Free DSST Math for Liberal Arts Practice Questions

Sample Practice Questions

Try these 10 sample questions from the DSST Math for Liberal Arts practice bank. Each includes the answer and explanation. Continue with the interactive practice above to review the full question set.

1. 1Which of the following numbers is an irrational real number?

   1. A.√25
   2. B.√18Correct answer: B
   3. C.0.125
   4. D.−7

   Explanation: The source states, "For any integer n > 0, the square root √n is either a whole number (√n ∈ Z; n is a perfect square); or √n is irrational" 18 is not a perfect square, so √18 is irrational. The other values are rational: 5, 1/8, and −7.

   Reference: Math 310: Square Roots — Proposition, Square Roots

2. 2Let S = {x | x is an integer and 2 < x ≤ 5}. Which roster represents S?

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

   Explanation: The source states, "choosing all of the elements of the universal set that satisfy a specified condition." Among integers, 3, 4, and 5 satisfy 2 < x ≤ 5.

   Reference: Sets — Set-builder notation

3. 3In SI, which base unit is used to measure length?

   1. A.Kilogram
   2. B.MeterCorrect answer: B
   3. C.Ampere
   4. D.Kelvin

   Explanation: NIST states, "Meter – Unit of Length" The meter is the SI base unit of length; the other units measure mass, time, and temperature, respectively.

   Reference: Definitions of SI Base Units — Meter – Unit of Length

4. 4Evaluate 18 − 3 × (2 + 2).

   1. A.6Correct answer: A
   2. B.12
   3. C.30
   4. D.60

   Explanation: The DOE handbook states, "Perform all math operations within the sets of parentheses first." First evaluate 2 + 2 = 4, then multiply 3 × 4 = 12 and subtract from 18 to obtain 6.

   Reference: DOE Fundamentals Handbook: Mathematics, Volume 1 — Module 1, p. 16, Hierarchy of Mathematical Operations

5. 5Solve the system x + y = 10 and x − y = 2. What is (x, y)?

   1. A.(4, 6)
   2. B.(6, 4)Correct answer: B
   3. C.(8, 2)
   4. D.(5, 5)

   Explanation: The source states, "If one of the equations is replaced by a new equation formed by adding the two original equations, the solution is unchanged." Adding gives 2x = 12, so x = 6 and y = 4.

   Reference: It's in the System: Concepts and Explanation — Solving Systems of Linear Equations

6. 6What is the product rule for logarithms in base b? Choose the identity valid whenever u and v are positive, b > 0 and b ≠ 1.

   1. A.The log of uv equals log u plus log vCorrect answer: A
   2. B.The log of uv equals log u minus log v
   3. C.The log of uv equals log u times log v
   4. D.The log of uv equals log u plus twice log v

   Explanation: The DOE study guide states, "log a (u ⋅ v) = log a u + log a v" The product rule adds the two logarithms. All logarithms in the options have base b.

   Reference: DOE Fundamental Academic Training Study Guide: Basic Mathematics and Algebra — Module 1.01, p. 1.01-33, Properties of Logarithms

7. 7A menu offers 4 main courses and 3 desserts. If a meal consists of one of each, how many different meals are possible?

   1. A.7
   2. B.12Correct answer: B
   3. C.16
   4. D.24

   Explanation: The source states, "the total number of leaves on a tree is the number of leaves per branch times the number of branches" There are 4 choices followed by 3 choices for each, so 4 × 3 = 12.

   Reference: SticiGui: Counting — Summary, Fundamental Rule of Counting

8. 8On a standard horizontal real number line, which number lies furthest to the left?

   1. A.−1.2Correct answer: A
   2. B.0.4
   3. C.−0.7
   4. D.1.1

   Explanation: The source states, "numbers on the number line increase from left to right" The smallest value, −1.2, is furthest left.

   Reference: Yale National Initiative: Number Line Unit — Learning Objectives

9. 9Let T = {4, 6, 8}. Which statement correctly expresses that 6 is a member of T?

   1. A.6 is a subset of T
   2. B.T is an element of 6
   3. C.6 is an element of TCorrect answer: C
   4. D.T is equal to 6

   Explanation: The source states, "The symbol ∈ is used to indicate an element of a set, whereas the symbol ⊆ is used to indicate a subset." The roster lists 6, so 6 ∈ T; the other statements confuse membership, subset, and equality.

   Reference: Sets — Subsets

10. 10For measurements of mass, what is the International System's base unit?

    1. A.Meter
    2. B.Kelvin
    3. C.Second
    4. D.KilogramCorrect answer: D

    Explanation: NIST states, "Kilogram – Unit of Mass" The kilogram measures mass; the other units measure length, temperature, and time.

    Reference: Definitions of SI Base Units — Kilogram – Unit of Mass