20 Mathematics Knowledge (MK) Practice Questions & Answers
Every Mathematics Knowledge (MK) practice question from the ASVAB Practice Test, with the correct answer and a short explanation.
Start practice test →1. Solve for x: 3x - 7 = 8
- A.x = 5✓ Answer
- B.x = 3
- C.x = 1
- D.x = 15
Add 7 to both sides to isolate the term with x, giving 3x = 15; then divide both sides by 3 to get x = 5. Inverse operations undo addition and multiplication.
Source: ASVAB Mathematics Knowledge — linear equations (inverse operations)Report a problem with this question
2. What is the value of 2 + 3 × 4?
- A.24
- B.20
- C.9
- D.14✓ Answer
By the order of operations (PEMDAS), multiplication is performed before addition, so 3 × 4 = 12 first, then 2 + 12 = 14. Doing addition first would wrongly give 20.
Source: ASVAB Mathematics Knowledge — order of operations (PEMDAS)Report a problem with this question
3. A right triangle has legs of length 6 and 8. What is the length of the hypotenuse?
- A.10✓ Answer
- B.14
- C.12
- D.48
By the Pythagorean theorem, a² + b² = c², so c² = 6² + 8² = 36 + 64 = 100, and c = √100 = 10. The theorem relates the legs to the hypotenuse in any right triangle.
Source: ASVAB Mathematics Knowledge — Pythagorean theoremReport a problem with this question
4. Which of the following is a prime number?
- A.39
- B.91
- C.37✓ Answer
- D.51
A prime number has exactly two distinct factors, 1 and itself. 37 cannot be divided evenly by any integer other than 1 and 37, whereas 51 = 3 × 17, 91 = 7 × 13, and 39 = 3 × 13.
Source: ASVAB Mathematics Knowledge — prime numbers and factorsReport a problem with this question
5. Factor completely: x² - 5x + 6
- A.(x - 2)(x - 3)✓ Answer
- B.(x - 1)(x - 6)
- C.(x + 2)(x + 3)
- D.(x - 5)(x + 6)
Find two numbers that multiply to +6 and add to -5; those are -2 and -3. So x² - 5x + 6 = (x - 2)(x - 3), which expands back to the original trinomial.
Source: ASVAB Mathematics Knowledge — factoring quadraticsReport a problem with this question
6. What is the value of 2⁵?
- A.16
- B.25
- C.10
- D.32✓ Answer
An exponent tells how many times the base is used as a factor, so 2⁵ = 2 × 2 × 2 × 2 × 2 = 32. It is not 2 × 5 = 10, a common error.
Source: ASVAB Mathematics Knowledge — exponentsReport a problem with this question
7. What is the area of a circle with radius 5? (Use A = πr²)
- A.5π
- B.25π✓ Answer
- C.50π
- D.10π
The area of a circle is A = πr². Squaring the radius gives r² = 5² = 25, so the area is 25π. Using 2r instead of r² would wrongly give 10π.
Source: ASVAB Mathematics Knowledge — area of a circleReport a problem with this question
8. Solve the inequality: 2x + 3 > 11
- A.x < 7
- B.x < 4
- C.x > 7
- D.x > 4✓ Answer
Subtract 3 from both sides to get 2x > 8, then divide by 2 to get x > 4. Because we divide by a positive number, the inequality direction stays the same.
Source: ASVAB Mathematics Knowledge — solving inequalitiesReport a problem with this question
9. What is the volume of a cube with edge length 4?
- A.48
- B.16
- C.12
- D.64✓ Answer
The volume of a cube is the edge length cubed, V = s³ = 4³ = 64. All three dimensions are equal, so you multiply 4 × 4 × 4.
Source: ASVAB Mathematics Knowledge — volume of a cubeReport a problem with this question
10. Simplify: (x³)²
- A.x⁸
- B.x⁹
- C.x⁵
- D.x⁶✓ Answer
When a power is raised to another power, you multiply the exponents: (x³)² = x^(3×2) = x⁶. Adding the exponents instead would wrongly give x⁵.
Source: ASVAB Mathematics Knowledge — power of a power ruleReport a problem with this question
11. What is the sum of the interior angles of a pentagon?
- A.360°
- B.720°
- C.540°✓ Answer
- D.450°
The sum of interior angles of an n-sided polygon is (n - 2) × 180°. For a pentagon n = 5, so (5 - 2) × 180° = 3 × 180° = 540°.
Source: ASVAB Mathematics Knowledge — interior angle sum of polygonsReport a problem with this question
12. What is the length of the diagonal of a square whose side is 5?
- A.5√2✓ Answer
- B.25
- C.5
- D.10
A diagonal splits the square into two right triangles with legs of 5, so by the Pythagorean theorem the diagonal is √(5² + 5²) = √50 = 5√2. The diagonal of a square is always side × √2.
Source: ASVAB Mathematics Knowledge — diagonal of a square (Pythagorean theorem)Report a problem with this question
13. What is √144?
- A.12✓ Answer
- B.72
- C.24
- D.14
The square root of 144 is the number that, when multiplied by itself, gives 144. Since 12 × 12 = 144, √144 = 12.
Source: ASVAB Mathematics Knowledge — square rootsReport a problem with this question
14. A triangle has a base of 10 and a height of 6. What is its area?
- A.60
- B.30✓ Answer
- C.36
- D.16
The area of a triangle is A = ½ × base × height = ½ × 10 × 6 = 30. Forgetting the factor of ½ would wrongly give 60.
Source: ASVAB Mathematics Knowledge — area of a triangleReport a problem with this question
15. What is the value of ∛27 (the cube root of 27)?
- A.6
- B.27
- C.3✓ Answer
- D.9
The cube root of 27 is the number that, cubed, equals 27. Since 3 × 3 × 3 = 27, the cube root is 3.
Source: ASVAB Mathematics Knowledge — cube rootsReport a problem with this question
16. In a right triangle, one acute angle measures 35°. What is the measure of the other acute angle?
- A.65°
- B.45°
- C.55°✓ Answer
- D.145°
The three angles of any triangle sum to 180°. The right angle is 90°, so the two acute angles must total 90°; therefore the other is 90° - 35° = 55°.
Source: ASVAB Mathematics Knowledge — triangle angle sumReport a problem with this question
17. What is the perimeter of a rectangle with length 9 and width 4?
- A.36
- B.13
- C.26✓ Answer
- D.22
The perimeter of a rectangle is P = 2(length + width) = 2(9 + 4) = 2 × 13 = 26. Multiplying length by width instead gives the area (36), not the perimeter.
Source: ASVAB Mathematics Knowledge — perimeter of a rectangleReport a problem with this question
18. What is the slope of the line passing through the points (1, 2) and (3, 8)?
- A.1/3
- B.6
- C.3✓ Answer
- D.2
Slope is the change in y divided by the change in x: (8 - 2)/(3 - 1) = 6/2 = 3. It measures how steeply the line rises per unit of horizontal distance.
Source: ASVAB Mathematics Knowledge — slope in coordinate geometryReport a problem with this question
19. What is the value of 5! (5 factorial)?
- A.15
- B.120✓ Answer
- C.20
- D.25
A factorial is the product of all positive integers up to that number, so 5! = 5 × 4 × 3 × 2 × 1 = 120. It is not 5 × 5 = 25.
Source: ASVAB Mathematics Knowledge — factorialsReport a problem with this question
20. What is the volume of a cylinder with radius 3 and height 10? (Use V = πr²h)
- A.900π
- B.60π
- C.30π
- D.90π✓ Answer
The volume of a cylinder is V = πr²h. Squaring the radius gives r² = 3² = 9, then 9 × 10 = 90, so V = 90π. The radius must be squared, not just multiplied.
Source: ASVAB Mathematics Knowledge — volume of a cylinderReport a problem with this question
Practice questions modeled on the ASVAB content domains. Not affiliated with or endorsed by the U.S. Department of Defense, USMEPCOM, or any branch of the U.S. Armed Forces. Study the official practice materials at officialasvab.com. Official ASVAB →