Joining the Military

Mathematics Knowledge Practice Test

Free · No signup

High school math: algebra, geometry and number rules, no calculator. 15 questions in 31 minutes.

Reviewed by Guilherme Correia, active-duty U.S. Air Force

1. Choose a test

2. Choose a version

Four versions, no question repeated between them. Take a new one each time so the score measures what you learned, not what you remember.

3. Choose the timing

Free, no signup. Your answers stay on this device.

Sample Mathematics Knowledge questions, with the answers

The first 3 of the 15 questions in version A of this subtest, exactly as the test asks them. Every question on the test comes with an explanation like these after you answer.

  1. 1. What is the value of 20 - 12 ÷ 4 + 3 × 2?

    • A. 10
    • B. 23
    • C. 11
    • D. 8

    Answer: B. Division and multiplication come before addition and subtraction: 12 ÷ 4 = 3 and 3 × 2 = 6. That leaves 20 - 3 + 6, worked left to right: 17 + 6 = 23. Working the whole line left to right, starting with 20 - 12, gives 10, the most tempting wrong choice.

    Remember: PEMDAS: parentheses, exponents, then multiplication and division left to right, then addition and subtraction left to right.

  2. 2. What is 3/8 written as a percent?

    • A. 37.5%
    • B. 3.75%
    • C. 0.375%
    • D. 266.7%

    Answer: A. Divide 3 by 8 to get the decimal 0.375, then multiply by 100 by moving the decimal point two places to the right: 37.5%. Putting a percent sign on the decimal without moving the point gives 0.375%, the most tempting wrong choice, and moving it only one place gives 3.75%. Dividing 8 by 3 instead gives about 266.7%.

    Remember: Fraction to percent: divide the top by the bottom, then move the decimal point two places to the right.

  3. 3. Which of the following is equal to 5^3 × 5^4?

    • A. 5^12
    • B. 25^7
    • C. 5^7
    • D. 25^12

    Answer: C. When powers with the same base are multiplied, keep the base and add the exponents: 3 + 4 = 7, so the product is 5^7 (three fives times four fives is seven fives). Multiplying the exponents gives 5^12, the most tempting wrong choice. The base stays 5; it does not become 25.

    Remember: Same base, multiplying: add the exponents. A power raised to a power: multiply the exponents.

The format of all ten subtests, how the AFQT is scored and how to study for it are on the ASVAB practice test hub.

What Mathematics Knowledge covers

Order of operations, fractions and percent, exponents and roots, scientific notation, equations and inequalities, factoring, angles and triangles, the Pythagorean theorem, circles, area and volume, primes and factors, and probability.

It is one of the four subtests that make up your AFQT. Take all four together for the full practice and an estimated AFQT range.

FAQ

ASVAB practice test: frequently asked questions

Can you use a calculator on the ASVAB?
No. The testing program states that you cannot use a calculator when taking the ASVAB, because the ability to do math by hand may be required on the job. This practice test is built the same way: every math question can be solved on scratch paper.
How many questions is Mathematics Knowledge on the ASVAB, and how long do you get?
15 questions in 31 minutes on the computer version given at a MEPS or MET site (the CAT-ASVAB), without tryout questions; the paper version has 25 in 24 minutes. This practice test uses the computer format and limit. Source: officialasvab.com, What to Expect.
What does the ASVAB Mathematics Knowledge subtest cover?
Order of operations, fractions and percent, exponents and roots, scientific notation, equations and inequalities, factoring, angles and triangles, the Pythagorean theorem, circles, area and volume, primes and factors, and probability.
Does Mathematics Knowledge count toward the AFQT, and which jobs use it?
Yes. Mathematics Knowledge is one of the four AFQT subtests (AR + MK + 2 x VE, where VE comes from Word Knowledge and Paragraph Comprehension), so it affects whether you can enlist at all. It feeds these service composites: Army line scores: Clerical (CL, VE+AR+MK), Electronics (EL, GS+AR+MK+EI), Field Artillery (FA, AR+CS+MK+MC), General Maintenance (GM, GS+AS+MK+EI), Skilled Technical (ST, GS+VE+MK+MC). Navy composites: Administration 1 (Admin 1, MK + VE), Administration 2 (Admin 2, CS + MK + VE), Specialized 2 (Spec 2, GS + MK + VE), Specialized 4 (Spec 4, AR + GS + MK + VE), Mechanical 2 (Mech 2, AO + AS + MK), Operations 1 (Ops 1, AR + AS + MK + VE), Operations 3 (Ops 3, AO + AR + MK + VE), Operations 4 (Ops 4, CS + MC + MK + VE), Technical 1 (Tech 1, AR + MC + MK + VE), Technical 2 (Tech 2, AR + EI + GS + MK). Air Force MAGE composites: Administrative (A, VE + MK), Electronic (E, AR + MK + EI + GS). Marine Corps line scores: Electrical (EL, AR + EI + GS + MK), Clerical (CL, VE + MK).
Is the ASVAB timed?
Yes. On the computer version given at a MEPS or MET site, each of the ten subtests has its own time limit. Without tryout questions: General Science 15 questions in 12 minutes, Arithmetic Reasoning 15 in 55, Word Knowledge 15 in 9, Paragraph Comprehension 10 in 27, Mathematics Knowledge 15 in 31, Electronics Information 15 in 10, Auto Information 10 in 7, Shop Information 10 in 6, Mechanical Comprehension 15 in 22 and Assembling Objects 15 in 18: 135 questions in 197 minutes. The testing program says almost all examinees finish each subtest before the time expires. The at-home PiCAT has no time limits on the individual subtests.
Can you go back to a question on the ASVAB?
Not on the computer version. The testing program says that because the CAT-ASVAB is adaptive, you cannot change an answer once you have moved on to the next question. On the paper version you can review your answers within a subtest. The timed mode of this practice test works like the computer version.
What is the AFQT, and is it a different test?
It is not a separate test. The AFQT is a score computed from four ASVAB subtests: Arithmetic Reasoning, Mathematics Knowledge, Word Knowledge and Paragraph Comprehension. DoD's technical bulletin gives the formula as AR + MK + 2 times VE, where VE combines Word Knowledge and Paragraph Comprehension. The result is reported as a percentile from 1 to 99 against a national sample of 18 to 23 year olds tested in 1997. The officer selection tests, such as the AFOQT, are different exams.
Do the science and technical subtests count toward the AFQT?
No. The AFQT uses only Arithmetic Reasoning, Mathematics Knowledge, Word Knowledge and Paragraph Comprehension. General Science, Electronics Information, Auto and Shop Information, Mechanical Comprehension and Assembling Objects feed the composite scores (line scores) each service uses to decide which jobs you qualify for, so they matter once your AFQT gets you in. On the computer test Auto and Shop are separate subtests, combined into one Auto and Shop (AS) score.

Keep going

Next steps

Army ASVAB Jobs

Every MOS and its line score

Air Force ASVAB Jobs

Every AFSC and its minimum

Navy ASVAB Ratings

Every rating and its line score

First-Year Pay

What you earn in your first year

officialasvab.com (What to Expect, Scores, FAQs, CAT-ASVAB, PiCAT, retest policy), ASVAB Technical Bulletin No. 4, Segall (2004), DoDI 1145.01, and each service's recruiting site, read October 3, 2026

Results are estimates. Always verify with your finance office.

Reviewed by Guilherme Correia · Military Toolkit editorial

Military Toolkit is not affiliated with the Department of Defense or the ASVAB testing program. The questions are original practice material, not ASVAB questions.