ASVAB Math Knowledge Practice Test

Algebra and geometry without a calculator. Here are 10 ASVAB mathematics knowledge questions, each with the answer and the reason.

Updated 2026-11-14 by the Tigertest team. Covers eight of the CAT-ASVAB subtests in test order with the real time limits. Assembling Objects uses figures and is not included. Minimum AFQT scores vary by branch and change with recruiting needs.

1.
Solve for x: 3x + 7 = 22
- A.
  x = 3
- B.
  x = 7
- C.
  x = 15
- D.
  x = 5
Answer: D.
Subtract 7 from both sides to get 3x = 15, then divide by 3: x = 5. The answer 15 stops one step early.
2.
Simplify: (x³)(x⁴)
- A.
  x⁷
- B.
  x¹²
- C.
  2x⁷
- D.
  x¹
Answer: A.
When multiplying powers with the same base, add the exponents: 3 + 4 = 7, so the product is x⁷. Multiplying the exponents (x¹²) is the rule for raising a power to a power, not for multiplying.
3.
Solve for x: 2(x - 3) = 10
- A.
  x = 2
- B.
  x = 5
- C.
  x = 6.5
- D.
  x = 8
Answer: D.
Divide both sides by 2 to get x - 3 = 5, then add 3: x = 8. Alternatively distribute: 2x - 6 = 10, so 2x = 16 and x = 8.
4.
Which of the following is a prime number?
- A.
  21
- B.
  27
- C.
  33
- D.
  29
Answer: D.
A prime has exactly two factors, 1 and itself. 29 cannot be divided evenly by any whole number other than 1 and 29. 21 = 3 × 7, 27 = 3 × 9, and 33 = 3 × 11.
5.
Simplify: 5(2a - 3) + 4a
- A.
  10a - 15
- B.
  14a - 15
- C.
  14a - 3
- D.
  10a - 3
Answer: B.
Distribute the 5: 10a - 15. Then add 4a: 14a - 15. Forgetting to multiply -3 by 5 gives the wrong constant, and forgetting to add 4a gives 10a.
6.
What is the area of a circle with a radius of 3 centimeters? (Use 3.14 for pi.)
- A.
  28.26 square centimeters
- B.
  9.42 square centimeters
- C.
  18.84 square centimeters
- D.
  113.04 square centimeters
Answer: A.
Area is pi × r²: 3.14 × 3² = 3.14 × 9 = 28.26 square centimeters. The answer 18.84 is the circumference (2 × pi × r), and 113.04 uses the radius squared as 36.
7.
A right triangle has legs of 6 and 8. What is the length of the hypotenuse?
- A.
  10
- B.
  12
- C.
  14
- D.
  100
Answer: A.
By the Pythagorean theorem, c² = 6² + 8² = 36 + 64 = 100, so c = √100 = 10. The answer 100 forgets to take the square root, and 14 simply adds the legs.
8.
What is the supplement of a 115-degree angle?
- A.
  25 degrees
- B.
  65 degrees
- C.
  75 degrees
- D.
  245 degrees
Answer: B.
Supplementary angles add to 180 degrees: 180 - 115 = 65. The answer 25 would be the complement if the angle were 65, but complements only exist for angles under 90.
9.
Solve for x: 3(x + 2) = 2x + 11
- A.
  x = 3
- B.
  x = 5
- C.
  x = 7
- D.
  x = 17
Answer: B.
Distribute: 3x + 6 = 2x + 11. Subtract 2x from both sides: x + 6 = 11. Subtract 6: x = 5.
10.
What is the least common multiple of 6 and 8?
- A.
  2
- B.
  14
- C.
  24
- D.
  48
Answer: C.
Multiples of 6 are 6, 12, 18, 24 and multiples of 8 are 8, 16, 24, so the smallest shared multiple is 24. The answer 2 is the greatest common factor, and 48 is a common multiple but not the least.

Drill every mathematics knowledge question in the ASVAB Mathematics Knowledge drill: questions you miss come back until you have mastered them. Then take a timed practice test with the Mathematics Knowledge section in it.

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