FINAL EXAM REVIEW 2011
Multiple Choice Evaluate the expression for the given value of the variable(s). ____
____
____
1.
4(3h − 6) 1+h a. 32
; h = −2
2. −x 2 − 4x − 4; x = –3 a. 3
b.
48
c.
−48
d.
30
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.
d.
−12c − 7d
5. If a = b, then a – c ____ equals b – c. a. always b. sometimes
c.
−7c + 12d
never
Solve the equation. ____
____
____
____
6. 6(x − 0.8) − 0.2 (5x − 4) = 6 a. –0.5 b. –2 7. 9x 2 + 16 = 0 4 4 a. − i, i 3 3 16 16 b. − i, i 9 9
a.
x + 10 − 7 = −5 14
b.
–8
0.5
d.
3 3 − i, i 4 4 4 4 − , 3 3
c. d.
14, –14 –4, 4
c.
4
c.
8. x 2 + 18x + 81 = 25 a. 14, 4 b. –4, –14 9.
c.
1
d.
2
d.
–6
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 7 b. x = ; a ≠ 0, b ≠ −9 a+b+9
c. d.
7 ; a + b ≠ −9 a+b+9 −2 x = ; a ≠ −b a+b x =
Solve the inequality. Graph the solution set. ____ 11. 2 + 2k ≤ 8 a. k ≥ 3
b.
k≤5
c.
k≤3
d.
k≥5
c.
b≥1
d.
no solutions
____ 12. 26 + 6b ≥ 2(3b + 4) a.
all real numbers
b.
b≤1
1 2
1 2
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
2
FINAL EXAM REVIEW 2011 Solve the compound inequality. Graph the solution set. ____ 14. −2 ≤ 2x − 4 < 4 a. 0 ≤ x < − 2
b.
1≤x< 4
c.
1≤x<0
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 < x < 18 c. 5.5 ≤ x ≤ 9 b. 5.5 < x < 9 d. 11 ≤ x ≤ 18 ____ 16. Students tested the acidity of the campus pond over a three-day period. On Monday and Tuesday, the pH values were 6.75 and 7.86. Find the range of pH values for Wednesday’s reading that will result in a mean pH greater than 7.1 and less than 7.6. a. 7.01 < x < 7.5 c. 21.3 < x < 22.8 b. 6.69 < x < 8.19 d. 10.65 < x < 11.4 ____ 17. An absolute value equation ____ has an extraneous solution. a. always b. sometimes
c.
never
Solve the inequality. Graph the solution. ____ 18. | 2x + 3 | ≥ 19 a. x ≤ −22 or x ≥ 16
c.
x ≤ −11 or x ≥ 8
d.
x ≥ −11 or x ≤ 8
| 1| ____ 19. 2 | x + | < 9 | 4| 3 3 a. −4 < x < 4 8 8
c.
3 3 x < −4 or x > 4 8 8
3 1 −4 < x < 4 4 4
d.
3 1 x < −4 or x > 4 4 4
b.
b.
x ≤ −8 or x ≥ 8
3
FINAL EXAM REVIEW 2011 ____ 20. Suppose f (x) = 4x − 2 and g (x) = −2x + 1. f (5) . Find the value of g (−3) 5 4 a. 1 b. 2 c. 9 7
−2
d.
2
d.
3
Find the slope of the line through the pair of points.
1 1 1 ____ 21. (− , 0) and (− , − ) 3 2 2 a.
−3
b.
1 3
c.
−
1 3
____ 22. Find the point-slope form of the equation of the line passing through the points (–6, –4) and (2, –5). 1 1 a. y + 4 = (x – 2) c. y + 5 = − (x + 6) 8 8 1 1 b. y + 4 = − (x + 6) d. y + 4 = (x + 6) 8 8 Find the slope of the line.
1 ____ 23. y = − x − 4 2 1 a. − 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
4
FINAL EXAM REVIEW 2011 Graph the inequality. ____ 26. 4x – 2y < –3 a.
b.
c.
d.
5
FINAL EXAM REVIEW 2011 Graph the absolute value inequality. ____ 27. y < |x + 2| – 2 a.
c.
b.
d.
6
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. ÔÏÔÔ a + c = 52 ÔÏÔÔ a + c = 52 Ô Ô a. ÔÌ ; 39 adults; 25 children c. ÔÌ ; 25 adults; 39 children ÔÔ a = c + 3 ÔÔ c = a + 3 Ó Ó ÔÏÔÔ a + c = 52 ÔÏÔÔ a + c = 52 Ô Ô b. ÔÌ ; 39 adults, 13 children d. ÔÌ ; 13 adults, 39 children ÔÔ a = 3c ÔÔ c = 3a Ó Ó Solve the system.
ÔÏÔÔ −4x + 4y = −8 Ô ____ 30. ÔÌ ÔÔ x − 4y = −7 Ó a. (3, 5)
b.
(5, 3)
c.
7
(–3, –5)
d.
(–5, –3)
FINAL EXAM REVIEW 2011
ÔÏÔÔ 0.18f − 0.3g = 3 Ô ____ 31. ÌÔ ÔÔ 0.15g − 0.9f = −5.55 Ó a. f = –7, g = 5 b. f = –5, g = –7
c. d.
f = 5, g = 7 f = 5, g = –7
ÔÏÔÔ −x + 2y = 10 Ô ____ 32. ÔÌ ÔÔ −3x + 6y = 11 Ó a. infinite solutions b. (–5, 2)
c. d.
(5, –2) no solutions
c.
(1, 11, 5)
ÔÏÔÔ 2x ÔÔ ÔÔ ____ 33. ÔÌÔ 6x ÔÔÔ ÔÔ 3x ÔÓ a.
− 2y + z = −15 − 3y − z = −19 − y − z = −6 (1, 8, 0)
b.
(–3, 2, –5)
8
d.
(–1, 3, 4)
FINAL EXAM REVIEW 2011 Solve the system of inequalities by graphing.
ÏÔÔ ÔÔ x ≥ −2 ____ 34. ÌÔ ÔÔ y > 3 Ó a.
b.
c.
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) b.
2
8x + 12x − 16
____ 37. x 2 + 14x + 48 a. (x + 6)(x − 8) b. (x + 8)(x − 6)
c. d.
8x(−2x − 3) −4(−2x 2 − 3x + 4)
c. d.
(x − 8)(x − 6) (x + 6)(x + 8)
9
FINAL EXAM REVIEW 2011 ____ 38. x 2 − 6x + 8 a. (x + 4)(x + 2) b. (x − 2)(x − 4)
c. d.
(x − 4)(x + 2) (x − 2)(x + 4)
____ 39. 3x 2 + 26x + 35 a. (x + 5)(3x + 7) b. (3x + 7)(x − 5)
c. d.
(3x + 5)(x − 7) (3x + 5)(x + 7)
____ 40. 9x 2 − 16 a. (3x + 4)(−3x − 4)
c. d.
(−3x + 4)(3x − 4) (3x − 4) 2
____ 41. x 3 + 216 a. (x − 6)(x 2 + 6x + 36) b. (x + 6)(x 2 − 6x + 36)
c. d.
(x − 6)(x 2 − 6x + 36) (x + 6)(x 2 + 6x + 72)
____ 42. c 3 − 512 a. −(c − 8)(c 2 + 8c + 64) b. (c − 8)(c 2 + 8c + 64)
c. d.
(c + 8)(c 2 + 8c + 64) (c − 8)(c 2 − 8c − 64)
b.
(3x + 4)(3x − 4)
10
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.
____ 45. Find the missing value to complete the square. x 2 + 2x + ____ a. 2 b. 1 c.
–36i
d.
36i
4
d.
8
Solve the quadratic equation by completing the square. ____ 46. x 2 + 10x + 14 = 0 a. −10 ± 6 b. 100 ± 11
c. d.
11
5 ±6 −5 ±
11
FINAL EXAM REVIEW 2011 Rewrite the equation in vertex form. ____ 47. y = x 2 + 10x + 16 a. b.
y = (x + 5) 2 + 41 y = (x + 10) 2 − 9
y = (x + 10) 2 + 11 y = (x + 5) 2 − 9
c. d.
Use the Quadratic Formula to solve the equation. ____ 48. 4x 2 − x + 3 = 0 a.
1 ± 8
47 8
c.
1 i 47 ± 8 8
b.
8±
i 94 8
d.
1 i 47 ± 4 4
____ 49. Write 4x2(–2x2 + 5x3) in standard form. Then classify it by degree and number of terms. a. 2x + 9x4; quintic binomial c. 2x5 – 8x4; quintic trinomial 5 4 b. 20x – 8x ; quintic binomial d. 20x5 – 10x4; 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. b.
quadratic model cubic model
c. d.
linear model 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 ____ 52. Solve x 4 − 34x 2 = −225. a. no solution b. 3, –5
c. d.
d.
x–5
3, –3, 5, –5 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
12
FINAL EXAM REVIEW 2011 Multiply and simplify if possible. ____ 56.
____ 57.
4
3 ⋅ 4 −3 a. –3
b.
3
Ê ˆ 7x ÁÁÁ x − 7 7 ˜˜˜ Ë ¯ a. x 7 − 49 x b. 7x − 49x
c.
3 4 −3
c.
x 7 −x − 42x
d.
d.
not possible
49
Rationalize the denominator of the expression. Assume that all variables are positive.
6x 8 y 9
____ 58.
5x 2 y 4
5 30x 10 y 13
b.
____ 59.
30y
x3 y2
a.
5x 2 y 4
2+ 3
3
c.
5x 3 y 2
d.
none of these
30y
3
6
a.
2 3 6 + 9 3 18 6
c.
23 6 + 93 4 6
b.
2 3 36 + 33 2 6
d.
2 3 36 + 33 4 6
Simplify. ____ 60. − 5 − 3 36 + 6 5 a.
c.
5 5 − 18 5 5 − 3 36
b. 1
d.
−5 5 − 18 none of these
20
c.
20
d.
3
c.
3
d.
1
____ 61. 20 2 ⋅ 20 2 1
a. 1
20 4
b.
1
1
3
____ 62. 3 ⋅ 9 3 a. 9
b.
3
13
3
FINAL EXAM REVIEW 2011 Multiply.
Ê ˆ2 ____ 63. ÁÁÁ −5 − 3 ˜˜˜ Ë ¯ a. 28 + 10 3 b.
d.
28 − 10 3
Ê ˆÊ ____ 64. ÁÁÁ 8 − 2 ˜˜˜ ÁÁÁ 9 + Ë ¯Ë a. 72 − 10 b.
c.
−13 + 5 3 25 − 10 3
ˆ 5 ˜˜˜ ¯ c.
72 + 8 5 − 9 2 − 1
10
d.
72 − 2 10 72 − 3 −
c.
−
10
1
____ 65. (−2x + 6) 5 = (−8 + 10x) 5 7 2 a. b. 6 3
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 b. log 1, 296 = 4
c. d.
____ 70. Write the equation log 32 8 = a.
32
3 in exponential form. 5
3
3
5
5
= 8
b.
log 1, 296 = 4 ⋅ 6 log 4 1, 296 = 6
8
= 32
c.
ÊÁ 3 ˜ˆ 32 ÁÁ ˜˜ = 8 ÁÁ 5 ˜˜ Ë ¯
5
d.
8 3 = 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 b. Product Property
c. d.
Difference Property Power Property
____ 72. log 4 7 + log 4 2 = log 4 14 a. Quotient Property b. Power Property
c. d.
Addition Property Product Property
14
FINAL EXAM REVIEW 2011 Write the expression as a single logarithm. ____ 73. 4 log x − 6 log (x + 2) x a. 24 log x+2 b. log x 4 (x + 2) 6
c.
log x(x + 2) 24
d.
none of these
c.
log 7 2 − log 7 n
d.
−n log 7 2
c.
log 3 11 + 3 log 3 p
d.
11 log 3 p 3
Expand the logarithmic expression. ____ 74. log 7 a. b.
n 2 log 7 n − log 7 2 log 7 n log 7 2
____ 75. log 3 11p 3 a. log 3 11 ⋅ 3 log 3 p b. ____ 76. log b a. b.
log 3 11 − 3 log 3 p
57 74 1 log 57 + 2 b 1 log 57 − 2 b
1 log 74 2 b 1 log 74 2 b
c. d.
log b 57 − log b 74 log b
1 (57 − 74) 2
____ 77. A construction explosion has an intensity I of 4.85 × 10 −2 W/m2. Find the loudness of the sound in decibels if I L = 10 log and I o = 10 −12 W/m2. Round to the nearest tenth. I0 a. b.
146.9 decibels 115.8 decibels
____ 78. Solve log(4x + 10) = 3. 7 a. − b. 4
495 2
c. d.
106.9 decibels 48.5 decibels
c.
250
____ 79. Solve 3 log 2x = 4. Round to the nearest ten-thousandth. a. 10.7722 b. 5 c. 2.7826
d.
990
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
15
FINAL EXAM REVIEW 2011
____ 82.
p 2 − 4p − 32 p+4 −p + 8; p ≠ −4 p − 8; p ≠ −4
a. b.
c. d.
−p − 8; p ≠ 4 p + 8; p ≠ 4
Multiply or divide. State any restrictions on the variables.
4a 5 ____ 83.
7b 4 a. b.
____ 84.
2b 2 ⋅
2a 4 4a 9 , a ≠ 0, b ≠ 0 7b 6 4a , a ≠ 0, b ≠ 0 7b2
x 2 − 16
c. d.
7b2 4a
, a ≠ 0, b ≠ 0
4 9 6 a b , a ≠ 0, b ≠ 0 7
x 2 + 5x + 4
÷ x 2 + 5x + 6 x 2 − 2x − 8 (x − 4) 2 ; x ≠ − 3, − 1 a. (x + 3)(x + 1) (x + 4) 2 (x + 1)
b.
(x + 2) 2 (x + 3) (x − 4) 2
c.
(x + 3)(x + 1) 1
d.
(x + 3)(x + 1)
; x ≠ − 3, − 2, 4
; x ≠ − 4, − 3, − 2, − 1, 4
; x ≠ − 4, − 3, − 2, − 1, 4
Add or subtract. Simplify if possible.
____ 85.
b 2 − 2b − 8 2
b +b−2 a.
6 −
b−1
b − 10
c.
2
b.
b − 2b − 14 b2 + b − 2
d.
16
b−4 b−1 b − 10 b−1
FINAL EXAM REVIEW 2011 Simplify the complex fraction.
4 ____ 86.
x+3 1 +3 x 12x + 4 a. x 2 + 3x 4x b. 3x + 9
4x c. d.
2
3x + 10x + 3 not here
4x x+ y
____ 87.
7 3x 15x 2 a.
b.
7y
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 a.
−
=
g−5 g−8
22 3
b.
22
c.
d.
−22
____ 89. Use the graph to write an equation for the parabola.
a.
y = −
b.
y =
x2 4
x2 4
x2 2
c.
y =
d.
y = 2x 2
17
14
FINAL EXAM REVIEW 2011 ____ 90. Write an equation for the translation of x 2 + y 2 = 25, 2 units right and 4 units down. 2 2 2 2 a. (x + 2) + ÁËÊ y + 4ˆ˜¯ = 25 c. (x + 2) + ÁËÊ y − 4ˆ˜¯ = 25 2 2 2 2 b. (x − 2) + ÁËÊ y + 4ˆ˜¯ = 25 d. (x − 2) + ÁËÊ y − 4ˆ˜¯ = 25 ____ 91. Write an explicit formula for the sequence 7, 2, –3, –8, –13, ... Then find a 14 . c. a n = −5n + 12; –58 a. a n = −5n + 12; –53 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
yes, 4
d.
no
Is the sequence geometric? If so, identify the common ratio. ____ 95. 6, 12, 24, 48, ... a. yes, 2
b.
yes, –2
c.
Find the missing term of the geometric sequence. ____ 96. 45, a.
, 1620, ... 9720
____ 97. 1250, a.
1200
b.
51
c.
6
d.
270
b.
650
c.
250
d.
125
, 50, ...
____ 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 1 1 1 + + + +… 5 10 20 40 a. It diverges; it has a sum. b. It diverges; it does not have a sum.
c. d.
18
It converges; it has a sum. It converges; it does not have a sum.
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. d.
19
mean = 47.5; standard deviation = 9.4 mean = 47.5; standard deviation = 88.9
