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ASVAB Mathematics Knowledge Practice Questions and Study Tips
Mathematics Knowledge tests high school math concepts directly, without the word problems. It is one of the four AFQT subtests. Expect algebra, geometry and number rules, with no calculator.
| Questions (paper ASVAB) | 25 |
|---|---|
| Time limit | 24 minutes |
| Abbreviation | MK |
| Counts toward AFQT? | Yes, it is one of the four AFQT subtests. |
The computer version of the ASVAB (CAT-ASVAB) has fewer questions and adjusts the difficulty to your answers, but it covers the same material.
What the Mathematics Knowledge subtest covers
- Algebra: solving equations and inequalities, factoring, exponents
- Geometry: area, perimeter, volume, angles and the Pythagorean theorem
- Number rules: fractions, decimals, square roots, order of operations
- Multiplying polynomials and simplifying expressions
Mathematics Knowledge practice questions
Try these 18 questions written in the ASVAB style. They cover algebra, geometry and number rules. Work each one on scratch paper before you open the answer.
1. Solve for x: 3x − 7 = 11
- 4
- 5
- 6
- 7
Show answer
C. 6 Add 7 to both sides to get 3x = 18, then divide by 3 to get x = 6.
2. What is the area of a circle with a radius of 4?
- 8π
- 12π
- 16π
- 64π
Show answer
C. 16π Area = πr² = π × 4² = 16π.
3. Multiply: (x + 3)(x − 2)
- x² + x − 6
- x² − x − 6
- x² + 5x − 6
- x² − 6
Show answer
A. x² + x − 6 x·x + x·(−2) + 3·x + 3·(−2) = x² + x − 6.
4. Solve for x: 2(x − 4) = 10
- 7
- 9
- 3
- 12
Show answer
B. 9 Divide both sides by 2: x − 4 = 5, so x = 9.
5. Evaluate: 3² + 4 × 5 − 6 ÷ 2
- 22
- 14
- 26
- 32
Show answer
C. 26 Exponents first, then multiplication and division, then addition and subtraction: 9 + 20 − 3 = 26.
6. A right triangle has legs of 6 and 8. How long is the hypotenuse?
- 14
- 10
- 12
- 48
Show answer
B. 10 a² + b² = c²: 36 + 64 = 100, and √100 = 10. (6-8-10 is the 3-4-5 triangle doubled.)
Want to know where you stand? The free 25-question diagnostic covers all nine subtests and shows your weakest one. No account needed to start.
7. A box is 4 feet long, 5 feet wide and 3 feet high. What is its volume?
- 12 cubic feet
- 47 cubic feet
- 60 cubic feet
- 94 cubic feet
Show answer
C. 60 cubic feet Volume = length × width × height = 4 × 5 × 3 = 60 cubic feet. (94 is the surface area.)
8. Which values of x solve x² − 9 = 0?
- 3 only
- 9 only
- 3 and −3
- 9 and −9
Show answer
C. 3 and −3 x² = 9, and both 3² and (−3)² equal 9.
9. Factor: x² + 7x + 12
- (x + 2)(x + 6)
- (x + 3)(x + 4)
- (x + 1)(x + 12)
- (x − 3)(x − 4)
Show answer
B. (x + 3)(x + 4) Find two numbers that multiply to 12 and add to 7: 3 and 4.
10. Simplify: x³ · x⁴
- 2x⁷
- x¹²
- 7x
- x⁷
Show answer
D. x⁷ When you multiply powers with the same base, add the exponents: 3 + 4 = 7.
11. Solve: 5 − 2x > 11
- x > −3
- x < −3
- x > 3
- x < 3
Show answer
B. x < −3 Subtract 5: −2x > 6. Dividing by a negative number flips the sign: x < −3.
12. Two angles of a triangle measure 50° and 65°. What is the third angle?
- 115°
- 75°
- 65°
- 55°
Show answer
C. 65° The angles of a triangle add to 180°: 180 − 50 − 65 = 65°.
Want to know where you stand? The free 25-question diagnostic covers all nine subtests and shows your weakest one. No account needed to start.
13. Simplify: √50
- 5√2
- 2√5
- 25√2
- 10√5
Show answer
A. 5√2 √50 = √(25 × 2) = √25 × √2 = 5√2.
14. Divide: 3/4 ÷ 3/8
- 9/32
- 1/2
- 6
- 2
Show answer
D. 2 Multiply by the reciprocal: 3/4 × 8/3 = 24/12 = 2.
15. What is the slope of the line through (1, 2) and (3, 8)?
- 3
- 1/3
- 2
- 6
Show answer
A. 3 Slope = change in y ÷ change in x = (8 − 2) ÷ (3 − 1) = 6 ÷ 2 = 3.
16. A circle has a diameter of 10. What is its circumference?
- 5π
- 10π
- 20π
- 25π
Show answer
B. 10π Circumference = π × diameter = 10π. (25π is the area.)
17. Which is 0.00045 written in scientific notation?
- 4.5 × 10⁴
- 4.5 × 10⁻³
- 4.5 × 10⁻⁵
- 4.5 × 10⁻⁴
Show answer
D. 4.5 × 10⁻⁴ Move the decimal point 4 places right to get 4.5, so the power of 10 is −4.
18. If a = 3 and b = −2, what is a² − 2ab + b²?
- 1
- 5
- 13
- 25
Show answer
D. 25 9 − 2(3)(−2) + 4 = 9 + 12 + 4 = 25. Shortcut: the expression is (a − b)² = 5² = 25.
Rules to know by heart
Mathematics Knowledge tests rules more than calculation. If you know these, most questions take seconds.
- Exponents: x³ · x⁴ = x⁷ (add), x⁶ ÷ x² = x⁴ (subtract), (x³)² = x⁶ (multiply), x⁰ = 1 and x⁻² = 1/x².
- Multiplying binomials: (a + b)(c + d) = ac + ad + bc + bd. Multiply every term by every term.
- Special products: (a + b)² = a² + 2ab + b², (a − b)² = a² − 2ab + b², and (a + b)(a − b) = a² − b².
- Negative numbers: two negatives multiply to a positive, and subtracting a negative is the same as adding.
- Fractions: to divide, multiply by the reciprocal. To add, find a common denominator first.
- Angles: a straight line is 180°, a triangle 180°, a four-sided shape 360°. Vertical angles are equal.
- Primes: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29. 1 is not prime, and 2 is the only even prime.
- Perfect squares: know 1² to 15² (up to 225). They make square roots and the Pythagorean theorem fast.
The area, volume and coordinate formulas are on the free ASVAB formula sheet.
How Mathematics Knowledge differs from Arithmetic Reasoning
Both are math and both count toward the AFQT, but they test different skills. Arithmetic Reasoning gives you a story and asks you to choose the right math. Mathematics Knowledge gives you the math directly, as an equation or a figure, and asks you to apply a rule. If you do well on one and poorly on the other, study the skill that is missing: setting up problems for Arithmetic Reasoning, or rules and formulas for Mathematics Knowledge.
Question types students miss most
- Inequalities. When you multiply or divide both sides by a negative number, flip the inequality sign.
- Order of operations. Exponents, then multiplication and division from left to right, then addition and subtraction.
- Square roots of non-perfect squares. Pull out the largest perfect square: √50 = 5√2.
- Area versus perimeter versus volume. The wrong measurement is almost always one of the answer choices.
- Equations with two answers. x² = 9 has two solutions, 3 and −3.
Common mistakes
- Dropping a negative sign when you distribute or multiply.
- Using the diameter where the formula needs the radius.
- Adding exponents when you should multiply them: (x³)² is x⁶, while x³ · x² is x⁵.
- Forgetting to check an answer by plugging it back into the original equation.
Time strategy
The paper test gives you 24 minutes for 25 questions, a little under a minute each. Questions you can answer from a memorized formula should take 20 to 30 seconds, which buys time for multi-step algebra.
On equations, plugging the answer choices back in is often faster than solving. Start with the middle value so you can tell whether to go higher or lower. On the computer test (CAT-ASVAB) you can't go back, so answer every question.
A 7-day plan for Mathematics Knowledge
- Day 1: Take the free diagnostic for a baseline, then review fractions, exponents and order of operations.
- Day 2: Solving one- and two-step equations and inequalities.
- Day 3: Multiplying and factoring polynomials.
- Day 4: Area, perimeter and volume. Memorize the formulas from the ASVAB formula sheet.
- Day 5: Angles, triangles and the Pythagorean theorem.
- Day 6: Square roots, scientific notation, slope and coordinates.
- Day 7: 25 mixed questions in 24 minutes, then redo every miss.
Tips for the Mathematics Knowledge subtest
- Memorize the core formulas: area of a circle, triangle and rectangle, the Pythagorean theorem and volume of a box.
- On equations, you can plug each answer back in to see which one works.
- Watch your signs. A dropped negative is the most common mistake.
Questions people ask
How many questions are on ASVAB Mathematics Knowledge?
The paper ASVAB has 25 Mathematics Knowledge questions with a 24-minute time limit. The computer version has fewer questions.
Does Mathematics Knowledge count toward the AFQT?
Yes, it is one of the four AFQT subtests.
What formulas do I need for ASVAB Mathematics Knowledge?
Area and perimeter of rectangles, triangles and circles, volume of a box and cylinder, the Pythagorean theorem, slope, and the angle sums of triangles and polygons. They are all on our free ASVAB formula sheet.
Is ASVAB Mathematics Knowledge hard?
It covers high school algebra and geometry, not advanced math. Most people who struggle have forgotten formulas or rules, which comes back quickly with a week or two of practice.
Free download: print the ASVAB formula sheet with every math formula you need to know by heart, since no calculator or formula sheet is allowed on test day.
Find your weakest subtest in about 20 minutes. The free 25-question diagnostic covers all nine ASVAB subtests. No card needed.
Take the free ASVAB diagnostic