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Mathematics Knowledge (MK) AFQT

Mathematics Knowledge (MK) tests your grasp of core math concepts and is one of the four AFQT subtests that decide whether you qualify to enlist. Here is exactly what it covers and how to prepare.

Practice questions

Original Mathematics Knowledge questions in the ASVAB style. Pick an answer for instant feedback and an explanation, then keep going in the app.

  1. Solve for x: 3(x - 4) = 2x + 5

    1. x = 7
    2. x = 12
    3. x = 17
    4. x = 1

    Distribute to get 3x - 12 = 2x + 5. Subtract 2x from both sides: x - 12 = 5, then add 12: x = 17.

  2. Simplify the expression (2x^3)^4.

    1. 8x^7
    2. 16x^12
    3. 16x^7
    4. 8x^12

    Raise each factor to the 4th power: 2^4 = 16 and (x^3)^4 = x^(3*4) = x^12, giving 16x^12.

  3. A right triangle has legs measuring 9 and 12. What is the length of the hypotenuse?

    1. 15
    2. 21
    3. 18
    4. 13

    By the Pythagorean theorem, the hypotenuse equals the square root of (9^2 + 12^2) = square root of (81 + 144) = square root of 225 = 15.

  4. A cylinder has a radius of 3 and a height of 10. What is its volume?

    1. 30π
    2. 60π
    3. 90π
    4. 900π

    Volume of a cylinder is π times radius squared times height: π(3^2)(10) = π(9)(10) = 90π.

  5. Which of the following is the complete factorization of x^2 - 7x + 12?

    1. (x - 2)(x - 6)
    2. (x - 3)(x - 4)
    3. (x + 3)(x + 4)
    4. (x - 1)(x - 12)

    We need two numbers that multiply to 12 and add to -7: those are -3 and -4, so the factorization is (x - 3)(x - 4).

  6. What is the sum of 2/3 and 1/4?

    1. 3/7
    2. 11/12
    3. 5/12
    4. 3/12

    Use a common denominator of 12: 2/3 = 8/12 and 1/4 = 3/12, so the sum is 8/12 + 3/12 = 11/12.

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What it measures

Mathematics Knowledge (MK) measures your understanding of high-school-level math concepts and how well you can apply rules and formulas. Unlike Arithmetic Reasoning, which wraps math in word problems, MK tests the math itself directly: solving equations, working with fractions and exponents, and knowing geometry facts.

MK is one of the four AFQT subtests, along with Arithmetic Reasoning (AR), Word Knowledge (WK), and Paragraph Comprehension (PC). Your scores on these four are combined into the AFQT score, which determines whether you are eligible to enlist and in which category you fall. Because AFQT decides your basic qualification, MK directly affects your enlistment. It is also part of many line score combinations used to qualify for specific military jobs, so a strong MK score opens more career options.

What's on it

Topics and skills you will see

  • Number properties: factors, multiples, prime numbers, order of operations (PEMDAS), and positive and negative numbers
  • Fractions, decimals, and percentages: simplifying, converting, and operating with each
  • Exponents and roots: squares, cubes, square roots, and the basic exponent rules
  • Algebra: solving linear equations for a variable, evaluating expressions, factoring, and simple inequalities
  • Geometry: perimeter, area, and volume; angles; properties of triangles, circles, rectangles, and other shapes; the Pythagorean theorem
  • Basic formulas and definitions: knowing terms like mean, median, radius, diameter, and how to plug values into a formula

How to study it

Memorize the core formulas and rules first. MK rewards recall. Make flashcards for area and perimeter of common shapes, the area and circumference of a circle, volume of a box, the Pythagorean theorem, and the exponent rules. Also lock in the order of operations (PEMDAS). If a formula is in your memory, the question becomes plug-and-solve.

Practice by working problems, not just reading. Math is a skill you build by doing. Set a timer and do sets of problems, then review every mistake to find the concept you missed. Rework any problem you got wrong until you can solve it cleanly without help. Aim for a mix of algebra and geometry so no topic stays weak.

Show your steps and check the answer. The most common MK mistakes are careless ones: dropping a negative sign, misreading an exponent, or breaking the order of operations. Write out each step instead of doing it in your head, and plug your answer back into the original equation when you can. On the CAT-ASVAB you cannot skip and return, so answer each question deliberately before moving on.

Avoid the trap answers. Multiple-choice options often include the result of a common error, so a wrong answer can look "right." Do not pick the first choice that resembles your number without finishing the full calculation. When you are unsure, plug the answer choices back into the problem to see which one works, and eliminate options that are obviously too large or too small before you guess.

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