Free GED® Mathematical Reasoning Test Practice Questions

Sample Practice Questions

Try these 10 sample questions from the GED® Mathematical Reasoning Test practice bank. Each includes the answer and explanation. Continue with the interactive practice above to review the full question set.

1. 1Which list orders 0.6, 5/8, 0.58, and 3/4 from least to greatest?

   1. A.0.58, 0.6, 5/8, 3/4Correct answer: A
   2. B.0.58, 5/8, 0.6, 3/4
   3. C.0.6, 0.58, 3/4, 5/8
   4. D.5/8, 0.6, 0.58, 3/4

   Explanation: The text states, "To compare a decimal to a fraction, we will first convert the fraction to a decimal and then compare the decimals." Here 5/8 = 0.625 and 3/4 = 0.75, giving 0.58 < 0.6 < 0.625 < 0.75.

   Reference: Prealgebra 2e: Decimals and Fractions — Order Decimals and Fractions, introductory explanation

2. 2After combining like terms, which expression is equivalent to (3/4)x + (1/2)x − 2?

   1. A.(5/4)x minus 2Correct answer: A
   2. B.(4/6)x minus 2
   3. C.(3/8)x minus 2
   4. D.(5/4)x plus 2

   Explanation: The text says to "Add the coefficients of the like terms". Since 3/4 + 1/2 = 5/4, the expression becomes (5/4)x − 2.

   Reference: Prealgebra 2e: Key Concepts — Section 2.2, Combine like terms

3. 3Two alarms sound together at noon. One repeats every 12 minutes and the other every 18 minutes. How many minutes after noon will they next sound together?

   1. A.6 minutes
   2. B.24 minutes
   3. C.36 minutesCorrect answer: C
   4. D.216 minutes

   Explanation: The text defines the least common multiple: "The smallest number that is a multiple of two numbers is called the least common multiple (LCM)." Multiples of 12 are 12, 24, 36, and multiples of 18 are 18, 36. Their first common positive multiple is 36.

   Reference: Prealgebra 2e: Key Terms — Chapter 2, least common multiple

4. 4Evaluate 2x² − 3x + 1 when x = −2.

   1. A.3
   2. B.7
   3. C.11
   4. D.15Correct answer: D

   Explanation: The source states, "To evaluate an algebraic expression means to find the value of the expression when the variable is replaced by a given number." Substituting −2 gives 2(4) − 3(−2) + 1 = 15.

   Reference: Prealgebra 2e: Key Terms — Chapter 2, evaluate

5. 5What is the distance on a number line between −3.5 and 2.25?

   1. A.1.25 units
   2. B.negative 5.75 units
   3. C.5.25 units
   4. D.5.75 unitsCorrect answer: D

   Explanation: The GED guide directs finding the distance between two rational numbers, "including using the absolute value of their difference." Here |−3.5 − 2.25| = |−5.75| = 5.75 units.

   Reference: Assessment Guide for Educators: Mathematical Reasoning — p. 7, Q.1.d

6. 6A delivery service charges a fixed $6 fee plus $2 for each mile. If m is the number of miles, which expression gives the charge in dollars?

   1. A.2m + 6Correct answer: A
   2. B.6m + 2
   3. C.2(m + 6)
   4. D.6(m + 2)

   Explanation: The GED formula sheet gives "total cost = (number of units) × (price per unit)". Mileage costs 2m dollars, and adding the fixed $6 gives 2m + 6.

   Reference: Assessment Guide for Educators: Mathematical Reasoning — p. 12, Mathematics Formula Sheet, total cost

7. 7A teacher has 42 red tiles and 30 blue tiles. She wants identical groups with no tiles left over, and each group must contain the same number of red tiles and the same number of blue tiles. What is the greatest number of groups she can make?

   1. A.3 groups
   2. B.6 groupsCorrect answer: B
   3. C.7 groups
   4. D.12 groups

   Explanation: The book says, "The greatest common factor (GCF) of two or more expressions is the largest expression that is a factor of all the expressions." The greatest common factor of 42 and 30 is 6, so six groups contain seven red and five blue tiles each.

   Reference: Prealgebra 2e: Introduction to Factoring Polynomials — Greatest Common Factor, definition

8. 8Use multiplication to write the binomial product (x + 3)(x − 2) as an expanded polynomial.

   1. A.x^2 plus x minus 6Correct answer: A
   2. B.x^2 minus x minus 6
   3. C.x^2 plus 5x minus 6
   4. D.x^2 plus x plus 6

   Explanation: The text recommends, "Use the FOIL method for multiplying two binomials." Multiplying the four pairs gives x² − 2x + 3x − 6 = x² + x − 6.

   Reference: Prealgebra 2e: Key Concepts — Section 10.3, Multiply Polynomials

9. 9Which expression is equivalent to 5³ × 5⁴?

   1. A.5^7Correct answer: A
   2. B.5^12
   3. C.25^7
   4. D.10^7

   Explanation: The product property says, "To multiply with like bases, add the exponents." The base remains 5 and 3 + 4 = 7.

   Reference: Prealgebra 2e: Key Concepts — Section 10.2, Product Property of Exponents

10. 10Which factored expression equals x² + 7x + 12?

    1. A.(x plus 3)(x plus 4)Correct answer: A
    2. B.(x minus 3)(x minus 4)
    3. C.(x plus 2)(x plus 6)
    4. D.(x plus 3)(x minus 4)

    Explanation: The text states, "Splitting a product into factors is called factoring." Expanding (x + 3)(x + 4) yields x² + 7x + 12.

    Reference: Prealgebra 2e: Introduction to Factoring Polynomials — Find the Greatest Common Factor of Two or More Expressions, factoring definition