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Name: __________________________ Date: _____________
1. Which graph represents the interval?
(, –1]
A)
]
(

–1
B)
)
(

–1
C)
]
[

–1
D)
)
–1
E)
]
–1
2. Reduce the index of the radical.
15 y 24
1
A) y
9
9
B) y
5
C)
y8
D)
9
y
E)
y9
3. Find the greatest common factor of the expression.
45t5m4, 150t2m9, 30t9
A) 3t2 B) 3t2m4 C) 15t2m4
D) 15t9m9 E) 15t2
4. Evaluate the expression without using a calculator.
–4 / 3
1
 
8
1
A) 16

B)
1
6
1
C) 6
D) 16 E) –16
Page 1
5. Give a verbal description of the subset of real numbers represented by the interval.
[–4, 1)
A) all integers between –4 and 1, including –4 but not including 1
B) all integers between –4 and 1, including 1 but not including –4
C) all real numbers between –4 and 1, including –4 but not including 1
D) all real numbers between –4 and 1, including 1 but not including –4
E) all real numbers between –4 and 1, including –4 and 1
6. Perform the multiplication and simplify.
n2  1
n+5
2
2
6n + 23n – 35
7 n + 9n + 2
A)
n +1
, n  1, n  –5
 6n – 7  7n + 2 
n –1
, n  –1, n  –5
 6n – 7  7n – 2 
E)
n –1

, n  1, n  –5
 6n + 7  7n + 2
D)
n –1
, n  –1, n  –5
 6n – 7  7n + 2 
C)
n +1
, n  –1, n  –5
 6n – 7  7n – 2 
B)
7. Plot the two real numbers on the real number line. Then place the appropriate inequality symbol (< or >)
between them.
2, 1
A) 2 < 1 B) 2 > 1
8.
1 13
  40  0
2
x
Find all solutions of x
.
A) x  –5, – 8
9.
B) x  –5,8
1 1
x   ,
5 8
C)
D)
1 1
,
13 3
log 4 20  log 4 5 without using a calculator.
5
B) 1 C) 5 D) 2 E) 4
Find the exact value of
1
A) 2
x
Page 2
x
E)
1 1
,
13 3
10. Determine which numbers in the set are rational numbers.
2
,
3
4.3636..., – 8,
A)
B)
C)
D)
E)
37,
36
, – 5.040040004...,
5
36
, – 5.040040004...
5
36
– 8,
, – 5.040040004...,
5
36
, 36
5
36
– 8,
, 36
5
2
36
– 8,  ,
3
5
36
4.3636..., – 8,
4.3636...,
–8,
37,
4.3636...,
4.3636...,
36
11. Rationalize the denominator. Then simplify your answer.
4
33
16
A) 33
12.
8
B) 33
4 33
C) 33
2 33
D) 33
E)
37
33
1
f ( x)  ln x at x  14.67
5
Evaluate the function
. Round to 3 decimal places. (You may use your
calculator.)
A) 1.237 B) 0.537 C) 1.218 D) –0.322 E) undefined
13. Evaluate the expression.
32 
3
B) –18 C) –729 D)
A) 3

1
729
1
E) 729
14. Use a calculator to evaluate the expression. (Round your answer to three decimal places.)
7.96 10–1 
1/ 4
A) 1.990 10–1
B) 9.446 10–1
15.
Rewrite the logarithmic equation
36
A) 6
1/ 36
 – 2 B) 6
C) 4.476 100 D) 2.987 100 E) 1.990101
log 6
 – 2 C)
1
–2
36
in exponential form.
6
–2
1

36
Page 3
 1 
 
D)  36 
–2
6 –2  
6
E)
1
36
16. Simplify the radical expression.
3 81q8u –9
3q 3 3q5
A)
17.
u u6
Solve:
18.
3q 3 3q 2
u
C)
u3
B)
27q 3 3q5
27q 6 3 3q 2
u9
D)
E)
u u6
–9  x – 9  –3 2  x   2
x–
A)
3q 2 3 3q 2
1
8
x–
B)
73
6
x
C)
89
8
x–
D)
73
12
x
E)
89
12
2
2
3 
2
9

x+   y +  
4 
5
25 .
Determine the center and radius of the circle represented by the equation 
A)
D)
3
2
 2
 3
3
3
– , – 
– , – 
5
4
4
5
 ; radius: 5
 ; radius: 5
center: 
center: 
3 2
9
 , 
4
5
 ; radius: 25
center: 
C)
3 2
9
–
 , 
center:  4 5  ; radius: 25
B)
E)
2 3
3
–
 , 
5
4
 ; radius: 5
center: 
19. Write the polynomial in standard form.
–5 + 4x2 + 7x
A) –5 + 7 x + 4 x 2
B) 4 x 2 + 7 x – 5
C) 7 x – 5 + 4 x 2
D) 4 x 2 – 5 + 7 x
E) –5 + 4 x 2 + 7 x
20. Factor the perfect square trinomial.
9y2 + 24y + 16
A) (3y – 4)(3y + 4) B) (9y – 4)(y + 4) C) (–3y + 4)2 D) (3y + 4)2 E) (3y – 4)2
21. Write the rational expression in simplest form.
6n – 48n2
56n – 7
A) 6n
, n0
7
B) 6n
1
, n
7
8
C)
6n
1
 , n
7
8
D)
6n
1
, n , n0
7
8
E)
6n
 , n0
7
Page 4

22. Find the value(s) of x for which f (x) = g (x).
f (x) = x2 – 14x + 34
7
A) 34, 48, 2
23.
g (x) = –2x + 7
7
B) 34, –14, 2
7
C) 3, 9 D) –3, –9 E) –20, 2
7  x – 8  7 x – 49
Solve:
A) x  7
B) –7  x  8
C) x  –48
D) x  –8
E) no solution
25. Identify the degree and leading coefficient of the polynomial.
–6x4y + 8x2y2 + xy5
A) degree: 5
leading coefficient: 1
B) degree: 6
leading coefficient: 1
C) degree: 6
leading coefficient: –6
D) degree: 5
E) degree: 4
leading coefficient: –6
leading coefficient: –6
27. Factor the expression by removing the common factor with the smaller exponent.
x3 + 7x–1
x4 + 7
A) x3(1 + 7x2) B) x(x2 + 7)
C) x(x4 + 7) D)
x
x2 + 7
x
E)
28. Determine which numbers in the set are whole numbers.
36
8
, –16, 13,
9
9
A) 16, – 20, 0, –16, 13
16, – 20, 0,
D)
36
8
, 13,
9
9
E)
36
16, 0,
, 13
9
B) 16, 13
16, 0,
C) 16, 0, 13
29. Perform the division and simplify.
9u 2 – 12u + 3

u –1
9u 2 – 17u – 2 9u 2 + 73u + 8
A) 3  3u – 1 u + 8 
1
, u  1, u  –
u+2
9
B) 3  3u – 1 u – 8 
1
, u  1, u 
u–2
9
C) 3  3u + 1 u + 8 
1
, u  –1, u  –
u–2
9
D)
3  3u – 1 u + 8 
E)
u–2
3  3u – 1 u + 8 
u–2
Page 5
, u  1, u  –
, u2
1
9
–8  x + 9 
30.
9
Write a verbal description of the algebraic expression
without using the variable.
A) 9 more than the product of –8 and some number, divided by 9 .
B) 9 less than the product of –8 and some number, divided by 9 .
C) The quotient of –8 and 9 , divided by the sum of a number and 9 .
D) The quotient of –8 and 9 , times the sum of a number and 9 .
E) 9 less than the product of –8 and the sum of a number and 9 .
31. Perform the subtraction and simplify.
7x
3

x5 5 x
7x + 3
7x – 3
A) 5  x
B) x + 5
7x + 3
C) x + 5
7x + 3
D) x  5
7x – 3
E) x  5
32. Find the slope-intercept form of the equation of the line that passes through the given point and has the
indicated slope.
point: (–1, 7)
slope: m = –4
A) y = –4x + 7 B) y = –4x + 27 C) y = –4x + 3 D) y = –4x – 1 E) y = –4x – 8
33.
x
Evaluate the function f ( x)  1.7 at x = 2.7. Round to 3 decimal places.
A) 5.412 B) 4.590 C) 14.611 D) 4.190 E) 2.890
34.
Expand the expression
as a sum, difference, and/or constant multiple of logarithms.
A)
B)
C)
D)
E)
35. Plot the two real numbers on the real number line. Then place the appropriate inequality symbol (< or >)
between them.
1
3
– , –
5
16
1
3
– –
16
A) 5
–
B)
1
3
–
5
16
Page 6
36.
5–2 
Rewrite the exponential equation
A)
1
–2
25
B) log 2 25  – 2
log5
1
25 in logarithmic form.
D) log 25 5  – 2
E)
log5
1
2
25
C) log5 25  – 2
37. Factor by grouping.
r3 – 9r2 + 6r – 54
A) r2 + 6(r – 9)
B) (r2 + 6)2(r – 9)
C) (r2 + 6)(r – 9)
D) (r2 – 6)(r + 9)
E) (r2 + 6)(r – 9)2
39. Use the One-to-One Property to solve the following equation for x.
23x  128
128
64

3
A) 3
B)
7
C) 3
3
D) 7
E) 2
40. Find (if possible) the supplement of 117 .
A) 27 B) 63 C) 57 D) 87 E) not possible
41.
2
Determine the vertex of the graph of the quadratic function f ( x)  x – 6 .
A)
 0, 6 
B)
 –6,0
C)
 –6, –6
 0, –6
D)
E)
 6, 0 
42. Approximate the numbers and place the correct symbol (< or >) between them.
A) –1.5 < 0 B) –1.5 < –1 C) –1.5 < 1 D) –1.5 > 1
E) –1.5 > 0
43. Find ( f  g )(x).
f ( x)  7 x2 + 7 x
A)
g ( x)  –3  x
D)
7 x2 + 7 x
, x3
–3  x
B)
7 x2 + 7 x
( f / g )( x) 
, x  –3
–3  x
C)
7 x2 + 7 x
( f / g )( x) 
, x0
–3  x
( f / g )( x) 
E)
Page 7
( f / g )( x) 
7x + 7
, x0
–3
( f / g )( x)  –
7 x2
– 7, x  0
3
44. Find ( f + g)(x).
f (x) = 7x2 + x – 1
g(x) = 3x2 – 3x + 1
A) ( f + g)(x) = 4x4 + 4x2 – 2
B) ( f + g)(x) = 10x4 – 2x2
C) ( f + g)(x) = 4x2 + 4x – 2
D) ( f + g)(x) = 10x2 – 2x
E) ( f + g)(x) = –10x2 + 2x
46. The value of an investment is presently $9436.14. It had been paying 8% compounded continuously since
the investment was made 8 years ago. How much was invested originally?
A) $4546.87 B) $4975.61 C) $5923.86 D) $6821.06 E) $2161.69
47.
2
Solve the equation ln x  ln(e ) for x using the One-to-One Property.
e
A)
2
C) 2 D) e
B) e
E) The equation has no solution.
48. Factor out the common factor.
12n – 4
A) 4(8n) B) 4(3n) C) 4(3n – 1)
D) 12(n – 1) E) 12(n + 1)
49. Use inequality notation to describe the set.
q is positive
A) q   B) q   C) q  0 D) q  0 E) q  0
51. Factor the sum or difference of cubes.
27x3 + 8
A) (3x – 2)3
B) (3x + 2)3
C) (3x + 2)(9x2 – 6x + 4)
D) (3x + 2)(9x2 + 6x + 4)
E) (3x – 2)(9x2 – 6x + 4)
52. Use a calculator to approximate the number. (Round your answer to three decimal places.)
5 625
A) 3.624 B) 3125.000 C) 25.000 D) 125.000 E) 630.000
53. Use the One-to-One Property to solve the following equation for x.
5 x1
1
 
3
4
A) 5
 27

B)
3
5
1
C) 5

D)
2
5
1
E) 3
54. Use a calculator to approximate the number. (Round your answer to three decimal places.)
 12 
 
7
–9 / 2
11/ 9
 5
 
 7
A) –0.574 B) 0.007 C) 0.001 D) 0.751 E) 11.971
55. Evaluate the expression for the given value of x.
3x 4
A) –48
x = –4
–
B)
1
768
1
C) 768
D) 768 E) –768
Page 8
56. Find the area of the shaded region in the figure. Write your result as a polynomial in standard form.
A) 7x2 + 17x
B) 7x2 + 23x
C) 9x2 + 17x
D) 9x2 + 23x
E) 8x2 + 18x
57. Evaluate the function for the indicated values.
f ( x)  3 x + 9 – 2
1
 
6
(i) f (4)
(ii) f (–2.4)
A) (i) 38
(ii) 16
B) (i) 38
(ii) 16
C) (i) 37
(ii) 19
58.
Evaluate the function
(iii) f
(iii) 25
(iii) 28
(iii) 28
D) (i) 37
E) (i) 37
f ( x)  log 2 x at x 
(ii) 19
(ii) 16
(iii) 25
(iii) 25
1
2 without using a calculator.
1
A) 0 B) –1 C) –2 D) 2 E) 2
59. Simplify the radical expression.
175q9 – 7 7q9
A)
–245q 4 q
B)
–2q 4 7q
C)
–35q 4 7q
9
D) –7q 182
9
E) –6q 182
60. Evaluate the expression.
x7
, x  –7
x7
A) 7
61.
B) x C) x
Find f g .
f (x) = 4x – 9
A) ( f g )( x) 
B) ( f
C) ( f
D) 1 E) 1
g (x) = x + 2
D) ( f
4x – 1
g )( x)  4x – 7
E)
g )( x)  4x2 – x – 18
Page 9
g )( x)  3x – 11
( f g )( x)  3x – 7
62. Perform the operation.
Add 6.2x5 – 8.4x4 – 6.7x and –8.3x5 + 0.9x – 5.1.
A) –2.1x5 – 7.5x4 – 11.8x
B) –2.1x10 – 7.5x5 – 11.8x
C) –2.1x5 – 7.5x – 11.8
D) –2.1x5 – 8.4x4 – 5.8x – 5.1
E) –2.1x10 – 8.4x4 – 5.8x2 – 5.1
63. State whether the polynomial is a monomial, binomial, or trinomial.
7x3y2
A) monomial B) binomial C) trinomial
64. Estimate the slope of the line.
A)
B)
C)
D)
E)
Page 10
65. Use the Vertical Line Test to determine in which of the graphs y is not a function of x.
A) x
B) x
C) x
D) x
E)
All of the choices (A, B, C, and D) represent functions.
67. Determine whether the function is even, odd, or neither.
A)
B)
C)
Page 11
68.
Solve the equation log(1  x)  log(10) for x using the One-to-One Property.
A) 11 B) –9 C) –11 D) 0 E) The equation has no solution.
69. Evaluate the function at the specified value of the independent variable and simplify.
q (y) = 2y + 5
q (–0.1)
A) –0.2y + 10 B) –5.2 C) 4.8 D) –0.1y + 5 E) –0.1y – 5
70.
5
Determine which of the following values of x is a solution to the equation
A) x  –3
x–
B)
3
5
C) x  –4
D) x  5
1
6
x+4
.
E) x  3
71. Identify the rule of algebra illustrated by the statement.
–2r + 9r = (–2 + 9)r
A) associative property of addition
D) commutative property of multiplication
B) commutative property of addition
E) distributive property
C) associative property of multiplication
72.
2
Solve ln x  ln 7  0 for x.
B)  7, 7
A) 49
73.
49
C) e
Identify the the value of the function
A) 10
B) 1010
C) 101/2
1
D) 2
7/2
D) e
E) no solution
f ( x)  log10 10 .
E) undefined
74. Determine which numbers in the set are irrational numbers.
17
19
, 0,
, 9, 5.090990999..., 6
4
6
17 19
,
, 9, 6
4
6
17
19
, 0,
, 9, 6
4
6
17 19
,
, 5.090990999..., 6
4
6
17 19
1.222...,
,
, 9, 5.090990999..., 6
4
6
17 19
,
, 6
4
6
1.222...,
A)
B)
C)
D)
E)
Page 12
75. Does the table describe a function?
Input value
2001 2002 2003 2004 2005
Output value
A) yes
76.
70
40
60
50
B) no
log 6 17 in terms of the natural logarithm.
ln17
ln 6
log 6 e E) ln17
B) ln17 C) ln 6 ln17 D)
Rewrite the logarithm
ln17
A) ln 6
77.
40
Find g f .
f (x) = x + 8
A) ( g f )( x) 
g (x) = x2
x2 + 8
B)
( g f )( x)  x2 – 64
C)
( g f )( x)  x2 + 64
D)
( g f )( x)  x2 + 8x + 64
E)
( g f )( x) 
x2 + 16x + 64
79. Write the slope-intercept form of the equation of the line through the given point parallel to the given line.
point: (–4, 5)
line: –30x – 6y = 0
A)
D) y = –5x – 15
1
77
y
B)
x+
30
15
1
29
y  x+
5
5
C)
y = –30x + 125
E)
80. Completely factor the expression.
2(7 + 9n)2 + (n + 6)(7 + 9n)
A) (7 + 9n)2 + (n + 6)
B) 3(7 + 9n)(n + 6)
C) (7 + 9n)(19n + 20)
y = –5x + 21
D) (7 + 9n)3(n + 8)
E) 3(7 + 9n)3(n + 6)
81. Completely factor the expression.
2n3 + 128
A) 2(n + 4)2(n – 4)
B) 2(n + 4)(n – 4)2
C) 2(n – 4)(n2 + 4n + 16)
D) 2(n + 4)(n2 + 4n + 16)
E) 2(n + 4)(n2 – 4n + 16)
Page 13
82. Create and complete a table to find the x and y coordinates of points that lie on the graph of the
2
equation y  x – 4 x . Plot at least 5 points along with the graph of the equation.
A)
B)
C)
Page 14
D)
E)
Page 15
83.
Simplify the expression
A)
2  log5 7
B)
log5 175 .
35log5 2
C) 7
2log5 7
D)
E) The expression cannot be simplified.
84. Evaluate the expression without using a calculator.
81 –3 / 4
1
A) –27 B) 81 C) –81 D) 27
85.
x x
7x
 7
55
Solve: 11 5
385
55
x–
x–
13 B)
6
A)

E)
1
27
C) x  –55
x–
D)
6
55
x
E)
385
9
86. Evaluate the expression.
46
45
6
A) 5

B)
1
4
1
C) 4
D) 4 E) –4
88. Approximate the numbers and place the correct symbol (< or >) between them.
–4
A)
1
1
1
4 1
2
B) 2
1
–4  –1
2
C)
–5
D)
1
1
1
–4  –1
2
2
E)
89. Determine two coterminal angles (one positive and one negative) for   –478 .
A) 152 , – 208
D) 242 , –118
B) 332 , – 388
E) 242 , – 298
C) 152 , – 298
90. After 2 years, an investment of $400 compounded annually at an interest rate r will yield an amount of
400(1 + r)2.
Write this polynomial in standard form.
A) 800 + 800r
D) 400r2 + 800r + 400
2
B) 160,000 + 320,000r + 160,000r
E) 400r2 + 400r + 400
2
C) 400 + 800r + 400r
91. Simplify the expression.
–5r 3 –3r 7


13
A) 45r
13
B) 135r
3
24
C) 135r
24
D) 15r
Page 16
24
E) 45r
92.
log 3
A) log142
93.
log3 142 in terms of the common logarithm (base 10).
log142
log142
log 3 10 E) log142
B) log 3
C) log 3 log142 D)
Rewrite the logarithm
Find three ordered pairs satisfying y  4 x – 3 .
A)  4, 25  5,17   6, 21
,
,
B)  4,13  5, 21  6, 21
,
,
C)  4,13  5,17   6, 21
,
,
D)
E)
5,17 ,  6, 29 ,  7, 25
5,17 ,  6, 21 ,  7,33
94. List the terms of the expression:
11u
–3
6
11u
–4u 2 – 6
A)
,
–4u 2 –
u2 u
B)
,
11
–4 – 6 –3
C)
,
,
11u
–4u 2 – 6 –3
D)
,
,
E)
–4u 2
95. State whether the polynomial is a monomial, binomial, or trinomial.
–6x2 + 3 – 8y2
A) monomial B) binomial C) trinomial
96. Factor the trinomial by grouping.
5z2 – 22z + 8
A) (z – 4)(5z – 2)
B) (z + 4)(5z + 2)
C) (z – 4)(5z – 2)2
D) (z – 4)2(5z – 2)
E) z – 4(5z – 2)
97. A rectangular playground of length x and width y has a perimeter of 640 feet. Determine the equation for
the area of the playground in terms of x.
A) A  640x
2
B) A  640 x  x
C) A  640  x
2
D) A  320 x  x
2
E) A  320  x
99. An investment is expected to pay 8% per year compounded continuously. If you want the value of the
investment to be $400,000 after 25 years, how much should you invest initially? Round to the nearest
dollar.
A) $13,534 B) $27,067 C) $54,134 D) $108,268 E) $173,835
100. Factor the difference of two squares.
81  (p – 6) 2
A) (p + 3)(15 p) B) (p + 3)(–9 p)
101.
C) (–9 p)2 D) (15 p)2 E) (p + 3)2
4
3
Find all solutions of x – 6 x  x – 6  0 .
A)
1  3 i
D)
x  1,
2
B)
1 3 i
x  6,  1,
2
C)
1  3 i
x  –6, 1,
2
E)
Page 17
x  –6,1,
x  6,  1
1 2 i
3
102.
x+2
5
4
Which of the following is not a solution to the inequality
?
x

–22
x

–24
x

15
x

13
x

2
A)
B)
C)
D)
E)
103.
)  23 . Round to 3 decimal places.
Solve for x: 7(10
A) 2.517 B) 0.517 C) 1.362 D) –1.362 E) no solution
–5 
x2
104. Multiply.
(–x + 8)(7x – 6)
A) 6x + 2 B) 6x2 + 2
C) 55x – 48 D) 6x2 + 8x + 2
E) –7x2 + 62x – 48
105. An initial investment of $3000 grows at an annual interest rate of 5% compounded continuously. How
long will it take to double the investment?
A) 13.86 years B) 14.86 years C) 14.40 years D) 13.40 years E) 1 year
106. Evaluate the expression.
4–1 + 4–3
1
17
A) 34 B) 64
–
C)
1
34
–
D)
17
64
E) –16
107. Evaluate the expression.
2–6
A) 4
108.
B) –4 C) 8 D) –8 E) 12
The point
cos .
 3, 4  is on the terminal side of an angle in standard position. Determine the exact value of
cos   
A)
5
3
cos  
B)
4
3
cos  
C)
3
4
cos   
D)
4
3
cos  
E)
109. Find the special product.
(7x – 6)(7x + 6)
A) 14x B) 14x2 C) 49x2 – 36 D) 49x2 + 36 E) 49x2 – 84x – 36
110. Find ( fg )(x).
f ( x)  –7 x
g ( x)  –5 x – 9
A) ( fg )( x)  x 35 + 3 7 x
D)
( fg )( x)  35x2 – 9
B) ( fg )( x)  3 x 35 + 7 x
E)
( fg )( x)  35x2 + 63x
C) ( fg )( x) 
–12 x – 9
Page 18
3
5
111. Find ( f  g )(x).
f ( x) 
A)
B)
C)
112.
7x
5x + 4
( f  g )( x) 
( f  g )( x) 
( f  g )( x) 
6
x
7x + 6
4x + 4
D)
7 x + 34
5x + 4
E)
( f  g )( x) 
( f  g )( x) 
7 x 2 + 30 x – 24
5x2 + 4 x
7 x 2 + 30 x + 24
5x2 + 4 x
7 x + 26
5x + 4
Find all solutions of
A) x  3
113.
g ( x)  –
x  x – 5  1.
B) x  3
C) x  6
D) x  9
E) x  –3
Write the standard form of the equation of the circle whose diameter has endpoints of
 –2, 10 .
A)
B)
C)
 x + 5   y – 6   25
2
2
 x + 5   y – 6   5
2
2
 x – 6    y + 5  25
2
D)
2
E)
 –8, 2 and
 x + 6    y – 5  25
2
2
 x – 5   y + 6   5
2
2
114. Write the rational expression in simplest form.
54 y 4
24 y5
9 y4
A) 4 y
115.
5
, y0
27 y
, y0
B) 12
18
, y0
C) 8 y
9
, y0
D) 4 y
27
, y0
E) 12 y
3
 1 
log3  
 27  .
Simplify the expression
A) 3
B) –9
C) 0 D) –81 E) The expression cannot be simplified.
116. Find the slope and y-intercept of the equation of the line.
3y + 15x = 12
A) slope: –15;
y-intercept: 12
D) slope: 4;
B) slope: 12;
y-intercept: –15
E) slope: –5;
C) slope: –15;
y-intercept: 3
y-intercept: –5
y-intercept: 4
117. Give a verbal description of the subset of real numbers represented by the inequality.
–5  x  8
A) all real numbers less than –5 and greater than 8
B) all real numbers between –5 and 8 not including –5 or 8
C) all real numbers between –5 and 8, including –5 but not including 8
D) all real numbers between –5 and 8, including 8 but not including –5
E) all real numbers between –5 and 8, including –5 and 8
Page 19
118. Assuming that the graph shown has y-axis symmetry, sketch the complete graph.
A)
B)
C)
Page 20
D)
E)
Page 21
119. Perform the operation.
 –5x + 4  –9 x2 – 5x + 8
A) 45 x3 + 25 x 2 – 40 x + 8
B) 34 x 2 – 60 x + 32
C)
120.
D) 45 x3 – 11x 2 – 60 x + 8
E) 45 x3 – 11x 2 – 60 x + 32
45 x3 + 61x 2 – 20 x + 32
2
Write the quadratic function, f ( x)  x + 8 x + 25 , in standard form.
A) f ( x)   x + 4 2 – 9
D) f ( x)  x – 9



B)
f ( x)   x + 4  + 9
C)
f ( x)    x – 9  + 4
E)
2

2
–4
f ( x)    x – 4  – 9
2
2
121. Use inequality notation to describe the set.
q is at least –4 but less than 6
A) 6  q  –4 B) 6  q  –4 C) –4  q  6 D) –4  q  6 E) –4  q  6
122.
123.
log
1.877
1/ 3
Evaluate the logarithm
using the change of base formula. Round to 3 decimal places.
A) 0.630 B) –0.692 C) –1.745 D) –0.573 E) 0.273
log7 714 using the change of base formula. Round to 3 decimal places.
Evaluate the logarithm
A) 6.571 B) 0.296 C) 3.377 D) 12.786 E) 2.854
124. Simplify the expression.
2
3
4 3
   
 w  w
72
5
A) w
432
5
B) w
432
6
C) w
72
43
6
D) w
6
E) w
125. Evaluate the expression for the given value of x.
6x0
A) 0
126.
x=2
B) 6 C) –6 D) –12 E) 12
Approximate the solution to ln( x  3)  ln x  3 . Round to 3 decimal places.
A) –0.950 B) 0.750 C) 0.157 D) 20.086 E) 0.003
128. Completely factor the expression.
6m3 + 5m2 – 6m
A) m(2m – 3)(3m + 2)
B) m(2m + 3)(3m – 2)
C) (2m2 + 3m)(3m – 2)
D) (2m2 – 3m)(3m + 2)
E) (2m + 3)(3m2 – 2m)
129. Find the greatest common factor of the expression.
60, 18, 30
A) 3 B) 6 C) 18 D) 12 E) 15
Page 22
130. Find all real values of x such that f (x) = 0.
f ( x)  25x2  64
5
8
64



25
A) 8 B) 5 C)
131.

D)
64
25
8
E) 5
x / 2
 0.0052 . Round to 3 decimal places.
Solve for x: 3
A) 9.574 B) 10.518 C) 12.715 D) –12.715 E) –4.787
132. Determine which of the given expressions is a polynomial.
A) 8x 2 – 7 x – 5
D) 2
B) 8 x 3 – 7 x 2 – 5 x 1
E)
x3 + 8 x 2 – 7 x – 5
13
2
x – 7 x 2 – 5 x 1
13
C) 8 x – 7 x – 5
133. Factor the perfect square trinomial.
n2 +
10
25
n
7
49
 10 
n+ 
7
A) 
2
5

n+ 
7
B) 
2
5

n – 
7
C) 
2
 10 
n – 
7
D) 
2
5 
5

 n +  n – 
7 
7
E) 
134. Perform the operation and write the result in standard form.
7x3 – 1   –2x3 + 2x – 5
A) 9 x3 + 2 x – 6
B) 9 x3 – 2 x + 4
D) 9 x6 + 2 x – 6
E) 5 x6 + 2 x – 6
C) 9 x6 – 2 x + 4
Page 23
135. Match the inequality –1  x  1 with its graph.
A)
–1
1
–1
1
B)
C)
1
D)
–1
1
–1
1
E)
136. Determine which numbers in the set are integers.
3.3, 14, 6 , 0, 7.0, – 4
A) 14, 0, 7.0, – 4
B) 3.3, 14, 0, 7.0, – 4
C) 14, 0
137.
D) 14, 6 , 0, – 4
E) 14, 0, – 4
2
Solve: x – 4 x – 12  0
A)
 , – 4
B)
 –2,  
C)
 –2,6
D)
 ,6
E)
 6,  
138. Place the correct symbol (<, >, or =) between the pair of real numbers.
2
A)
 –2
 2   –2
B)
 2   –2
C)
 2   –2
139.
f ( x)  x 2 – x +
Determine the vertex of the graph of the quadratic function
1 3
 , 
A)  2 2 
5

 –1, 
4
B) 
140. Factor the trinomial.
u2 – u – 6
A) u(u – 1) – 6 B) u(u – 7)
 1 5
– , 
C)  2 4 
 1 3
– ,– 
D)  4 4 
C) (u + 3)(u + 2)
5
4.
1 
 ,1
E)  2 
D) (u – 3)(u + 2) E) (u + 3)(u – 2)
Page 24
141. Evaluate the expression for the given value of x.
2x –1
2
–
3
A)
142.
x = –3
2
B) 3
1
C) 6
D) –6 E) 6
log7 x  log7 4 to the logarithm of a single term.
log7 4x C) log 7 4 x D) log 7 x 4 E) log7  x + 4
B)
Condense the expression
7
A) log(4 x)
143. Identify the rules of algebra illustrated by the statement.
sy + ts = sy + st = s(y + t) = s(t + y)
A) distributive property; commutative property of addition; associative property of addition
B) associative property of multiplication; commutative property of addition; associative property of
addition
C) commutative property of multiplication; distributive property; commutative property of addition
D) associative property of multiplication; distributive property; associative property of addition
E) commutative property of multiplication; associative property of addition; commutative property of
addition
144.
2
Use the quadratic formula to solve x + 12 x + 22  0 .
A) x  6  14
D)
B)
C)
145.
x  –20  14
x  –6  14
Condense the expression
5
x
log  
 y
A)
146.
147.
E)
5  log x  log y 
5x
log
5y
B)
x5
log
y
C)
x  20  14
x  –160  14
to the logarithm of a single term.
x5
log
5 y
D)
E)
5  log x  log y 
x
1
  8
Solve  2 
for x.

1
A) 1 B)
C) 3
Find all solutions of
2 14
x– ,
3 3
A)
D) 2
–3x – 6  8
E) no solution
.
14 2
x– ,
3 3
B)
x–
C)
14
3
148. Is the interval bounded or unbounded?
–3 < x < –1
A) unbounded B) bounded
Page 25
9 11
x– ,
8 6
D)
x–
E)
2
3
149. What is the justification in each of the indicated steps shown below in the solution of the linear equation
–8  x – 4 + 3  4
A) ?1
?2
B) ?1
?2
C) ?1
?2
D) ?1
?2
E) ?1
?2
?
–8  x – 4 + 3  4
–8x + 32 + 3  4
–8x + 35  4
–8x + 35 – 35  4 – 35
–8x  –31
–8 x –31

–8
–8
31
x
8
Write original equation.
?1
Simplify.
?2
Simplify.
Divide both sides by –8 .
Simplify.
Associative Property.
Subtract –35 from both sides.
Commutative Property.
Add –35 to both sides.
Distributive Property.
Add –35 to both sides.
Combine like terms.
Add –35 to both sides.
Clear parentheses.
Subtract –35 from both sides.
150. Write the rational expression in simplest form.
v 2  16
v 2 + 4v – 32
A) v – 4
, v4
v–8
B) v – 4
, v4
v +8
C) v – 4
, v  –4
v +8
D)
E)
v+4
, v  –4
v +8
v+4
, v4
v +8
151. Write the polynomial in standard form.
–3x3 y 3 + 2 x 2 y 5 – 7 x6 y 2
A) 2 x 2 y 5 – 3x3 y 3 – 7 x 6 y 2
B) 2 x 2 y 5 – 7 x 6 y 2 – 3x3 y 3
C) –7 x6 y 2 + 2 x 2 y 5 – 3x3 y 3
D) –7 x6 y 2 – 3x3 y 3 + 2 x 2 y 5
E) –3x3 y 3 – 7 x 6 y 2 + 2 x 2 y 5
152. Identify the degree and leading coefficient of the polynomial.
–1 – 9x2 + 7x
A) degree: 3
leading coefficient: 7
D) degree: 2
B) degree: 2
leading coefficient: 9
E) degree: 2
C) degree: 3
leading coefficient: 9
Page 26
leading coefficient: –9
leading coefficient: –1
153. Factor by grouping.
45q6 – 20q4 + 18q2 – 8
A) 5q4 + 2(9q2 – 4)
B) (5q4 + 2)(9q2 – 4)2
C) (5q4 + 2)2(9q2 – 4)
D) (5q4 + 2)(9q2 – 4)
E) (5q4 – 2)(9q2 + 4)
154. Place the correct symbol (<, >, or =) between the pair of real numbers.
  –8
A)
  –8  –8
–8
B)
  –8  –8
C)
  –8  –8
155. Factor out the common factor.
2n(8n – 3) – (8n – 3)
A) (8n – 3)2n
B) (8n – 3)2n – 1
C) (8n – 3)2n + 1
D) (8n – 3)(2n – 1)
E) (8n – 3)(2n + 1)
156. Perform the operations and simplify.
u 3 / 2 m7 / 6
 um 5 / 6
2 / 3 1/ 3
A) u m
3/ 2 1/ 3
B) u m
1/ 2 1/ 3
C) u m
m1/ 3
u1/ 2
1/ 2
D) u
1/ 3
E) m
157. Factor the sum or difference of cubes.
q3 + 27
A) (q + 3)(q2 – 3q + 9)
B) (q – 3)(q2 + 3q + 9)
C) (q + 3)(q2 + 3q + 9)
D) (q – 3)3
E) (q + 3)3
158. Rewrite the expression with positive exponents and simplify.
 –4z 2   4z –4 
–4
1
16
A) 24z
159.
2
24
128
16
16
B) z
C) z
16
1
16
D) 16z
16
E) z
2
Write the quadratic function, f ( x)   x + 10 x – 17 , in standard form.
A) f ( x)   x + 5 2 + 8
D) f ( x)   x – 5


B)
f ( x)   x – 8  – 5
C)
f ( x)   x – 5  – 8
E)
2
2
Page 27

 +8
2
f ( x)    x + 8  – 5
2
160. Identify the rules of algebra illustrated from left to right by the following statement.
(p – 9) + 9 = p + (–9 + 9) = p + 0 = p
A) commutative property of addition; additive inverse property; additive identity property
B) associative property of addition; additive inverse property; additive identity property
C) commutative property of addition; additive identity property; additive inverse property
D) associative property of addition; additive identity property; additive inverse property
E) distributive property; additive identity property; additive inverse property
161. Perform the operation and write the result in standard form.

8x –6 – 3x 2

3
A) –24 x – 48 x
2
C) –48 x – 24 x
3
B) 24 x – 48 x
2
D) –48 – 24x
2
E) –48 + 24x
162. Rewrite the expression with positive exponents and simplify.
 y –8   y 6
 –8   
 n  n 


2
2
A) y
n 48
y 48
y2
48
C) y
48
D) n
2
E) n
1
n
2 2
B) y n
163. Plot the points and find the slope of the line passing through the pair of points.
(–1, 1), (3, –4)
–
A) slope:
4
5
4
B) slope: 5
–
C) slope:
2
7
–
D) slope:
5
4
5
E) slope: 4
164. Find the special product.
(4x – 2)2
A) 16x2 – 16x + 4 B) 16x2 – 8x + 4 C) 8x2 – 4 D) 16x2 – 4 E) 16x2 + 4
165. Factor the expression by removing the common factor with the smaller exponent.
8x4(7x – 1)1/4 – 3(7x – 1)–3/4
1/ 4
A)
D) 56 x5 – 8 x 4 – 3
5
4
56x
 7 x – 1
– 8x – 3

 7 x – 11/ 4
 7 x – 13/ 4 56 x5 – 8x4 – 3
B)
C)
E)
56 x17 – 8 x16 – 3
 7 x – 11/ 4
56 x5 – 8 x 4 – 3
 7 x – 13 / 4
166.
Using the figure below, if   35  and y  6 , determine the exact value of x.
r
y

x
x
A)
35
tan 6
x
B)
6
cot 35
x
C)
6
tan 35
Page 28
x
D)
6
sin 35
x
E)
35
csc 6
168.
Graph the given function
A)
B)
C)
D)
E)
Page 29
169.
2
Determine which of the following values of x is a solution to the equation x – 2 x – 24  0 .
A) x  –6, x  –4
B) x  6
C) x  6, x  –4
D) x  6, x  4
E) x  4
170. Identify the rules of algebra illustrated from left to right by the following statement.
1
1
 3v     3  v  1 v  v
3
3 
A) associative property of multiplication; multiplicative inverse property; multiplicative identity
property
B) commutative property of multiplication; multiplicative inverse property; multiplicative identity
property
C) associative property of multiplication; multiplicative identity property; multiplicative inverse
property
D) commutative property of multiplication; multiplicative identity property; multiplicative inverse
property
E) distributive property; multiplicative identity property; multiplicative inverse property
171. Which investment option will pay the most interest?
A) 11.6% compounded annually
B) 11.4% compounded semiannually
C) 11.2% compounded quarterly
D) 11.0% compounded continuously
E) These investments all pay the same amount of interest.
172. Find (if possible) the complement of 110 .
A) 20 B) 70 C) 50 D) 80 E) not possible
173. Factor the trinomial.
9m2 – 30m + 16
A) (9m + 8)(m + 2)
B) (9m – 8)(m – 2)
C) (3m + 8)(3m – 2)
174.
D) (3m + 8)(3m + 2)
E) (3m – 8)(3m – 2)
1
[log 4 x  log 4 7]  [log 4 y ]
Condense the expression 5
to the logarithm of a single term.
log 4
A)
 7 x 5
y
log 4
B)
7x
5y
log 4 5
C)
7x
y
log 4
D)
5 7x
y
E)
log 4 5 7 x  log 4 y
175. The length L of the hypotenuse of a right triangle is
L  x2  y 2
where x and y are the lengths of the other two sides. Find the length of the hypotenuse when the other
12
sides measure 1 unit and 5 units.
17
169
A) 1 unit B) 2 units C) 25 units D)
17
13
5 units E) 5 units
Page 30
176.
y  3x – 3
Find the slope and y-intercept of the equation of the line.
A)
D) slope: –3; y-intercept: 3
1
slope: 3 ; y-intercept: –3
B)
–
E) slope: 3; y-intercept: 3
1
3 ; y-intercept: 3
slope:
C) slope: 3; y-intercept: –3
177. Evaluate the expression for the given value of x.
2
expression: 9 x – 4 x – 4
value: x = –3
A) –46 B) 89 C) –73 D) 81 E) –54
178. Evaluate the expression for the given value of x.
x5
expression: x  5
A)
1

5
B) 1
5
value: x = –5
D) not possible since numerator is 0
E) not possible since denominator is 0
C) 0
179.
2
Solve ln x  3 for x.
9
A) e
3
B) 10
3
C) e
3/ 2 3/ 2
D) e , e
E) no solution
180. Factor the difference of two squares.
49y2  4
A) (49y + 2)(49y  2)
B) (49y + 4)(49y  4)
C) (7y  2)2
D) (7y  2)2
E) (7y + 2)(7y  2)
181. Determine which numbers in the set are natural numbers.
–10, 3, 15,
A) 3, 15,
B) 3, 15,
49, 0, – 9,
49, 0,
26
D) 3, 15
26
E)
49
–10, 3, 15, 0, – 9
C) 3, 15, 0
182.
Write the standard form of the equation of the parabola that has a vertex at
the point
A)
 6,3 .
D)
3
2
 x + 8 + 6
196
2
2
f ( x)   x + 8  – 5
49
1
2
f ( x)   x – 8  – 5
8
f ( x) 
B)
C)
E)
Page 31
 –8, –5 and passes through
5
2
 x + 5 + 3
6
5
2
f ( x)  –  x + 5  – 6
64
f ( x)  –
183.
The ordered pair
A)
x+2
 2, 2  is a solution point for which equation below?
D)
y
B)
2
y  x – 2x – 8
C)
y  2 x – 4
E)
2
y
1 3
x – 4x2
2
y
x2 + 2 x – 4
x
184. Determine the quadrant in which a 133 angle lies.
A) 1st quadrant B) 2nd quadrant C) 3rd quadrant D) 4th quadrant
185. Perform the addition and simplify.
8
2
x + 6 x – 16

3
2
x +x–6
11
 x + 8 x – 2 x + 3
B)
11x + 48
 x + 8 x – 2 x + 3
C)
11x
 x – 8 x + 2 x + 3
A)
D)
E)
11x
 x + 8 x + 2 x – 3
11
2 x 2 + 7 x – 22
186. Which graph represents the inequality?
–9 x  –6
A)
)
–9
[
–6
B)
[
]
–9
–6
C)
]
(
–9
–6
D)
)
(
–9
–6
E)
]
[
–9
–6
187. Completely factor the expression.
2s2  8
A) (2s – 4)(s + 2)
B) (2s + 4)(s – 2)
C) (2s + 4)(s + 2)
D) 2(s + 2)(s – 2)
E) 2(s + 4)(s – 4)
Page 32
188. Determine which of the given expressions is NOT a polynomial.
A) 2 x 2 – 5 x 1 + 3
D) –9 x 6 + 2 x 4 – 5 x 2 + 3
B) 2 x3 – 5 x 2 + 3
E) 6 3
2
13
C)
x + 2 x – 5x + 3
7 x2 + 3
189. List the coefficients of the variable terms in the expression:
–7 7 s 2 – 14s + 14
A) –7 7 , –14 , 14
B) –7 7s 2
C) –7 7s 2 , –14s , 14
D) –7 7
E) –7 7 , –14
190. Approximate the solution to ln 2 x  3.2 . Round to 3 decimal places.
A) 4.953 B) 12.266 C) 3.893 D) 0.470 E) 792.447
191. Factor out the common factor.
55z3 – 11z2 + 88z
A) 11(5z3 – z2 + 8z)
B) 11z(5z2 – z + 8)
C) z(55z 2 – 11z + 88)
D) 55z(z 2 – z + 8)
E) 55(5z3 – z2 + 8z)
192. Solve: –6    x + 3  4
A) –7  x  3
B) –9  x  –7
C) –3  x  –7
Page 33
D) –7  x  9
E) no solution
Answer Key
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.
39.
40.
41.
42.
43.
44.
45.
46.
47.
48.
49.
50.
51.
52.
53.
E
C
E
E
C
B
B
C
B
D
C
B
E
B
C
B
E
D
B
D
C
C
E
A
B
E
D
E
D
D
D
C
D
D
A
A
C
B
C
B
D
C
B
D
A
B
D
C
E
B
C
A
D
Page 34
54.
55.
56.
57.
58.
59.
60.
61.
62.
63.
64.
65.
66.
67.
68.
69.
70.
71.
72.
73.
74.
75.
76.
77.
78.
79.
80.
81.
82.
83.
84.
85.
86.
87.
88.
89.
90.
91.
92.
93.
94.
95.
96.
97.
98.
99.
100.
101.
102.
103.
104.
105.
106.
107.
D
D
A
E
B
B
D
A
D
A
C
D
E
C
B
C
A
E
B
D
C
A
A
E
C
D
C
E
A
A
D
A
D
B
E
D
D
C
B
C
D
C
A
D
E
C
A
B
B
A
E
A
B
A
Page 35
108.
109.
110.
111.
112.
113.
114.
115.
116.
117.
118.
119.
120.
121.
122.
123.
124.
125.
126.
127.
128.
129.
130.
131.
132.
133.
134.
135.
136.
137.
138.
139.
140.
141.
142.
143.
144.
145.
146.
147.
148.
149.
150.
151.
152.
153.
154.
155.
156.
157.
158.
159.
160.
161.
E
C
E
E
D
A
D
B
E
D
A
E
B
C
D
C
B
B
C
E
B
B
B
A
D
B
B
D
A
C
C
E
D
A
B
C
C
A
C
B
B
C
E
C
D
D
B
D
A
A
D
D
B
A
Page 36
162.
163.
164.
165.
166.
167.
168.
169.
170.
171.
172.
173.
174.
175.
176.
177.
178.
179.
180.
181.
182.
183.
184.
185.
186.
187.
188.
189.
190.
191.
192.
A
D
A
C
C
C
D
C
A
B
E
E
D
E
C
B
C
D
E
B
B
E
B
B
C
D
A
E
B
B
A
Page 37