Free ACCUPLACER Quantitative Reasoning, Algebra, and Statistics Practice Questions

Sample Practice Questions

Try these 10 sample questions from the ACCUPLACER Quantitative Reasoning, Algebra, and Statistics practice bank. Each includes the answer and explanation. Continue with the interactive practice above to review the full question set.

1. 1Multiply the fractions 2/3 and 5/8 and reduce the resulting product.

   1. A.5/12Correct answer: A
   2. B.7/11
   3. C.10/11
   4. D.3/4

   Explanation: OpenStax states, "To multiply fractions, we multiply the numerators and multiply the denominators." Thus (2 × 5)/(3 × 8) = 10/24 = 5/12.

   Reference: Prealgebra 2e: Multiply and Divide Fractions — Multiply Fractions, Fraction Multiplication rule

2. 2A class has 12 students who commute and 8 who live on campus. What is the ratio of commuters to all students?

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

   Explanation: OpenStax states, "A ratio compares two numbers or two quantities that are measured with the same unit." The requested comparison is 12 to 20, which simplifies to 3:5.

   Reference: Prealgebra 2e: Ratios and Rate — Ratios, comparison definition

3. 3Using the product rule, rewrite x³ × x⁵ as a single power.

   1. A.x^2
   2. B.x^8Correct answer: B
   3. C.x^15
   4. D.2x^8

   Explanation: OpenStax states, "To multiply with like bases, add the exponents." Thus x³ × x⁵ = x⁸.

   Reference: Elementary Algebra 2e: Multiplication Properties of Exponents — Product Property for Exponents, rule for like bases

4. 4After substituting x = −4 into 3x − 2, which numerical result follows?

   1. A.negative 14Correct answer: A
   2. B.negative 10
   3. C.10
   4. D.14

   Explanation: OpenStax says, "To evaluate an expression, substitute that number for the variable in the expression and then simplify the expression." Substituting −4 gives 3(−4) − 2 = −14.

   Reference: Elementary Algebra 2e: Use the Language of Algebra — Evaluate an Expression, substitution rule

5. 5Find the unknown value that makes 3x + 5 equal to 20.

   1. A.5Correct answer: A
   2. B.15
   3. C.25/3
   4. D.75

   Explanation: The source advises, "Use all the usual algebraic methods for solving equations, such as adding or subtracting the same quantity to or from both sides, or multiplying or dividing both sides of the equation by the same quantity." Subtract 5 from both sides and divide by 3: x = 5.

   Reference: Algebra and Trigonometry: Functions and Function Notation — Solve for the Output Variable, equal operations on both sides

6. 6What is the slope of the line through (1, 3) and (5, 11)?

   1. A.1/2
   2. B.2Correct answer: B
   3. C.4
   4. D.8

   Explanation: The source says, "Take the ratio of rise to run to find the slope." The rise is 11 − 3 = 8 and the run is 5 − 1 = 4, so the slope is 2.

   Reference: Elementary Algebra 2e: Graphs Key Concepts — Chapter 4, Understand Slope of a Line

7. 7A coin is tossed twice, with outcomes recorded in order. Which set is the sample space?

   1. A.{HH, HT, TH, TT}Correct answer: A
   2. B.{H, T}
   3. C.{HH, HT, TT}
   4. D.{HH, TT}

   Explanation: The source defines the sample space as "the set of all possible outcomes of an experiment". Two ordered tosses have four possible outcomes: HH, HT, TH, and TT.

   Reference: Introductory Statistics 2e: Probability Key Terms — Chapter 3, Sample Space

8. 8What is the mean of 4, 6, 8, and 10?

   1. A.6
   2. B.7Correct answer: B
   3. C.8
   4. D.14

   Explanation: The source illustrates a mean: "add the 50 weights together and divide by 50." Here (4 + 6 + 8 + 10)/4 = 7.

   Reference: Introductory Statistics 2e: Measures of the Center of the Data — Section 2.5, Measures of the Center of the Data

9. 9A rectangular garden is 9 meters long and 4 meters wide. What is its perimeter?

   1. A.13 m
   2. B.18 m
   3. C.26 mCorrect answer: C
   4. D.36 m

   Explanation: The source says the rectangle perimeter is "the sum of twice the length and twice the width." Thus 2(9) + 2(4) = 26 meters.

   Reference: Prealgebra 2e: Properties of Rectangles, Triangles, and Trapezoids — Properties of Rectangles, perimeter

10. 10The width of a rectangular enclosure is w, and its length is w + 3. Express the distance around it in terms of w.

    1. A.2w + 3
    2. B.2w + 6
    3. C.4w + 3
    4. D.4w + 6Correct answer: D

    Explanation: The source states the perimeter is "the sum of twice the length and twice the width." Thus 2(w + 3) + 2w = 4w + 6.

    Reference: Prealgebra 2e: Properties of Rectangles, Triangles, and Trapezoids — Properties of Rectangles, perimeter