ASVAB Mathematics Knowledge Practice

One of the subtests you will find on the ASVAB is the Mathematics Knowledge test. The following sample questions will give you an idea of what you need to know for test day.

Sample questions

Mathematics Knowledge

Time: 24 minutes for 25 questions

Directions: Mathematics Knowledge is the fifth subtest on the ASVAB. The questions are designed to test your ability to solve general mathematical problems. Each question is followed by four possible answers. Decide which answer is correct, and then mark the corresponding space on your answer sheet. Use your scratch paper for any figuring you want to do. You may not use a calculator.

1. (–5)³ =

   • (A)–125

   • (B)–15

   • (C)15

   • (D)125

2. If 42 < 2x, which is true about the value of x?

   • (A)x is less than 21.

   • (B)x is greater than 21.

   • (C)x is less than or equal to 21.

   • (D)x is greater than or equal to 21.

3. 473 + 220 + 27 =

   • (A)710

   • (B)620

   • (C)720

   • (D)711

4. In the decimal 45.21, which digit is in the tenths place?

   • (A)4

   • (B)5

   • (C)2

   • (D)1

5. What are the coordinates of point P?

   

   Credit: Illustration by Thomson Digital

   • (A)(–3, –2)

   • (B)(3, –2)

   • (C)(–3, 2)

   • (D)(2, –3)

6. Express 11/4 as a decimal.

   • (A)2.25

   • (B)2.5

   • (C)2.75

   • (D)3.25

7. If –2 + y = 8, then y =

   • (A)–10

   • (B)–6

   • (C)6

   • (D)10

8. A circle has a circumference of 9.24 centimeters. What is the diameter of the circle?

   • (A)1.5 cm

   • (B)3 cm

   • (C)3.14 cm

   • (D)6 cm

9. What is 28 percent of 40?

   • (A)9.4

   • (B)10.2

   • (C)11.2

   • (D)12.5

10. Which is equal to 10³ × 10^–6 × 10²?

    • (A)10

    • (B)100

    • (C)0.1

    • (D)0.01

Answers and explanations

1. A. –125

   The value of (–5)³ is equal to –5 multiplied by itself three times:

   (–5)³ = (–5)(–5)(–5) = 25(–5) = –125

2. B. x is greater than 21.

   To get x alone on one side of the inequality, divide both sides of the inequality 42 < 2x by 2:

   

3. C. 720

   This one is simple addition.

4. C. 2

   The digit 4 is in the tens place, the digit 5 is in the ones place, the digit 2 is in the tenths place, and the digit 1 is in the hundredths place.

5. C. (–3, 2)

   Locate point P by starting at the origin and moving along the x-axis until you’re even with point P. That’s the –3 mark, so –3 is your x coordinate. Now move along the y-axis until you reach point P. It’s at the 2 mark, so 2 is the y coordinate.

   

   Credit: Illustration by Thomson Digital

6. C. 2.75

   Divide 11 by 4 using long division.

   

7. D. 10

   To get y by itself on one side of the equal sign, add 2 to both sides of the equation: –2 + y + 2 = 8 + 2. The –2 and 2 on the left side cancel each other, so y = 10.

8. 8 B. 3 cm

   The formula for the circumference of a circle is C = πd. Substitute 9.24 for C and 3.14 for π and then solve for d by dividing both sides by 3.14.

   

9. C. 11.2

   Write 28 percent as a decimal: 28 percent = 28/100 = 0.28. Multiply: 0.28(40) = 11.2.

10. C. 0.1

    To multiply terms with the same base, add the exponents:

    10^{3 + (–6) + 2} = 10^–1

    Simplify: