A rectangular room measures 14 feet long and 9 feet wide. What is the area of the room?

Correct answer: 126 square feet. Area of a rectangle = length × width = 14 × 9 = 126 square feet.

Solve for x: 3x − 7 = 14

Correct answer: x = 7. Isolate the variable in two steps. Add 7 to both sides to undo the subtraction: 3x = 21. Divide both sides by 3 to undo the multiplication: x = 7. The choice x = 3 comes from dividing the original 14 by 3 and ignoring the −7 entirely. The choice x = 5 comes from subtracting 7 from 14 first (14 − 7 = 7), then dividing the wrong direction. The choice x = 9 comes from sign confusion, treating −7 as +7 and computing (14 − 7)÷3 backwards or 21÷3 with an extra add.

What is the value of 2⁵?

Correct answer: 32. An exponent counts how many times the base multiplies itself. 2⁵ = 2 × 2 × 2 × 2 × 2 = 32. Build it stepwise: 2×2 = 4, ×2 = 8, ×2 = 16, ×2 = 32. The choice 10 comes from confusing exponentiation with multiplication and computing 2 × 5. The choice 16 is 2⁴, one factor short. The choice 25 comes from swapping base and exponent and computing 5² instead of 2⁵.

What is ³⁄₄ divided by ³⁄₈?

Correct answer: 2. Dividing by a fraction means multiplying by its reciprocal: ³⁄₄ × ⁸⁄₃ = 24⁄12 = 2.

What is the perimeter of a square with a side length of 11 inches?

Correct answer: 44 inches. Perimeter of a square = 4 × side = 4 × 11 = 44 inches.

Solve for y: 5y + 3 = 2y + 18

Correct answer: y = 5. Subtract 2y from both sides: 3y + 3 = 18. Subtract 3: 3y = 15. Divide: y = 5.

A right triangle has legs measuring 6 cm and 8 cm. What is the length of the hypotenuse?

Correct answer: 10 cm. By the Pythagorean theorem: c² = 6² + 8² = 36 + 64 = 100. c = √100 = 10 cm.

Correct answer: 36. Convert the percent to a decimal and multiply: 15% = 0.15, so 0.15 × 240 = 36. Cross-check by computing 10% of 240 = 24, then 5% = 12, sum = 36. The choice 30 comes from using 12.5% (an off-by-one in the percent). The choice 40 comes from misreading 15% as 1/6 of 240. The choice 42 comes from adding 12 + 30 or other small slips in mental math.

Simplify: (3x²)(4x³)

Correct answer: 12x⁵. Multiply coefficients: 3 × 4 = 12. Add exponents: x² × x³ = x⁵. Result: 12x⁵.

What is the circumference of a circle with a diameter of 10 inches? (Use π ≈ 3.14)

Correct answer: 31.4 inches. Circumference uses C = πd, where d is the diameter. C = 3.14 × 10 = 31.4 inches. The choice 15.7 inches uses the radius (5) instead of the diameter, computing πr. The choice 78.5 inches applies the area formula πr² with r = 5, mixing area and circumference. The choice 314 inches uses d² instead of d, computing π × 100.

If the ratio of boys to girls in a class is 3:5 and there are 24 boys, how many girls are in the class?

Correct answer: 40. Find the value of one ratio unit. 3 units = 24 boys, so 1 unit = 8. Girls = 5 units = 5 × 8 = 40. The choice 32 adds 8 to the boy count instead of scaling the girl ratio. The choice 36 mixes up the ratio direction (3/5 × something) and lands near 40. The choice 48 treats the ratio 3:5 as parts of 8, then multiplies the boy count by the total ratio (24 × 8/4) or doubles the boys.

Evaluate: |−18| + |5|

Correct answer: 23. Absolute value removes the sign: |−18| = 18, |5| = 5. Sum = 18 + 5 = 23.

How many free Mathematics Knowledge practice questions are here?

This page has 12 free ASVAB Mathematics Knowledge questions, each with the correct answer and a full worked explanation. They're free to use with no account required.

Does Mathematics Knowledge count toward my AFQT score?

Yes. Mathematics Knowledge is one of the four AFQT subtests (AR, WK, PC, MK), so it directly affects your enlistment eligibility.

What does the Mathematics Knowledge subtest cover?

Pure math: algebra, geometry, and number theory. One of the 4 AFQT subtests. Unlike AR, these are straight math problems, not word problems. On the CAT-ASVAB it has 15 questions with about 23 minutes to answer them. Topics include: Algebra, geometry, fractions, exponents, equations.

Are these the same as the real ASVAB questions?

No. These are original practice questions calibrated to match the style and difficulty of the real ASVAB. The actual test is a secure exam, so no one publishes its live items. Practicing this format is the closest legitimate prep.

Free ASVAB Mathematics Knowledge Practice Test

12 Mathematics Knowledge (MK) practice questions, each with a worked explanation of the right answer.

Last updated May 2026

The ASVAB Mathematics Knowledge (MK) subtest covers algebra, geometry, fractions, exponents, equations. On the computer-adaptive CAT-ASVAB it has 15 questions with about 23 minutes to answer. It is one of the four AFQT subtests, so it directly affects your enlistment eligibility. Work the 12 questions below, then read each explanation. Understanding why the answer is right is what raises your score.

Question 1· Mathematics Knowledge
A rectangular room measures 14 feet long and 9 feet wide. What is the area of the room?
- A.46 square feet
- B.92 square feet
- C.126 square feet
- D.132 square feet
Show answer & explanationHide answer
Correct answer: C. 126 square feet
Why: Area of a rectangle = length × width = 14 × 9 = 126 square feet.
Question 2· Mathematics Knowledge
Solve for x: 3x − 7 = 14
- A.x = 3
- B.x = 5
- C.x = 7
- D.x = 9
Show answer & explanationHide answer
Correct answer: C. x = 7
Why: Isolate the variable in two steps. Add 7 to both sides to undo the subtraction: 3x = 21. Divide both sides by 3 to undo the multiplication: x = 7. The choice x = 3 comes from dividing the original 14 by 3 and ignoring the −7 entirely. The choice x = 5 comes from subtracting 7 from 14 first (14 − 7 = 7), then dividing the wrong direction. The choice x = 9 comes from sign confusion, treating −7 as +7 and computing (14 − 7)÷3 backwards or 21÷3 with an extra add.
Question 3· Mathematics Knowledge
What is the value of 2⁵?
- A.10
- B.16
- C.25
- D.32
Show answer & explanationHide answer
Correct answer: D. 32
Why: An exponent counts how many times the base multiplies itself. 2⁵ = 2 × 2 × 2 × 2 × 2 = 32. Build it stepwise: 2×2 = 4, ×2 = 8, ×2 = 16, ×2 = 32. The choice 10 comes from confusing exponentiation with multiplication and computing 2 × 5. The choice 16 is 2⁴, one factor short. The choice 25 comes from swapping base and exponent and computing 5² instead of 2⁵.
Question 4· Mathematics Knowledge
What is ³⁄₄ divided by ³⁄₈?
- A.½
- B.1
- C.2
- D.9⁄32
Show answer & explanationHide answer
Correct answer: C. 2
Why: Dividing by a fraction means multiplying by its reciprocal: ³⁄₄ × ⁸⁄₃ = 24⁄12 = 2.
Question 5· Mathematics Knowledge
What is the perimeter of a square with a side length of 11 inches?
- A.22 inches
- B.33 inches
- C.44 inches
- D.121 inches
Show answer & explanationHide answer
Correct answer: C. 44 inches
Why: Perimeter of a square = 4 × side = 4 × 11 = 44 inches.
Question 6· Mathematics Knowledge
Solve for y: 5y + 3 = 2y + 18
- A.y = 3
- B.y = 5
- C.y = 7
- D.y = 9
Show answer & explanationHide answer
Correct answer: B. y = 5
Why: Subtract 2y from both sides: 3y + 3 = 18. Subtract 3: 3y = 15. Divide: y = 5.
Question 7· Mathematics Knowledge
A right triangle has legs measuring 6 cm and 8 cm. What is the length of the hypotenuse?
- A.7 cm
- B.10 cm
- C.12 cm
- D.14 cm
Show answer & explanationHide answer
Correct answer: B. 10 cm
Why: By the Pythagorean theorem: c² = 6² + 8² = 36 + 64 = 100. c = √100 = 10 cm.
Question 8· Mathematics Knowledge
What is 15% of 240?
- A.30
- B.36
- C.40
- D.42
Show answer & explanationHide answer
Correct answer: B. 36
Why: Convert the percent to a decimal and multiply: 15% = 0.15, so 0.15 × 240 = 36. Cross-check by computing 10% of 240 = 24, then 5% = 12, sum = 36. The choice 30 comes from using 12.5% (an off-by-one in the percent). The choice 40 comes from misreading 15% as 1/6 of 240. The choice 42 comes from adding 12 + 30 or other small slips in mental math.
Question 9· Mathematics Knowledge
Simplify: (3x²)(4x³)
- A.7x⁵
- B.12x⁵
- C.12x⁶
- D.7x⁶
Show answer & explanationHide answer
Correct answer: B. 12x⁵
Why: Multiply coefficients: 3 × 4 = 12. Add exponents: x² × x³ = x⁵. Result: 12x⁵.
Question 10· Mathematics Knowledge
What is the circumference of a circle with a diameter of 10 inches? (Use π ≈ 3.14)
- A.15.7 inches
- B.31.4 inches
- C.78.5 inches
- D.314 inches
Show answer & explanationHide answer
Correct answer: B. 31.4 inches
Why: Circumference uses C = πd, where d is the diameter. C = 3.14 × 10 = 31.4 inches. The choice 15.7 inches uses the radius (5) instead of the diameter, computing πr. The choice 78.5 inches applies the area formula πr² with r = 5, mixing area and circumference. The choice 314 inches uses d² instead of d, computing π × 100.
Question 11· Mathematics Knowledge
If the ratio of boys to girls in a class is 3:5 and there are 24 boys, how many girls are in the class?
- A.32
- B.36
- C.40
- D.48
Show answer & explanationHide answer
Correct answer: C. 40
Why: Find the value of one ratio unit. 3 units = 24 boys, so 1 unit = 8. Girls = 5 units = 5 × 8 = 40. The choice 32 adds 8 to the boy count instead of scaling the girl ratio. The choice 36 mixes up the ratio direction (3/5 × something) and lands near 40. The choice 48 treats the ratio 3:5 as parts of 8, then multiplies the boy count by the total ratio (24 × 8/4) or doubles the boys.
Question 12· Mathematics Knowledge
Evaluate: |−18| + |5|
- A.−13
- B.13
- C.23
- D.−23
Show answer & explanationHide answer
Correct answer: C. 23
Why: Absolute value removes the sign: |−18| = 18, |5| = 5. Sum = 18 + 5 = 23.

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What's on the ASVAB Mathematics Knowledge subtest

Pure math: algebra, geometry, and number theory. One of the 4 AFQT subtests. Unlike AR, these are straight math problems, not word problems.

Common topics you'll see:

Fractions, decimals & percentages
Exponents & square roots
Geometry (area, perimeter, volume)
Basic algebra & solving equations
Inequalities
Order of operations
Ratios & proportions
Scientific notation
Probability basics
Coordinate geometry

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FAQ

How many free Mathematics Knowledge practice questions are here?: This page has 12 free ASVAB Mathematics Knowledge questions, each with the correct answer and a full worked explanation. They're free to use with no account required.
Does Mathematics Knowledge count toward my AFQT score?: Yes. Mathematics Knowledge is one of the four AFQT subtests (AR, WK, PC, MK), so it directly affects your enlistment eligibility.
What does the Mathematics Knowledge subtest cover?: Pure math: algebra, geometry, and number theory. One of the 4 AFQT subtests. Unlike AR, these are straight math problems, not word problems. On the CAT-ASVAB it has 15 questions with about 23 minutes to answer them. Topics include: Algebra, geometry, fractions, exponents, equations.
Are these the same as the real ASVAB questions?: No. These are original practice questions calibrated to match the style and difficulty of the real ASVAB. The actual test is a secure exam, so no one publishes its live items. Practicing this format is the closest legitimate prep.

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