Mathematics Knowledge practice: ASVAB algebra and geometry
Ten questions in two sets of five on equations, exponents, fractions, triangles, circles, polygons, inequalities and volume. Pencil and paper only, as on the real test.
Correct answers
0 / 5
0 of 5 answered: the explanations appear below as you go.
| Subtests covered | MK |
Practice items written by Radif Partners for this site, not real ASVAB questions. A share of correct answers does not convert into a standard score or an AFQT percentile.
Prepared by Radif Partners · Method · official sources read on October 22, 2026 · published formulas and tables
Mathematics Knowledge (MK) is the ASVAB subtest of high school math stated directly, without a story: solve an equation, simplify an exponent, find an area, a volume or an angle. Where Arithmetic Reasoning tests whether you can set up a problem, MK tests whether you know the rule. The computer version gives 15 questions in 31 minutes, about 124 seconds each, and the paper version 25 questions in 24 minutes, about 58 seconds each. MK counts once in the AFQT sum AR + MK + 2 × VE, and it enters the Air Force A and E areas and the Marine Corps EL and CL line scores. A candidate with AR 50 and VE 53 who raises MK from 41 to 47 moves the AFQT from 45 to 51 and the Air Force Administrative percentile from 37 to 49. No calculator is allowed. The ten questions are written by Radif Partners, they are not real ASVAB items, and a score on them does not convert into an AFQT.
What Mathematics Knowledge covers
The ten questions on this page sample the main topics of the subtest. In algebra: a linear equation (3x + 7 = 25), an exponent (2 to the fifth), the product rule for powers, a quadratic solved by factoring and an inequality. In geometry: the area of a circle, the hypotenuse of a right triangle, the interior angles of a hexagon and the volume of a box. One question adds two fractions with different denominators. The real subtest stays within the same high school range, as the Official ASVAB sample questions show, but the computer version adapts and may serve harder items if you answer well.
Time and method
The Official ASVAB fact sheet gives 15 MK questions in 31 minutes on the computer test, about 124 seconds each, and 25 in 24 minutes on paper, about 58 seconds each. Because no calculator is allowed, keep the arithmetic light: work with fractions and with pi left as a symbol whenever the choices do, as in an answer written 16π. Check by substitution when you can. If x = 6 is offered for 3x + 7 = 25, compute 18 + 7 and you are done in five seconds, faster than solving.
Common traps, with examples
- Adding fractions straight across. 3/4 + 2/3 is not 5/7. Put both over 12: 9/12 + 8/12 = 17/12.
- Multiplying exponents that should be added. x³ times x⁴ is x⁷, not x¹². Exponents multiply only when a power is raised to another power, as in (x³)⁴.
- Flipping the inequality. In 2(x − 3) > 4x + 2, the x terms end up as −2x > 8. Dividing by −2 reverses the sign: x < −4. Forgetting this is one of the most frequent algebra errors.
- Area versus circumference. For a radius of 4, the area is πr² = 16π and the circumference 2πr = 8π. Both are usually among the choices.
- Polygon angles. The interior angles of an n-sided polygon add up to (n − 2) × 180. A hexagon gives 720 degrees, not 360, which is the sum of the exterior angles.
Where MK counts
MK enters the AFQT once, in the sum AR + MK + 2 × VE read in the 1997 conversion table. It weighs half as much as VE there, but it is the subtest that most often holds back candidates who read well. Take a candidate with AR 50, VE 53, GS 49 and EI 47. With MK 41, the AFQT is 45; with MK 47, it becomes 51. The Air Force Administrative percentile moves from 37 to 49 and the Electrical percentile from 35 to 41, because MK appears in A = MK + VE; E = GS + AR + MK + EI. In the Marine Corps, MK is part of EL = GS + AR + MK + EI; CL = MK + VE. The line score calculator shows the effect on every composite, and the Air Force page explains how the four areas open jobs.
A study plan for MK
Write one page with every formula from the list above and recite it until you can rebuild it from memory. Then work by topic: one session on equations and inequalities, one on exponents and roots, one on plane geometry, one on volume and polygons. End each session with a mixed timed set, since the real test does not announce the topic. Arithmetic Reasoning uses the same skills inside stories, so the Arithmetic Reasoning page is the next step, and the study plan page shows how many MK points your AFQT target needs. Finish with the mixed practice test.