ExamView - FINAL EXAM REVIEW 2011.tst

FINAL EXAM REVIEW 2011
Multiple Choice
Evaluate the expression for the given value of the variable(s).
____ 1.
4(3h − 6)
;h = −2
1 +h
a. 32 b. 48 c. −48 d. 30
____ 2. −x 2 − 4x − 4; x = –3
a. 3 b. –1 c. 11 d. –17
____
3. The expression −16t 2 + 1800 models the height of an object t seconds after it has been dropped from a height
of 1800 feet. Find the height of an object after falling for 4.8 seconds.
a. 2168.64 ft b. 1431.36 ft c. 1723.2 ft d. 7698.24 ft
Simplify by combining like terms.
____
4. 4c − 4d + 8c − 3d
a. 12c + 7d b. 12c − 7d c. −12c − 7d d. −7c + 12d
____ 5. If a = b, then a – c ____ equals b – c.
a. always b. sometimes c. never
Solve the equation.
____ 6. 6(x − 0.8) − 0.2( 5x − 4) = 6
a. –0.5 b. –2 c. 0.5 d. 2
____ 7. 9x 2 + 16 = 0
a. − 4 3 i, 4 3 i c. −3 4 i, 3 4 i
b. − 16 16
i,
9 9 i d. −4 3 , 4 3
____ 8. x 2 + 18x + 81 = 25
a. 14, 4 c. 14, –14
b. –4, –14 d. –4, 4
____ 9. x + 10 − 7 = −5
a. 14 b. –8 c. 4 d. –6
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FINAL EXAM REVIEW 2011
Solve for x. State any restrictions on the variables.
____ 10. ax + bx +9 =7
2
a. x =
a + b ; a≠b c. x = 7
a + b +9 ; a + b ≠ −9
7
b. x =
a + b +9 ; a ≠ 0, b ≠ −9 d. x = −2
a + b ; a ≠ −b
Solve the inequality. Graph the solution set.
____ 11. 2 + 2k ≤ 8
a. k ≥ 3 c. k ≤ 3
b. k ≤ 5 d. k ≥ 5
____ 12. 26 + 6b ≥ 2(3b + 4)
a. all real numbers c. b ≥ 1 1 2
b. b ≤ 1 1 2
d. no solutions
Solve the problem by writing an inequality.
____ 13. A club decides to sell T-shirts for $12 as a fund-raiser. It costs $20 plus $8 per T-shirt to make the T-shirts.
Write and solve an equation to find how many T-shirts the club needs to make and sell in order to profit at
least $100.
a. 12x − ( 8x + 20) ≥ 100; x ≥ 30 c. (8x + 20) − 12x ≥ 100; x ≥ 20
b. 12x − 8x + 20 ≥ 100; x ≥ 20 d. 12x − 8(x + 20) ≥ 100; x ≥ 20
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FINAL EXAM REVIEW 2011
Solve the compound inequality. Graph the solution set.
____ 14. −2 ≤ 2x − 4 < 4
a. 0 ≤ x < − 2 c. 1 ≤ x < 0
b. 1 ≤ x < 4 d. 3 ≤ x < 6
____ 15. The perimeter of a square garden is to be at least 22 feet but not more than 36 feet. Find all possible values
for the length of its sides.
a. 11 41 4
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FINAL EXAM REVIEW 2011
____ 20. Suppose f ( x) = 4x − 2 and g( x) = −2x + 1.
f( 5)
Find the value of
g( −3) .
a. 1 5 9
b. 2 4 7
c. −2 d. 2
Find the slope of the line through the pair of points.
____ 21. (− 1 3 , 0) and (−1 2 , −1 2 )
a. −3 b.
1
3
c. − 1 3
d. 3
____ 22. Find the point-slope form of the equation of the line passing through the points (–6, –4) and (2, –5).
a. y + 4 = 1 8 (x – 2) c. y + 5 = −1 (x + 6)
8
b. y + 4 = − 1 8 (x + 6) d. y + 4 = 1 (x + 6)
8
Find the slope of the line.
____ 23. y = − 1 2 x − 4
a. − 1 2
b.
1
2
c. –4 d. none of these
____ 24. x = a
a. a b. 0 c. undefined d. 1
____ 25. A 3-mi cab ride costs $3.00. A 6-mi cab ride costs $4.80. Find a linear equation that models cost c as a
function of distance d.
a. c = 0.80d + 1.20 c. d = 0.60c + 1.80
b. c = 1.00d + 1.80 d. c = 0.60d + 1.20
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FINAL EXAM REVIEW 2011
Graph the inequality.
____ 26. 4x – 2y < –3
a. c.
b. d.
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FINAL EXAM REVIEW 2011
Graph the absolute value inequality.
____ 27. y < |x + 2| – 2
a. c.
b. d.
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FINAL EXAM REVIEW 2011
____ 28. y ≥ |x + 3| – 2
a. c.
b. d.
____ 29. A group of 52 people attended a ball game. There were three times as many children as adults in the group.
Set up a system of equations that represents the numbers of adults and children who attended the game and
solve the system to find the number of children who were in the group.
Ï
Ï
a + c = 52
a.
Ô
Ì ; 39 adults; 25 children c.
Ôa + c = 52
Ì ; 25 adults; 39 children
ÓÔ
a = c + 3
ÓÔ
c = a + 3
Ï
Ï
a + c = 52
b.
Ô
Ì ; 39 adults, 13 children d.
Ôa + c = 52
Ì ; 13 adults, 39 children
ÓÔ
a = 3c
ÓÔ
c = 3a
Solve the system.
____ 30.
Ï
Ô−4x + 4y = −8
Ì
ÓÔ
x − 4y = −7
a. (3, 5) b. (5, 3) c. (–3, –5) d. (–5, –3)
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FINAL EXAM REVIEW 2011
____ 31.
____ 32.
____ 33.
Ï
Ô0.18f − 0.3g = 3
Ì
ÓÔ
0.15g − 0.9f = −5.55
a. f = –7, g = 5 c. f = 5, g = 7
b. f = –5, g = –7 d. f = 5, g = –7
Ï
Ô−x + 2y = 10
Ì
ÓÔ
−3x + 6y = 11
a. infinite solutions c. (5, –2)
b. (–5, 2) d. no solutions
Ï
2x − 2y + z = −15
Ô
Ì6x − 3y − z = −19
ÓÔ
3x − y − z = −6
a. (1, 8, 0) b. (–3, 2, –5) c. (1, 11, 5) d. (–1, 3, 4)
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FINAL EXAM REVIEW 2011
Solve the system of inequalities by graphing.
____ 34.
Ï
Ôx ≥ −2
Ì
ÓÔ
y > 3
a. c.
b. d.
____ 35. Equivalent systems of two linear equations ____ have the same solutions.
a. always b. sometimes c. never
Factor the expression.
____ 36. 8x 2 + 12x − 16
a. −2(−4x 2 + 12x − 16) c. 8x(−2x − 3)
b. 8x 2 + 12x − 16 d. −4(−2x 2 − 3x + 4)
____ 37. x 2 + 14x + 48
a. (x + 6)(x − 8) c. (x − 8)(x − 6)
b. (x + 8)(x − 6) d. (x + 6)(x + 8)
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FINAL EXAM REVIEW 2011
____ 38. x 2 −6x +8
a. (x + 4)(x + 2) c. (x − 4)(x + 2)
b. (x − 2)(x − 4) d. (x − 2)(x + 4)
____ 39. 3x 2 + 26x + 35
a. (x + 5)(3x + 7) c. (3x + 5)(x − 7)
b. (3x + 7)(x − 5) d. (3x + 5)(x + 7)
____ 40. 9x 2 − 16
a. (3x + 4)(−3x − 4) c. (−3x + 4)(3x − 4)
b. (3x + 4)(3x − 4) d. (3x − 4) 2
____ 41. x 3 + 216
a. (x − 6)(x 2 + 6x + 36) c. (x − 6)(x 2 − 6x + 36)
b. (x + 6)(x 2 − 6x + 36) d. (x + 6)(x 2 + 6x + 72)
____ 42. c 3 − 512
a. −(c − 8)(c 2 + 8c + 64) c. (c + 8)(c 2 + 8c + 64)
b. (c − 8)(c 2 + 8c + 64) d. (c − 8)(c 2 − 8c − 64)
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FINAL EXAM REVIEW 2011
____ 43. Identify the graph of the complex number −3 − 2i.
a. c.
b. d.
Simplify the expression.
____ 44. (−6i)(−6i)
a. 36 b. –36 c. –36i d. 36i
____ 45. Find the missing value to complete the square.
x 2 + 2x + ____
a. 2 b. 1 c. 4 d. 8
Solve the quadratic equation by completing the square.
____ 46. x 2 + 10x + 14 = 0
a. −10 ± 6 c. 5 ± 6
b. 100 ± 11 d. −5 ± 11
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FINAL EXAM REVIEW 2011
Rewrite the equation in vertex form.
____ 47. y = x 2 + 10x + 16
a. y = (x + 5) 2 + 41 c. y = (x + 10) 2 + 11
b. y = (x + 10) 2 − 9 d. y = (x + 5) 2 − 9
Use the Quadratic Formula to solve the equation.
____ 48. 4x 2 − x + 3 = 0
a.
1
8 ± 47
8
b. 8 ± i 94
8
c.
d.
1
8 ± i 47
8
1
4 ± i 47
4
____ 49. Write 4x 2 (–2x 2 + 5x 3 ) in standard form. Then classify it by degree and number of terms.
a. 2x + 9x 4 ; quintic binomial c. 2x 5 – 8x 4 ; quintic trinomial
b. 20x 5 – 8x 4 ; quintic binomial d. 20x 5 – 10x 4 ; quartic binomial
____ 50. Use a graphing calculator to determine which type of model best fits the values in the table.
x –6 –2 0 2 6
y –6 –2 0 2 6
a. quadratic model c. linear model
b. cubic model d. none of these
____ 51. Determine which binomial is a factor of −2x 3 + 14x 2 − 24x + 20.
a. x + 5 b. x + 20 c. x – 24 d. x – 5
____ 52. Solve x 4 − 34x 2 = −225.
a. no solution c. 3, –3, 5, –5
b. 3, –5 d. 3, –3
____ 53. Find a quadratic equation with roots –1 + 4i and –1 – 4i.
a. x 2 − 2x + 17 = 0 c. x 2 + 2x + 17 = 0
b. x 2 + 2x − 17 = 0 d. x 2 − 2x − 17 = 0
____ 54. Use the Binomial Theorem to expand (d − 3b) 3 .
a. d 3 − 3d 2 b + 3db 2 − b 3
b. d 3 + 3d 2 b + 3db 2 + b 3
c. d 3 + 9d 2 b + 27db 2 + 27b 3
d. d 3 − 9d 2 b + 27db 2 − 27b 3
____ 55. Determine the probability of getting four heads when tossing a coin four times.
a. 0.5 b. 0.375 c. 0.25 d. 0.0625
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FINAL EXAM REVIEW 2011
Multiply and simplify if possible.
4
____ 56. 3
⋅
4
−3
4
a. –3 b. 3 c. 3 −3
Ê
ˆ
____ 57. 7x x −7 7
Ë
Á
¯
˜
a. x 7 − 49 x c. x 7 − x 49
b. 7x − 49x d. − 42x
d. not possible
Rationalize the denominator of the expression. Assume that all variables are positive.
____ 58.
a.
b.
6x 8 y 9
5x 2 y 4
x 3 y 2 30y
5
c. 5x 3 y 2 30y
30x 10 y 13
d. none of these
5x 2 y 4
____ 59.
3
2 + 3
3
6
a.
b.
3
2 6
3
2 36
3
+ 9 18
6
3
+ 3 2
6
c.
d.
3
2 6
3
2 36
3
+ 9 4
6
3
+ 3 4
6
Simplify.
____ 60. − 5 − 3 36 + 6 5
1
____ 61. 20 2
⋅ 20
a. 5 5 − 18 c. −5 5 − 18
b. 5 5 − 3 36 d. none of these
1
2
1
a.
4
20
b. 20 c. 20 d. 1
1
____ 62. 3 3
⋅ 9
1
3
3
a. 9 b. 3
c. 3 d. 3
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FINAL EXAM REVIEW 2011
Multiply.
____ 63.
2
Ê ˆ
−5 − 3
Ë
Á
¯
˜
a. 28 + 10 3 c. −13 + 5 3
b. 28 − 10 3 d. 25 − 10 3
____ 64.
Ê ˆ
8 − 2
Ë
Á
¯
Ê
Ë
Á 9 + 5 ˆ
¯
˜
a. 72 − 10 c. 72 − 2 10
b. 72 + 8 5 − 9 2 − 10 d. 72 − 3 − 10
____ 65. ( −2x + 6)
5 = ( −8 + 10x)
7
a.
b.
6
1
1
5
2
3
c. − 1 4
d.
6
7
____ 66. Let f(x) = 3x + 2 and g(x) = x − 3. Find f(x) – g(x).
a. 2x – 5 b. 2x + 5 c. 4x – 1 d. 2x – 1
____ 67. Let f(x) = −2x − 7 and g(x) = −4x + 3. Find (f û g)(−5).
a. 23 b. –53 c. –9 d. 3
____ 68. How much money invested at 5% compounded continuously for 3 years will yield $820?
a. $952.70 b. $818.84 c. $780.01 d. $705.78
Write the equation in logarithmic form.
____ 69. 6 4 = 1, 296
a. log 6
1, 296=4 c. log 1, 296 = 4 ⋅ 6
b. log 1, 296=4 d. log 4
1, 296=6
____ 70. Write the equation log 32
8= 3 in exponential form.
5
3
3
a.
5
32 = 8 b.
5
8 = 32 c.
Ê 3 ˆ
Ë
Á 5 ¯
˜
32
5
= 8 d.
3
8 = 32
State the property or properties of logarithms used to rewrite the expression.
____ 71. log 5
6 − log 5
2 = log 5
3
a. Quotient Property c. Difference Property
b. Product Property d. Power Property
____ 72. log 4
7 + log 4
2 = log 4
14
a. Quotient Property c. Addition Property
b. Power Property d. Product Property
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FINAL EXAM REVIEW 2011
Write the expression as a single logarithm.
____ 73. 4 log x − 6 log (x + 2)
a.
x
24 log
x + 2
c. log x(x + 2) 24
b. log x 4 (x + 2) 6 d. none of these
Expand the logarithmic expression.
n
____ 74. log 7
2
a. log 7
n − log 7
2 c. log 7
2 − log 7
n
b.
log 7
n
log 7
2
d. −n log 7
2
____ 75. log 3
11p 3
a. log 3
11 ⋅ 3 log 3
p c. log 3
11 + 3 log 3
p
b. log 3
11 − 3 log 3
p d. 11 log 3
p 3
57
____ 76. log b
74
1
a.
2 log 57 + 1 b
2 log 74 c. log 57 − log 74
b b b
1
b.
2 log 57 − 1 b
2 log 74 d. log 1
b b
(57 − 74)
2
____ 77. A construction explosion has an intensity I of 4.85×10 −2 W/m 2 . Find the loudness of the sound in decibels if
L=10 log I
I 0
and I o
= 10 −12 W/m 2 . Round to the nearest tenth.
a. 146.9 decibels c. 106.9 decibels
b. 115.8 decibels d. 48.5 decibels
____ 78. Solve log(4x + 10) = 3.
a. − 7 4
b.
495
2
c. 250 d. 990
____ 79. Solve 3 log 2x= 4. Round to the nearest ten-thousandth.
a. 10.7722 b. 5 c. 2.7826 d. 0.6309
____ 80. Solve log 3x + log 9 = 0. Round to the nearest hundredth if necessary.
a. 0.33 b. 0.04 c. 3 d. 27
____ 81. Solve 2 log 4 − log 3 + 2 log x − 4 = 0. Round to the nearest ten-thousandth.
a. 12.3308 b. 43.3013 c. 86.6025 d. 1875
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FINAL EXAM REVIEW 2011
____ 82.
p 2 − 4p − 32
p + 4
a. −p + 8; p ≠ −4 c. −p − 8; p ≠ 4
b. p − 8; p ≠ −4 d. p + 8; p ≠ 4
Multiply or divide. State any restrictions on the variables.
____ 83.
____ 84.
4a 5
7b 4 ⋅ 2b 2
2a 4
a.
b.
4a 9
7b , a≠0, b≠0 c. 7b 2
6 4a
, a≠0, b≠0
4a
7b , a≠0, b≠0 d. 4
2 7 a9 b 6 , a≠0, b≠0
x 2 − 16
x 2 + 5x + 6 ÷ x 2 + 5x + 4
x 2 − 2x − 8
a.
b.
c.
d.
(x − 4) 2
(x + 3)(x + 1) ; x ≠ − 3, − 1
(x + 4) 2 (x + 1)
; x ≠ − 3, − 2, 4
(x + 2) 2 (x + 3)
(x − 4) 2
; x ≠ − 4, − 3, − 2, − 1, 4
(x + 3)(x + 1)
1
; x ≠ − 4, − 3, − 2, − 1, 4
(x + 3)(x + 1)
____ 85.
Add or subtract. Simplify if possible.
b 2 − 2b − 8
b 2 + b − 2 − 6
b − 1
a. b − 10 c.
b.
b 2 − 2b − 14
b 2 + b − 2
d.
b − 4
b − 1
b − 10
b − 1
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FINAL EXAM REVIEW 2011
Simplify the complex fraction.
____ 86.
4
x + 3
1
x + 3
a.
b.
12x + 4
x 2 + 3x
4x
3x + 9
c.
4x
3x 2 + 10x + 3
d. not here
x + 4x y
____ 87.
7
3x
a.
15x 2
7y
b.
7x(y + 4)
3xy
c.
3x 2 (y + 4)
7y
d.
3(y + 4)
7y
Solve the equation. Check the solution.
____ 88.
g + 4
g − 2 = g − 5
g − 8
a. − 22
3
b. 22 c. −22 d. 14
____ 89. Use the graph to write an equation for the parabola.
a. y = − x 2
4
b. y= x 2
4
c. y= x 2
2
d. y= 2x 2
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FINAL EXAM REVIEW 2011
____ 90. Write an equation for the translation of x 2 + y 2 = 25, 2 units right and 4 units down.
a. ( x + 2) + Ê
Ë
Á y + 4ˆ¯˜ = 25 c. ( x + 2) + Ê
Ë
Á y − 4ˆ¯˜ = 25
b. ( x − 2) + Ê
Ë
Á y + 4ˆ¯˜ = 25 d. ( x − 2) + Ê
Ë
Á y − 4ˆ¯˜ = 25
____ 91. Write an explicit formula for the sequence 7, 2, –3, –8, –13, ... Then find a 14
.
a. a n
= −5n + 12; –53 c. a n
= −5n + 12; –58
b. a n
= −5n + 7; –58 d. a n
= −5n + 7; –63
____ 92. Viola makes gift baskets for Valentine’s Day. She has 13 baskets left over from last year, and she plans to
make 12 more each day. If there are 15 work days until the day she begins to sell the baskets, how many
baskets will she have to sell?
a. 193 baskets c. 205 baskets
b. 156 baskets d. 181 baskets
____ 93. Find the 50th term of the sequence 5, –2, –9, –16, ...
a. –352 b. –343 c. –338 d. –331
____ 94. Find the arithmetic mean a n
of a n − 1
= 3.9, a n + 1
= 7.1.
a. 11 b. 5.5 c. 3.7 d. 1.6
Is the sequence geometric? If so, identify the common ratio.
____ 95. 6, 12, 24, 48, ...
a. yes, 2 b. yes, –2 c. yes, 4 d. no
Find the missing term of the geometric sequence.
____ 96. 45, , 1620, ...
a. 9720 b. 51 c. 6 d. 270
____ 97. 1250, , 50, ...
a. 1200 b. 650 c. 250 d. 125
____ 98. The sequence 15, 21, 27, 33, 39, ..., 75 has 11 terms. Evaluate the related series.
a. 420 c. 210
b. 495 d. 480
Does the infinite geometric series diverge or converge? Explain.
____ 99.
1
5 + 1 10 + 1 20 + 1 40 + …
a. It diverges; it has a sum. c. It converges; it has a sum.
b. It diverges; it does not have a sum. d. It converges; it does not have a sum.
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FINAL EXAM REVIEW 2011
Find the mean and standard deviation of the of data. Round to the nearest tenth.
____ 100. 62, 37, 48, 67, 44, 58, 47, 47
a. mean = 51.3;
standard deviation = 9.4
b. mean = 51.3;
standard deviation = 88.9
c. mean = 47.5;
standard deviation = 9.4
d. mean = 47.5;
standard deviation = 88.9
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