Algebra II Semester 2 Practice Final _18 Pages

Name: ________________________ Class: ___________________ 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
q − 8
a.
q − 3
q − 7
b.
q − 3
c. q − 8
d.
q 2 − 2q − 36
q 2 + 2q − 15
2. Write a polynomial function in standard form with
zeros at –4, 2, and –5.
a. f(x) = x 3 + 7x 2 + 2x − 40
b. f(x) = x 3 + 7x 2 + 2x − 6
c. f(x) = x 3 − 3x 2 − 120x − 6
d. f(x) = x 3 − 40x 2 + 7x + 2
3. Simplify.
− 10 + 2 4 − 3 10
a. 4 10 + 4
b. −4 10 + 2 4
c. −4 10 + 4
d. none of these
4. Multiply.
Ê ˆ Ê ˆ
−2 − 10
Ë
Á
¯
˜ −3 + 10
Ë
Á
¯
˜
a. 16 + 6 10
b. −4 + 6 10
c. −4 + 10
d. −15 − 5 10
5. Rationalize the denominator of the expression.
a.
b.
7 − 3
7 + 3
4 − 2 21
4
10 − 2 21
4
c.
−4 − 21
4
d. −1
6. Write an exponential function y = ab x for a graph
that includes (1, 17.5) and (–1, 2.8).
a. y = 2.5(7) x
b. y = 5(3.5) x
c. y = 7(2.5) x
d. y = 3.5(5) x
7. Write 2x 3 + 2x 2 – 40x in factored form.
a. 2x(x + 5)(x – 4)
b. 5x(x – 4)(x + 2)
c. –4x(x + 2)(x + 5)
d. 2x(x – 4)(x – 5)
8. For the function f(x) = (5 − 6x) 2 , find f −1 .
a. f −1 (x) =±
b. f −1 (x) =±
5 + x
6
5 + x
6
c. f −1 (x) = 5 ± x
6
d. f −1 (x) = 5 ± x
6
1

ID: A
9. Solve. Check for extraneous solutions.
6x = 24 − 12x
a.
2
3
b. −1
c.
2
and −1
3
d. − 2 3
10. Find the product ( 5x − 3)(x − 5x + 2).
a. 5x 4 − 3x 3 + 25x 2 − 5x − 6
b. 5x 4 − 3x 3 − 25x 2 + 25x − 6
c. 5x 3 − 28x 2 + 25x − 6
d. 5x 3 + 22x 2 − 5x − 6
11. Factor the expression.
x 3 − 27
a. (x − 3)(x 2 − 3x + 18)
b. (x − 3)(x 2 + 3x + 9)
c. (x + 3)(x 2 + 3x + 9)
d. (x + 3)(x 2 − 3x + 9)
12. Solve the equation. Check the solution.
5
3k + 1 k =−3
8
a.
3
b. − 8 9
c. − 16
9
d. − 1 2
13. Find the center and radius of the circle with
equation ( x + 8) + Ê
Ë
Á y − 8ˆ¯˜ = 16.
a. (8, –8); 16
b. (–8, 8); 4
c. (8, –8); 4
d. (–8, 8); 16
14. Solve the equation.
x − 9 − 10 =−5
a. 25
b. 34
c. 16
d. 14
15. Solve log(3x + 11) = 2.
a.
89
3
b.
100
3
c. −3
d. 89
16. Divide using synthetic division.
(x 4 − 18x 3 + 44x 2 + 55x − 28) ÷ (x − 4)
a. x 3 + 10x 2 + 68x + 41
b. x 3 − 18x 2 + 10x + 41
c. x 3 − 14x 2 − 12x + 7
d. x 3 − 12x 2 + 7x − 14
17. Solve the equation. Check the solution.
d + 7
d − 4 = d − 5
d + 2
1
a.
3
17
b.
c.
9
17
5
d. − 17
5
18. Divide 4x 3 + 2x 2 − 2x + 3 by x + 3.
a. 4x 2 + 14x − 32, R 87
b. 4x 2 − 10x + 28
c. 4x 2 + 14x − 32
d. 4x 2 − 10x + 28, R –81
3
19. Simplify 48a 13 b 12
positive.
a. 2a 4 3
b a
b. 6a 4 b 4 3
2a
c. 2a 4 b 4 6a
3
d. none of these
. Assume that all variables are
2

ID: A
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.
a. 2.977; log 2
7.874
b. 4.127; log 2
7.874
c. 1.792; log 2
31
d. 2.977; log 2
31
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
a. direct variation; y = 9x
b. inverse variation; y = 9 x
c. neither
22. Expand the logarithmic expression.
log 8
3d 2
a. 3log 8
d 2
b. log 8
3 ⋅ 2 log 8
d
c. log 8
3 − 2 log 8
d
d. log 8
3 + 2 log 8
d
23. Let f(x) = 4x + 6 and g(x) = 2x + 7. Find
(f û g)(5).
a. 74
b. 26
c. 59
d. 17
24. Rationalize the denominator of the expression.
3
4
3
7
a.
3
28
7
b.
3
196
7
c.
3
7 28
d. none of these
25. In how many different orders can you line up 6
cards on a shelf
a. 6
b. 720
c. 120
d. 1
26. Write an equation for the translation of y = −7
x
that has the asymptotes x = –2 and y = –7.
a. y =
−7
x − 2 − 7
b. y =
−7
x + 2 − 7
c. y =
−7
x − 7 − 2
d. y =
−7
x + 7 − 2
27. The values (5.1, 10) and (x, 3) are from an inverse
variation. Find the missing value and round to the
nearest hundredth.
a. 17.00
b. 1.53
c. 51.00
d. 153.00
28. Solve 27x 3 + 343 = 0. Find all complex roots.
a.
7 21 ± 21 3
,
3 18
b. no solution
c. − 7 3 , 7 3
d. − 7 21 ± 21i 3
,
3 18
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.
a. 6w 2 ; quadratic monomial
b. 2w 5 + w 4 − 3w 3 ; quintic trinomial
c. 2w 4 + w 3 − 3w 2 ; quartic trinomial
d. 2w 3 + w 2 − 3w; cubic trinomial
3

ID: A
30. Use synthetic division to find P(–4) for
P(x) = x 4 + 8x 3 + 2x 2 + 5x − 9.
a. –253
b. –4
c. –73
d. 765
31. Expand the logarithmic expression.
log 4
8k 4
a. log 4
8 − 4 log 4
k
b. log 4
8 + 4 log 4
k
c. log 4
8 ⋅ 4 log 4
k
d. 8log 4
k 4
32. Divide using synthetic division.
(x 4 − 12x 3 + 20x 2 + 36x − 45) ÷ (x − 3)
a. x 3 − 9x 2 − 7x + 15
b. x 3 − 7x 2 + 15x − 9
c. x 3 + 6x 2 + 34x + 6
d. x 3 − 12x 2 + 6x + 6
33. Use natural logarithms to solve the equation. Round
to the nearest thousandth.
2e 4x + 11 = 22
a. 0.426
b. –2.151
c. 0.300
d. 0.701
34. Solve the equation.
x + 9 − 8 =−4
a. –5
b. 16
c. 25
d. 7
35. Use natural logarithms to solve the equation. Round
to the nearest thousandth.
8e 4x + 11 = 30
a. 0.216
b. 0.409
c. 0.092
d. –2.420
36. Multiply or divide. State any restrictions on the
variables.
x 2
x − 4 ⋅ x 2 + x − 20
x 2 + 4x
a.
b.
c.
d.
x 2 + 5x
x + 4 , x ≠ 4, − 4
x 2 + 5x
, x ≠ 4, 0, − 4
x + 4
x + 5
, x ≠ 4, 0, − 4
x + 4
x + 5
x + 4 , x ≠ 4, − 4
37. Write the equation in logarithmic form.
4 2 = 16
a. log 16 = 2
b. log 16 = 2 ⋅ 4
c. log 4
16 = 2
d. log 2
16 = 4
4

ID: A
38. Find the foci of the ellipse with the equation x 2
9 + y 2
= 1. Graph the ellipse.
49
a. foci (0, ± 2 10) c. foci (0, ± 58)
b. foci (0, ± 58) d. foci (0, ± 2 10)
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.
x
a.
2
9 + y 2
25 = 1
b.
c.
d.
40. Write an equation for the translation of
x 2 + y 2 = 49, 4 units right and 2 units down.
a. ( x + 4) + Ê
Ë
Á y − 2ˆ¯˜ = 49
b. ( x − 4) + Ê
Ë
Á y − 2ˆ¯˜ = 49
c. ( x − 4) + Ê
Ë
Á y + 2ˆ¯˜ = 49
d. ( x + 4) + Ê
Ë
Á y + 2ˆ¯˜ = 49
x 2
5 + y 2
3 = 1
x 2
3 + y 2
5 = 1
x 2
25 + y 2
5

ID: A
41. Use the Pascal’s Triangle to expand the bionomial 42. Multiply or divide. State any restrictions on the
(d + 2b) 3 .
variables.
a. d 3 − 6d 2 b + 12db 2 − 8b 3
t 2
b. d 3 + 3d 2 b + 3db 2 + b 3
c. d 3 − 3d 2 b + 3db 2 − b
t + 2 ⋅ t2 + t − 2
t 2 − 3t
3
d. d 3 + 6d 2 b + 12db 2 + 8b 3 t 2 − t
a.
t − 3 , t ≠ −2, 3
b.
c.
d.
t 2 − t
, t ≠ −2, 0, 3
t − 3
t − 1
, t ≠ −2, 0, 3
t − 3
t − 1
t − 3 , t ≠ −2, 3
43. Factor the expression.
x 4 − 25x 2 + 144
a. (x − 4)(x + 4)(x − 3)(x + 3) c. (x − 4)(x − 4)(x + 3)(x + 3)
b. (x − 4)(x − 3)(x 2 ) d. no solution
44. Divide and simplify.
3
120x 27
3
3x
3
a. 24x 26
b. 2x 8 24x 2
c. 5x 2 3
2x 8
d. 2x 8 3
5x 2
45. Solve ln(4x − 4) = 8. Round to the nearest
thousandth.
a. 2,981.958
b. 746.239
c. 2,976.958
d. 744.239
46. Simplify.
1
3
3
⋅ 9
a. 9
1
3
b.
3
3
c. 3
d. 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.
a. y = 6z
wx ; 12
b. y = 8wx
z ; 64
c. y = 6wx
z ; 48
d. y = 8z
wx ; 1
48. Multiply.
2
Ê ˆ
−5 − 3
Ë
Á
¯
˜
a. 28 + 10 3
b. 28 − 10 3
c. −13 + 5 3
d. 25 − 10 3
6

ID: A
49. Graph the equation.
16x 2 + 4y 2 = 49
a.
c.
The graph is an ellipse. The center is at
the origin. It has two lines of symmetry,
the x-axis and the y-axis.
The graph is a circle. The center is at the
origin. Every line through the origin is a
line of symmetry.
b.
d.
The graph is an ellipse. The center is at
the origin. It has two lines of symmetry,
the x-axis and the y-axis.
50. Use a graphing calculator. Use the graph of y = e x
to evaluate e 1.7 to four decimal places.
a. 5.4739
b. 4.6211
c. 2.7183
d. 0.1827
The graph is a circle. The center is at the
origin. Every line through the origin is a
line of symmetry.
51. Simplify the rational expression. State any
restrictions on the variable.
p 2 − 4p − 32
p + 4
a. −p + 8; p ≠ −4
b. p − 8; p ≠ −4
c. −p − 8; p ≠ 4
d. p + 8; p ≠ 4
7

ID: A
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)
x
a.
2
25 + y 2
16 = 1
b.
c.
d.
x 2
16 + y 2
25 = 1
x 2
5 + y 2
4 = 1
x 2
4 + y 2
5 = 1
53. Find the inverse of y = 7x 2 + 7.
a. y =±
b. x =
x − 7
7
y − 7
7
x + 7
c. y =±
7
d. y 2 = x + 7
7
54. Rationalize the denominator of the expression.
Assume that all variables are positive.
7x 9 y 7
a.
b.
2x 3 y 2
x 3 y 2
2
14y
14x 12 y 9
2x 3 y 2
c. 2x 3 y 2 14y
d. none of these
55. Write the equation in logarithmic form.
6 4 = 1, 296
a. log 6
1, 296 = 4
b. log 1, 296 = 4
c. log 1, 296 = 4 ⋅ 6
d. log 4
1, 296 = 6
56. Suppose that x and y vary inversely, and x = 7 when
y = 11. Write the function that models the inverse
variation.
a. y = 1.57x
b. y = 77
x
c. y = 4 x
d. y = 18
x
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
a. direct variation; y = 14x
b. inverse variation; y = 504
x
c. neither
58. Describe the combined variation that is modeled by
the formula or equation.
y =
w
2x 2
a. y varies directly as w and inversely as x.
b. y varies directly as w and inversely as the
square of 2x.
c. y varies directly as the square of x and inversely
as w.
d. y varies directly as w and inversely as the
square of x.
59. Describe the combined variation that is modeled by
the formula or equation.
a = F m
a. a varies directly as F and inversely as m.
b. a varies directly as m and inversely as F.
c. a varies directly as F and m.
d. y varies inversely as F and m.
8

ID: A
60. Graph the conic section.
4x 2 − 9y 2 = 144
a. c.
b. d.
61. Write an equation of an ellipse with center (3, –3),
vertical major axis of length 12, and minor axis of
length 6.
a.
b.
c.
d.
( x + 3) 2
6
( x − 3) 2
12
( x + 3) 2
36
( x − 3) 2
9
−
Ê
Ë
Á y − 3 ˆ¯˜ 2
12
= 1
+
Ê
Ë
Á y + 3 ˆ¯˜ 2
6
= 1
−
Ê
Ë
Á y − 3 ˆ¯˜ 2
9
= 1
+
Ê
Ë
Á y + 3 ˆ¯˜ 2
36
= 1
62. Write an equation of a hyperbola with vertices (3,
–2) and (–9, –2), and foci (7, –2) and (–13, –2).
a.
Ê
(x − 3) 2 Ë
Á y − 2 ˆ¯˜ 2
−
36 64
= 1
b.
Ê
(x − 3) 2 Ë
Á y − 2 ˆ¯˜ 2
−
12 16
= 1
c.
Ê
(x + 3) 2 Ë
Á y + 2 ˆ¯˜ 2
−
12 16
= 1
d.
Ê
(x + 3) 2 Ë
Á y + 2 ˆ¯˜ 2
−
36 64
= 1
9

ID: A
63. Sketch the asymptotes and graph the function.
2
y =
x + 2 − 3
a. c.
b. d.
64. Simplify the rational expression. State any
restrictions on the variable.
q 2 + 11q + 24
q 2 − 5q − 24
q + 8
a. ; q ≠ −3, q ≠ −8
q − 8
−(q + 8)
b.
q − 8 ; q ≠ 8
c.
d.
q + 8
q − 8 ; q ≠ −3, q ≠ 8
−(q + 8)
q − 8 ; q ≠ −3, q ≠ 8
65. Solve the equation. Check the solution.
−2
x + 4 = 4
x + 3
a. − 13
6
b. −11
c. − 8 3
d. − 11
3
10

ID: A
66. Multiply or divide. State any restrictions on the
variables.
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)
67. Add or subtract. Simplify if possible.
w 2 + 2w − 24
w 2 + w − 30 + 8
w − 5
w − 4
a.
w − 5
b.
w 2 + 2w − 16
w 2 + w − 30
c. w + 4
d.
w + 4
w − 5
69. Simplify the complex fraction.
3
4y − 2 y
1
y + 3 2y
a.
20
3
b. − 1 2
c. −2
d.
3
20
70. Solve the equation. Check the solution.
a
a 2 − 36 + 2
a − 6 = 1
a + 6
a. –9
b. –6
c. –9 and –6
d. 6
71. Write an exponential function for the graph.
68. State the property or properties of logarithms used
to rewrite the expression.
log 625x 4 = 1 log 5x
5
a. Commutative Property
b. Product Property
c. Quotient Property
d. Power Property
a. y = 0.5(2) x
b. y = 2(0.5) x
c. y = (2 ⋅ 0.5) x
d. y = 2(5) x
11

ID: A
72. Graph y = 76 () x + 2 + 1.
a. c.
b. d.
73. Evaluate the logarithm.
1
log 5
625
a. –3
b. 5
c. –4
d. 4
74. Write the equation log 32
8 = 3 5
a.
3
5
32 = 8
b.
3
5
8 = 32
c.
32
Ê 3 ˆ
Ë
Á 5 ¯
˜
= 8
5
d.
3
8 = 32
in exponential form.
12

ID: A
75. State the property or properties of logarithms used
to rewrite the expression.
log 5
6 − log 5
2 = log 5
3
a. Quotient Property
b. Product Property
c. Difference Property
d. Power Property
76. State the property or properties of logarithms used
to rewrite the expression.
2log6 + log 1 = log 12
3
a. Power Property and Product Property
b. Quotient Property and Product Property
c. Quotient Property only
d. Power Property only
77. Write the expression as a single logarithm.
5log b
q + 2log b
y
a. log b
(q 5 y 2 )
b. ( 5 + 2) log Ê
b Ë
Áq + yˆ¯˜
c. log Ê b
q 5 + y 2 ˆ
Ë
Á
¯
˜
d. log Ê b
qy 5 + 2 ˆ
Ë
Á
¯
˜
78. Write the expression as a single logarithm.
log 3
4 − log 3
2
79. Expand the logarithmic expression.
n
log 7
2
a. log 7
n − log 7
2
b.
log 7
n
log 7
2
c. log 7
2 − log 7
n
d. −n log 7
2
80. Expand the logarithmic expression.
57
log b
74
a.
1
2 log 57 + 1 b
2 log 74 b
b.
1
2 log 57 − 1 b
2 log 74 b
c. log b
57 − log b
74
1
d. log b
(57 − 74)
2
81. Solve 15 2x = 36. Round to the nearest
ten-thousandth.
a. 0.6616
b. 2.6466
c. 1.7509
d. 1.9091
82. Use the Change of Base Formula to solve 2 2x = 90.
Round to the nearest ten-thousandth.
a. 7.6133
b. 9.3658
c. 3.2459
d. 12.9837
83. Write the expression as a single natural logarithm.
3ln3 + 3lnc
a. ln( 27 + c 3 )
b. ln 9c 3
c. ln 27c
d. ln 27c 3
84. Find all the real square roots of 0.0004.
a. 0.00632 and –0.00632
b. 0.06325 and –0.06325
c. 0.0002 and –0.0002
d. 0.02 and –0.02
13

ID: A
85. Find the real-number root.
− 125
3
343
25
a.
49
b. − 125
343
c. − 125
1029
d. − 5 7
86. Multiply and simplify if possible.
6 ⋅ 2
a. 2 3
b. 12
c. 3 2
d. not possible
87. Multiply and simplify if possible.
Ê
ˆ
7x x − 7 7
Ë
Á
¯
˜
a. x 7 − 49 x
b. 7x − 49x
c. x 7 − x 49
d. − 42x
88. Divide and simplify.
3
3
162
2
3
a. 3 3
3
b. 162
3
c. 3 3
d. 3 3
89. Divide and simplify.
90x 18
2x
a. 3x 8 5x
b. 18x 17
c. 5x 3x 8
d. none of these
90. Rationalize the denominator of the expression.
Assume that all variables are positive.
6x 8 y 9
a.
b.
5x 2 y 4
x 3 y 2
5
30y
30x 10 y 13
5x 2 y 4
c. 5x 3 y 2 30y
d. none of these
91. Rationalize the denominator of the expression.
Assume that all variables are positive.
3
2 + 3
a.
b.
c.
d.
3
6
3
2 6
3
2 36
3
2 6
3
2 36
3
+ 9 18
6
3
+ 3 2
6
3
+ 9 4
6
3
+ 3 4
6
92. Add if possible.
4
2 2x
4
a. 8 4x
4
+ 6 2x
4
b. 16 2x
4
c. 8 2x
d. not possible to simplify
93. Add if possible.
3
4 3x
3
a. 9 13x
3
b. 27 3x
3
+ 5 10x
c. 27 10x
3
d. not possible to simplify
14

ID: A
94. Subtract if possible.
4
4
2 5a − 6 5a
4
a. −20 5a
4
b. 8 5a
4
c. −4 5a
d. not possible to simplify
95. Simplify.
1
20 2
⋅ 20
1
1
2
a.
4
20
b. 20
c. 20
d. 1
8
96. Write the exponential expression 3x in radical
form.
8
a. 3 x 3
8
b. 3x 3
3
c. 3 x 8
3
d.
8 8
3 x 3
97. Solve the equation.
2
( x − 7)
3 = 4
a. 11
b. 15; –1
c. –3
d. 1; –1
98. Solve the equation.
1
( −2x + 6)
5 = ( −8 + 10x)
a.
7
6
b.
2
3
c. − 1 4
d.
6
7
1
5
3
99. Let f(x) = −3x − 6 and g(x) = 5x + 2. Find f(x) +
g(x).
a. 2x – 4
b. –8x – 8
c. –8x – 4
d. 2x – 8
100. Let f(x) = x 2 + 2x − 1 and g(x) = 2x − 4. Find
2f(x) – 3g(x).
a. 2x 2 − 2x − 14
b. −3x 2 − 2x − 1
c. 2x 2 − 2x + 10
d. −3x 2 − 2x − 7
101. Let f(x) = x 2 + 6 and g(x) = x + 8 . Find
x
Ê
Ë
Á g û f ˆ¯˜ ( −7).
a. − 55
7
384
b.
7
295
c.
49
63
d.
55
102. Find the inverse of y = 7x 2 − 3.
x + 3
a. y =±
7
y + 3
b. x =
7
c. y 2 = x − 3
7
x − 3
d. y =±
7
103. For the function f(x) = x + 9, find (f û f −1 )(5).
a. 14
b. 5
c. –5
d. 25
15

ID: A
104. Let f(x) = 4 + 5x and g(x) = 2x − 1. Find f(g(x))
and g(f(x)).
a. f(g(x)) = 10x – 1; g(f(x)) = 10x + 7
b. f(g(x)) = 7x + 3; g(f(x)) = 10x + 7
c. f(g(x)) = –7x – 3; g(f(x)) = –10x + 7
d. f(g(x)) = –10x – 7; g(f(x)) = 7x + 3
105. Evaluate the logarithm.
1
log 3
243
a. –4
b. 3
c. –5
d. 5
106. Graph the function.
y = x + 3
a. c.
b. d.
107. Classify –3x 5 – 2x 3 by degree and by number of
terms.
a. quintic binomial
b. quartic binomial
c. quintic trinomial
d. quartic trinomial
108. Classify –7x 5 – 6x 4 + 4x 3 by degree and by number
of terms.
a. quartic trinomial
b. quintic trinomial
c. cubic binomial
d. quadratic binomial
16

ID: A
109. Write the polynomial 6x 2 − 9x 3 + 3
in standard
3
form.
a. −3x 3 + 2x 2 + 1
b. 2x 2 − 3x 3 + 1
c. −3x 3 + 2x 2
d. 2x 2 − 3x 3
110. Find the zeros of f(x) = (x + 3) 2 (x − 5) 6 and state
the multiplicity.
a. 2, multiplicity –3; 5, multiplicity 6
b. –3, multiplicity 2; 6, multiplicity 5
c. –3, multiplicity 2; 5, multiplicity 6
d. 2, multiplicity –3; 6, multiplicity 5
111. Divide using synthetic division.
(x 3 + 4 − 11x + 3x 2 ) ÷ (6 + x)
a. x 2 − 5x, R 70
b. x 2 − 5x, R –62
c. x 2 − 3x + 7, R 46
d. x 2 − 3x + 7, R –38
112. Solve x 4 − 34x 2 = −225.
a. no solution
b. 3, –5
c. 3, –3, 5, –5
d. 3, –3
113. Evaluate the expression.
5!
a. 24
b. 120
c. 15
d. 720
114. Evaluate the expression.
7!
4! 3!
a. 13
b. 35
c. 79
d. 840
115. Use Pascal’s Triangle to expand the binomial.
(s − 5v) 5
a. s 5 − 5s 4 v + 10s 3 v 2 − 10s 2 v 3 + 5sv 4 − v 5
b. s 5 + 125s 4 v − 1250s 3 v 2 + 6250s 2 v 3 − 15625sv 4 + 15625v 5
c. s 5 − 25s 4 v + 250s 3 v 2 − 1250s 2 v 3 + 3125sv 4 − 3125v 5
d. s 5 − 25s 4 + 250s 3 − 1250s 2 + 3125s − 3125
116. Simplify.
− 2 − 2 25 − 6 2
a. 7 2 − 10
b. −7 2 − 2 25
c. −7 2 − 10
d. none of these
117. Divide and simplify.
225x 24
3x
a. 5x 11 3x
b. 75x 23
c. 3x 5x 11
d. none of these
118. Multiply.
2
Ê ˆ
6 + 5
Ë
Á
¯
˜
a. 41 − 12 5
b. 17 + 6 5
c. 36 − 12 5
d. 41 + 12 5
119. Write 5x 3 – 5x 2 – 30x in factored form.
a. 5x(x – 3)(x – 2)
b. 2x(x – 3)(x + 5)
c. 5x(x + 2)(x – 3)
d. –3x(x + 5)(x + 2)
17

ID: A
3
120. Simplify 162a 13 b 6
positive.
a. 3a 4 3
b a
b. 6a 4 b 2 3
3a
c. 3a 4 b 2 3
6a
d. none of these
. Assume that all variables are
121. Write an exponential function y = ab x for a graph
that includes (0, 4) and (1, 14).
a. y = 7(2) x
b. y = 4(3.5) x
c. y = 2(7) x
d. y = 3.5(4) x
125. Solve the equation. Check the solution.
k + 5
k + 8 = k + 4
k − 5
a. − 19
4
b. − 7 4
c. − 7 12
d.
7
4
122. Simplify.
1
10
3
⋅ 100
a. 10
b. 10
c. 100
3
d. 10
1
3
123. Write a polynomial function in standard form with
zeros at –5, –2, and –4.
a. f(x) = x 3 + 40x 2 + 11x + 38
b. f(x) = x 3 + 11x 2 + 38x + 13
c. f(x) = x 3 + 11x 2 + 38x + 40
d. f(x) = x 3 + 14x 2 + 240x + 13
124. Find the inverse of y = 6x 2 − 2.
a. y 2 = x − 2
6
b. y =±
c. x =
d. y =±
x − 2
6
y + 2
6
x + 2
6
18