Algebra 2 Semester 2 Practice Final Summer 13

Name: ________________________ Period: ___________________ Date: __________
ID: A
Algebra II Semester 2 Practice Final Exam (Chapters 6-10)
1. Add or subtract. Simplify if possible.
q 2 − 2q − 35
q 2 + 2q − 15 − 1
q − 3
2. Write a polynomial function in standard form with
zeros at –4, 2, and –5.
3. Simplify.
− 10 + 2 4 − 3 10
4. Multiply.
Ê ˆ Ê ˆ
−2 − 10
Ë
Á
¯
˜ −3 + 10
Ë
Á
¯
˜
5. Rationalize the denominator of the expression.
7 − 3
7 + 3
6. Write an exponential function y = ab x for a graph
that includes (1, 17.5) and (–1, 2.8).
7. Write 2x 3 + 2x 2 – 40x in factored form.
8. For the function f(x) = (5 − 6x) 2 , find f −1 .
9. Solve. Check for extraneous solutions.
6x = 24 − 12x
10. Find the product ( 5x − 3)(x 3 − 5x + 2).
11. Factor the expression.
x 3 − 27
12. Solve the equation. Check the solution.
5
3k + 1 k =−3
13. Find the center and radius of the circle with
equation ( x + 8) 2 + Ê
Ë
Á y − 8ˆ¯˜ 2
= 16.
14. Solve the equation.
x − 9 − 10 =−5
15. Solve log(3x + 11) = 2.
16. Divide using synthetic division.
(x 4 − 18x 3 + 44x 2 + 55x − 28) ÷ (x − 4)
17. Solve the equation. Check the solution.
d + 7
d − 4 = d − 5
d + 2
18. Divide 4x 3 + 2x 2 − 2x + 3 by x + 3.
3
19. Simplify 48a 13 b 12
positive.
. Assume that all variables are
20. Use the Change of Base Formula to evaluate
log 4
62. Then convert log 4
62 to a logarithm in base
2. Round to the nearest thousandth.
21. Is the relationship between the variables in the table
a direct variation, an inverse variation, or neither?
If it is a direct or inverse variation, write a function
to model it.
x 0 1 2 3
y 0 9
9
2
3
22. Expand the logarithmic expression.
log 8
3d 2
23. Let f(x) = 4x + 6 and g(x) = 2x + 7. Find
(f û g)(5).
24. Rationalize the denominator of the expression.
3
4
3
7
25. In how many different orders can you line up 6
cards on a shelf?
1

ID: A
26. Write an equation for the translation of y = −7
x
that has the asymptotes x = –2 and y = –7.
27. The values (5.1, 10) and (x, 3) are from an inverse
variation. Find the missing value and round to the
nearest hundredth.
28. Solve 27x 3 + 343 = 0. Find all complex roots.
29. Zach wrote the formula w(w – 1)(2w + 3) for the
volume of a rectangular prism he is designing, with
width w, which is always has a positive value
greater than 1. Find the product and then classify
this polynomial by degree and by number of terms.
30. Use synthetic division to find P(–4) for
P(x) = x 4 + 8x 3 + 2x 2 + 5x − 9.
31. Expand the logarithmic expression.
log 4
8k 4
32. Divide using synthetic division.
(x 4 − 12x 3 + 20x 2 + 36x − 45) ÷ (x − 3)
33. Use natural logarithms to solve the equation. Round
to the nearest thousandth.
2e 4x + 11 = 22
34. Solve the equation.
x + 9 − 8 =−4
35. Use natural logarithms to solve the equation. Round
to the nearest thousandth.
8e 4x + 11 = 30
36. Multiply or divide. State any restrictions on the
variables.
x 2
x − 4 ⋅ x 2 + x − 20
x 2 + 4x
37. Write the equation in logarithmic form.
4 2 = 16
38. Find the foci of the ellipse with the equation x 2
9 + y 2
49
= 1. Graph the ellipse.
39. Write an equation in standard form of an ellipse
that has a vertex at (–3, 0), a co-vertex at (0, –5),
and is centered at the origin.
40. Write an equation for the translation of
x 2 + y 2 = 49, 4 units right and 2 units down.
41. Use the Pascal’s Triangle to expand the bionomial
(d + 2b) 3 .
42. Multiply or divide. State any restrictions on the
variables.
t 2
t + 2 ⋅ t2 + t − 2
t 2 − 3t
43. Factor the expression.
x 4 − 25x 2 + 144
44. Divide and simplify.
3
120x 27
3
3x
45. Solve ln(4x − 4) = 8. Round to the nearest
thousandth.
46. Simplify.
1
3
3
⋅ 9
1
3
47. Suppose that y varies jointly with w and x and
inversely with z and y = 160 when w = 5, x = 24
and z = 6. Write the equation that models the
relationship. Then find y when w = 4, x = 10 and z
= 5.
2

ID: A
48. Multiply.
Ê ˆ
−5 − 3
Ë
Á
¯
˜
49. Graph the equation.
16x 2 + 4y 2 = 49
2
50. Use a graphing calculator. Use the graph of y = e x
to evaluate e 1.7 to four decimal places.
51. Simplify the rational expression. State any
restrictions on the variable.
p 2 − 4p − 32
p + 4
52. Write an equation of an ellipse in standard form
with the center at the origin and with the given
characteristics.
vertices at (–5, 0) and co-vertices (0, 4)
53. Find the inverse of y = 7x 2 + 7.
54. Rationalize the denominator of the expression.
Assume that all variables are positive.
7x 9 y 7
2x 3 y 2
56. Suppose that x and y vary inversely, and x = 7 when
y = 11. Write the function that models the inverse
variation.
57. Is the relationship between the variables in the table
a direct variation, an inverse variation, or neither?
If it is a direct or inverse variation, write a function
to model it.
x 6 10 11 15
y 84 140 154 210
58. Describe the combined variation that is modeled by
the formula or equation.
y =
w
2x 2
59. Describe the combined variation that is modeled by
the formula or equation.
a = F m
55. Write the equation in logarithmic form.
6 4 = 1, 296
60. Graph the conic section.
4x 2 − 9y 2 = 144
61. Write an equation of an ellipse with center (3, –3),
vertical major axis of length 12, and minor axis of
length 6.
62. Write an equation of a hyperbola with vertices (3,
–2) and (–9, –2), and foci (7, –2) and (–13, –2).
63. Sketch the asymptotes and graph the function.
2
y =
x + 2 − 3
3

ID: A
64. Simplify the rational expression. State any
69. Simplify the complex fraction.
restrictions on the variable.
3
q 2 + 11q + 24
4y − 2 y
q 2 − 5q − 24
1
y + 3 2y
65. Solve the equation. Check the solution.
−2
x + 4 = 4
70. Solve the equation. Check the solution.
x + 3
a
a 2 − 36 + 2
a − 6 = 1
a + 6
66. Multiply or divide. State any restrictions on the
variables.
x 2 − 16
x 2 + 5x + 6 ÷ x 2 71. Write an exponential function for the graph.
+ 5x + 4
x 2 − 2x − 8
67. Add or subtract. Simplify if possible.
w 2 + 2w − 24
w 2 + w − 30 + 8
w − 5
68. State the property or properties of logarithms used
to rewrite the expression.
log 20 625x 4 = 1 5 log 5x
72. Graph y = 76 () x + 2 + 1.
73. Evaluate the logarithm.
log 5
1
625
74. Write the equation log 32
8 = 3 5
in exponential form.
Write the expression as a single logarithm.
5log b
q + 2log b
y
78. Write the expression as a single logarithm.
log 3
4 − log 3
2
75. State the property or properties of logarithms used
to rewrite the expression.
log 5
6 − log 5
2 = log 5
3
76. State the property or properties of logarithms used
to rewrite the expression.
2log6 + log 1 3
= log 12
77.
79. Expand the logarithmic expression.
log 7
n
2
80. Expand the logarithmic expression.
57
log b
74
81. Solve 15 2x = 36. Round to the nearest
ten-thousandth.
4

ID: A
82. Use the Change of Base Formula to solve 2 2x = 90.
Round to the nearest ten-thousandth.
83. Write the expression as a single natural logarithm.
3ln3 + 3lnc
84. Find all the real square roots of 0.0004.
85. Find the real-number root.
− 125
3
343
86. Multiply and simplify if possible.
6 ⋅ 2
87. Multiply and simplify if possible.
Ê
ˆ
7x x − 7 7
Ë
Á
¯
˜
88. Divide and simplify.
3
3
162
2
89. Divide and simplify.
90x 18
2x
90. Rationalize the denominator of the expression.
Assume that all variables are positive.
6x 8 y 9
5x 2 y 4
91. Rationalize the denominator of the expression.
Assume that all variables are positive.
3
2 + 3
3
6
92. Add if possible.
4
2 2x
4
+ 6 2x
93. Add if possible.
3
4 3x
3
+ 5 10x
94. Subtract if possible.
4
4
2 5a − 6 5a
95. Simplify.
1
20 2
⋅ 20
1
2
8
96. Write the exponential expression 3x in radical
form.
97. Solve the equation.
2
( x − 7)
3 = 4
98. Solve the equation.
1
1
( −2x + 6)
5 = ( −8 + 10x)
5
99. Let f(x) =−3x − 6 and g(x) = 5x + 2. Find f(x) +
g(x).
100. Let f(x) = x 2 + 2x − 1 and g(x) = 2x − 4. Find
2f(x) – 3g(x).
101. Let f(x) = x 2 + 6 and g(x) = x + 8 . Find
x
Ê
Ë
Á g û f ˆ¯˜ ( −7).
102. Find the inverse of y = 7x 2 − 3.
103. For the function f(x) = x + 9, find (f û f −1 )(5).
104. Let f(x) = 4 + 5x and g(x) = 2x − 1. Find f(g(x))
and g(f(x)).
105. Evaluate the logarithm.
log 3
1
243
3
106. Graph the function.
y = x + 3
5

ID: A
107. Classify –3x 5 – 2x 3 by degree and by number of
terms.
108. Classify –7x 5 – 6x 4 + 4x 3 by degree and by number
of terms.
109. Write the polynomial 6x 2 − 9x 3 + 3
in standard
3
form.
110. Find the zeros of f(x) = (x + 3) 2 (x − 5) 6 and state
the multiplicity.
111. Divide using synthetic division.
(x 3 + 4 − 11x + 3x 2 ) ÷ (6 + x)
112. Solve x 4 − 34x 2 =−225.
113. Evaluate the expression.
5!
114. Evaluate the expression.
7!
4! 3!
115. Use Pascal’s Triangle to expand the binomial.
(s − 5v) 5
116. Simplify.
− 2 − 2 25 − 6 2
117. Divide and simplify.
225x 24
3x
125. Solve the equation. Check the solution.
k + 5
k + 8 = k + 4
k − 5
118. Multiply.
Ê ˆ
6 + 5
Ë
Á
¯
˜
2
119. Write 5x 3 – 5x 2 – 30x in factored form.
3
120. Simplify 162a 13 b 6
positive.
. Assume that all variables are
121. Write an exponential function y = ab x for a graph
that includes (0, 4) and (1, 14).
122. Simplify.
1
10 3
⋅ 100
1
3
123. Write a polynomial function in standard form with
zeros at –5, –2, and –4.
124. Find the inverse of y = 6x 2 − 2.
6

ID: A
Algebra II Semester 2 Practice Final Exam (Chapters 6-10)
Answer Section
1. ANS:
q − 8
q − 3
REF: 9-5 Adding and Subtracting Rational Expressions
OBJ: 9-5.1 Adding and Subtracting Rational Expressions TOP: 9-5 Example 4
KEY: simplifying a rational expression | subtracting rational expressions
2. ANS:
f(x) = x 3 + 7x 2 + 2x − 40
REF: 6-2 Polynomials and Linear Factors
OBJ: 6-2.2 Factors and Zeros of a Polynomial Function TOP: 6-2 Example 5
KEY: polynomial function | standard form of a polynomial | zeros of a polynomial function
3. ANS:
−4 10 + 4
REF: 7-3 Binomial Radical Expressions
TOP: 7-3 Example 3
4. ANS:
−4 + 10
OBJ: 7-3.1 Adding and Subtracting Radical Expressions
KEY: like radicals | simplifying a radical expression
REF: 7-3 Binomial Radical Expressions OBJ: 7-3.2 Multiplying and Dividing Binomial Radical Expressions
TOP: 7-3 Example 4
KEY: binomial radical expressions | simplifying a radical expression | multiplying binomial radical expressions
5. ANS:
10 − 2 21
4
REF: 7-3 Binomial Radical Expressions OBJ: 7-3.2 Multiplying and Dividing Binomial Radical Expressions
TOP: 7-3 Example 6
KEY: binomial radical expressions | conjugates | multiplying binomial radical expressions | simplifying a radical
expression
6. ANS:
y = 7(2.5) x
REF: 8-1 Exploring Exponential Models OBJ: 8-1.1 Exponential Growth
TOP: 8-1 Example 3
KEY: exponential function | growth factor
7. ANS:
2x(x + 5)(x – 4)
REF: 6-2 Polynomials and Linear Factors
OBJ: 6-2.1 The Factored Form of a Polynomial TOP: 6-2 Example 2
KEY: factoring a polynomial | polynomial
1

ID: A
8. ANS:
f −1 (x) = 5 ±
6
x
REF: 7-7 Inverse Relations and Functions
TOP: 7-7 Example 4
9. ANS:
2
3
REF: 7-5 Solving Radical Equations
TOP: 7-5 Example 4
10. ANS:
5x 4 − 3x 3 − 25x 2 + 25x − 6
OBJ: 7-7.1 The Inverse of a Function
KEY: domain | inverse relations and functions | range
OBJ: 7-5.1 Solving Radical Equations
KEY: radical equation | extraneous solutions
REF: Page 414 OBJ: 6-2.2 Multiplying Polynomials NAT: 12.5.3.c
TOP: 6-2 Multiplying Polynomials KEY: multiplying polynomials
11. ANS:
(x − 3)(x 2 + 3x + 9)
REF: 6-4 Solving Polynomial Equations
TOP: 6-4 Example 3
12. ANS:
OBJ: 6-4.2 Solving Equations by Factoring
KEY: polynomial | factoring a polynomial
− 8 9
REF: 9-6 Solving Rational Equations
TOP: 9-6 Example 2
13. ANS:
(–8, 8); 4
OBJ: 9-6.1 Solving Rational Equations
KEY: rational equation
REF: 10-3 Circles OBJ: 10-3.2 Using the Center and Radius of a Circle
TOP: 10-3 Example 4
KEY: center of a circle | circle | equation of a circle | radius | translation
14. ANS:
34
REF: 7-5 Solving Radical Equations OBJ: 7-5.1 Solving Radical Equations
TOP: 7-5 Example 1 KEY: radical equation |
15. ANS:
89
3
REF: 8-5 Exponential and Logarithmic Equations
OBJ: 8-5.2 Solving Logarithmic Equations
TOP: 8-5 Example 6
KEY: logarithmic equation | properties of logarithms
2

ID: A
16. ANS:
x 3 − 14x 2 − 12x + 7
REF: 6-3 Dividing Polynomials
TOP: 6-3 Example 3
17. ANS:
1
3
REF: 9-6 Solving Rational Equations
TOP: 9-6 Example 1
18. ANS:
4x 2 − 10x + 28, R –81
REF: 6-3 Dividing Polynomials
TOP: 6-3 Example 1
19. ANS:
2a 4 b 4 3
6a
OBJ: 6-3.2 Using Synthetic Division
KEY: division of polynomials | polynomial | synthetic division
OBJ: 9-6.1 Solving Rational Equations
KEY: rational equation
OBJ: 6-3.1 Using Long Division
KEY: polynomial | division of polynomials
REF: 7-2 Multiplying and Dividing Radical Expressions OBJ: 7-2.1 Multiplying Radical Expressions
TOP: 7-2 Example 2
KEY: multiplying radical expressions | simplifying a radical expression
20. ANS:
2.977; log 2
7.874
REF: 8-5 Exponential and Logarithmic Equations
OBJ: 8-5.2 Solving Logarithmic Equations
TOP: 8-5 Example 5
KEY: Change of Base Formula | evaluating logarithms
21. ANS:
inverse variation; y = 9 x
REF: 9-1 Inverse Variation
TOP: 9-1 Example 2
22. ANS:
log 8
3 + 2log 8
d
OBJ: 9-1.1 Using Inverse Variation
KEY: rational function | inverse variation
REF: 8-4 Properties of Logarithms OBJ: 8-4.1 Using the Properties of Logarithms
TOP: 8-4 Example 3
KEY: properties of logarithms | expanding logarithms | Product Property of Logarithms | Power Property of
Logarithms
23. ANS:
74
REF: 7-6 Function Operations
TOP: 7-6 Example 3
OBJ: 7-6.2 Composition of Functions
KEY: composition of functions | operations with functions
3

ID: A
24. ANS:
3
196
7
REF: 7-2 Multiplying and Dividing Radical Expressions OBJ: 7-2.2 Dividing Radical Expressions
TOP: 7-2 Example 5
KEY: divide radical expressions | simplifying a radical expression
25. ANS:
720
REF: 6-7 Permutations and Combinations
TOP: 6-7 Example 1
26. ANS:
−7
y =
x + 2 − 7
OBJ: 6-7.1 Permutations
KEY: permutation | factorial | problem solving
REF: 9-2 The Reciprocal Function Family
OBJ: 9-2.2 Graphing Translations of Reciprocal Functions TOP: 9-2 Example 5
KEY: asymptote | translation
27. ANS:
17.00
REF: 9-1 Inverse Variation
TOP: 9-1 Example 3
28. ANS:
− 7 21 ± 21i 3
,
3 18
REF: 6-4 Solving Polynomial Equations
TOP: 6-4 Example 4
29. ANS:
2w 3 + w 2 − 3w; cubic trinomial
REF: 6-1 Polynomial Functions
TOP: 6-1 Example 1
30. ANS:
–253
REF: 6-3 Dividing Polynomials
TOP: 6-3 Example 5
31. ANS:
log 4
8 + 4log 4
k
OBJ: 9-1.1 Using Inverse Variation
KEY: inverse variation | pair of values
OBJ: 6-4.2 Solving Equations by Factoring
KEY: factoring a polynomial | polynomial function
OBJ: 6-1.1 Exploring Polynomial Functions
KEY: degree of a polynomial | polynomial
OBJ: 6-3.2 Using Synthetic Division
KEY: division of polynomials | polynomial | synthetic division
REF: 8-4 Properties of Logarithms OBJ: 8-4.1 Using the Properties of Logarithms
TOP: 8-4 Example 3
KEY: properties of logarithms | expanding logarithms | Product Property of Logarithms | Power Property of
Logarithms
4

ID: A
32. ANS:
x 3 − 9x 2 − 7x + 15
REF: 6-3 Dividing Polynomials
TOP: 6-3 Example 3
33. ANS:
0.426
REF: 8-6 Natural Logarithms
TOP: 8-6 Example 4
34. ANS:
7
OBJ: 6-3.2 Using Synthetic Division
KEY: division of polynomials | polynomial | synthetic division
OBJ: 8-6.2 Natural Logarithmic and Exponential Equations
KEY: exponential equation | properties of logarithms
REF: 7-5 Solving Radical Equations OBJ: 7-5.1 Solving Radical Equations
TOP: 7-5 Example 1 KEY: radical equation |
35. ANS:
0.216
REF: 8-6 Natural Logarithms
TOP: 8-6 Example 4
36. ANS:
x 2 + 5x
, x ≠ 4, 0, − 4
x + 4
OBJ: 8-6.2 Natural Logarithmic and Exponential Equations
KEY: exponential equation | properties of logarithms
REF: 9-4 Rational Expressions OBJ: 9-4.2 Multiplying and Dividing Rational Expressions
TOP: 9-4 Example 3
KEY: simplifying a rational expression | restrictions on a variable | multiplying rational expressions
37. ANS:
log 4
16 = 2
REF: 8-3 Logarithmic Functions as Inverses
OBJ: 8-3.1 Writing and Evaluating Logarithmic Expressions TOP: 8-3 Example 2
KEY: logarithm | logarithmic form
5

ID: A
38. ANS:
foci (0, ± 2 10)
REF: 10-4 Ellipses
OBJ: 10-4.2 Finding and Using the Foci of an Ellipse
TOP: 10-4 Example 3
KEY: co-vertex of an ellipse | ellipse | equation of an ellipse | graphing | foci of an ellipse | major axis of an ellipse
| minor axis of an ellipse
39. ANS:
x 2
9 + y 2
25 = 1
REF: 10-4 Ellipses
OBJ: 10-4.1 Writing the Equation of an Ellipse
TOP: 10-4 Example 1
KEY: ellipse | equation of an ellipse | vertex of an ellipse | co-vertex of an ellipse | minor axis of an ellipse | major
axis of an ellipse
40. ANS:
( x − 4) 2 + Ê
Ë
Á y + 2ˆ¯˜ 2
= 49
REF: 10-3 Circles OBJ: 10-3.1 Writing the Equation of a Circle
TOP: 10-3 Example 2
KEY: center of a circle | circle | equation of a circle | radius
41. ANS:
d 3 + 6d 2 b + 12db 2 + 8b 3
REF: 6-8 The Binomial Theorem
TOP: 6-8 Example 3
42. ANS:
t 2 − t
, t ≠ −2, 0, 3
t − 3
OBJ: 6-8.2 The Binomial Theorem
KEY: Pascal's Triangle | binomial expansion
REF: 9-4 Rational Expressions OBJ: 9-4.2 Multiplying and Dividing Rational Expressions
TOP: 9-4 Example 3
KEY: simplifying a rational expression | restrictions on a variable | multiplying rational expressions
6

ID: A
43. ANS:
(x − 4)(x + 4)(x − 3)(x + 3)
REF: 6-4 Solving Polynomial Equations
TOP: 6-4 Example 5
44. ANS:
2x 8 3
5x 2
OBJ: 6-4.2 Solving Equations by Factoring
KEY: factoring a polynomial | polynomial
REF: 7-2 Multiplying and Dividing Radical Expressions OBJ: 7-2.2 Dividing Radical Expressions
TOP: 7-2 Example 4
KEY: simplifying a radical expression | divide radical expressions | rationalize the denominator
45. ANS:
746.239
REF: 8-6 Natural Logarithms
TOP: 8-6 Example 3
46. ANS:
3
REF: 7-4 Rational Exponents
TOP: 7-4 Example 1
47. ANS:
y = 8wx
z ; 64
REF: 9-1 Inverse Variation
TOP: 9-1 Example 5
48. ANS:
28 + 10 3
OBJ: 8-6.2 Natural Logarithmic and Exponential Equations
KEY: natural logarithmic equation | properties of logarithms
OBJ: 7-4.1 Simplifying Expressions with Rational Exponents
KEY: rational exponent
OBJ: 9-1.2 Using Combined Variation
KEY: direct variation | combined variation | joint variation
REF: 7-3 Binomial Radical Expressions OBJ: 7-3.2 Multiplying and Dividing Binomial Radical Expressions
TOP: 7-3 Example 4
KEY: binomial radical expressions | multiplying binomial radical expressions | simplifying a radical expression
7

ID: A
49. ANS:
The graph is an ellipse. The center is at the origin. It has two lines of
symmetry, the x-axis and the y-axis.
REF: 10-1 Exploring Conic Sections
TOP: 10-1 Example 2
50. ANS:
5.4739
OBJ: 10-1.1 Graphing Equations of Conic Sections
KEY: conic sections | graphing | ellipse | domain | range
REF: 8-2 Properties of Exponential Functions
OBJ: 8-2.2 The Number e
TOP: 8-2 Example 4
KEY: exponential function | graphing | the number e
51. ANS:
p − 8; p ≠ −4
REF: 9-4 Rational Expressions OBJ: 9-4.1 Simplifying Rational Expressions
TOP: 9-4 Example 1
KEY: rational expression | simplifying a rational expression | restrictions on a variable
52. ANS:
x 2
25 + y 2
16 = 1
REF: 10-4 Ellipses
OBJ: 10-4.1 Writing the Equation of an Ellipse
TOP: 10-4 Example 1
KEY: co-vertex of an ellipse | ellipse | equation of an ellipse | major axis of an ellipse | minor axis of an ellipse |
vertex of an ellipse
53. ANS:
y =±
x − 7
7
REF: 7-7 Inverse Relations and Functions
OBJ: 7-7.1 The Inverse of a Function
TOP: 7-7 Example 2 KEY: inverse relations and functions |
8

ID: A
54. ANS:
x 3 y 2
2
14y
REF: 7-2 Multiplying and Dividing Radical Expressions OBJ: 7-2.2 Dividing Radical Expressions
TOP: 7-2 Example 5
KEY: divide radical expressions | simplifying a radical expression
55. ANS:
log 6
1, 296 = 4
REF: 8-3 Logarithmic Functions as Inverses
OBJ: 8-3.1 Writing and Evaluating Logarithmic Expressions TOP: 8-3 Example 2
KEY: logarithm | logarithmic form
56. ANS:
y = 77
x
REF: 9-1 Inverse Variation
TOP: 9-1 Example 1
57. ANS:
direct variation; y = 14x
OBJ: 9-1.1 Using Inverse Variation
KEY: rational function | inverse variation
REF: 9-1 Inverse Variation
OBJ: 9-1.1 Using Inverse Variation
TOP: 9-1 Example 2
KEY: rational function | direct variation
58. ANS:
y varies directly as w and inversely as the square of x.
REF: 9-1 Inverse Variation
TOP: 9-1 Example 4
59. ANS:
a varies directly as F and inversely as m.
REF: 9-1 Inverse Variation
TOP: 9-1 Example 4
OBJ: 9-1.2 Using Combined Variation
KEY: direct variation | inverse variation | combined variation
OBJ: 9-1.2 Using Combined Variation
KEY: direct variation | inverse variation | combined variation
9

ID: A
60. ANS:
REF: 10-5 Hyperbolas
OBJ: 10-5.1 Graphing Hyperbolas Centered at the Origin
TOP: 10-5 Example 1
KEY: hyperbola | equation of a hyperbola | graphing | transverse axis of a hyperbola | vertices of a hyperbola |
asymptotes of a hyperbola
61. ANS:
( x − 3) 2 Ê
Ë
Á y + 3 ˆ¯˜ 2
+ = 1
9 36
REF: 10-6 Translating Conic Sections OBJ: 10-6.1 Writing Equations of Translated Conic Sections
TOP: 10-6 Example 1
KEY: conic sections | co-vertex of an ellipse | equation of an ellipse | major axis of an ellipse | minor axis of an
ellipse | translation | vertex of an ellipse
62. ANS:
Ê
(x + 3) 2 Ë
Á y + 2 ˆ¯˜ 2
− = 1
36 64
REF: 10-6 Translating Conic Sections OBJ: 10-6.1 Writing Equations of Translated Conic Sections
TOP: 10-6 Example 2
KEY: conic sections | equation of a hyperbola | hyperbola | translation | transverse axis of a hyperbola | vertices of
a hyperbola
10

ID: A
63. ANS:
REF: 9-2 The Reciprocal Function Family
OBJ: 9-2.2 Graphing Translations of Reciprocal Functions TOP: 9-2 Example 4
KEY: graphing | asymptote
64. ANS:
q + 8
q − 8 ; q ≠ −3, q ≠ 8
REF: 9-4 Rational Expressions OBJ: 9-4.1 Simplifying Rational Expressions
TOP: 9-4 Example 1
KEY: rational expression | simplifying a rational expression | restrictions on a variable
65. ANS:
− 11
3
REF: 9-6 Solving Rational Equations
TOP: 9-6 Example 1
66. ANS:
(x − 4) 2
; x ≠ − 4, − 3, − 2, − 1, 4
(x + 3)(x + 1)
REF: 9-4 Rational Expressions
TOP: 9-4 Example 4
67. ANS:
w + 4
w − 5
OBJ: 9-6.1 Solving Rational Equations
KEY: rational equation
OBJ: 9-4.2 Multiplying and Dividing Rational Expressions
KEY: restrictions on a variable | dividing rational expressions
REF: 9-5 Adding and Subtracting Rational Expressions
OBJ: 9-5.1 Adding and Subtracting Rational Expressions TOP: 9-5 Example 3
KEY: simplifying a rational expression | adding rational expressions
11

ID: A
68. ANS:
Power Property
REF: 8-4 Properties of Logarithms
TOP: 8-4 Example 1
69. ANS:
OBJ: 8-4.1 Using the Properties of Logarithms
KEY: properties of logarithms | Power Property of Logarithms
− 1 2
REF: 9-5 Adding and Subtracting Rational Expressions OBJ: 9-5.2 Simplifying Complex Fractions
TOP: 9-5 Example 5
KEY: complex fraction | simplifying a rational expression | simplifying a complex fraction
70. ANS:
–9
REF: 9-6 Solving Rational Equations
TOP: 9-6 Example 2
71. ANS:
y = 0.5(2) x
OBJ: 9-6.1 Solving Rational Equations
KEY: rational equation | no solutions
REF: 8-1 Exploring Exponential Models OBJ: 8-1.1 Exponential Growth
TOP: 8-1 Example 3
KEY: exponential function | graphing | growth factor
72. ANS:
REF: 8-2 Properties of Exponential Functions
OBJ: 8-2.1 Comparing Graphs
TOP: 8-2 Example 2
KEY: exponential function | graphing
73. ANS:
–4
REF: 8-3 Logarithmic Functions as Inverses
OBJ: 8-3.1 Writing and Evaluating Logarithmic Expressions TOP: 8-3 Example 3
KEY: evaluating logarithms
12

ID: A
74. ANS:
3
5
32 = 8
REF: 8-3 Logarithmic Functions as Inverses
OBJ: 8-3.1 Writing and Evaluating Logarithmic Expressions TOP: 8-3 Example 3
KEY: logarithmic form | logarithm | exponential form
75. ANS:
Quotient Property
REF: 8-4 Properties of Logarithms
TOP: 8-4 Example 1
76. ANS:
Power Property and Product Property
REF: 8-4 Properties of Logarithms
TOP: 8-4 Example 1
77. ANS:
log b
(q 5 y 2 )
OBJ: 8-4.1 Using the Properties of Logarithms
KEY: properties of logarithms | Quotient Property of Logarithms
OBJ: 8-4.1 Using the Properties of Logarithms
KEY: properties of logarithms
REF: 8-4 Properties of Logarithms OBJ: 8-4.1 Using the Properties of Logarithms
TOP: 8-4 Example 2
KEY: properties of logarithms | logarithm | Product Property of Logarithms | Power Property of Logarithms
78. ANS:
log 3
2
REF: 8-4 Properties of Logarithms OBJ: 8-4.1 Using the Properties of Logarithms
TOP: 8-4 Example 2
KEY: properties of logarithms | simplifying a logarithm | Quotient Property of Logarithms
79. ANS:
log 7
n − log 7
2
REF: 8-4 Properties of Logarithms OBJ: 8-4.1 Using the Properties of Logarithms
TOP: 8-4 Example 3
KEY: properties of logarithms | expanding logarithms | Quotient Property of Logarithms
80. ANS:
1
2 log 57 − 1 b
2 log 74 b
REF: 8-4 Properties of Logarithms OBJ: 8-4.1 Using the Properties of Logarithms
KEY: properties of logarithms | expanding logarithms | Power Property of Logarithms | Quotient Property of
Logarithms
81. ANS:
0.6616
REF: 8-5 Exponential and Logarithmic Equations
OBJ: 8-5.1 Solving Exponential Equations
TOP: 8-5 Example 1
KEY: exponential equation
13

ID: A
82. ANS:
3.2459
REF: 8-5 Exponential and Logarithmic Equations
OBJ: 8-5.2 Solving Logarithmic Equations
TOP: 8-5 Example 5
KEY: exponential equation | Change of Base Formula
83. ANS:
ln 27c 3
REF: 8-6 Natural Logarithms
TOP: 8-6 Example 1
84. ANS:
0.02 and –0.02
OBJ: 8-6.1 Natural Logarithms
KEY: simplifying a natural logarithm | properties of logarithms
REF: 7-1 Roots and Radical Expressions OBJ: 7-1.1 Roots and Radical Expressions
TOP: 7-1 Example 1
KEY: square root | real roots
85. ANS:
− 5 7
REF: 7-1 Roots and Radical Expressions OBJ: 7-1.1 Roots and Radical Expressions
TOP: 7-1 Example 2
KEY: real roots
86. ANS:
2 3
REF: 7-2 Multiplying and Dividing Radical Expressions OBJ: 7-2.1 Multiplying Radical Expressions
TOP: 7-2 Example 1
KEY: multiplying radical expressions | simplifying a radical expression
87. ANS:
x 7 − 49 x
REF: 7-2 Multiplying and Dividing Radical Expressions OBJ: 7-2.1 Multiplying Radical Expressions
TOP: 7-2 Example 3
KEY: multiplying radical expressions | simplifying a radical expression
88. ANS:
3
3 3
REF: 7-2 Multiplying and Dividing Radical Expressions OBJ: 7-2.2 Dividing Radical Expressions
TOP: 7-2 Example 4
KEY: simplifying a radical expression | divide radical expressions | rationalize the denominator
89. ANS:
3x 8 5x
REF: 7-2 Multiplying and Dividing Radical Expressions OBJ: 7-2.2 Dividing Radical Expressions
TOP: 7-2 Example 4
KEY: simplifying a radical expression | divide radical expressions | rationalize the denominator
14

ID: A
90. ANS:
x 3 y 2
5
30y
REF: 7-2 Multiplying and Dividing Radical Expressions OBJ: 7-2.2 Dividing Radical Expressions
TOP: 7-2 Example 5
KEY: divide radical expressions | simplifying a radical expression
91. ANS:
3
2 36
3
+ 3 4
6
REF: 7-3 Binomial Radical Expressions OBJ: 7-3.2 Multiplying and Dividing Binomial Radical Expressions
TOP: 7-3 Example 6
KEY: binomial radical expressions | multiplying binomial radical expressions | rationalize the denominator
92. ANS:
4
8 2x
REF: 7-3 Binomial Radical Expressions OBJ: 7-3.1 Adding and Subtracting Radical Expressions
TOP: 7-3 Example 1
KEY: binomial radical expressions | adding radical expressions | like radicals
93. ANS:
not possible to simplify
REF: 7-3 Binomial Radical Expressions OBJ: 7-3.1 Adding and Subtracting Radical Expressions
TOP: 7-3 Example 1
KEY: binomial radical expressions | adding radical expressions | like radicals
94. ANS:
4
−4 5a
REF: 7-3 Binomial Radical Expressions OBJ: 7-3.1 Adding and Subtracting Radical Expressions
TOP: 7-3 Example 1
KEY: binomial radical expressions | adding radical expressions | like radicals
95. ANS:
20
REF: 7-4 Rational Exponents
TOP: 7-4 Example 1
96. ANS:
8
3 x 3
REF: 7-4 Rational Exponents
TOP: 7-4 Example 2
97. ANS:
15; –1
REF: 7-5 Solving Radical Equations
TOP: 7-5 Example 2
OBJ: 7-4.1 Simplifying Expressions with Rational Exponents
KEY: rational exponent
OBJ: 7-4.1 Simplifying Expressions with Rational Exponents
KEY: rational exponent | radical form
OBJ: 7-5.1 Solving Radical Equations
KEY: radical equation | rational exponent
15

ID: A
98. ANS:
7
6
REF: 7-5 Solving Radical Equations
TOP: 7-5 Example 5
99. ANS:
2x – 4
OBJ: 7-5.1 Solving Radical Equations
KEY: extraneous solutions | radical equation | rational exponent
REF: 7-6 Function Operations
OBJ: 7-6.1 Operations with Functions
TOP: 7-6 Example 1
KEY: addition and subtraction of functions | operations with functions
100. ANS:
2x 2 − 2x + 10
REF: 7-6 Function Operations
OBJ: 7-6.1 Operations with Functions
TOP: 7-6 Example 2
KEY: addition and subtraction of functions | operations with functions
101. ANS:
63
55
REF: 7-6 Function Operations
TOP: 7-6 Example 3
102. ANS:
y =±
x + 3
7
OBJ: 7-6.2 Composition of Functions
KEY: composition of functions | operations with functions
REF: 7-7 Inverse Relations and Functions
OBJ: 7-7.1 The Inverse of a Function
TOP: 7-7 Example 2 KEY: inverse relations and functions |
103. ANS:
5
REF: 7-7 Inverse Relations and Functions
TOP: 7-7 Example 6
104. ANS:
f(g(x)) = 10x – 1; g(f(x)) = 10x + 7
REF: 7-6 Function Operations
TOP: 7-6 Example 3
105. ANS:
–5
OBJ: 7-7.1 The Inverse of a Function
KEY: composition of functions | inverse relations and functions
OBJ: 7-6.2 Composition of Functions
KEY: composition of functions | operations with functions
REF: 8-3 Logarithmic Functions as Inverses
OBJ: 8-3.1 Writing and Evaluating Logarithmic Expressions TOP: 8-3 Example 3
KEY: evaluating logarithms
16

ID: A
106. ANS:
REF: 7-8 Graphing Radical Functions
TOP: 7-8 Example 2
107. ANS:
quintic binomial
REF: 6-1 Polynomial Functions
TOP: 6-1 Example 1
108. ANS:
quintic trinomial
REF: 6-1 Polynomial Functions
TOP: 6-1 Example 1
109. ANS:
−3x 3 + 2x 2 + 1
REF: 6-1 Polynomial Functions
TOP: 6-1 Example 1
110. ANS:
–3, multiplicity 2; 5, multiplicity 6
OBJ: 7-8.1 Radical Functions
KEY: domain | graphing | range | radical function | translation
OBJ: 6-1.1 Exploring Polynomial Functions
KEY: polynomial | degree of a polynomial
OBJ: 6-1.1 Exploring Polynomial Functions
KEY: degree of a polynomial | polynomial
OBJ: 6-1.1 Exploring Polynomial Functions
KEY: polynomial | standard form of a polynomial
REF: 6-2 Polynomials and Linear Factors
OBJ: 6-2.2 Factors and Zeros of a Polynomial Function TOP: 6-2 Example 6
KEY: polynomial function | zeros of a polynomial function | multiplicity | multiple zero
111. ANS:
x 2 − 3x + 7, R –38
REF: 6-3 Dividing Polynomials
TOP: 6-3 Example 3
112. ANS:
3, –3, 5, –5
REF: 6-4 Solving Polynomial Equations
TOP: 6-4 Example 6
OBJ: 6-3.2 Using Synthetic Division
KEY: division of polynomials | polynomial | synthetic division
OBJ: 6-4.2 Solving Equations by Factoring
KEY: factoring a polynomial | polynomial
17

ID: A
113. ANS:
120
REF: 6-7 Permutations and Combinations
TOP: 6-7 Example 1
114. ANS:
35
KEY: factorial
OBJ: 6-7.1 Permutations
REF: 6-7 Permutations and Combinations
TOP: 6-7 Example 1
KEY: factorial
115. ANS:
s 5 − 25s 4 v + 250s 3 v 2 − 1250s 2 v 3 + 3125sv 4 − 3125v 5
OBJ: 6-7.1 Permutations
REF: 6-8 The Binomial Theorem
TOP: 6-8 Example 2
116. ANS:
−7 2 − 10
REF: 7-3 Binomial Radical Expressions
TOP: 7-3 Example 3
117. ANS:
5x 11 3x
OBJ: 6-8.1 Binomial Expansion and Pascal's Triangle
KEY: Pascal's Triangle | binomial expansion
OBJ: 7-3.1 Adding and Subtracting Radical Expressions
KEY: like radicals | simplifying a radical expression
REF: 7-2 Multiplying and Dividing Radical Expressions OBJ: 7-2.2 Dividing Radical Expressions
TOP: 7-2 Example 4
KEY: simplifying a radical expression | divide radical expressions | rationalize the denominator
118. ANS:
41 + 12 5
REF: 7-3 Binomial Radical Expressions OBJ: 7-3.2 Multiplying and Dividing Binomial Radical Expressions
TOP: 7-3 Example 4
KEY: binomial radical expressions | multiplying binomial radical expressions | simplifying a radical expression
119. ANS:
5x(x + 2)(x – 3)
REF: 6-2 Polynomials and Linear Factors
OBJ: 6-2.1 The Factored Form of a Polynomial TOP: 6-2 Example 2
KEY: factoring a polynomial | polynomial
120. ANS:
3a 4 b 2 3
6a
REF: 7-2 Multiplying and Dividing Radical Expressions OBJ: 7-2.1 Multiplying Radical Expressions
TOP: 7-2 Example 2
KEY: multiplying radical expressions | simplifying a radical expression
18

ID: A
121. ANS:
y = 4(3.5) x
REF: 8-1 Exploring Exponential Models OBJ: 8-1.1 Exponential Growth
TOP: 8-1 Example 3
KEY: exponential function | growth factor
122. ANS:
10
REF: 7-4 Rational Exponents
TOP: 7-4 Example 1
123. ANS:
f(x) = x 3 + 11x 2 + 38x + 40
OBJ: 7-4.1 Simplifying Expressions with Rational Exponents
KEY: rational exponent
REF: 6-2 Polynomials and Linear Factors
OBJ: 6-2.2 Factors and Zeros of a Polynomial Function TOP: 6-2 Example 5
KEY: polynomial function | standard form of a polynomial | zeros of a polynomial function
124. ANS:
y =±
x + 2
6
REF: 7-7 Inverse Relations and Functions
OBJ: 7-7.1 The Inverse of a Function
TOP: 7-7 Example 2 KEY: inverse relations and functions |
125. ANS:
− 19
4
REF: 9-6 Solving Rational Equations
TOP: 9-6 Example 1
OBJ: 9-6.1 Solving Rational Equations
KEY: rational equation
19