Free ASVAB Mathematics Knowledge Practice Test

Mathematics Knowledge practice questions

1. Question 1

   If 4x − 7 = 21, what is the value of x?

   1. A.3.5
   2. B.5
   3. C.7
   4. D.14
   Show answer

   Correct answer: C. 7

   Add 7 to both sides to get 4x = 28, then divide by 4: x = 7.

2. Question 2

   Two angles are supplementary. If one angle measures 68°, what is the measure of the other angle?

   1. A.112°
   2. B.22°
   3. C.122°
   4. D.292°
   Show answer

   Correct answer: A. 112°

   Supplementary angles add up to 180°, so the other angle is 180° − 68° = 112°.

3. Question 3

   Simplify: (2x³)(5x⁴)

   1. A.7x⁷
   2. B.10x¹²
   3. C.7x¹²
   4. D.10x⁷
   Show answer

   Correct answer: D. 10x⁷

   Multiply the coefficients (2 × 5 = 10) and add the exponents of x (3 + 4 = 7), giving 10x⁷.

4. Question 4

   A rectangle is 9 cm long and 4 cm wide. What is its perimeter?

   1. A.36 cm
   2. B.26 cm
   3. C.13 cm
   4. D.22 cm
   Show answer

   Correct answer: B. 26 cm

   Perimeter = 2 × (length + width) = 2 × (9 + 4) = 2 × 13 = 26 cm.

5. Question 5

   Which of the following is the complete factorization of x² − 3x − 28?

   1. A.(x + 7)(x − 4)
   2. B.(x − 7)(x + 4)
   3. C.(x − 14)(x + 2)
   4. D.(x − 4)(x − 7)
   Show answer

   Correct answer: B. (x − 7)(x + 4)

   Find two numbers that multiply to −28 and add to −3: −7 and 4. So x² − 3x − 28 = (x − 7)(x + 4).

6. Question 6

   A right triangle has legs of length 9 and 12. What is the length of the hypotenuse?

   1. A.21
   2. B.√63
   3. C.13
   4. D.15
   Show answer

   Correct answer: D. 15

   By the Pythagorean theorem, c² = 9² + 12² = 81 + 144 = 225, so c = √225 = 15.

7. Question 7

   What is the value of 3a² − 2b when a = −2 and b = 5?

   1. A.2
   2. B.26
   3. C.−22
   4. D.22
   Show answer

   Correct answer: A. 2

   Substitute: 3(−2)² − 2(5) = 3(4) − 10 = 12 − 10 = 2. Remember that (−2)² = 4, which is positive.

8. Question 8

   The circumference of a circle is 18π inches. What is the area of the circle?

   1. A.36π square inches
   2. B.18π square inches
   3. C.81π square inches
   4. D.324π square inches
   Show answer

   Correct answer: C. 81π square inches

   Circumference = 2πr, so 2πr = 18π gives r = 9. Area = πr² = π(9²) = 81π square inches.

9. Question 9

   Which inequality describes all solutions of −3x + 5 > 17?

   1. A.x > −4
   2. B.x < 4
   3. C.x > 4
   4. D.x < −4
   Show answer

   Correct answer: D. x < −4

   Subtract 5 to get −3x > 12. Dividing both sides by −3 reverses the inequality sign, so x < −4.

10. Question 10

    If 2x + 3y = 12 and x − y = 1, what is the value of x + y?

    1. A.5
    2. B.4
    3. C.6
    4. D.7
    Show answer

    Correct answer: A. 5

    From x − y = 1, x = y + 1. Substitute: 2(y + 1) + 3y = 12, so 5y = 10 and y = 2; then x = 3, and x + y = 5.

11. Question 11

    A cylinder has a radius of 3 feet and a height of 10 feet. What is its volume?

    1. A.30π cubic feet
    2. B.90π cubic feet
    3. C.60π cubic feet
    4. D.180π cubic feet
    Show answer

    Correct answer: B. 90π cubic feet

    Volume of a cylinder = πr²h = π(3²)(10) = π(9)(10) = 90π cubic feet.

12. Question 12

    What is the value of √144 − √49?

    1. A.√95
    2. B.25
    3. C.5
    4. D.9
    Show answer

    Correct answer: C. 5

    √144 = 12 and √49 = 7, so the difference is 12 − 7 = 5. Note that √144 − √49 is not the same as √(144 − 49).

13. Question 13

    What is the positive solution of 2x² − 5x − 12 = 0?

    1. A.4
    2. B.3/2
    3. C.6
    4. D.3
    Show answer

    Correct answer: A. 4

    Factor: 2x² − 5x − 12 = (2x + 3)(x − 4). Setting each factor to zero gives x = −3/2 or x = 4, so the positive solution is 4.

14. Question 14

    The three angles of a triangle are in the ratio 2 : 3 : 4. What is the measure of the largest angle?

    1. A.40°
    2. B.60°
    3. C.90°
    4. D.80°
    Show answer

    Correct answer: D. 80°

    Let the angles be 2k, 3k and 4k. Then 9k = 180°, so k = 20° and the largest angle is 4 × 20° = 80°.

15. Question 15

    Simplify (x² − 9)/(x² + 5x + 6), assuming the denominator is not zero.

    1. A.(x − 3)/(x + 3)
    2. B.−9/(5x + 6)
    3. C.(x − 3)/(x + 2)
    4. D.(x + 3)/(x + 2)
    Show answer

    Correct answer: C. (x − 3)/(x + 2)

    Factor the top and bottom: (x − 3)(x + 3) / [(x + 2)(x + 3)]. Cancel the common factor (x + 3) to get (x − 3)/(x + 2).

Tips for ASVAB Mathematics Knowledge

• Memorize the core formulas: area and perimeter, circle area and circumference, volume, and the Pythagorean theorem.
• Plug the answer choices back into the equation when solving directly is slow.
• Watch negative signs and order of operations — they are the most common source of wrong answers.
• No calculator is allowed, so keep perfect squares and common fraction–decimal conversions in memory.

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