ASVAB Math Practice Test 2024 Free Printable PDF Worksheet: Mathematics Knowledge (MK) Question Answers Free Download for Armed Services Vocational Aptitude Battery exam and Armed Forces Qualification Test (AFQT) exam preparation online.

Mathematics Knowledge (MK) tests the ability to solve problems by applying knowledge of mathematical concepts and applications. The problems focus on concepts and algorithms and involve number theory, numeration, algebraic operations and equations, geometry and measurement, and probability. Mathematics Knowledge is one factor that characterizes mathematics comprehension and assesses logical thinking.

Actual Exam Content in MK Part

Test Type

No. of Items

Time Limit

ASVAB Paper-and-Pencil

15

24

CAT-ASVAB Test

15

23

ASVAB Mathematics Knowledge Practice Test 2024

The following ASVAB Mathematics Knowledge Practice Test is only for reference purposes; it’s not an actual exam test question. You can download our free ASVAB Math Practice Question in PDF (printable and editable). This will help you make better ASVAB Test Prep offline. You can also use these files (PDF, DOC) as worksheets.

Q7. Factor the following expression: y² − 16y + 48

A. (y − 1)(y +48)

B. (y − 4)(y − 12)

C. (y − 4)(y + 4)

D. (y +1)(y − 16)

View Correct Answer

Answer: B

Note the minus sign in the middle term and the plus sign in the third term. This should tell you that the factors will contain a minus sign in
each term. In this problem, the fact that the two terms will have a minus sign should lead you to the correct answer, as only one answer has a minus sign in each term. However, not all questions of this type will have that kind of clue. Note that the first term in each factor will be y. Now you need to find two numbers that multiply to 48 and add to 16. Those numbers are 4 and 12. This gives the factors (y − 4)(y − 12)

Q8. Solve for x. 12x + 6 = 8x +10

A. x = 1

B. x = 2

C. x = 4

D. x = 6

View Correct Answer

Answer: A

To solve such problems, move all the terms with an unknown to one side of the equal sign and the numbers to the other.

Q9. Solve for the two unknowns.
3y + 3x = 24
6y + 3x = 39

A. y = 3; x = 5

B. y = 4; x = 6

C. y = 5; x = 3

D. y = 6; x = 2

View Correct Answer

Answer: C

Set each equation equal to zero. Next, arrange one of the equations so that when it is subtracted from or added to the other equation, one of the terms becomes zero and drops out of the equation. Next, solve for the remaining unknown.

Q10. x¹² / x^{4}

A. x^{−}^{4}

B. x^{8}

C. x^{18}

D. x^{−16}

View Correct Answer

Answer: B

To divide numbers with exponents, subtract the exponents. In this problem, subtract the 4 from the 12, leaving x^{8} as the correct answer.

Q11. Solve for y.

y² + 7y = −10

A. y = −5; y = −2

B. y = 1; y = −10

C. y = −2; y = 6

D. y = 5; y = −1

View Correct Answer

Answer: A

Set the equation to equal zero:

Q12. Multiply: \frac{6y}{11} × \frac{2}{5x}

A. 6y + 5x =22

B. 22y / 5x

C. 5y/ 22x

D. 22y / 55x

View Correct Answer

Answer: D

multiply fractions, multiply the numerators and denominators.

Q13. Divide: \frac{6x}{11} ÷ \frac{2}{5y}

A. 3y + 11x =2

B. 15xy / 11

C. 12/ 22xy

D. 11y / 25x

View Correct Answer

Answer: B

To divide fractions, invert the second term and multiply.

Q14. \sqrt[3]27

A. 3

B. 4

C. 5

D. 2.25

View Correct Answer

Answer: A

The cube root is the number that, when multiplied by itself three times, results in the answer. In this instance, 3 × 3 × 3 = 27, so the cube root of 27 = 3.

To answer most questions of this type on the ASVAB, you just need to memorize some basic cubes. It would be wise to memorize all the cubes from 2 to 10, just to prepare for ASVAB test item possibilities

Q15. Solve for g \fracgh =a

A. ga / h

B. g =a/h

C. g = ah

D. g = a ÷ h

View Correct Answer

Answer: C

Isolate the variable of interest on one side of the equation. In this problem, you must multiply each side by h, leaving g on the left side of the
equation and h on the right side. Therefore, the answer is g = ah.

Q16. Which of the following is an equilateral triangle?

View Correct Answer

Answer: D

An equilateral triangle has three equal sides and angles, so D is the correct answer.

Q17. What is the perimeter of the following rectangle?

A. 12 m

B. 18 m

C. 24 m

D. 12 m

View Correct Answer

Answer: C

To find the perimeter of a quadrilateral, add the lengths of the four sides. In this instance, 9 meters + 9 meters + 3 meters + 3 meters + 24
meters, the correct answer

Q18. What is the circumference of the following circle?

A. 6.56 m

B. 12.56 m

C. 25.12 m

D. 35.12 m

View Correct Answer

Answer: C

The formula for the circumference of a circle is Πd. The figure gives the radius, which is one-half the length of the diameter. To find the diameter, multiply the radius by 2. In this problem, the diameter is 8 meters. Multiplying 8 by Π gives the correct answer of 25.12 meters.

Q19. In the following equilateral triangle, what is the measure of ∠1?

A. 30°

B. 45°

C. 60°

D. 90°

View Correct Answer

Answer: C

An equilateral triangle has three equal angles. A triangle has a total of 180°, so each angle must be 60°.

20. If ∠1 is 34°, what is the measure of ∠2?

A. 56°

B. 110°

C. 146°

D. 180°

View Correct Answer

Answer: C

A straight line or straight angle is 180°. So if ∠1 is 34°, ∠2 is the difference between 180° and 34°, or 146°.

Q21. In the following right triangle, what is the length of side AB?

A. 3 m

B. 5 m

C. 7 m

D. 12 m

View Correct Answer

Answer: B

∠C is a right angle, so you can employ the Pythagorean Theorem

Q22. What is the area of the following triangle?

A. 8 ft²

B. 12 ft²

C. 15 ft²

D. 16 ft²

View Correct Answer

Answer: D

This is a right triangle, so 4 ft is the height of the triangle and 8 ft is the base. The formula for the area of a triangle is ½ bh.

Q23. What is the diameter of the following circle?

A. 40 cm

B. 80 cm

C. 160 cm

D. 640 cm

View Correct Answer

Answer: C

The diameter is 2r. r = 80 cm, so the diameter is 160 cm.

Q24. If lines A and B are parallel and are intersected by line C and ∠2 is 30°, what is the measure of ∠7?

A. 30°

B. 50°

C. 112°

D. 130°

View Correct Answer

Answer: A

∠2 and ∠7 are alternate exterior angles and therefore are equal in measure. So both ∠2 and ∠7 are 30°.

Q25. What is the volume of a cylinder with a height of 15 m and a radius of 5 m?

A. 235.50 m³

B. 1,177.50 m³

C. 1,280.25 m³

D. 1,340.25 m³

View Correct Answer

Answer: B

The formula for finding the volume of a cylinder is V = ∏r ² h.