ASVAB Math Knowledge: formulas, practice and a free drill

Mathematics Knowledge (MK) tests high school math with no story around it: algebra, exponents, roots, geometry and number rules. It has 15 questions in 31 minutes on the CAT and 25 in 24 minutes on paper, with no calculator and no formula sheet. It is a quarter of your AFQT, and most questions come down to knowing about fifteen rules and formulas.

15 / 31 min
CAT questions and time: 25 / 24 min
paper questions and time: 25%
of the AFQT: 12 free
timed drill questions

Last checked 20 October 2026 · Question counts and times from the official ASVAB site

Start the free Mathematics Knowledge drill

12 questions, 11:31 on the clock, every answer explained. No sign-up.

By the LifeScore Editorial Team · Updated 20 October 2026 · How we check facts · How this is scored

Free ASVAB-style drill

Try 12 Mathematics Knowledge questions against the paper clock

25 questions in 24 minutes is the real paper pace, so 12 questions get 11:31. Original questions, scored on our server, with every answer explained at the end. It is a taster of one subtest, not an AFQT estimate: for that, take the full free practice test.

12
questions
11:31
time limit
Free
every answer explained

How many questions are on ASVAB Mathematics Knowledge, and how long do you get?

15 questions in 31 minutes on the CAT-ASVAB and 25 questions in 24 minutes on the paper ASVAB, with no calculator on either.

ASVAB Mathematics Knowledge: the official format, and what our drill copies
CAT-ASVAB (computer)	15 questions in 31 minutes, about 124 seconds eachPublished by the ownerOfficial ASVAB, "The CAT-ASVAB"
Paper ASVAB (P&P)	25 questions in 24 minutes, about 58 seconds eachPublished by the ownerOfficial ASVAB, "What to expect when you take the ASVAB"
Calculator	Not allowed on either versionPublished by the ownerDepartment of Defense, "The use of calculators on the ASVAB" (2026 note)
Weight in the AFQT	A quarter: AFQT = AR + MK + 2 × VEPublished by the ownerOfficial ASVAB, "ASVAB Technical Bulletin No. 1" (AFQT formula)
Guessing	Paper: no penalty, so never leave a blank. CAT: unfinished questions are scored as random guesses, so do not click through at the endPublished by the ownerOfficial ASVAB, "ASVAB scoring"
Our free drill	12 original questions, 11:31 on the clock (the paper pace), every answer explainedLifeScore

What does ASVAB Mathematics Knowledge test?

The official description is high school mathematics. Unlike Arithmetic Reasoning there is little reading: you get an equation to solve, a shape to measure or an expression to simplify. That makes it the most knowledge-based of the four AFQT subtests: if you know the rule, the question is quick; if you do not, no strategy will find it.

On paper you get 25 questions in 24 minutes, about 58 seconds each. On the CAT you get 15 in 31 minutes, about 124 seconds each, with questions that get harder as you get them right. No formula sheet is given on either version, so the formulas below have to be in your head.

MK is one of the four AFQT subtests and a quarter of the AFQT formula. It is also inside the Army CL, EL, FA, GM and ST line scores, most Navy rating sums (some count it twice, written 2MK), the Air Force Administrative and Electronics composites, and the Marine Corps EL and CL scores.

See which jobs ask for which scores, branch by branch: Army jobs, Navy jobs, Air Force jobs, Marine Corps jobs.

What formulas do you need for ASVAB Math Knowledge?

No formula sheet is provided, so learn these by heart. Together they cover most of the geometry and algebra the subtest asks about.

Formulas and rules to memorise (our list)
Topic	Rule or formula	Example
Exponents: multiply	aᵐ × aⁿ = aᵐ⁺ⁿ	3² × 3³ = 3⁵
Exponents: power of a power	(aᵐ)ⁿ = aᵐⁿ	(2³)² = 2⁶
Square roots	√(a × b) = √a × √b	√72 = √36 × √2 = 6√2
Linear equations	Do the same to both sides	4x − 9 = 2x + 7 gives x = 8
Factoring	x² + bx + c = (x + p)(x + q), p + q = b, pq = c	x² − 5x + 6 = (x − 2)(x − 3)
Pythagorean theorem	a² + b² = c²	legs 6 and 8 give 10
Circle	Area πr², circumference 2πr	r = 5: area 25π
Rectangle and triangle	Area lw and ½bh	base 10, height 4: 20
Box (rectangular solid)	Volume lwh	2 × 3 × 4 = 24
Cylinder	Volume πr²h	r = 2, h = 5: 20π
Angles	Straight line 180°, triangle 180°, full turn 360°	supplementary angles add to 180°
Order of operations	Brackets, exponents, × and ÷, + and −	2 + 3 × 4 = 14

Write the formula on your scratch paper before you put numbers in. It is the same habit as in Arithmetic Reasoning, and it catches the circumference-for-area slip.

What do ASVAB Mathematics Knowledge questions look like?

Like these 7, which we wrote in the style of the official description: the first two are worked open, the rest hide the answer until you try. None is a real ASVAB question.

ASVAB-style question 1 · Linear equation
If 4x − 9 = 2x + 7, what is x?
1. A1
2. B4
3. C8
4. D16
Worked answer
C: 8. Subtract 2x from both sides and add 9: 2x = 16, so x = 8.
1. Collect the x terms: 4x − 2x = 2x.
2. Collect the numbers: 7 + 9 = 16.
3. 2x = 16, so x = 8. Check: 32 − 9 = 23 and 16 + 7 = 23.
The trap: 16, stopping at 2x = 16. Finish the last step.
ASVAB-style question 2 · Exponents
Which is equal to 3² × 3³?
1. A3⁵
2. B3⁶
3. C9⁵
4. D9⁶
Worked answer
A: 3⁵. When you multiply powers of the same base, add the exponents: 3²⁺³ = 3⁵.
1. Same base, multiplication: add the exponents.
2. 2 + 3 = 5.
3. Check: 9 × 27 = 243, and 3⁵ = 243.
The trap: 3⁶, from multiplying the exponents. That rule is for a power of a power, (3²)³.
ASVAB-style question 3 · Geometry
A right triangle has legs of 6 and 8. How long is the hypotenuse?
1. A7
2. B10
3. C14
4. D100
Show the worked answer
B: 10. 6² + 8² = 36 + 64 = 100, and √100 = 10.
1. Write a² + b² = c².
2. 36 + 64 = 100.
3. c = √100 = 10.
The trap: 100, forgetting the square root. Or 14, adding the legs. The hypotenuse is always shorter than the two legs added together.
ASVAB-style question 4 · Geometry
What is the area of a circle with a radius of 5?
1. A10π
2. B25π
3. C50π
4. D100π
Show the worked answer
B: 25π. Area is πr², so π × 5² = 25π.
1. Write A = πr².
2. r² = 25.
3. A = 25π.
The trap: 10π, the circumference (2πr). Or 100π, from squaring the diameter. Write the formula first.
ASVAB-style question 5 · Factoring
What are the solutions of x² − 5x + 6 = 0?
1. Ax = 2 and x = 3
2. Bx = −2 and x = −3
3. Cx = 1 and x = 6
4. Dx = −1 and x = 6
Show the worked answer
A: x = 2 and x = 3. x² − 5x + 6 = (x − 2)(x − 3), which is zero when x = 2 or x = 3.
1. Find two numbers that multiply to 6 and add to −5: −2 and −3.
2. So the equation is (x − 2)(x − 3) = 0.
3. Each bracket can be zero: x = 2 or x = 3. Check: 4 − 10 + 6 = 0.
The trap: x = −2 and x = −3, the numbers in the brackets rather than the solutions. Set each bracket to zero.
ASVAB-style question 6 · Angles
Two angles are supplementary, and one is three times the other. What is the larger angle?
1. A45°
2. B90°
3. C120°
4. D135°
Show the worked answer
D: 135°. Supplementary angles add to 180°. With x and 3x, 4x = 180, so x = 45 and the larger is 135°.
1. Supplementary means the two add to 180°.
2. Call them x and 3x: 4x = 180, so x = 45.
3. The larger is 3 × 45 = 135°.
The trap: 45°, the smaller angle. Read which one the question asks for.
ASVAB-style question 7 · Roots
Which is equal to √72?
1. A6√2
2. B4√3
3. C9√2
4. D2√6
Show the worked answer
A: 6√2. 72 = 36 × 2, so √72 = √36 × √2 = 6√2.
1. Find the largest perfect square that divides 72: 36.
2. √72 = √36 × √2.
3. = 6√2. Check: 6² × 2 = 72.
The trap: 9√2, from 72 = 9 × 8 and taking 9 out without its square root. Only perfect squares come out of the root, as their roots.

4 more Mathematics Knowledge drills, and full mocks

The free drill is one set. The ASVAB Pass Pack has 16 subtest drills across the four AFQT subjects, 6 full ASVAB-style mocks and a score predictor.

The ASVAB Pass Pack gives you 6 full mocks on the real clock, 16 drills of 12 questions for the sections that cost you points, and a predictor that turns your mocks into the odds of reaching your target. One payment, no subscription, and your free score stays free.

Prep courses for these tests usually cost $19 to $129. The ASVAB Pass Pack is US$39 (£29), once.

See the ASVAB Pass Pack How our questions are built and checked

6
timed mocks: 16
topic drills: 1
score predictor

How do you get a better ASVAB Mathematics Knowledge score?

MK gives no formula sheet. The table above is short enough to learn in a week; write it out from memory once a day. The rest of our method is below.

Our method, in order of how much it usually helps

Learn the formulas cold
MK gives no formula sheet. The table above is short enough to learn in a week; write it out from memory once a day.
Write the formula first
Before numbers, write the rule. It is three seconds that stops area-for-circumference and add-for-multiply slips.
Check by substitution
For equations, put your answer back in. If both sides match, you are right. On paper, you can also test the options in the equation when algebra stalls.
Estimate geometry
A hypotenuse is longer than either leg and shorter than both added. A circle of radius 5 has area a bit over 75. Rough numbers rule out options.
Pace yourself: about 58 seconds on paper
Most MK questions are quick if you know the rule. Do those first; mark the ones you need to work out and come back within the subtest.
Know your squares and roots
Squares up to 15² and the roots of perfect squares save time on Pythagoras, roots and factoring questions.

What are the most common ASVAB Mathematics Knowledge mistakes?

Exponent rules mixed up: multiply powers: add exponents. Power of a power: multiply them. Different bases: no shortcut.

The traps we see most often, and the fix

Exponent rules mixed up
Multiply powers: add exponents. Power of a power: multiply them. Different bases: no shortcut.
Stopping one step early
2x = 16 is not the answer; x is. Read what the question asks for.
Sign errors
Moving a term across the equals sign changes its sign. Subtracting a negative adds. Most algebra mistakes are here.
Radius versus diameter
Many circle questions give the diameter. Halve it before using πr².
Brackets versus solutions
In (x − 2)(x − 3) = 0 the solutions are 2 and 3, not −2 and −3.

How should you study for ASVAB Mathematics Knowledge in a week?

Start with the free drill to find your weak spots, spend five days on them, then retake the drill. Twenty to forty minutes a day is enough to see a change.

A 7-day Mathematics Knowledge plan (ours)
Day	What to do
Day 1	Take the free drill below. List the rules you did not know, not just the questions you missed.
Day 2	Exponents, roots and order of operations: learn the rules, then 20 questions.
Day 3	Linear equations and inequalities: 20 questions, checking each answer by substitution.
Day 4	Factoring and quadratics: 15 questions. Write the multiply-add pair for each.
Day 5	Geometry: area, perimeter, volume, Pythagoras and angles. Write every formula from memory first.
Day 6	A timed mixed set at the paper pace (58 seconds a question), no calculator.
Day 7	Retake the drill. Rewrite the formula table from memory; anything you miss goes on tomorrow's list.

Then put it together: the how to pass the ASVAB guide plans all four AFQT subjects, the free ASVAB-style practice test gives an estimated AFQT, and what is a good ASVAB score shows what each branch asks for. The other subtest guides: Arithmetic Reasoning, Word Knowledge, Paragraph Comprehension.

Frequently asked questions

How many questions are on ASVAB Mathematics Knowledge?

15 on the CAT-ASVAB, with 31 minutes, and 25 on the paper ASVAB, with 24 minutes, per the official ASVAB site.

What math is on ASVAB Math Knowledge?

High school math: algebra (equations, inequalities, factoring), exponents and roots, geometry (area, volume, angles, Pythagoras) and number rules. Word problems belong to Arithmetic Reasoning.

Do you get a formula sheet on the ASVAB?

No. Formulas such as the area of a circle or the Pythagorean theorem have to be memorised. The table on this page lists the ones worth learning.

Can you use a calculator on ASVAB Math Knowledge?

No. Calculators are not allowed on either version of the ASVAB. You get scratch paper.

What is the difference between Math Knowledge and Arithmetic Reasoning?

Arithmetic Reasoning is word problems: you have to work out what to calculate. Mathematics Knowledge is math rules asked directly: you have to know how. Each is a quarter of the AFQT.

How can I improve my Math Knowledge score fast?

Learn the formula table on this page by heart, then practise the four most common topics: exponents, linear equations, factoring and basic geometry. Knowing a rule turns a hard question into a quick one.

Make Mathematics Knowledge your strongest subtest

16 subtest drills, 6 full ASVAB-style mocks and a predictor for the score your job needs.