Free CLEP College Mathematics Practice Questions

Sample Practice Questions

Try these 10 sample questions from the CLEP College Mathematics practice bank. Each includes the answer and explanation. Continue with the interactive practice above to review the full question set.

1. 1What is the solution of 3x − 7 = 11?

   1. A.x = 4
   2. B.x = 6Correct answer: B
   3. C.x = 12
   4. D.x = 18

   Explanation: "We may add, subtract, multiply, or divide an equation by a number or an expression as long as we do the same thing to both sides of the equal sign." Adding 7 to both sides gives 3x = 18, and dividing by 3 gives x = 6.

   Reference: College Algebra 2e: Linear Equations in One Variable — Section 2.2, How To: Given a linear equation

2. 2A meal offers 3 choices of soup and 4 choices of sandwich. How many meals contain one soup and one sandwich?

   1. A.7
   2. B.12Correct answer: B
   3. C.24
   4. D.64

   Explanation: "We can tack on additional tasks by multiplying the number of ways to accomplish those tasks to our previous product." Multiply the 3 soup choices by the 4 sandwich choices to obtain 12 meals.

   Reference: Contemporary Mathematics: The Multiplication Rule for Counting — The Multiplication Rule for Counting, explanation following the cake and frosting table

3. 3A pie chart has a 90-degree sector for transit users. What percentage of the whole does this sector represent?

   1. A.20%
   2. B.25%Correct answer: B
   3. C.40%
   4. D.90%

   Explanation: "A pie chart displays data concerning one categorical variable by partitioning a circle into “slices” that represent the proportion in each category." A 90-degree sector is 90/360 = 25% of the circle.

   Reference: STAT 200: Describing Data, Part 1 — Visual Representations, Pie Charts

4. 4A price rises from $120 to $150. What is the percentage increase?

   1. A.20%
   2. B.25%Correct answer: B
   3. C.30%
   4. D.80%

   Explanation: "(3.1) Percent Change: \[ \Delta \% = \frac{\text{New − Old}}{\text{Old}} \times 100 \nonumber \]" The increase is 30 on an original price of 120, so 30/120 = 25%.

   Reference: Business Math: Formula Sheet — Appendix 16.4, formula 3.1

5. 5A triangle has base 10 cm and perpendicular height 6 cm. What is its area?

   1. A.16 cm²
   2. B.30 cm²Correct answer: B
   3. C.60 cm²
   4. D.120 cm²

   Explanation: "The area of a triangle is equal to one-half of its base times its height." Half of 10 × 6 is 30 square centimeters.

   Reference: Elementary College Geometry: The Area of a Triangle — Section 6.3, Theorem 1

6. 6What is the converse of 'If a figure is a square, then it is a rectangle'?

   1. A.If a figure is not a square, then it is not a rectangle
   2. B.If a figure is a rectangle, then it is a squareCorrect answer: B
   3. C.If a figure is not a rectangle, then it is not a square
   4. D.A figure is a square and a rectangle

   Explanation: "The converse of the conditional statement \(P \to Q\) is the conditional statement \(Q \to P\)." The converse exchanges the hypothesis and conclusion; it need not be true merely because the original statement is true.

   Reference: Discrete Structures: Logically Equivalent Statements — Preview Activity: Converse and Contrapositive, converse definition

7. 7How is the number 3 + √2 classified?

   1. A.An integer
   2. B.A rational non-integer
   3. C.An irrational numberCorrect answer: C
   4. D.A non-real number

   Explanation: "It is not hard to see that the sum of any rational number plus \(\sqrt{2}\) is also irrational." Since 3 is rational, 3 + √2 is irrational and real.

   Reference: An Introduction to Number Theory: Rational and Irrational Numbers — Rational and Irrational Numbers, paragraph after the irrationality proof

8. 8Which inequality gives all solutions of −2x + 5 > 11?

   1. A.x is greater than negative 3
   2. B.x is less than positive 3
   3. C.x is less than negative 3Correct answer: C
   4. D.x is greater than positive 3

   Explanation: "The one exception is when we multiply or divide by a negative number; doing so reverses the inequality symbol." Subtracting 5 gives −2x > 6; dividing by −2 reverses the sign, giving x < −3.

   Reference: College Algebra 2e: Linear Inequalities and Absolute Value Inequalities — Section 2.7, Using the Properties of Inequalities

9. 9How many different two-person committees can be chosen from five people if the committee has no assigned roles?

   1. A.5
   2. B.20
   3. C.25
   4. D.10Correct answer: D

   Explanation: "Permutations are used to count subsets when order matters; combinations work when order doesn't matter." Order is irrelevant, so 5 × 4 / 2 = 10 committees.

   Reference: Contemporary Mathematics: Chapter 7 Key Concepts — Chapter 7, Key Concepts

10. 10In a frequency histogram, the bar for the interval 10 to under 20 has height 7. What does that height represent?

    1. A.7 observations in that intervalCorrect answer: A
    2. B.7 intervals in the data
    3. C.An average value of 7
    4. D.A maximum value of 7

    Explanation: "The heights of the bars either reflect the frequency or the relative frequency (percents) of encountering that range of numbers in the data" With a frequency scale, bar height 7 counts the seven observations in that interval.

    Reference: STAT 100: Getting the Big Picture and Summaries — Histograms, explanation of frequency bars