cos x
y sin 2x
Graph the function.
10. 11. 12. 13.
14. 15. 16. y 17. y tan 2x
3
y cos y tan 4x
y 5 sin x
1
y cos x
y 2 cos 3x
sin 2x
1
2x y sin 2x
3
π
4
4 x
Write an equation of the form where and
with the given amplitude and period.
18. 19. Amplitude: 20.
Period:
Respiration Cycle After exercising for a few minutes, a person has a
respiratory cycle for which the velocity, v (in liters per second), of air flow is
approximated by v 1.75 sin where t is time in seconds. Inhalation occurs
when v > 0 and exhalation occurs when v < 0.
2 t,
y a sin bx, a > 0
b > 0,
1
Amplitude: 3
3
Amplitude: 12
Period: 4
Period: 7
3
21. Find the time for one full respiratory cycle.
22. Find the number of cycles per minute.
23. Sketch the graph of the velocity function.
x
1
2 x
π
8
x
4
1
y
2π
y 1
y
1
4 sin 2x
1
3 sin 6x
Algebra 2 15
Chapter 14 Resource Book
x
Lesson 14.1

Answer Key
Practice C
1. A 2. C 3. B 4. amplitude: 8, period:
5. amplitude: 1, period: 6. amplitude:
period: 7. amplitude: 3, period:
8. amplitude: 4, period: 1
1
9. amplitude: 10 period: 8
10. y
11. y
,
1
2 ,
2
1
12. y
13.
1
14. y
15.
1
3π
2
1
2
2π
16. y 17.
1
1
24
18. 19. y
20. y 5 sin 16x 21. about 2.22 sec
2 1
sin
3 6 x
x
y 6 sin
5
x
x
x
x
1
1
1
y
y
1
4
2
6
1
π
y
π
32
x
x
x
x
2

Lesson 14.1
LESSON
14.1
Practice C
For use with pages 831–837
16 Algebra 2
Chapter 14 Resource Book
NAME _________________________________________________________ DATE ___________
Match the function with its graph.
1. 2. y 4 tan 3. y 4 tan 2 x
1
y 4 tan 2x
A. y
B. y
C.
2
Find the amplitude and period of the graph of the function.
4. 5. 6.
7. y 3 sin 8. y 4 sin 2x
9.
1
y 8 sin x
y cos 4x
3 x
π
8
Graph the function.
10. 11. 12. 13.
14. 15. 16. 17. y 1
y y 3 sin 2x
y 2 tan 6x
1
2 cos 4x
1
y 3 cos y 2 tan 8x
3 sin x
1
2x 1
y sin 3
1
y 2 cos x
x
Write an equation of the form y a sin bx, where a > 0 and
b > 0, with the given amplitude and period.
18. Amplitude: 6
Period: 10
2
19. Amplitude:
3
20. Amplitude: 5
Period: Period:
8
21. Pendulum Motion The motion of a pendulum can be modeled by
y A cos 32t
L ,
where y is the directed length (in feet) of the arc, A is
the length (in feet) of the arc from which the pendulum is released, L is
the length (in feet) of the pendulum, and t is the time in seconds. How
many seconds does it take a 2 foot pendulum that is released with an
initial arc of 4 inches to swing through one complete cycle?
L
A
x
2 x
2
12
1
8
x
y 1
y
1
10 cos 4x
1
2 cos 2x
y
2
Copyright © McDougal Littell Inc.
All rights reserved.
π
x

Answer Key
Practice A
1. shift up 5 units 2. reflect in x-axis, shift left
units 3. shift right shift down 4 units
4
4. B 5. A 6. C
7. y
8. y
units,
9. y
10.
11. y 12.
13.
15.
16. July, January
Temperature
T
80
70
60
50
40
30
20
10
1
1
π
2
1
π
π
4
y 5 3 sin 1
2 x
14.
y 1 3 tan 4x
0
0 1 2 3 4 5 6 7 8 9 10 11
Month
x
x
x
t
1
1
y
π
2
π
2
1
y 2 cos x
2
y
π
2
x
x
x

Lesson 14.2
LESSON
14.2
Practice A
For use with pages 840–847
26 Algebra 2
Chapter 14 Resource Book
NAME _________________________________________________________ DATE ___________
Describe how the graph of y sin x
or y cos x can be
transformed to produce the graph of the given function.
1. y 5 sin x
2. y cosx
3.
Match the function with its graph.
4. y 2 sin2x
5. y 2 sinx
6. y 2 sinx
A. y
B. y
C.
1
π
2
Graph the function.
x
7. 8. y 4
9. y 3 sinx 2
10. y 2 2 cosx
11. y 3 tan x
12. y 3 tanx
1
y cosx
2 cos x
Write an equation of the graph described.
13. The graph of y 3 sin translated down 5 units
14. The graph of y cos x translated up 2 units and left units
1
2x 15. The graph of y 3 tan 4x translated down 1 unit and right units, and
2
then reflected in the line y 1
16. Average Temperature A model for the average daily temperature, T
(degrees Fahrenheit), in Kansas City, Missouri, is given by
T 54 25.2 sin ,
where t 0 represents January 1, t 1 represents February 1, and so on.
Sketch the graph of this function. Which month has the highest average
temperature? The lowest average temperature?
2
t 4.3 12
1
π
4
x
y 4 cosx 4
2
y
π
2
Copyright © McDougal Littell Inc.
All rights reserved.
x

Answer Key
Practice B
1. reflect in x-axis, shift left units
4
2. shift left shift up 2 units
2 units,
3. shift right shift down 2 units
4. y
5.
1
6. y
7.
1
8. y
9.
1
10. y
11.
1
12. y
13. y 8 3 tan 2x
1
π
2
2π
π
2
1
π
units,
x
x
x
x
x
1
1
y
y
π
2
π
2
1
y
1
y
π
4
1
x
x
x
x
6
14.
15.
16. Minimum of 1 at
Maximum of 5 at
17. y 3 sin 1
3 x
x
y 6 sin
x 0,
3
,
2 2
1
y 5
x
2 1
cos 6x
2

LESSON
14.2
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice B
For use with pages 840–847
Describe how the graph of y sin x or y cos x can be
transformed to produce the graph of the given function.
Graph the function.
4.
1
y sinx
2
5. y tan 2x
6.
7. y 2 cosx 8. y 3 sin x
9. y 1 3 tan x
10. 11. y 12. y 2 cosx
1
1
y 1 sin x
cosx
4 2
Write an equation of the graph described.
13. The graph of translated up 8 units and then reflected in the
line
14. The graph of translated down 5 units and right unit
15. The graph of y 6 sin translated left units and reflected in the x-axis
1
y
6
1
y 3 tan 2x
y 8
cos 6x
2
16. Minimum and Maximum Values What are the minimum and maximum
values of y 3 2 cos 2x? Write two x-values at which the minimum
occurs. Write two x-values at which the maximum occurs.
17. Write an equation of the graph below.
1
y
π
4
1. y cosx 2. y 2 sinx 3. y 2 cosx
2
2
2 x
x
2
y 1 cos 1
4 x
Algebra 2 27
Chapter 14 Resource Book
Lesson 14.2

Answer Key
Practice C
1. shift left shift up 4 units 2. reflect
in x-axis, shift right units 3. reflect in x-axis,
2
shift left shift down 1 unit
4
4. y
5. y
units,
6. y
7.
8. y
9.
10. y
11.
12.
1
1
1
1
π
π
8
π
2
π
2
y
1
units,
13.
14.
15. y 1 1
cos 3x
4 3
π
2
x
x
x
x
x
1
1
2
y
y
π
2
π
4
4π
1
y
y 2 tan
y 10 3 sin 2x
1
x
3
1
x
x
x
x
16. Brightest: 25th, 65th; Dimmest: 5th, 45th
Brightness
17.
Distance from
top (feet)
y
16
12
8
4
0
0 10203040506070
d 375 tan 230;
d
250
200
150
100
50
0
0
Time (days)
5 101520253035θ
Angle (degrees)
t

Lesson 14.2
LESSON
14.2
Practice C
For use with pages 840–847
28 Algebra 2
Chapter 14 Resource Book
NAME _________________________________________________________ DATE ___________
Describe how the graph of y sin x or y cos x can be
transformed to produce the graph of the given function.
1. y 4 sinx
2. y cosx 3.
Graph the function.
4. y 4 sin 5. y cosx 6. y 2 cos 4x
1
2 x
7. y 3 sin 2x
8. y 1 sinx
9.
10. 11. y tan 12. y 2 tan x
1
2 x
y tanx
Write an equation of the graph described.
13. The graph of translated right units and reflected in
the x-axis
14. The graph of translated down 10 units and reflected in the
line
15. The graph of y translated up 1 unit, left units, and then
3
reflected in the line y 1
1
y 2 tan
y 3 sin 2x
y 10
cos 3x
4 1
3x 16. Stars Suppose that the brightness of a distant star is given by
y 10.5 5.2 cos ,
where t is given in days. Sketch the graph for 0 ≤ t ≤ 80. Which day(s) is
the brightness the greatest? Which day(s) is the brightness the least?
17. Mountain Climbing You are standing 375 feet from the base of a
230 foot cliff. Your friend is rappelling down the cliff. Write and graph a
model for your friend’s distance d from the top as a function of her angle
of elevation .
t
40 20
You
θ
2
375 ft
230 ft
2
2
y 1 sinx 4
y 4 cos 1
4 x
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice A
1.
cot 3
csc 4
5
sin
4,
4
5, tan 4
3, sec 5
2.
csc 2, cot 1
3.
4.
5.
6. sin 8
17, cos 15
17, tan 8
csc
15,
17
sec 15
17
sin
8 ,
15
17, cos 8
17, tan 15
cot
8 ,
3
csc 4
5
cos
4,
3
5, sin 4
5, tan 4
cot
3,
4
csc 3
5
sin
3,
3
5, cos 4
5, sec 5
4,
sec 17
15 ,
7. cos x 8. sec x 9. cot x 10.
11. sec 12. sin x
2 tan x
x
13.
tan x cot x
14.
15.
16. sin2 x sin4 x sin2 x 1 sin2 1 sin x1 sin x 1 sin
x
2 x cos2 cos x
cos x cot x cos x
sin x
1 sin x1 sin x
x
1 cos 2 xcos 2 x cos 2 x cos 4 x
17.
1 sin2 x sin2 cos x
2 x sin2
x
1
sec2 x tan2 x
sec2 1 tan
x
2 x
1 tan2 x 1 tan2 x
sec2 x
1 2 sin 2 x
18.
cos 1
, tan 1, sec 2,
2
1 1
cot x tan x
tan x cos x
1
sin x sin x 1 sin2 x
sin x cos2 x
sin x
cos
2 x cos x tan
2
sin x cos x cot x sin x cos x
sin2 x cos 2 x
sin x
cot 15
8
1
csc x
sin x
x
3,
cos x
sin x
19.
t
t 0
x 3 2.1 0 2.1
y 0 2.8 4 2.8
5
4
sin 2 t cos 2 t x2
9
1
y
4
1
2
3
x
3
x 3 2.1 0 2.1
y 0 2.8 4 2.8
2
4
7
4
y2
1,
16
ellipse

LESSON
14.3
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice A
For use with pages 848–854
Find the values of the other five trigonometric functions of
1. cos 2.
3 3
, < < 2
5 2
3
3. tan , 0 < < 4.
4 2
3
5. cot 8 , < < 2
6.
15 2
Simplify the expression.
sin 1
3
, < <
2 2
sec 5
, < <
3 2
csc 17
, < <
8 2
7. cot x sin x
8. cos x sin x tan x
9.
10. 11. 12.
sin2 x tan2 x cos2 sinx
x
cosx
cot
sin
x cos x
2
x 2
cos
x 2
Verify the identity.
13. 14.
15. 16.
17. 18. cos
19. Conic Sections Complete the table of values for the parametric
equations x 3 cos t and y 4 sin t. Then sketch the graph in the
xy-plane. Then use a trigonometric identity to verify that the graph is a
circle, an ellipse, or a hyperbola.
1 tan
x cos x tan x csc x
2 2 2 x
1 tan2 x 1 2 sin2 sin
x
2 x sin4 x cos2 x cos4 1 sin x1 sinx cos x
2 1 1
tan x cot x
tan x cot x
1
sin x cot x cos x
sin x
x
t 0
x
y
4
2
3
4
5
4
3
2
7
4
.
Algebra 2 41
Chapter 14 Resource Book
Lesson 14.3

Answer Key
Practice B
1. cos 8 15
, tan , sec 17
17 8 8 ,
csc 17
15 ,
2. sin 3 4 5
, cos , sec
5 5 4 ,
csc 5
3 ,
3.
csc 2
3 ,
4.
csc 5
2 ,
5. 1 6. csc x 7. tan 8. sin x 9. sin x
2 x
10. csc x 11.
1
csc x
sin x
12.
sec2 x
sec x
13.
14.
cos x csc x tan x cos x csc x cos x tan x
cot 4
3
sin 3
, tan 3, sec 2,
2
cos 1
2
, sin , tan 2,
5 5
tan2 x
sec x sec2 x 1
sec x
tan
x sin x cot x sin x
2
cos x
sin x cos x
sin x
cos x sin x
cos x cot x sin x
sin x cos x
15. sin circle
2 t cos2 t y2 x2
1,
16 16
16. hyperbola
17.
r2 cos2 x R2 r2 R2 r2 1 cos2 r cos x
x
2 1 sec
R rR r
2 t tan2 t x2
9 1 ,
R 2 r 2 sin 2 x
cot 8
15
cot 1
3
cot 1
2
sec x cot x 1 cos x
cos x sin x
1
sec x cos x
sec x
y2

Lesson 14.3
LESSON
14.3
Practice B
For use with pages 848–854
42 Algebra 2
Chapter 14 Resource Book
NAME _________________________________________________________ DATE ___________
Find the values of the other five trigonometric functions of .
1. sin 2.
15 3
, < <
17 2
3. cos 1,
< <
4.
2 2
Simplify the expression.
cos
5. 6. 7.
2 x
sec x cot x sin x
sin x
sin x
sin 3 x cos
8. 9. csc x csc x cos 10.
2 x
2 x cos2 x
Verify the identity.
11. sec x cot x csc x
12.
tan 3
, 0 < <
4 2
sec 5, 3
2
tan 2 x
sec x
sec x cos x
13. tan 14. cos x csc x tan x cot x sin x
x sin x cos x
2
Use a graphing calculator set in parametric mode to graph the
parametric equations. Use a trigonometric identity to determine
whether the graph is a circle, an ellipse, or a hyperbola. (Use a
square viewing window.)
15. 16.
17. Plumbing While drawing the plans for the plumbing of a new house, the
contractor finds it necessary for two water pipes to be joined at right
angles. The expression is used. Show that this
expression can be written as R2 r2 sin2 r cos x
x.
2 x 4 cos t, y 4 sin t
x 3 sec t, y tan t
R rR r
< < 2
1 cos 2 x
cos 2 x
1 sec x
sin x tan x
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice C
1. sin 8
, cos 15,
sec 17
17 17 15 ,
csc 17
8 ,
2. sin 4
4
, cos 3,
tan
5 5 3 ,
sec 5
3 ,
3.
4. cos
csc 2, cot 3 5. 1 6. cos x
3
1
2
, tan , sec
2 3 3 ,
cot 1
csc
6
37
6 ,
7. 8. 9.
10.
11.
2 sec2 x 1 sin2 x sin2 x cos2 2 sec
x
2 x 2 sec2 x sin2 x sin2 x cos2 cos
x
2 sin sec x csc x
x
2 cot x
2 x
2 sec
2 1 1
2 x cos2 x 1 2 cos2 x
cos2 1
x
12.
cot 15
8
cot 3
4
sin 6
, tan 6, sec 37,
37
1 sec x 1 sec x
sin x tan x sin x tan x
1
1
cos x cos x 1
sin x sin x cos x sin x
sin x
cos x
13.
tan
14.
3 x 1
tan x 1 tan x 1tan2 2 3 cos
x tan x 1
tan x 1
2 x sin2 x sin2 x 2 3 cos2 2 3 cos
x
2 x1 cos2 2 cos
x
2 x 3 cos4 cos x 1 1
csc x
sin x cos x 1 sin x
x
tan 2 x tan x 1
15. sin ellipse
2 t cos2 t x2 y2
1,
25 1
16. 1 sec hyperbola
2 t tan2 t x2
16 1 ,
17.
x 3
2 , 1 1 cos2 x
18. x 3
4 , tan2 x 1
y2

LESSON
14.3
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice C
For use with pages 848–854
Find the values of the other five trigonometric functions of .
1. tan 2.
8
, < <
15 2
1
3. cos , 0 < < 4.
37 2
Simplify the expression.
cot x
5. sin 6. 7.
csc x
x sec x
2
csc x csc x sin
8. 9. 10.
2 x
sec
sec x tan x
sin x cot x 2
cos
x 2 2 x
cot2 x
Verify the identity.
11. 12.
2 sec2 x 2 sec2 x sin2 x sin2 x cos2 x 1
13. 2 cos 14.
2 x 3 cos4 x sin2 x 2 3 cos2 x
csc 5 3
, < <
4 2
sin 1
, < <
2 2
1 sec x
csc x
sin x tan x
Use a graphing calculator set in parametric mode to graph the
parametric equations. Use a trigonometric identity to determine
whether the graph is a circle, an ellipse, or a hyperbola. (Use a
square viewing window.)
15. x 5 cos t, y sin t
16. x 4 sec t, y tan t
Counterexamples Show that the equation is not an identity (for all
values of x) by finding a value of x for which the equation is not
true.
17.
18. tan2 sin x 1 cos
x tan x
2 x
sec2
x 1
2
tan 3 x 1
tan x 1 tan2 x tan x 1
Algebra 2 43
Chapter 14 Resource Book
Lesson 14.3

Answer Key
Practice A
1. yes 2. yes 3. yes 4. yes 5. yes 6. yes
7. 2n,2 2n
3 3
8.
n
4 2
9.
10.
6
3 2 4
11. , , , 12.
2 2 3 3
5 7 11
13. , , , 14.
6 6 6 6
3 5 7
15. , , , 16.
4 4 4 4
7
n, 5
6 n
2n, 2n, 3
2 2n
11
17. , , 18.
6 6 2
3
19. 1.46, 4.82 20. 21. 0, ,
22. about 14.0 or about 0.245 radian
2
5
,
6 6
3 2 4
, , ,
2 2 3 3
2
4
,
3 3
2 4 5
, , ,
3 3 3 3
3 5
, , ,
2 2 3 3

LESSON
14.4
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice A
For use with pages 855–861
Verify that the given x-value is a solution of the equation.
1. 3 tan 2.
2 2x 1 0, x 5
12
5. 2 cos 6.
2 x 1 0, x 5
4
Find the general solution of the equation.
7. 8.
9. 10. sin2 3 sec x sin x 0
2 2 sin
x 4 0
2 3 csc x 2 0
x 1 0
Solve the equation in the interval
11. 12.
13. 14.
15. 16.
17. 18. 2 cos x 4 cos
19. Use a graphing calculator to approximate the solutions of 9 cos x 2 3
in the interval 0 ≤ x < 2. Round your answer to two decimal places.
20. Find the x-intercept(s) of the graph of y 3 sin x 3 in the interval
0 ≤ x < 2.
2 2 cos x 0
2 4 cos
x sin x 1 0
2 1 2 sin x 1
2 2 sin
x 0
2 2 sec x 5 cos x 1 0
2 x tan2 2 sin
x 3 0
2 2 cos x 2 cos x
2 x cos x
21. Find the points of intersection of the graphs of the given functions in the
interval 0 ≤ x < 2.
y sin x 1
y 2 sin 2 x 1
0 ≤ x < 2.
22. Kite Find the angle in the kite shown at the right
by solving the equation cot 16 tan .
2 sin 2 x sin x 1 0, x
2
3. 4. 2 sin2 sec x sin x 0, x 0
4 x 4 sec2 x 0, x 5
3
sec 2 x 2 tan x 4, x 7
4
1 ft
θ
4 ft
θ
Algebra 2 55
Chapter 14 Resource Book
Lesson 14.4

Answer Key
Practice B
7
1. 2n, 2n
2.
4 4
3.
6
4. 5.
6. 7. 8.
9. 10. 0, ,
0, ,
11
,
6 6
5
,
3 3
5
,
4 4
5 7 11
, , ,
6 6 6 6
5
2n, 2n
6 6
5 7 11
, , ,
6 6 6 6
3 5 7
, , ,
4 4 4 4
3
3 3
11. , , , 12.
2 2 4 4
13. 0.26, 1.31, 1.83, 2.88 14.
2n, 11
6 2n
2n
7
5 7 11
, , ,
6 6 6 6
15. 16. 5 3 7 11
, , , ,
3 3 2 2 6 6
3 5
, , ,
2 2 3 3

Lesson 14.4
LESSON
14.4
Practice B
For use with pages 855–861
56 Algebra 2
Chapter 14 Resource Book
NAME _________________________________________________________ DATE ___________
Find the general solution of the equation.
1. 2 cos x 1 0
2. 7 sec x 7 0
3. 5 cos x 3 3 cos x
4. csc x 2 0
Solve the equation in the interval
0 ≤ x < 2.
5. 6.
7. 8.
9. 10.
11. 12.
13. Use a graphing calculator to approximate the solutions of in
the interval Round your answer to two decimal places.
14. Find the x-intercept(s) of the graph of y 2 cos x 4 cos in the
interval 0 ≤ x < 2.
15. Find the points of intersection of the graphs of the given functions in the
interval 0 ≤ x < 2.
y sin x tan x
y 2 cos x
16. In calculus, it can be shown that the function y 2 sin x cos 2x has
minimum and maximum values when 2 cos x 4 cos x sin x 0. Find all
solutions of 2 cos x 4 cos x sin x 0 in the interval 0 ≤ x < 2. Verify
your solutions with a graphing calculator.
2 3 tan
0 ≤ x < .
x
2 3 sec
2x 1
2 3 tan
2 cos x sin x cos x 0
x 4 0
3 2 sin
2 csc x 17 15 csc x
sec x csc x 2 csc x 0
2 csc x 2 cos x csc x 3 csc x
x tan x 0
4 x sin2 2 cot x 0
4 x cot2 x 15 0
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice C
5
1. 2n, 2n
2.
3 3
5
3. 2n, 2n 4.
6 6
5.
3
6. 7.
8. 9. 0, ,
10.
5 7 11
, , ,
6 6 6 6
11.
5 3
, ,
6 6 2
5 3
2n, 2n, 2n
6 6 2
5
, ,
3 3
11
,
6 6
5 3
12. , , 13. 1.25, 2.36, 4.39, 5.50
6 6 2
2n, 2
3
2n, 4
3
2 4 5 5 7 11
14. , , , 15. , , ,
3 3 3 3 6 6 6 6
16. High tides of 8 feet at 6:00 A.M. and 6:00 P.M.,
low tides of 2 feet at 12:00 A.M. and 12:00 P.M.
6
n, 5
6 n
n
4
2n, 5
3 2n
2
,
3 3

LESSON
14.4
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice C
For use with pages 855–861
Find the general solution of the equation.
1. 2.
3. 4.
5. 6. csc2 4 sin x csc x 2 0
2 3 tan
3 sin x sin x 1
3 2 cot x 1 0
x 3 0
2 cos x 1 cos x
x 1 0
Solve the equation in the interval
7. 8.
9. 10.
11. 12.
13. Use a graphing calculator to approximate the solutions of
in the interval Round your answer to
two decimal places.
14. Find the x-intercept(s) of the graph of y sec4 x 4 sec2 sec 0 ≤ x < 2.
x.
2 sin x 2 cos
x 2 tan x 4
2 2 sin x 1 0
2 cot
x sin x 1
2 2 sin
3 sin x sec x 23 sin x 0
x 1 2
2 3 tan x 3 tan x csc x 3 tan x
x cos x 1 0
15. Find the points of intersection of the graphs of the given functions in the
interval 0 ≤ x < 2.
y 2 sec 2 x
y 3 tan 2 x
0 ≤ x < 2.
16. High Tide The depth of the Atlantic Ocean at a channel buoy off the
coast of Maine can be modeled by y 5 3 cos where y is the
water depth in feet and t is the time in hours. Consider a day in which
t 0 represents 12:00 midnight. For that day, when do the high and low
tides occur?
6 t
Algebra 2 57
Chapter 14 Resource Book
Lesson 14.4

Answer Key
Practice A
1. 2.
3. 4.
5. 6.
7. 8.
9. 10.
11. y 2 cos 12. y sin 3x
13. C
x
y 4 cos
y sin 2x 1 y 3 cos x 2
y 3 cos 4x y 5 sin 2x
y 2 sin 3x y 4 cos x
4
2 1
2x y 5 sin 4x
y 3 cos 2x
y 2 sin x

Lesson 14.5
LESSON
14.5
Practice A
For use with pages 862–868
68 Algebra 2
Chapter 14 Resource Book
NAME _________________________________________________________ DATE ___________
Write a function for the sinusoid.
1. y
2. y
3.
π
, 5
(0, 3)
4. y
5. y
6.
π
(2 π,
4)
, 2
4
Write a trigonometric function for the sinusoid with maximum at A
and minimum at B.
3
7. A0, 3, B 8. , 5 , B , 5
9.
4 4
, 3 4
10. A1, 4, B0, 4
11. A0, 2, B2, 6
12.
13. Blood Pressure Which of the following equations
represents the graph of a person’s blood pressure
shown at the right?
A.
B.
C.
2
2
( 8 )
π
8
2π
(0, 4)
P 120 40 sin 2t 2
P 100 20 cos 2t 2
P 100 20 sin
2t 2
D. P 120 20 sin t 2
x
x
3π
( , 5
8 )
1
1
A
π
4
π
2
( )
π
( , 3
2 )
3π
( , 0
4 )
Blood pressure
x
x
P
140
120
100
80
60
40
20
0
0 1 2 3 4 5 6 7
Time (seconds)
2
1
y
y
1
2
(0, 1)
1
A
A
, 1 , B 2 6
, 2 , B 2 6
t
1
( 2,
2)
3
( 2,
2)
(1, 5)
, 2
, 1
Copyright © McDougal Littell Inc.
All rights reserved.
x
x

Answer Key
Practice B
1. 2.
3. 4.
5. 6.
7. 8.
9. 10.
11. 12. y 3 cos
13. h 2 cos 4t 8
1
2x y y sin 2x 1
y 10 sin x 5
1
y 2 cos y 3 sin 2x 3
y cos x 2 y 4 cos 3x
2 cos x
1
y 3 sin
y 2 cos 4x y 5 sin x
3x 1
1
2x y 4 cos 2x

LESSON
14.5
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice B
For use with pages 862–868
Write a function for the sinusoid.
1. y
(0, 4)
2. y ( π,
3)
3.
2
4. y
5. y
6.
3π
6 ( , 5
2 )
4 (0, 3)
ππ
2
π
2
π
( , 4
2 )
π
( , 5
2 )
x
x
Write a trigonometric function for the sinusoid with maximum at A
and minimum at B.
A
x
(3 π,
1)
7. 8. 9.
10. A 11. A0.5, 5, B1.5, 15 12.
13. Number Wheel Your lucky number appears at the very bottom
of a vertical number wheel with a radius of 2 feet. The wheel is
positioned 6 feet above the ground and is rotating at a rate of 120
revolutions per minute. Write a model for the height h (in feet) of
your lucky number as a function of time t (in seconds).
Your
lucky
number
1
A0, 1, B1, 3
, 4 , B0, 4
3
3
, 2 , B , 0
4 4
1
π
π
x
(3 π,
3)
1 A0, , 2 B, 1 2
A0, 3, B2, 3
7
1
2
2 ft
6 ft
y
y
1
( , 2
4 )
1
( , 0
4 )
1
4
3
( , 6
4 )
Algebra 2 69
Chapter 14 Resource Book
1
4
(0, 2)
x
x
Lesson 14.5

Answer Key
Practice C
1. 2.
3. 4.
5. 6.
7. 8.
9. 10.
11. 12. y
13. h 9 cos 2t 13
3
y 3 sin
y 5 sin x
3
2 sin 2x 2
1
2x y sin
y 4 cos 2x y 2 cos 4x
1
y 2 cos 3x 1
x
y
y 2 cos 2x 1
3
2 1
y 6 sin y 3 cos 2x
y 5 cos 3x
2 sin x 2
1
4x

Lesson 14.5
LESSON
14.5
Practice C
For use with pages 862–868
70 Algebra 2
Chapter 14 Resource Book
NAME _________________________________________________________ DATE ___________
Write a function for the sinusoid.
1. y
2. y
3.
(2 π,
6)
(0, 3)
2
4. y
5. y
6.
1
,
2
(0, 1)
1
2π
5
( 2 2)
1
3 3
( ,
2 2)
x
(6 π,
6)
x
Write a trigonometric function for the sinusoid with maximum at A
and minimum at B.
7. 8. 9.
10. 11. A 12.
13. Bicycle Pedaling On a bicycle, your right foot is on the lowest pedal,
which is 4 inches above the ground. The diameter of the circular pedaling
motion is 18 inches, and the rate is 60 revolutions per minute. Write a
model for the height h (in inches) of your left foot as a function of the
time t (in seconds).
3
A
A, 3, B3, 3
, 5 , B , 5
2 2 1
A0, 4, B , 4
, 2 , B0, 2
2 4
1
π
2
1
2
π
( , 3
2 )
1
( , 3
2 )
x
x
A0, 3, B3, 1
A 1
4
2
1
y
y
1
π
3
(0, 5)
(1, 2)
, 0 , B 3
π
( , 5
3 )
(3, 4)
, 3 4
Copyright © McDougal Littell Inc.
All rights reserved.
x
x
Lesson 13.1

Lesson 14.6
LESSON
14.6
Practice A
For use with pages 869–874
82 Algebra 2
Chapter 14 Resource Book
NAME _________________________________________________________ DATE ___________
Find the exact value of the expression.
1. 2. 3.
4. 5. 6. tan 5
sin
12
7
cos
12
11
sin 165
cos 345
tan 255
12
Evaluate the expression given with and
with 0 < v <
2 .
3
sin u 3 < u < 2
5 2
7
cos v
25
7. sin u v
8. cos u v
9. tan u v
10. sin u v
11. cos u v
12. tan u v
Simplify the expression. Do not evaluate it.
13.
sin x 14.
cos x 15. tan x
2
16. sin 40 cos 32 cos 40 sin 32
17.
tan 135 tan 40
18. 19.
1 tan 135 tan 40
sin 5
3
cos
3
tan 135 tan 41
1 tan 135 tan 41
Solve the equation for
20. 21.
22. sin x sin x 2
23. tan x cos x 0 2
24. Show that sin x y z
sin x cos y cos z sin y cos x cos z sin z cos x cos y sin x sin y sin z.
(Hint: Write x y z x y z.
sin
x 3 sin 0 ≤ x < 2.
x 1 3
cos x 4 cos
x 1 4
25. Use the result from Exercise 24 to find using 31 3 2 7
12 4 3 6 .
31
sin
12
2
5
cos sin
3 3
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice B
1. 2. 3.
4. 5. 6.
7. 8. 9. 10. 11.
12.
13
84 13. sin x 14.
tan x 1
tan x 1
15. sin x
84
85
13
77
36
85
36
85
77
2 6
4
2 6
4
3 2
2 3 2 6
2 6
4
85
16. 17. cos 18. tan 36
7
sin 70
12
7 5
19. tan 20. , 21. , 22. 0,
4 4 3 3
23
12
3
23. 24. cos u v cos u v
2
cos u cos v sin u sin v cos u cos v
sin u sin v 2 cos u cos v
25. sin u v sin u v sin u cos v
cos u sin v sin u cos v cos u sin v
2 sin u cos v 26. sin u v sin u v
sin u cos v cos u sin vsin u cos v
cos u sin v sin 2 u cos 2 v
sin u cos u sin v cos v sin u cos u sin v cos v
sin2 u sin2 u sin2 v sin2 v sin2 u sin2 sin
v
2 u 1 sin2 v sin2 v 1 sin2 cos
u
2 u sin2 v sin2 u cos2 v cos2 u sin2 v
sin
27. cos u v cos u v
cos u cos v sin u sin vcos u cos v
2 u sin2 v
cos2 u cos2 u sin2 v sin2 v cos2 u sin2 cos
v
2 u 1 sin2 v sin2 v 1 cos2 sin u sin v cos
u
2 u cos2 v sin2 u sin2 v
cos 2 u sin 2 v
5

LESSON
14.6
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice B
For use with pages 869–874
Find the exact value of the expression.
1. 2. 3.
4. 5. 6. sin 13
sec
12
19
tan
12
cos 105
sin 195
tan 165
12
Evaluate the expression given
with
2
with and
7. sin u v
8. cos u v
9. tan u v
10. sin u v
11. cos u v
12. tan u v
.
8
tan v
15
0 < x <
cos u
2
4
5
Simplify the expression. Do not evaluate it.
13. sin x 2
14.
tan x 15.
16. sin 20 cos 50 cos 20 sin 50
17.
tan 78 tan 42
18. 19.
1 tan 78 tan 42
Solve the equation for
20. 21.
sin x 6
22. tan x cos x 0
23. sin x sin x 2
sin
cos x 4
1
x 6 2
cos
x 1 4
Verify the identity.
< x < 3
0 ≤ x < 2.
2
24.
25.
26.
27. cos u v cos u v cos2 u sin2 sin u v sin u v sin
v
2 u sin2 cos u v cos u v 2 cos u cos v
sin u v sin u v 2 sin u cos v
v
4
cos
4
cos
3
tan 5
tan
3 4
1 tan 5
tan
3 4
3
cos x
2
sin sin
4 3
Algebra 2 83
Chapter 14 Resource Book
Lesson 14.6

Answer Key
Practice C
1. 2.
6 2
4
3. 6 2
2
2
4. 2 3 5. 2 6
6.
11. 12.
7.
13.
8. 9.
14.
10.
15. 16. 17. sin 1.8
18. 19. tan 20. 0,
3
cos
tan 20
8
5
117
44 sin x sin x
tan x 1
1 tan x
42
44
2 6
125
5 5 4
21. 22. 23.
24. 3 1
2 2 cot 5
,
3 3
0,
1
2
3
4
5
3
7
,
4 4
117
125

Lesson 14.6
LESSON
14.6
Practice C
For use with pages 869–874
84 Algebra 2
Chapter 14 Resource Book
NAME _________________________________________________________ DATE ___________
Find the exact value of the expression.
1. 2. 3.
4. 5. sec
6. csc 12
7
cot
12
11
sin 225
cos 375
sec 195
12
Evaluate the expression given with and
with < x < 3
2 .
< u <
7
cot v
24
csc u
2
5
3
7. sin u v
8. cos u v
9. tan u v
10. sin u v
11. cos u v
12. tan u v
Simplify the expression. Do not evaluate it.
13. sin x
3
14. cos x
2
15.
16. cos 17. sin 4.5 cos 2.7 cos 4.5 sin 2.7
2 2
cos sin sin
6 7 6 7
tan 60 tan 40
18. 19.
1 tan 60 tan 40
Solve the equation for
20. 21.
22.
23. sin x 4
24. Index of Refraction The index of refraction n of a
transparent material is the ratio of the speed of light in a
vacuum to the speed of light in the material. Triangular
prisms are often used to measure the index of refraction
1 sin
0 ≤ x < 2.
sin x sin x 0
cos x 2 1 cos x 2
tan x cos x 0 2 x 4
air
θ2 using the formula n
. For the prism at the
right, Write the index of refraction as a function
of cot 1
2 .
2 60.
2
sin 1 2 2 sin 1
2
tan
tan
4 8
1 tan
tan
4 8
light
prism
tan x 4
θ 1
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice A
2 3 2 2
1. 2. 3. 2 1
2
2
4. 5. 6.
7.
8.
9.
10.
11.
12. 13.
14.
15. cos 6x cos 23x cos2 3x sin2 1 sin x 2 sin
sin 10x sin 25x 2 sin 5x cos 5x
3x
2 4 sin x cos
2 cos x sec x
x
3 x 4 sin3 tan 2x x cos x
42
sin 2x
7
42
, cos 2x 7
9 9 ,
sin 2x 24
sin
, cos 2x 7 , tan 2x 24
25 25 7
u
sin
72 u 2 u
, cos , tan 7
2 10 2 10 2 u 10 u
, cos
2 10 2 310
u
, tan
10 2 1
2 6
4
2 3
2 2
2
3
16.
4 sin x x x x
cos 22 sin cos
2 2 2
2 sin 2 x
2
17. sin 3x sin 2x x
sin 2x cos x cos 2x sin x
2 sin x cos x cos x 1 2 sin 2 x sin x
2 sin x 1 sin2 x sin x 2 sin3 2 sin x cos
x
2 x sin x 2 sin3 x
3 sin x 4 sin3 x sin x 3 4 sin2 2 sin x 2 sin
x
3 x sin x 2 sin3 x
7 11
18. , , 19.
2 6 6
2 sin x
20. 0, 21. 300 ft; 36.9
3 5
, ,
4 4
5
, ,
3 3
2

Lesson 14.7
LESSON
14.7
Practice A
For use with pages 875–882
94 Algebra 2
Chapter 14 Resource Book
NAME _________________________________________________________ DATE ___________
Find the exact value of the expression.
1. 2. 3.
4. 5. 6. sin
tan
8
cos
12
7
sin 15
cos 22.5
tan 112.5
12
Find the exact values of sin
7.
4 3
cos u , < u < 2
5 2
8.
u u u
, cos , and tan
2 2 2 .
Find the exact values of sin 2x, cos 2x, and tan 2x.
9.
4
sin x , 0 < x <
5 2
10.
Rewrite the expression without double angles or half angles, given
that 0 < x < Then simplify the expression.
cos 2x
11. sin 4x
12. 13. cos 2x sin x
cos x
2 .
Verify the identity.
14. 15.
16. 17. sin 3x sin x 3 4 sin2 4 sin x
x
cos
x
cos 2 sin x
2 2 2 3x sin2 sin 10x 2 sin 5x cos 5x
3x cos 6x
Solve the equation for 0 ≤ x < 2.
18. cos 2x sin x
19. cos 2x cos x 0
20. sin 2x 2 sin x 0
21. Baseball A hit baseball leaves the bat at an angle of with the
horizontal, with a velocity of feet per second, and is caught by
an outfielder. If first find the distance the ball was hit and
then check your answer by finding Remember that r
where r is the horizontal distance traveled.
1
32 v0 2 v0 100
sin 0.60,
.
sin 2,
sin u 7
, < u <
25 2
cos x 1
, < x <
3 2
Copyright © McDougal Littell Inc.
All rights reserved.

Answer Key
Practice B
1. 2. 3.
4.
5.
6.
7. sin 2x
8. csc x sec x 9. cos x
24
sin 2x
24
, cos 2x 7 , tan 2x
25 25 7
24
sin
, cos 2x 7 , tan 2x 24
25 25 7
u 26 u
, cos
2 26 2 526
u
, tan
26 2 1
sin
5
u 310 u
, cos
2 10 2 10
u
, tan
10 2 3
2 1
2 2
2
2 2
2
10.
11. cos 4x cos 22x 2 cos2 2 cos
2x 1
2 x cos x 1
2cos 2xcos 2x 1
22 cos 2 x 12 cos 2 x 1 1
8 cos 4 x 8 cos 2 x 1
12.
2 sin 2 x
13.
sin 2 x 2 sin x cos x cos 2 x
1 2 sin x cos x 1 sin 2x
14. cos 3x cos x 2x
cos x cos 2x sin x sin 2x
2 cos3 x cos x 2 cos x 2 cos3 2 cos
x
3 x cos x 2 cos x 1 cos2 cos x 2 cos
x
2 x 1 2 sin2 x cos x
4 cos 3 x 3 cos x
5 7 11
15. , , , 16.
6 6 6 6
17.
4 sin x x x x
cos 22 sin cos
2 2 2
sin x cos x 2
2
2 sin x
3 5 3 7
, , , , ,
4 2 4 4 2 4
2
0, 2 4
,
3 3
18. 0, 3, 2
, 3
3 2 , , 1, 4
, 3
3
2

LESSON
14.7
Copyright © McDougal Littell Inc.
All rights reserved.
NAME _________________________________________________________ DATE ___________
Practice B
For use with pages 875–882
Find the exact value of the expression.
1. 2. sin 3.
5
tan 67.5
8
Find the exact values of sin u u u
, cos , and tan
2 2 2 .
3 3
4. tan u , < u < 5.
4 2
Find the exact values of
3
6. cos x , 0 < x < 7.
5 2
Rewrite the expression without double angles or half angles, given
that 0 < x < Then simplify the expression.
sin 2x
8. 2 csc 2x
9. 10. cos 2x cos x
2 sin x
2 .
Verify the identity.
sin 2x, cos 2x, and tan 2x.
11. 12.
cos 4x 8 cos4 x cos2 x 1
sin u 5 3
, < u < 2
13 2
sin x 4 3
, < x < 2
5 2
4 sin x x
cos 2 sin x
2 2
13. 14. cos 3x 4 cos3 sin x cos x x 3 cos x
2 1 sin 2x
Solve the equation for 0 ≤ x < 2.
15. sec 2x 2
16. cos 2x cos x
17. sin 2x sin x cos x
18. A graph of y cos 2x 2 cos x in the interval 0 ≤ x < 2
is shown in the figure. In calculus, it can be shown that the
function y cos 2x 2 cos x has turning points when
sin 2x sin x 0. Find the coordinates of these turning points.
y
1
cos 3
8
π
Algebra 2 95
Chapter 14 Resource Book
x
Lesson 14.7

Answer Key
Practice C
1. 3 2
2.
2 2
2
3.
4. ,
,
5.
50 5 19
sin ,
10
u
2
tan u
cos
50 10 5 5 1
10 2 2
u
2
50 10 5
sin
10
u
2
cos u
2
6.
7.
8. 9.
2
1 tan2 1 2 sin
x
2 x 4 sin4 sin 2x
x
24 7 24
, cos 2x , tan 2x
25 25 7
10. 11. cos x sin x2 1
2 cos x 1
cos 2 x 2 cos x sin x sin 2 x
1 2 sin x cos x 1 sin 2x
12.
cos 1 cos 2x
2 x sin2 xcos2 x sin2 x
cos 2x
13.
14.
2 cos2 6x sin2 6x cos2 cos 12x cos 26x 2 cos
6x
2 6x 1
cos 2 6x sin 2 6x
15. 0, , 16. 0,
7 11
,
6 6
17.
sin 2x 42
, cos 2x 7
9 9 ,
cos 4 x sin 4 x
2 cot x
cot 2 x 1
2 cos x sin x
cos2 x sin2 sin 2x
tan 2x
x cos 2x
50 5 19
10
cos x
2
sin x
5 7 3 11
, , , , ,
6 2 6 6 2 6
18. A 1
2 a2 sin ; 25 in. 2
,
cos2 x
sin2 1
x
2 3
2
tan u 19 10
2 9
tan 2x 42
7

Lesson 14.7
LESSON
14.7
Practice C
For use with pages 875–882
96 Algebra 2
Chapter 14 Resource Book
NAME _________________________________________________________ DATE ___________
Find the exact value of the expression.
1. 2. sin 3.
7
tan 15
8
Find the exact values of sin u u u
, cos , and tan
2 2 2 .
4. tan u 2, 0 < u < 5.
2
Find the exact values of
6. sec x 3, 7.
< x <
2
Rewrite the expression without double angles or half angles, given
that 0 < x < Then simplify the expression.
π
2 .
8. cos 2x 4 sin 9. cot x tan 2x
10.
4 x
Verify the identity.
11. 12.
13. 14. cos2 6x sin2 2 cot x
cot
6x cos 12x
2 cos
tan 2x
x 1 4 x sin4 cos x sin x x cos 2x
2 1 sin 2x
Solve the equation for 0 ≤ x < 2π.
15. cos 2x sin x 1
16. 2 tan x tan 2x
17. cot x tan 2x
18. Geometry An isosceles triangle has two equal sides of length a, and the
angle between them is , as shown in the figure below. Write the area A of
the triangle in terms of a and . Then find the area of the triangle when
a 10 inches and
30.
θ
θ
2
a a a a
sin 2x, cos 2x, and tan 2x.
cos
12
sin u 9 3
, < u < 2
10 2
cot x 4 3
, < x <
3 2
1 2 cos x
cos 2x
Copyright © McDougal Littell Inc.
All rights reserved.