CLEP College Mathematics Practice Test

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

Median = 29, Mode = 31

Median = 31, Mode = 29

Median = 31, Mode = 31

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?

x = 2 and x = 3

x = -2 and x = -3

x = 1 and x = 6

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)

160·pi

480·pi / 3

640·pi / 3

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?

45 square centimeters

135 square centimeters

75 square centimeters

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?

4/33

1/9

1/11

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 $\frac{2x - 8}{x - 7}$ ?

x >= 4 and x ≠ 7

x > 4

all real numbers except x = 7

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?

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)?

1/2

-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)?

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?

Explanation

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

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