CLEP College Algebra
Practice Test
Time—90 Minutes
60 Questions
1.
For each question below, choose the best answer from the
choices given.
(3x + 5)2 =
(A)
(B)
(C)
(D)
(E)
2
9x + 30x + 25
9x2 + 15x + 25
9x2 + 15
9x2 + 25
3x2 + 25
5.
x 2 - 16
Where defined, x + 5
x+4
x-5
(A)
2.
3.
16 – 3x + 2
4 + 3x – 2
4 + (3x + 2)
–(3x + 2)2
3x + 2
(C)
( x + 4)( x - 5)
3r3 + 34r + 20
3r3 + 34r – 20
3r3 – 34r + 20
3r3 – 34r – 20
13r3 + 34r + 20
6.
x+5
(D)
x − x − 20
x+5
(E)
x+5
x-5
Which of the following is a factor of 8x2 – 2x –28?
(A)
(B)
(C)
(D)
(E)
If a + b = 4, what is the value of |4 – a| + |4 – b|?
(A)
(B)
(C)
(D)
(E)
x+5
2
4r(2r2 – 6) – (5r3 – 12 + 10r) + 8 =
(A)
(B)
(C)
(D)
(E)
4.
(B)
( )( )
( x − 4)( x - 5)
Which of the following is a factor of
16 – (3x + 2)2?
(A)
(B)
(C)
(D)
(E)
1
x+5 x - 5
–4
0
4
8
It cannot be determined from the given
information.
7.
4x + 7
4x – 4
4x + 2
2x – 7
x+2
Of the following, which is greatest?
(A)
(B)
(C)
(D)
(E)
3
4(2 )
3
(42)
3
(24)
3
2(4 )
2
(34)
1
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CLEP College Algebra
8.
For every positive integer x,
(A)
(B)
(C)
(D)
(E)
feet high. The tennis ball hits the ground and
–1
0
x–1
x
2x
1
9.
10. Millie drops a tennis ball out a window that is h
x! + x =
( x – 1)!
bounces several times. The height of each bounce
3
the height of the previous bounce. For exis
5
ample, after the first bounce, the ball bounces to
3
a height of h feet. Which of the following rep5
resents the total number of feet the ball travels
3
Which of the following is equal to a −3b 3 a 4 b3 ?
between the first and eighth bounce?
10
9
(A) –b a
(B)
b
9
4
∞ 3
(A) ∑ h i
i =0 5
10
9
9
a4
 3
(B) ∑ h 
i =1  5 
9
(C)
a4
10
8  3
(C) ∑ h 
i =1  5 
b9
1
b3
(D)
a
(E)
i
 3
(D) ∑ 2 h  
i =1
 5
8
1
9
i
7
i
( )
10
a 4b 9
8
(E) ∑ (2 h) 3
i =1
5
i +1
2
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CLEP College Algebra
13. Which of the following are the solutions of the
equation 3x2 – x = x – 16?
(A) x = 3 and x = 16
(B) x = 16 and x = –8
(C)
2 + 2 47
2 − 2 47
and
6
6
(D)
−2 + 2i 47
−2 − 2i 47
and
3
3
(E)
2 + 2i 47
2 − 2i 47
and
6
6
11. Which of the lines in the figure above is the graph
of y = –5?
(A)
(B)
(C)
(D)
(E)
a
b
c
d
e
12. Which of the following gives all values of p for
which |p + 8| ≥ 12?
(A)
(B)
(C)
(D)
(E)
{p|p ≥ 12}
{p|4 ≤ p ≤ 20}
{p|–12 ≤ p ≤ 12}
{p|–20 ≤ p ≤ 4}
{p|p ≤ –20 or p ≥ 4}
14. The shaded region in the figure above represents
the intersection of the graphs of y ≥ x, x ≥ 1, and
which of the following inequalities?
(A)
(B)
(C)
(D)
(E)
y ≤ 2x + 3
y ≥ 2x + 3
y ≤ 2x – 3
y ≥ 4x – 3
y ≥ 4x + 3
3
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was not involved in the production of and does not endorse this product.
CLEP College Algebra
18. Janna opens a bank account with $5,000 and
makes no additional deposits or withdrawals.
During the same week, her friend Emily spends
$15,000 on a new car. At the end of each year,
$250 is added to Janna’s account, while the value
of Emily’s car decreases by $500 each year.
Which of the following systems of equations
could be used to find the number of years, y, that
it will take for the values of Janna’s bank account
(v1) and Emily’s car (v2) to be equal?
(A)
(B)
(C)
(D)
(E)
15. The figure above shows the graph of the line with
equation ax – by = 1. Which of the following must
be true?
(A)
(B)
(C)
(D)
(E)
19. If A = {50,65}, B = {45,50,60,75}, and C =
{30,40,50,60,70}, then (A ∪B) ∩ C
a = 1 and b < 0
a < 0 and b = 0
a < 0 and b < 0
a < 0 and b > 0
a > 0 and b < 0
(A)
(B)
(C)
(D)
(E)
16. The set of all values for b for which the equation
5x2 + bx + 5 = 0 has either one or two real roots is
defined by
(A)
(B)
(C)
(D)
(E)
the empty set
{50}
{60}
{50, 60}
{45, 50, 60, 65, 70}
20. Which of the following numbers are not
rational?
b < 10
b > 10
b ≤ –5 or b ≥ 5
b ≤ –10 or b ≥ 10
b < –10 or b > 10
I. i
II. 3.33
17. Which quadrants of the xy-plane contain points
of the graph of 5x + y < 6?
(A)
(B)
(C)
(D)
(E)
v1 = 5,000 + y and v2 = 15,000 – y
v1 = 5,000y + 250 and v2 = 15,000y – 500
v1 = 5,000 + 250y and v2 = 15,000 – 500y
v1 = 5,000 + 500y and v2 = 15,000 – 250y
v1 = 5,000 – 250y and v2 = 15,000 + 500y
II and IV only
I, II, and IV only
II, III, and IV only
I, II, and III only
I, II, III, and IV
III.
22
7
(A)
(B)
(C)
(D)
(E)
I only
I and II only
I and III only
II and III only
I, II, and III
4
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was not involved in the production of and does not endorse this product.
CLEP College Algebra
25. What is the 20th term of the arithmetic sequence
3x, 3x + 2, 3x + 4, …?
2 − 6i
is expressed in the form a + bi, then
2−i
what is the value of b?
21. When
(A)
(B)
(C)
(D)
(E)
22. If l > m > 0 > n, then each of the following must
be true EXCEPT
(A)
(B)
(C)
(D)
ln < lm
lm > mn
ln < m2 < lm
l4 > m 4 > n 4
(E)
l> m
x + 38
3x + 38
3x + 40
3x + 42
114
23. ( 3 i)5 =
r
p(r)
–4
–2
0
2
4
6
8
–958
98
50
–46
–286
1,922
15,698
(A) −9 3
(B) 9 3 i
26. The table above gives some of the values of a
fifth degree polynomial p(r). Based on the values
shown, what is the minimum number of real roots
of the equation p(r) = 0?
(C) 27i
(D) 9
(E) – 3 i
(A)
(B)
(C)
(D)
(E)
24. What are all real values of y for which
5
1 y
= + ?
y + 7 5 10
(A)
(B)
(C)
(D)
(E)
Five
Four
Three
Two
One
27. Monica drew a pattern with rows of triangles. The
last row had 35 triangles. The row above it had
33 triangles, and each row above had 2 fewer triangles than the row just below it. There is 1 triangle in the top row. How many triangles are in
the pattern in all?
y = –12
y = 3 and y = –3
y = 3 and y = –12
y = 12 and y = –12
There are no real solutions.
5
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was not involved in the production of and does not endorse this product.
CLEP College Algebra
31. If the remainder is 19 when x3 – 2x2 + lx – 8 is
divided by x – 3, then l =
28. What is the middle term in the expansion of
6
x

 + 2 x ?
3

(A)
20
27
(B)
160
27
(C)
20 x 6
27
(D)
160 x 6
27
(E)
80 x 6
3
(A)
(B)
(C)
(D)
(E)
29. If x = 5 is a solution to the equation 2x3 – ax2 + 4x
– 20 = 0, what is the value of a?
32. The figure above shows the graph of the function
f. What is the value of f(f (0))?
(A)
(B)
(C)
(D)
(E)
30. The first three terms of a geometric sequence are
1
1
1
, − , and
. Which of the following rep5
15
45
resents the nth term of the sequence?
(−1)
5(3)
n −1
(−1)
5(3)
n
n+1
(C)
(−1)
(D)
(−1)
(A)
(B)
(E)
0
3
5
6
9
1
2
3
4
5
33. In the xy-plane, what is the x-intercept of the graph
n −1
of y =
3
x − 15 ?
5
n
15n+1
n+1
15n-1
(−1)
5(3)
n
n-1
6
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CLEP College Algebra
34. Which of the following define y as a function
of x?
36. Which of the following could be the graph of
y = x2 + 8x + 12?
I.
(A)
II. 6x2 + 4y = 15
III.
(A)
(B)
(C)
(D)
(E)
x
y
–10
–5
5
10
8
–7
3
–7
(B)
None
I only
I and II only
II and III only
I, II, and III
(C)
35. If 52 + p = 25p, then p =
(D)
(E)
7
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CLEP College Algebra
41. If f (x) = 8 + 3x2, and f –1 represents the inverse
function of f, then f –1(x) =
37. If f (x) = 4x – 3 and g(x) = 3x + 3, then f (g(x)) =
(A)
(B)
(C)
(D)
(E)
12x2 + 3x – 9
12x + 9
12x + 15
x+3
7x
(A) 3 + 8x2
38. If log2(x – 6) = 5, then what is the value of x?
(A)
(B)
(C)
(D)
(E)
25
31
38
41
59
39. For a science experiment, Ajay starts with 8 milliliters of a solution at 9:00A.M. Every 20 minutes,
he doubles the amount of solution. Assuming no
solution evaporates, how many milliliters of solution will there be at 11:00A.M.?
(A)
(B)
(C)
(D)
(E)
42.
(B)
1
8 + 3x 2
(C)
8− x
3
(D)
x −8
3
(E)
x −8
3
3x − 2 x − 5
−
x + 4 3x + 2
(A)
256
512
1,024
2,048
4,096
(B)
(C)
40. Which of the following must be true?
I. ln12.5x = xln12.5
II. log6(pxr) = xlog6 p + log6r
III. log4 4x = 4x
(A)
(B)
(C)
(D)
(E)
(D)
(E)
I only
II only
I and II only
II and III only
I, II, and III
8 x 2 − 6 x − 24
x + 4 3x + 2
(
)(
)
(
8 x 2 + x + 16
x + 4 3x + 2
)(
)
(
2x − 7
x + 4 3x + 2
)(
)
(
x+5
x + 4 3x + 2
)
)(
2x + 3
−2 x − 2
8
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CLEP College Algebra
(E)
43. The graph of the function y = f (x) is shown in the
preceding diagram. Which of the following is the
graph of y = f (x – 2) + 2
44. (i – 4)(2 + i) + (3i – 6) =
(A)
(B)
(C)
(D)
(E)
–15 + i
–14 + i
–12 + i
–21
–3
(A)
45. f is an exponential function defined by f (x) = mnx,
where m and n are positive constants. If f (4) =
162 and f (3) = 54, what is the value of m?
46. Which of the following will result in a perfect
square for all integer values of x, when added to
9x2 + 16?
(B)
(A)
(B)
(C)
(D)
(E)
(C)
36x
24x
16x
12x
0
x+y=2
x2 + y2 = 52
47. For what values of x will (x, y) be a solution to
the above system of equations?
(A)
(B)
(C)
(D)
(E)
(D)
The system has no solutions.
x = – 6 and x = 4
x = 6 and x = – 4
x = 2 and x = 2
x = 7 and x = 3
9
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CLEP is a registered trademark of the College Entrance Examination Board, which
was not involved in the production of and does not endorse this product.
CLEP College Algebra
51. 3x(4x2 + 2) – (8 – 2x3 + 10x) – 4 =
(A)
(B)
(C)
(D)
(E)
10x3 – 4x – 4
14x3 + 4x + 4
14x3 – 4x + 12
14x3 – 4x – 12
14x3 + 16x – 12
1 3 4 7 
1 2 
52. If A =  , , B =  , , ,  , and
4 5 6 8 
4 5
1 1 3
C =  , , , then A ∪ B ∩ C is
2 4 4
(
1 
(A)  
4
48. Which of the points in the above figure represents the complex number –1 + 4i?
(A)
(B)
(C)
(D)
(E)
1 
(B)  
2
A
B
C
D
E
1 3
(C)  , 
4 4
1 2 3 4 7 
(D)  , , , , 
4 5 5 6 8 
(E) the empty set
49. What is the ending value of an investment if
$7,000 is invested at 3% compounded monthly
for 4 years? Round your answer to the nearest
dollar.
53. Which of the following numbers are rational?
I. 5
II. π
III. 6.8989…
50. For the function f (x) =log5x, which of the following must be true?
(A)
(B)
(C)
(D)
(E)
I. f (x) decreases with decreasing values of x
II. The domain is (–∞, 0)
III. The range is(–∞,∞)
(A)
(B)
(C)
(D)
(E)
)
I only
I and II only
II and III only
I and III only
I, II, and III
I only
III only
I and III only
II and III only
I, II, and III
10
Copyright © 2004 Thomson Peterson’s,
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CLEP is a registered trademark of the College Entrance Examination Board, which
was not involved in the production of and does not endorse this product.
CLEP College Algebra
54. The first three terms of a geometric sequence are
15, 7.5, and 3.75. Which of the following represents the nth term of the sequence?
56. Which of the points in the preceding figure represents the complex number –3 – 2i?
(A)
(B)
(C)
(D)
(E)
(A) 15(2n–1)
(B) 15(0.5n–1)
(C)
15
0.5n−1
57. The first three terms in an arithmetic sequence
(D) 15(–0.5n–1)
(E)
x
x
x
+ 5, + 12, and + 19 . What is the 15th
2
2
2
term in the sequence?
are
−15
2 n−1
(A) x + 50
55. If a + 5 = b, what is the value of |a – b| – |b – a|?
(A)
(B)
(C)
(D)
(E)
A
B
C
D
E
–10
–5
0
5
It cannot be determined from the given
information.
(B)
x
+ 96
2
(C)
x
+ 98
2
(D)
x
+ 103
2
(E)
x
+ 110
2
11
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CLEP College Algebra
I. i2
x
0
2
4
6
8
10
12
f(x)
20
–45
–80
–128
132
–160
90
II. 1
III. 2i
(A)
(B)
(C)
(D)
(E)
60. –5b(b2 + 2b) – (4 + 3b3 – 6b) + 7 =
58. The table above gives some values of a 5th degree polynomial f (x). Based on the values in the
table, what is the minimum number of real roots
of the equation f (x) = 0?
(A)
(B)
(C)
(D)
(E)
I only
II only
III only
I and II only
I, II, and III
(A)
(B)
(C)
(D)
(E)
Five
Four
Three
Two
One
–8b3 – 10b2 + 6b + 3
8b3 + 10b2 – 6b – 3
–8b3 – 10b2 + 3
2b3 – 10b2 + 6b + 3
2b3 – 10b2 + 3
59. Which of the following numbers are real?
12
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