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CLEP College Mathematics Practice Test

10 free sample questions with answers and explanations. See how you'd score on the real CLEP exam.

Question 1Unit 4: Data Analysis, Statistics & Probability

The ages of seven employees are: 24, 31, 29, 45, 31, 38, and 22. Which of the following correctly lists the median and mode of this data set? A) Median = 31, Mode = 31 B) Median = 29, Mode = 31 C) Median = 31, Mode = 29 D) Median = 38, Mode = 31

A
A) Median = 29, Mode = 31
B
B) Median = 31, Mode = 29
C
C) Median = 31, Mode = 31
D
D) Median = 38, Mode = 31

Explanation

Ordered: 22,24,29,31,31,38,45. Middle (4th) value = 31, so median = 31. Mode = 31 since it appears twice. Both equal 31.

Question 2Unit 3: Algebra & Functions

What are the solutions to the quadratic equation x^2 - 5x + 6 = 0?

A
A) x = 2 and x = 3
B
B) x = -2 and x = -3
C
C) x = 1 and x = 6
D
D) x = 2 and x = -3

Explanation

Factoring: (x - 2)(x - 3) = 0, so x = 2 or x = 3. The other options use wrong sign combinations.

Question 3Unit 5: Geometry

A cylinder has a radius of 4 cm and a height of 10 cm. A cone with the same radius and height is removed from the interior of the cylinder. What is the volume of the remaining solid, in cubic centimeters? (Use pi ≈ 3.14159)

A
A) 160·pi
B
B) 480·pi / 3
C
C) 640·pi / 3
D
D) 320·pi / 3

Explanation

Cylinder volume = pi·r^2·h = 160·pi; cone volume = (1/3)·pi·r^2·h = 160·pi/3; remaining = 160·pi − 160·pi/3 = 320·pi/3.

Question 4Unit 5: Geometry

Two similar triangles have corresponding sides in the ratio 3:5. If the area of the smaller triangle is 27 square centimeters, what is the area of the larger triangle?

A
A) 45 square centimeters
B
B) 135 square centimeters
C
C) 75 square centimeters
D
D) 225 square centimeters

Explanation

Since areas scale as the square of the side ratio, the area ratio is (3/5)^2 = 9/25, so larger area = 27 · (25/9) = 75 sq cm.

Question 5Unit 4: Data Analysis, Statistics & Probability

A bag contains 4 red marbles, 3 blue marbles, and 5 green marbles. If two marbles are drawn one at a time WITHOUT replacement, what is the probability that both marbles are red?

A
A) 4/33
B
B) 1/9
C
C) 1/11
D
D) 2/12

Explanation

P(red then red) = (4/12)·(3/11) = 12/132 = 1/11. Since drawn without replacement the second probability changes to 3/11.

Question 6Unit 3: Algebra & Functions

What is the domain of the function f(x) = sqrt(2x - 8) / (x - 7)?

A
A) x >= 4 and x ≠ 7
B
B) x > 4
C
C) all real numbers except x = 7
D
D) x >= 4

Explanation

sqrt(2x-8) requires 2x - 8 >= 0, so x >= 4; denominator x - 7 ≠ 0 excludes x = 7, giving x >= 4 and x ≠ 7.

Question 7Unit 3: Algebra & Functions

Solve the system of equations: 2x + 3y = 12 and x - y = 1. What is the value of x?

A
A) 2
B
B) 3
C
C) 4
D
D) 5

Explanation

From x - y = 1, x = y + 1. Substituting: 2(y+1) + 3y = 12 → 5y = 10 → y = 2, so x = 3.

Question 8Unit 3: Algebra & Functions

What is the slope of the line passing through the points (2, -3) and (6, 5)?

A
A) 1/2
B
B) -2
C
C) 4
D
D) 2

Explanation

Slope = (5 - (-3)) / (6 - 2) = 8 / 4 = 2, therefore the slope is 2.

Question 9Unit 3: Algebra & Functions

If f(x) = 3x^2 - 2x + 5, what is f(-1)?

A
A) 0
B
B) 6
C
C) 8
D
D) 10

Explanation

f(-1) = 3(-1)^2 - 2(-1) + 5 = 3(1) + 2 + 5 = 10, so the answer is 10.

Question 10Unit 1: Logic & Sets

In a class of 50 students, 30 play soccer, 22 play basketball, and 8 play both sports. How many students play neither soccer nor basketball?

A
A) 6
B
B) 8
C
C) 14
D
D) 44

Explanation

By inclusion-exclusion, |S ∪ B| = 30 + 22 - 8 = 44, so neither = 50 - 44 = 6 students.

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