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Mathematics Knowledge — ASVAB practice questions

40 multiple-choice questions and 16 flashcards on Mathematics Knowledge, about 13% of the ASVAB bank. Every one carries a written rationale.

Written and maintained by the CoStudy team · last updated 2026-09-29 · how we write and review questions

What this chapter covers

Mathematics Knowledge is one of 11 chapters in CoStudy's ASVAB bank, and it holds 40 of the bank's 300 multiple-choice questions — roughly 13% of the total. That proportion is not arbitrary: chapters follow the certifying body's published exam outline, and the number of questions in each is set by that domain's published weight, so the share of your practice time this chapter takes matches the share of the real exam it accounts for.

Studying by chapter is worth doing once you have a diagnostic score. A single overall percentage tells you whether you are close; it does not tell you which domain is dragging. Working a weak chapter in isolation, and re-testing it in isolation, is the fastest way to move a score that has stalled — and it is why the mock exams in CoStudy report by domain rather than as one number.

Free Mathematics Knowledge practice questions

5 questions drawn from this chapter, with the full rationale shown — the controlling principle behind the right answer, and why each wrong option tempts and fails.

If x + y = 12 and x - y = 4, what is the value of x?

  1. 4
  2. 6
  3. 8
  4. 16

Answer: C — 8

C) Right — adding the two equations eliminates y and gives 2x = 16, so x = 8. A) 4 is taken straight from the second equation's right side. B) 6 splits 12 evenly, ignoring the second equation. D) 16 stops at 2x = 16 without dividing by 2.

If 3x + 7 = 22, what is x?

  1. 3
  2. 5
  3. 7
  4. 15

Answer: B — 5

3x = 22 − 7 = 15. x = 5. A) Got 3 too early. B) Correct. C) That's 22 − 15. D) That's 3x, not x.

If sin θ = 3/5, what is cos θ for the same acute angle?

  1. 3/4
  2. 5/3
  3. 4/5
  4. 5/4

Answer: C — 4/5

3-4-5 triangle: cos θ = adjacent/hyp = 4/5. A) Tan. C) Correct. C/D) Reciprocals.

What is the value of 2^3 times 2^4?

  1. 49
  2. 64
  3. 128
  4. 4,096

Answer: C — 128

C) Right — multiplying like bases adds the exponents, so 2^7 equals 128. A) 49 multiplies the exponents 3 and 4 and then squares the result loosely, a confusion of base and exponent. B) 64 is 2^6, an off-by-one in adding the exponents. D) 4,096 is 2^12, from multiplying the exponents instead of adding them.

What is the volume of a cube with edge 4?

  1. 12
  2. 16
  3. 32
  4. 64

Answer: D — 64

A) That's 3 sides summed. B) That's a face area. C) Twice the face. D) 4³ = 64.

Mathematics Knowledge flashcards

1 cards from the 16 in this chapter.

20% of 80 = ?

16. (0.20 × 80.)

Practise the full chapter

These are a sample. The full Mathematics Knowledge chapter runs 56 items with per-chapter progress tracking, on the web and in the iOS app.

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