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. Evaluate: −3² + (−4)(−5) − 12 ÷ 4
- A.32
- B.11
- C.8✓ Answer
- D.26
Under the order of operations (PEMDAS) the exponent applies only to the 3 because there are no parentheses, so −3² = −9, not +9. Then multiplication and division are done left to right: (−4)(−5) = 20 and 12 ÷ 4 = 3, giving −9 + 20 − 3 = 8. Choosing 26 means the negative sign was squared along with the 3.
Source: ASVAB CEP Overview p.19, MK content area "number theory"; order of operations (PEMDAS) and sign rules for multiplication of two negativesReport a problem with this question
2. Which of the following numbers is prime?
- A.91
- B.87
- C.51
- D.61✓ Answer
A prime number has exactly two distinct positive factors, 1 and itself. 51 = 3 × 17, 87 = 3 × 29 and 91 = 7 × 13 are composite (the digit sums of 51 and 87 are divisible by 3). 61 has no factor of 2, 3, 5 or 7, and since 8² = 64 > 61 it is enough to test primes up to √61, so 61 is prime.
Source: ASVAB CEP Overview p.19, MK content area "number theory"; definition of prime vs. composite and the divisibility-by-3 digit-sum ruleReport a problem with this question
3. Simplify: √(48/3)
- A.4√3
- B.8
- C.16
- D.4✓ Answer
The order of operations requires the division inside the radical to be done first: 48 ÷ 3 = 16, and √16 = 4. The distractor 4√3 comes from simplifying √48 while ignoring the division, and 16 is the value one step before taking the root — no calculator is needed if the division is done first.
Source: ASVAB CEP Overview p.19, MK content area "numeration (radicals)"; DoD/OPA no-calculator policy note on order of operations inside a radicalReport a problem with this question
4. Simplify: (2x³)⁴
- A.8x¹²
- B.16x⁷
- C.2x¹²
- D.16x¹²✓ Answer
The power-of-a-product rule raises every factor inside the parentheses to the outside power: 2⁴ = 16 and (x³)⁴ = x^(3·4) = x¹², so the result is 16x¹². Adding the exponents (x⁷) or leaving the coefficient un-raised (2x¹²) are the standard errors.
Source: ASVAB CEP Overview p.19, MK content area "numeration (exponents)"; laws of exponents (ab)ⁿ = aⁿbⁿ and (xᵃ)ᵇ = x^(ab)Report a problem with this question
5. (4 × 10⁵)(2 × 10⁻³) =
- A.8 × 10⁸
- B.8 × 10²✓ Answer
- C.6 × 10²
- D.8 × 10⁻¹⁵
When multiplying numbers in scientific notation, multiply the coefficients and add the exponents of 10: 4 × 2 = 8 and 5 + (−3) = 2, giving 8 × 10². Adding the coefficients produces 6, and multiplying the exponents produces the impossible 10⁻¹⁵.
Source: ASVAB CEP Overview p.19, MK content area "numeration (scientific notation)"; product rule for exponents xᵃ·xᵇ = x^(a+b)Report a problem with this question
6. If 30% of x is 42, then x =
- A.12.6
- B.70
- C.140✓ Answer
- D.126
The percent relationship is part/whole = percent/100, so 0.30x = 42 and x = 42 ÷ 0.30 = 140. The distractor 12.6 is 30% of 42, which reverses the relationship and treats 42 as the whole instead of the part.
Source: ASVAB CEP Overview p.19, MK content area "numeration (percents)"; percent proportion part/whole = percent/100Report a problem with this question
7. 2/3 ÷ 4/9 =
- A.2/3
- B.8/27
- C.3/2✓ Answer
- D.27/8
Dividing by a fraction is the same as multiplying by its reciprocal: 2/3 × 9/4 = 18/12, which reduces to 3/2. The distractor 8/27 comes from multiplying straight across without inverting the second fraction.
Source: ASVAB CEP Overview p.19, MK content area "numeration (fractions)"; division of fractions by multiplying by the reciprocalReport a problem with this question
8. Solve for x: 5x − 7 = 3x + 9
- A.x = 16
- B.x = 8✓ Answer
- C.x = −8
- D.x = 1
Isolate the variable with inverse operations: subtracting 3x from both sides gives 2x − 7 = 9, adding 7 gives 2x = 16, and dividing by 2 gives x = 8. The distractor 16 is the value one step before the final division — a classic trap when rushing.
Source: ASVAB CEP Overview p.19, MK content area "algebraic operations and equations"; solving one-variable linear equations by inverse operationsReport a problem with this question
9. Solve the inequality: −4x + 3 > 19
- A.x > 4
- B.x < −4✓ Answer
- C.x < 4
- D.x > −4
Subtracting 3 from both sides gives −4x > 16. Dividing both sides by a negative number reverses the direction of the inequality, so x < −4. Forgetting to flip the sign is one of the most common MK errors and produces the distractor x > −4.
Source: ASVAB CEP Overview p.19, MK content area "algebraic operations and equations"; inequality rule — reverse the sign when multiplying or dividing by a negativeReport a problem with this question
10. For 3a − 5b ≠ 0, simplify: (9a² − 25b²)/(3a − 5b)
- A.9a² + 25b²
- B.3a² + 5b²
- C.3a + 5b✓ Answer
- D.3a − 5b
The numerator is a difference of squares: 9a² − 25b² = (3a + 5b)(3a − 5b). Because 3a − 5b ≠ 0, that common factor may be cancelled, leaving 3a + 5b. The stated restriction is exactly what makes the cancellation legal — division by zero would otherwise be undefined.
Source: ASVAB CEP Overview p.19, MK content area "algebraic operations and equations"; difference-of-squares factoring a² − b² = (a + b)(a − b)Report a problem with this question
11. (2x − 3)(x + 5) =
- A.2x² + 7x + 15
- B.2x² + 7x − 15✓ Answer
- C.2x² + 13x − 15
- D.2x² − 7x − 15
Using FOIL: 2x·x = 2x², 2x·5 = 10x, −3·x = −3x, and −3·5 = −15. Combining like terms gives 10x − 3x = 7x, so the product is 2x² + 7x − 15. The constant is negative because a negative times a positive is negative.
Source: ASVAB CEP Overview p.19, MK content area "algebraic operations and equations"; distributive property applied as FOIL for binomial productsReport a problem with this question
12. What are the solutions of x² − 7x + 12 = 0?
- A.1 and 12
- B.3 and 4✓ Answer
- C.2 and 6
- D.−3 and −4
Factor by finding two numbers whose product is +12 and whose sum is −7: those are −3 and −4, so x² − 7x + 12 = (x − 3)(x − 4). The zero-product property then gives x = 3 or x = 4. The factors carry minus signs, but the roots themselves are positive.
Source: ASVAB CEP Overview p.19, MK content area "algebraic operations and equations"; factoring trinomials and the zero-product propertyReport a problem with this question
13. If 2x + y = 11 and x − y = 1, then x =
- A.3
- B.7
- C.5
- D.4✓ Answer
Adding the two equations eliminates y because +y and −y cancel: 3x = 12, so x = 4 (substituting back gives y = 3). The distractor 3 is the value of y — misreading which variable is asked for is a frequent MK mistake.
Source: ASVAB CEP Overview p.19, MK content area "algebraic operations and equations"; solving a system of two linear equations by eliminationReport a problem with this question
14. What is the slope of the line through (−2, 5) and (4, −7)?
- A.−2✓ Answer
- B.2
- C.1/2
- D.−1/2
Slope is rise over run: m = (y₂ − y₁)/(x₂ − x₁) = (−7 − 5)/(4 − (−2)) = −12/6 = −2. The slope is negative because y decreases as x increases; the distractor −1/2 comes from inverting rise and run.
Source: ASVAB CEP Overview p.19, MK content area "geometry and measurement"; coordinate-geometry slope formula m = (y₂ − y₁)/(x₂ − x₁)Report a problem with this question
15. A square has a perimeter of 36 cm. What is its area?
- A.324 cm²
- B.18 cm²
- C.36 cm²
- D.81 cm²✓ Answer
A square's perimeter is P = 4s, so s = 36 ÷ 4 = 9 cm, and its area is A = s² = 9² = 81 cm². Area uses squared units; confusing perimeter with area (or squaring half the perimeter, which gives 324) is a common source of error.
Source: ASVAB CEP Overview p.19, MK content area "geometry and measurement"; square perimeter P = 4s and area A = s²Report a problem with this question
16. A circle has a circumference of 12π. What is its area?
- A.12π
- B.6π
- C.36π✓ Answer
- D.144π
From C = 2πr, 12π = 2πr gives r = 6. Then A = πr² = π(6²) = 36π. The distractor 144π comes from using 12 as the radius instead of first solving for r, and 6π mistakes the radius itself for the area.
Source: ASVAB CEP Overview p.19, MK content area "geometry and measurement"; circle formulas C = 2πr and A = πr²Report a problem with this question
17. What is the volume of a cylinder with radius 3 and height 10?
- A.30π
- B.90π✓ Answer
- C.180π
- D.900π
A cylinder's volume is the base area times the height: V = πr²h = π(3²)(10) = 90π. The distractor 30π omits squaring the radius, and 180π uses 2rh (the lateral-surface pattern) instead of r².
Source: ASVAB CEP Overview p.19, MK content area "geometry and measurement"; cylinder volume V = πr²hReport a problem with this question
18. In a right triangle the hypotenuse is 13 and one leg is 5. How long is the other leg?
- A.12✓ Answer
- B.18
- C.8
- D.√194
The Pythagorean theorem states a² + b² = c², where c is the hypotenuse, so b² = 13² − 5² = 169 − 25 = 144 and b = 12 — the familiar 5-12-13 triple. The distractor √194 comes from adding the squares instead of subtracting, and 8 from subtracting the sides directly.
Source: ASVAB CEP Overview p.19, MK content area "geometry and measurement"; Pythagorean theorem a² + b² = c² and the 5-12-13 tripleReport a problem with this question
19. The interior angles of a triangle are in the ratio 2:3:4. What is the measure of the largest angle?
- A.60°
- B.80°✓ Answer
- C.90°
- D.40°
The interior angles of any triangle sum to 180°, so 2x + 3x + 4x = 180, giving 9x = 180 and x = 20°. The largest angle is 4x = 80°. Note the triangle is acute, so 90° cannot be correct.
Source: ASVAB CEP Overview p.19, MK content area "geometry and measurement"; triangle interior-angle sum = 180°Report a problem with this question
20. A bag contains 4 red marbles and 6 blue marbles. Two marbles are drawn without replacement. What is the probability that both are red?
- A.2/15✓ Answer
- B.3/25
- C.4/25
- D.2/5
Probability is favorable outcomes over total outcomes, and because the draws are without replacement they are dependent: the first draw is 4/10 and the second is 3/9, since both the red count and the total drop by one. Multiplying gives 12/90 = 2/15. The distractor 4/25 assumes replacement, (4/10)².
Source: ASVAB CEP Overview p.19, MK content area "probability"; multiplication rule for dependent events without replacementReport a problem with this question
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