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ASVAB Practice: Mathematics Knowledge Sample Questions

One of the subtests on the ASVAB is the Mathematics Knowledge test. Take a look at the following sample questions to see what kind of knowledge you will need 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. Simplify: 2 + 2y + 4 + y

    • (A)3y + 6

    • (B)3y + 8

    • (C)8y

    • (D)2y2 + 6

  2. What is the value of x?

    [Credit: Illustration by Thomson Digital]
    Credit: Illustration by Thomson Digital
    • (A)54°

    • (B)34°

    • (C)58°

    • (D)38°

  3. (5 – 2)! =

    • (A)118

    • (B)12

    • (C)6

    • (D)3

  4. How many factors does the number 51 have?

    • (A)Four

    • (B)Three

    • (C)Two

    • (D)One

  5. The number 0.405 is what percent of 0.9?

    • (A)4.5 percent

    • (B)45 percent

    • (C)25 percent

    • (D)50 percent

  6. The measure of angle P is m°. What is the measure of the complement of angle P?

    • (A)(180 – m) °

    • (B)(90 – m) °

    • (C)(m – 90) °

    • (D)(m – 180) °

  7. What is the length b in the right triangle?

    [Credit: Illustration by Thomson Digital]
    Credit: Illustration by Thomson Digital
    • (A)4 cm

    • (B)5 cm

    • (C)6 cm

    • (D)7 cm

  8. Translate the following sentence into an equation: “x decreased by 11 is twice x.”

    • (A)11 – x = 2x

    • (B)x – 11 = 2

    • (C)11 – x = 2

    • (D)x – 11 = 2x

  9. The mean of 5, 7, 8, 10, 4, and x is 7.5. What is the value of x?

    • (A)7

    • (B)8

    • (C)10

    • (D)11

Answers and explanations

  1. A. 3y+ 6

    This expression has two pairs of like terms. First, 2 and 4 are like terms and have a sum of 6. The terms 2y and y are also like terms and have a sum of 3y (remember that y is the same as 1y).

  2. D. 38°

    The sum of the angles of a triangle is always equal to 180°. To find the value of x, subtract 34° and 108° from 180°: 180° – 34° – 108° = 38°.

  3. C. 6

    Using the order of operations, simplify inside the parentheses first: (5 – 2)! = 3!. The expression 3! is the product of all whole numbers from 3 down to 1: 3! = 3(2)(1) = 6.

  4. A. Four

    The factors of a number are all the numbers, including the number and 1, that divide into the number without a remainder. The number 51 has four factors: 1, 3, 17, and 51.

  5. B. 45 percent

    Write this sentence as an equation, using x to represent the percent you’re trying to find: 0.405 = 0.9x. Divide both sides by 0.9 to get x alone on one side of the equal sign.

    image2.jpg

    You convert the decimal 0.45 to a percent by multiplying 0.45 by 100: 0.45(100) = 45 percent.

  6. B. (90 –m

    If two angles are complementary, the sum of their measures is 90°. Because the measure of angle P is m°, you find the complement of angle P by subtracting its measure from 90°.

  7. D. 7 cm

    Because the triangle is a right triangle, you need the Pythagorean theorem: a2 + b2 = c2. You know the lengths of side a and the hypotenuse (c), so plug those values into the theorem and solve for b:

    image3.jpg

    Use the positive answer because a length is never negative.

  8. D. x– 11 = 2x

    When you decrease something, you’re subtracting from it. In this instance, you’re taking 11 away from x; that means you have x – 11. “Is” means “equals” in mathematical terms (and you know that every equation must have an equal sign). “Twice x” means 2x. Your equation will look like this: x – 11 = 2x.

  9. D. 11

    The mean is the sum of all values divided by the number of values, or the average. First, find the sum of the values: 5 + 7 + 8 + 10 + 4 + x = 34 + x. Because there are six values, you’ll set this side of the equation up as a fraction:

    image4.jpg

    You already know the answer to the equation is 7.5, so your equation will look like this:

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