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Updated July 2026 with official ASVAB sources

ASVAB Mathematics Knowledge Practice Test: 100 Questions

Use this original ASVAB Mathematics Knowledge practice test to build no-calculator math from zero. Official ASVAB sources describe Mathematics Knowledge as knowledge of high school mathematics principles. This page turns that public scope into a beginner study path, official timing context, 100 original questions, answer explanations, and internal links to ASVAB score and AFQT resources.

ASVAB Study Guide ASVAB Score Guide ASVAB Score Calculator AFQT Score Calculator Arithmetic Reasoning Practice Paragraph Comprehension Practice Word Knowledge Practice

Official Mathematics Knowledge Scope

Mathematics Knowledge, abbreviated MK, is the ASVAB subtest for high school mathematics principles. Official ASVAB materials place it in the Math domain and describe it separately from Arithmetic Reasoning. That distinction is important for SEO and for students. Arithmetic Reasoning asks you to translate word problems into arithmetic. Mathematics Knowledge asks whether you know the underlying math ideas: number operations, algebra, geometry, measurement, factors, exponents, roots, proportions, and basic data reasoning.

The ASVAB program does not publish a public textbook-style curriculum with a chapter-by-chapter Mathematics Knowledge syllabus. The latest dependable public facts are the official subtest description, official sample-question format, CAT-ASVAB timing, paper-and-pencil timing, calculator guidance, and official score explanations. This page uses those official facts for structure and writes original practice questions around the public MK skill description. The topic buckets below are study categories, not separate official score-report categories.

Original practice notice: These 100 questions are original NUM8ERS study questions. They are not real ASVAB test questions, not leaked questions, and not copied from official sample items. Use them to build the math principles that make official ASVAB questions feel familiar.

Timing and No-Calculator Context

Official CAT-ASVAB information lists Mathematics Knowledge as 15 scored questions with a 31-minute time limit when no tryout questions are present. The same official CAT table lists possible tryout questions and a longer time limit when they appear. Official ASVAB fact-sheet timing lists the paper-and-pencil Mathematics Knowledge section as 25 questions in 24 minutes. The official ASVAB FAQ explains that calculators are not allowed because the test assesses ability to perform basic math without one.

Version Official MK timing context Practice implication
CAT-ASVAB 15 scored Mathematics Knowledge questions; 31 minutes without tryout questions. Practice 15-question mixed sets once the topic skills are familiar.
CAT-ASVAB with possible tryouts Official CAT information lists possible tryout questions and extra time when they appear. Do not judge your test only by item count; keep solving carefully.
P&P-ASVAB 25 Mathematics Knowledge questions in 24 minutes on the official fact sheet. Practice 25-question sets after you can do arithmetic, algebra, and geometry without a calculator.

CAT-ASVAB behavior also matters. Official materials explain that the computer adaptive test chooses items based on prior responses and that answers cannot be reviewed or changed after submission. For MK, that means you should check signs, units, exponents, and answer-choice reasonableness before moving forward. Paper-and-pencil ASVAB allows review within the current section, but timing still rewards clean setup and scratch work.

How to Use This Practice Test

If you know nothing about ASVAB Mathematics Knowledge, do not start by timing all 100 questions. First learn the topic categories. Questions 1-20 build arithmetic, fractions, decimals, percents, signed numbers, exponents, and roots. Questions 21-40 focus on algebra, functions, inequalities, and coordinate ideas. Questions 41-55 focus on geometry. Questions 56-70 focus on data, probability, measurement, and percent. Questions 71-100 mix review concepts that commonly expose weak fundamentals.

  1. Work the first 25 questions without a timer and read every explanation.
  2. Write the missed topic beside each miss: fractions, percent, exponents, algebra, geometry, measurement, or data.
  3. Redo missed questions after 24 hours without opening the explanation.
  4. When your slow accuracy improves, take 15-question CAT-style mixed sets.
  5. Then take 25-question paper-style mixed sets.
  6. Use official scores, not raw practice counts, with the AFQT Score Calculator or ASVAB Score Calculator.

Mathematics Knowledge matters for AFQT because official score guidance lists MK as one of the four subtests used to compute AFQT, along with Arithmetic Reasoning, Word Knowledge, and Paragraph Comprehension. This page helps you practice MK skills. The ASVAB Score Guide explains official score types, and the ASVAB Study Guide explains the full testing process.

Beginner Mathematics Review

Mathematics Knowledge rewards clean principles. A student can lose points not because the math is advanced, but because the basics are unstable: a sign error, a missed exponent rule, a fraction added incorrectly, or an area formula confused with perimeter. The fastest improvement comes from building a small set of dependable habits.

Arithmetic and Order of Operations

Start with operations. Addition and subtraction combine or compare amounts. Multiplication is repeated grouping. Division separates a total into equal parts or asks how many groups fit. Order of operations tells you what to do first: parentheses, exponents, multiplication and division from left to right, then addition and subtraction from left to right. In 6 + 3 × 4, multiplication happens first, so the answer is 18, not 36. On a no-calculator test, write one line of work instead of doing everything in your head.

Fractions, Decimals, and Percents

Fractions are part-whole numbers. To add or subtract fractions, use a common denominator. To multiply fractions, multiply across and simplify. To divide fractions, multiply by the reciprocal. Decimal and percent conversions are core MK skills: 0.25 is 25%, 1/4 is 25%, 3/4 is 75%, and 0.08 is 8%. Percent means per hundred, so 15% of 200 is 30. Many wrong choices come from moving a decimal one place too far.

Signed Numbers

Positive and negative numbers appear in algebra and coordinate questions. Adding a negative moves left on a number line; subtracting a negative moves right. Multiplying or dividing two numbers with the same sign gives a positive result. Multiplying or dividing numbers with different signs gives a negative result. Absolute value is distance from zero, so |-9| = 9. Keep signs visible in your scratch work. A correct method with one missed negative sign still gives the wrong answer.

Exponents and Roots

An exponent tells how many times a base is used as a factor. 72 = 49, 23 = 8, and 50 = 1 when the base is not zero. Square roots reverse squaring: √81=9. When multiplying powers with the same base, add exponents: x2 × x3 = x5. When simplifying radicals and powers, check whether the answer has the right size. The square root of 81 cannot be 18 because 18 squared is far too large.

Algebra and Equations

Algebra questions ask you to keep an equation balanced. Whatever you do to one side, do to the other. If x + 7 = 19, subtract 7 from both sides and get x = 12. If 3x = 27, divide by 3. If an equation has variables on both sides, collect variables on one side and constants on the other. Combine like terms only when the variable part matches: 3a + 2a = 5a, but 3a + 2b cannot be combined.

Functions, Graphs, and Coordinate Ideas

A function rule such as f(x)=x2+1 gives an output when you substitute a value for x. If x=3, then f(3)=10. Coordinate points use ordered pairs (x,y). Positive x moves right, negative x moves left, positive y moves up, and negative y moves down. A line in the form y=mx+b has slope m and y-intercept b. For y=2x+5, the y-intercept is 5.

Geometry and Measurement

Geometry questions often check the difference between perimeter, area, and volume. Perimeter is distance around a shape. Area covers a flat surface. Volume fills a solid. Rectangle area is length times width. Triangle area is one half base times height. A circle's circumference is 2π r, and its area is π r2. A rectangular prism's volume is length times width times height. Angle facts also matter: a triangle has 180 degrees, a right angle has 90 degrees, complementary angles total 90 degrees, and supplementary angles total 180 degrees.

Data, Probability, and Number Properties

Mean is the average, found by adding values and dividing by the number of values. Median is the middle value after ordering. Range is the largest value minus the smallest. Probability is favorable outcomes divided by total possible outcomes. Number properties include prime numbers, factors, multiples, greatest common factor, and least common multiple. These topics are usually short, but they reward exact vocabulary.

Seven-Day MK Routine

Day 1: arithmetic, signed numbers, and fractions. Day 2: decimals, percents, ratios, and proportions. Day 3: exponents, roots, and simplifying expressions. Day 4: one-step and two-step equations. Day 5: geometry formulas and angle facts. Day 6: data, probability, and mixed review. Day 7: timed set and error log. For each miss, write the corrected rule, not just the answer. A useful error log says "I added denominators; correct rule is common denominator first" or "I used perimeter when the question asked for area." That level of detail prevents the same mistake from repeating.

No-Calculator Scratch-Work Method

The official no-calculator context changes how you should practice. You do not need beautiful notebook work, but you do need scratch work that is clear enough to stop a preventable error. Use one line for setup, one line for calculation, and one quick reasonableness check. For example, if the question asks for 15% of 200, write 0.15 × 200, calculate 30, then check that 15% should be less than 20% and more than 10%. Since 10% of 200 is 20 and 20% is 40, 30 is reasonable.

For fractions, do not rush into decimal conversion unless it makes the problem easier. Fractions such as 1/2, 1/4, 3/4, 1/5, 2/5, and 3/5 are often faster as fractions. If you see 3/5 of 30, divide by 5 first and multiply by 3. That gives 12 without long decimal work. If you see 5/8, decimal conversion may be useful because 5 ÷ 8 = 0.625 is a common benchmark. The skill is not memorizing every decimal; it is choosing the form that makes the arithmetic smaller.

For equations, rewrite the question vertically when signs are involved. A common MK mistake is losing a negative sign in a two-step equation. In 2y + 6 = 0, subtract 6 first, write 2y=-6, then divide by 2. Do not jump straight to the answer in your head if negatives are involved. The same habit helps with -2x=8. The answer is -4, and writing the division step keeps you from choosing positive 4.

For geometry, always name what is being asked before using a formula. Perimeter, area, and volume are not interchangeable. If a question asks for carpet cost, you likely need area. If it asks for fencing, you likely need perimeter. If it asks how much a box can hold, you likely need volume. Write the requested measure first: "area," "perimeter," or "volume." Then write the formula. This is slower for three seconds and faster for the whole test because it prevents using the wrong formula confidently.

For coordinate and function questions, substitute carefully. If f(x)=x2+1, then f(3) means replace every x with 3. It does not mean multiply f by 3. If the point is (3,-2), the first number is the horizontal location and the second number is the vertical location. A positive first number and negative second number put the point in Quadrant IV. These questions are usually short, so the danger is not time; the danger is reading symbols casually.

Common MK Traps and How to Fix Them

Trap 1: adding fraction denominators. Students often turn 2/3 + 1/6 into 3/9. That is not how fraction addition works. The denominator names the size of the pieces, so pieces must have the same name before adding. Convert 2/3 to 4/6, then add 4/6 + 1/6 = 5/6. The fix is simple: for addition or subtraction, ask "same denominator?" before doing anything else.

Trap 2: applying percent to the wrong base. Percent always depends on a base number. If a value increases from 40 by 10%, the 10% is based on 40, so the increase is 4 and the new value is 44. If a question asks what percent 12 is of 48, the base is 48, so 12/48 = 25%. Write the fraction as "part over base" before converting to a percent.

Trap 3: confusing exponent rules. x2 × x3 becomes x5, not x6, because the same base is being multiplied and the exponents are added. But (3x)(4x) becomes 12x2, because the coefficients multiply and the two x factors make x2. A useful rule is to treat numbers and variable powers separately, then combine them at the end.

Trap 4: treating an estimate like an exact answer. Estimation is a check, not a replacement for a calculation unless the question asks for the best estimate. If the question asks for 198 × 5 as an estimate, 1,000 is appropriate because 198 is close to 200. If the question asks for the exact answer, then 198 × 5 = 990. Read whether the prompt asks for exact value, simplified form, nearest tenth, or estimate.

Trap 5: forgetting that a no-calculator test still allows strategy. You can use mental math, simplification, cancellation, and answer-choice elimination. If choices are 1,000, 500, 200, and 2,000 for 198 × 5, exact multiplication is not required to know the best estimate. If choices for a right triangle with legs 6 and 8 include 10, recognize the common 6-8-10 triple. Efficient math is still valid math.

How MK and Arithmetic Reasoning Support Each Other

Mathematics Knowledge and Arithmetic Reasoning are separate subtests, but studying them together can help. MK gives you the rules: fractions, percent, equations, geometry, and number properties. AR asks you to apply arithmetic in word-problem situations. If you cannot simplify 12/18, a word problem involving a 12-out-of-18 ratio will be harder. If you cannot solve 2x + 3 = 11, an applied problem that hides the same equation will feel confusing. Use the ASVAB Arithmetic Reasoning Practice Test after this page to see whether your math principles transfer into word problems.

For AFQT planning, do not study MK alone. Official AFQT uses Arithmetic Reasoning, Mathematics Knowledge, Word Knowledge, and Paragraph Comprehension. A student with strong MK but weak reading may still lose AFQT ground. A student with strong verbal skills but weak no-calculator math may also be limited. This is why the internal ASVAB cluster separates pages by intent: this page fixes math principles, the AR page fixes word-problem translation, the Word Knowledge page fixes vocabulary, and the Paragraph Comprehension page fixes short-passage reading.

Before timing yourself, do one final untimed audit. Can you add fractions without adding denominators? Can you convert percent to decimal without moving the decimal the wrong way? Can you solve a two-step equation while keeping signs intact? Can you name the formula before calculating geometry? Can you explain why an answer is reasonable? If any answer is no, that topic should get another short review before timed practice. Timed practice is valuable only after the rule is clear enough to use under pressure.

ASVAB Mathematics Knowledge Practice Test: 100 Questions

Answer each question without a calculator. Open the explanation only after choosing an answer.

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  1. What is 18 + 27?
    1. 35
    2. 45
    3. 54
    4. 56
    Answer and explanation

    Answer: B. Add the ones and tens: 18 + 27 = 45.

  2. What is 72 - 19?
    1. 43
    2. 47
    3. 53
    4. 61
    Answer and explanation

    Answer: C. Subtract 20 and add 1 back: 72 - 20 + 1 = 53.

  3. What is 8 x 7?
    1. 56
    2. 54
    3. 48
    4. 64
    Answer and explanation

    Answer: A. 8 × 7 = 56.

  4. What is 144 divided by 12?
    1. 10
    2. 11
    3. 12
    4. 14
    Answer and explanation

    Answer: C. Since 12 × 12 = 144, the quotient is 12.

  5. Evaluate 6 + 3 × 4.
    1. 36
    2. 18
    3. 24
    4. 30
    Answer and explanation

    Answer: B. Multiply first: 3 × 4 = 12, then 6 + 12 = 18.

  6. Evaluate (20 - 8) ÷ 3.
    1. 4
    2. 6
    3. 8
    4. 12
    Answer and explanation

    Answer: A. Parentheses first: 20 - 8 = 12, and 12 ÷ 3 = 4.

  7. What is 2/3 + 1/6?
    1. 1/2
    2. 2/9
    3. 3/9
    4. 5/6
    Answer and explanation

    Answer: D. 2/3 = 4/6, and 4/6 + 1/6 = 5/6.

  8. What is 3/4 - 1/8?
    1. 1/8
    2. 1/2
    3. 5/8
    4. 7/8
    Answer and explanation

    Answer: C. 3/4 = 6/8, and 6/8 - 1/8 = 5/8.

  9. Which fraction is equal to 0.6?
    1. 1/6
    2. 3/5
    3. 2/3
    4. 6/100
    Answer and explanation

    Answer: B. 0.6 = 6/10 = 3/5.

  10. What is 25% of 80?
    1. 20
    2. 25
    3. 30
    4. 40
    Answer and explanation

    Answer: A. 25% is one fourth, and 80 ÷ 4 = 20.

  11. 15% written as a decimal is what?
    1. 1.5
    2. 0.015
    3. 0.15
    4. 15.0
    Answer and explanation

    Answer: C. Divide percent by 100: 15% = 0.15.

  12. Simplify the ratio 3:12.
    1. 1:4
    2. 1:3
    3. 2:5
    4. 3:4
    Answer and explanation

    Answer: A. Divide both parts by 3 to get 1:4.

  13. What is 5/8 as a decimal?
    1. 0.125
    2. 0.25
    3. 0.5
    4. 0.625
    Answer and explanation

    Answer: D. 5 ÷ 8 = 0.625.

  14. What is 2.5 × 4?
    1. 6
    2. 10
    3. 12
    4. 14
    Answer and explanation

    Answer: B. 2.5 × 4 = 10.

  15. What is -3 + 8?
    1. 5
    2. -5
    3. 11
    4. -11
    Answer and explanation

    Answer: A. Starting at -3 and moving 8 units right gives 5.

  16. What is -4 × 6?
    1. 24
    2. 10
    3. -10
    4. -24
    Answer and explanation

    Answer: D. A negative times a positive is negative: -4 × 6 = -24.

  17. What is |-9|?
    1. -9
    2. 9
    3. 0
    4. 18
    Answer and explanation

    Answer: B. Absolute value is distance from zero, so |-9| = 9.

  18. What is 72?
    1. 14
    2. 21
    3. 49
    4. 72
    Answer and explanation

    Answer: C. 72 = 7 × 7 = 49.

  19. What is √81?
    1. 9
    2. 18
    3. 27
    4. 40.5
    Answer and explanation

    Answer: A. The number whose square is 81 is 9.

  20. Evaluate 23 × 22.
    1. 8
    2. 16
    3. 24
    4. 32
    Answer and explanation

    Answer: D. Add exponents with the same base: 23 × 22 = 25 = 32.

  21. Solve x + 7 = 19.
    1. 10
    2. 12
    3. 19
    4. 26
    Answer and explanation

    Answer: B. Subtract 7 from both sides: x = 12.

  22. Solve 3x = 27.
    1. 9
    2. 18
    3. 24
    4. 30
    Answer and explanation

    Answer: A. Divide by 3: x = 9.

  23. Solve 2x - 5 = 11.
    1. 3
    2. 6
    3. 8
    4. 16
    Answer and explanation

    Answer: C. Add 5 to get 2x=16, then divide by 2 to get x=8.

  24. Solve x/4 + 2 = 7.
    1. 5
    2. 12
    3. 16
    4. 20
    Answer and explanation

    Answer: D. Subtract 2 to get x/4=5, so x=20.

  25. Solve 5(x + 2) = 35.
    1. 3
    2. 5
    3. 7
    4. 9
    Answer and explanation

    Answer: B. Divide by 5 to get x+2=7, so x=5.

  26. Solve 4x + 3 = 2x + 15.
    1. 6
    2. 8
    3. 9
    4. 12
    Answer and explanation

    Answer: A. Subtract 2x and 3 to get 2x=12, so x=6.

  27. If y = 2x + 1, what is y when x = 4?
    1. 7
    2. 8
    3. 9
    4. 10
    Answer and explanation

    Answer: C. Substitute 4: y = 2(4)+1 = 9.

  28. Solve the inequality x - 3 > 7.
    1. x < 4
    2. x > 10
    3. x > 7
    4. x < 10
    Answer and explanation

    Answer: B. Add 3 to both sides: x > 10.

  29. Solve -2x = 8.
    1. 4
    2. 2
    3. -2
    4. -4
    Answer and explanation

    Answer: D. Divide by -2: x = -4.

  30. Simplify 3a + 2a.
    1. 5a
    2. 6a
    3. a5
    4. 5a2
    Answer and explanation

    Answer: A. Combine like terms: 3a + 2a = 5a.

  31. Simplify 7x - 2x + 4.
    1. 9x+4
    2. 5x
    3. 5x+4
    4. 7x+2
    Answer and explanation

    Answer: C. Combine 7x - 2x to get 5x, then keep +4.

  32. Simplify x2 × x3.
    1. x6
    2. x5
    3. 2x5
    4. x9
    Answer and explanation

    Answer: B. Add exponents with the same base: x2+3=x5.

  33. Simplify (3x)(4x).
    1. 7x
    2. 12x
    3. 7x2
    4. 12x2
    Answer and explanation

    Answer: D. Multiply coefficients and variables: 3 × 4 = 12 and x × x = x2.

  34. Factor x2 - 9.
    1. (x-3)(x+3)
    2. (x-9)(x+1)
    3. (x+9)(x-1)
    4. (x-3)(x-3)
    Answer and explanation

    Answer: A. This is a difference of squares: x2 - 32 = (x-3)(x+3).

  35. Expand 2(x + 4).
    1. 2x+4
    2. x+8
    3. 2x+8
    4. 6x
    Answer and explanation

    Answer: C. Distribute 2 to both terms: 2x + 8.

  36. What is the slope of the line through (0,0) and (2,6)?
    1. 2
    2. 3
    3. 6
    4. 12
    Answer and explanation

    Answer: B. Slope is rise over run: (6-0)/(2-0)=3.

  37. What is the y-intercept of y = 2x + 5?
    1. 5
    2. 2
    3. -2
    4. -5
    Answer and explanation

    Answer: A. In y=mx+b, the y-intercept is b, which is 5.

  38. If f(x)=x2+1, what is f(3)?
    1. 7
    2. 8
    3. 10
    4. 12
    Answer and explanation

    Answer: C. f(3)=32+1=9+1=10.

  39. In which quadrant is the point (3,-2)?
    1. I
    2. II
    3. III
    4. IV
    Answer and explanation

    Answer: D. Positive x and negative y place the point in Quadrant IV.

  40. What kind of line is represented by y = 4?
    1. vertical
    2. horizontal
    3. diagonal only
    4. curved
    Answer and explanation

    Answer: B. y=4 has the same y-value for every x, so it is horizontal.

  41. What is the area of a rectangle with length 8 and width 5?
    1. 40
    2. 26
    3. 13
    4. 80
    Answer and explanation

    Answer: A. Rectangle area is length times width: 8 × 5 = 40.

  42. What is the perimeter of a rectangle with length 6 and width 4?
    1. 10
    2. 18
    3. 20
    4. 24
    Answer and explanation

    Answer: C. Perimeter is 2(6+4)=20.

  43. What is the area of a triangle with base 10 and height 6?
    1. 16
    2. 30
    3. 60
    4. 120
    Answer and explanation

    Answer: B. Triangle area is 1/2 × 10 × 6 = 30.

  44. Using π ≈ 3.14, what is the circumference of a circle with radius 5?
    1. 31.4
    2. 15.7
    3. 25
    4. 78.5
    Answer and explanation

    Answer: A. Circumference is 2π r = 2(3.14)(5)=31.4.

  45. What is the area of a circle with radius 3?
    1. 3π
    2. 6π
    3. 12π
    4. 9π
    Answer and explanation

    Answer: D. Circle area is π r2 = π(32)=9π.

  46. What is the volume of a rectangular prism with length 4, width 5, and height 6?
    1. 60
    2. 90
    3. 120
    4. 240
    Answer and explanation

    Answer: C. Volume is 4 × 5 × 6 = 120.

  47. What is the volume of a cube with side length 3?
    1. 9
    2. 27
    3. 36
    4. 81
    Answer and explanation

    Answer: B. Cube volume is 33 = 27.

  48. What is the perimeter of a square with side length 9?
    1. 36
    2. 18
    3. 27
    4. 81
    Answer and explanation

    Answer: A. A square has four equal sides, so 4 × 9 = 36.

  49. What is the area of a parallelogram with base 7 and height 5?
    1. 12
    2. 24
    3. 30
    4. 35
    Answer and explanation

    Answer: D. Parallelogram area is base times height: 7 × 5 = 35.

  50. A right triangle has legs 6 and 8. What is the hypotenuse?
    1. 8
    2. 9
    3. 10
    4. 14
    Answer and explanation

    Answer: C. 62+82=36+64=100, so the hypotenuse is 10.

  51. What is the sum of the angles in a triangle?
    1. 90 degrees
    2. 180 degrees
    3. 270 degrees
    4. 360 degrees
    Answer and explanation

    Answer: B. The interior angles of a triangle always sum to 180 degrees.

  52. How many degrees are in a right angle?
    1. 90
    2. 120
    3. 180
    4. 360
    Answer and explanation

    Answer: A. A right angle measures 90 degrees.

  53. Complementary angles add to how many degrees?
    1. 45
    2. 60
    3. 180
    4. 90
    Answer and explanation

    Answer: D. Complementary angles add to 90 degrees.

  54. Supplementary angles add to how many degrees?
    1. 45
    2. 90
    3. 180
    4. 360
    Answer and explanation

    Answer: C. Supplementary angles add to 180 degrees.

  55. A scale drawing uses 2 cm to represent 10 m. How many meters are represented by 5 cm?
    1. 15
    2. 25
    3. 30
    4. 50
    Answer and explanation

    Answer: B. 1 cm represents 5 m, so 5 cm represents 25 m.

  56. What is the mean of 4, 8, and 12?
    1. 6
    2. 7
    3. 8
    4. 10
    Answer and explanation

    Answer: C. Add and divide by 3: (4+8+12)/3 = 8.

  57. What is the median of 3, 7, 9, 10, and 12?
    1. 9
    2. 8
    3. 7
    4. 10
    Answer and explanation

    Answer: A. The middle number in order is 9.

  58. What is the range of 15, 22, 10, and 18?
    1. 8
    2. 10
    3. 11
    4. 12
    Answer and explanation

    Answer: D. Range is largest minus smallest: 22 - 10 = 12.

  59. What is the probability of rolling an even number on a fair six-sided die?
    1. 1/3
    2. 1/2
    3. 2/3
    4. 5/6
    Answer and explanation

    Answer: B. Even outcomes are 2, 4, and 6: 3/6 = 1/2.

  60. A bag has 3 red marbles and 7 blue marbles. What is the probability of picking a red marble?
    1. 7/10
    2. 1/2
    3. 3/10
    4. 3/7
    Answer and explanation

    Answer: C. There are 10 marbles total and 3 are red, so the probability is 3/10.

  61. How many minutes are in 2 hours?
    1. 120
    2. 90
    3. 100
    4. 160
    Answer and explanation

    Answer: A. One hour is 60 minutes, so 2 × 60 = 120.

  62. How many feet are in 1 yard?
    1. 1
    2. 2
    3. 12
    4. 3
    Answer and explanation

    Answer: D. One yard equals 3 feet.

  63. How many inches are in 5 feet?
    1. 50
    2. 60
    3. 72
    4. 120
    Answer and explanation

    Answer: B. One foot is 12 inches, so 5 × 12 = 60.

  64. 100 centimeters equals how many meters?
    1. 0.1
    2. 10
    3. 1
    4. 1000
    Answer and explanation

    Answer: C. 100 centimeters equals 1 meter.

  65. What is 1/4 as a percent?
    1. 25%
    2. 40%
    3. 50%
    4. 75%
    Answer and explanation

    Answer: A. 1/4 = 0.25 = 25%.

  66. What percent is 20 out of 50?
    1. 20%
    2. 25%
    3. 30%
    4. 40%
    Answer and explanation

    Answer: D. 20/50 = 0.4 = 40%.

  67. 30% as a fraction in simplest form is what?
    1. 3/100
    2. 3/10
    3. 1/30
    4. 30/10
    Answer and explanation

    Answer: B. 30% = 30/100 = 3/10.

  68. 0.08 written as a percent is what?
    1. 0.8%
    2. 80%
    3. 8%
    4. 800%
    Answer and explanation

    Answer: C. Multiply by 100: 0.08 = 8%.

  69. 12 is what percent of 48?
    1. 25%
    2. 30%
    3. 40%
    4. 48%
    Answer and explanation

    Answer: A. 12/48 = 1/4 = 25%.

  70. Increase 40 by 10%.
    1. 4
    2. 36
    3. 40
    4. 44
    Answer and explanation

    Answer: D. 10% of 40 is 4, so the increased value is 44.

  71. One angle in a linear pair is 65 degrees. What is the other angle?
    1. 65
    2. 115
    3. 125
    4. 180
    Answer and explanation

    Answer: B. Linear pairs sum to 180 degrees, so 180 - 65 = 115.

  72. Evaluate √49 + √16.
    1. 7
    2. 9
    3. 11
    4. 65
    Answer and explanation

    Answer: C. √49=7 and √16=4, so the sum is 11.

  73. What is 50?
    1. 1
    2. 0
    3. 5
    4. 25
    Answer and explanation

    Answer: A. Any nonzero number raised to the zero power equals 1.

  74. What is 10-1?
    1. 10
    2. 0.1
    3. -10
    4. 1
    Answer and explanation

    Answer: B. 10-1=1/10=0.1.

  75. Simplify 12/18.
    1. 3/4
    2. 4/5
    3. 1/3
    4. 2/3
    Answer and explanation

    Answer: D. Divide numerator and denominator by 6: 12/18 = 2/3.

  76. What is the reciprocal of 4/7?
    1. 4/7
    2. -4/7
    3. 7/4
    4. 11/4
    Answer and explanation

    Answer: C. The reciprocal flips numerator and denominator: 7/4.

  77. What is 3/5 of 10?
    1. 6
    2. 5
    3. 8
    4. 15
    Answer and explanation

    Answer: A. 10 × 3/5 = 6.

  78. What is (9/10) ÷ (3/5)?
    1. 1/2
    2. 3/2
    3. 2/3
    4. 27/50
    Answer and explanation

    Answer: B. Multiply by the reciprocal: (9/10)(5/3)=45/30=3/2.

  79. Solve the proportion x/6 = 4/3.
    1. 2
    2. 6
    3. 8
    4. 12
    Answer and explanation

    Answer: C. Multiply both sides by 6: x = 6(4/3)=8.

  80. What is 2/5 of 30?
    1. 6
    2. 10
    3. 15
    4. 12
    Answer and explanation

    Answer: D. 30 ÷ 5 = 6, and 6 × 2 = 12.

  81. What is 4.2 + 3.75?
    1. 7.95
    2. 7.55
    3. 8.05
    4. 8.75
    Answer and explanation

    Answer: A. Align decimals: 4.20 + 3.75 = 7.95.

  82. What is 6.5 - 2.8?
    1. 2.7
    2. 3.3
    3. 3.7
    4. 4.1
    Answer and explanation

    Answer: C. 6.5 - 2.8 = 3.7.

  83. What is 0.4 × 0.2?
    1. 0.8
    2. 0.08
    3. 0.06
    4. 0.02
    Answer and explanation

    Answer: B. 4 × 2 = 8, and two decimal places give 0.08.

  84. What is 3.6 ÷ 0.6?
    1. 6
    2. 0.6
    3. 3
    4. 60
    Answer and explanation

    Answer: A. 3.6 ÷ 0.6 = 36 ÷ 6 = 6.

  85. Round 47.86 to the nearest tenth.
    1. 47
    2. 48
    3. 47.8
    4. 47.9
    Answer and explanation

    Answer: D. The hundredths digit is 6, so 47.86 rounds to 47.9.

  86. Which number is prime?
    1. 21
    2. 27
    3. 29
    4. 33
    Answer and explanation

    Answer: C. 29 has no positive factors other than 1 and 29.

  87. What is the least common multiple of 6 and 8?
    1. 12
    2. 24
    3. 32
    4. 48
    Answer and explanation

    Answer: B. Multiples of 6 and 8 first meet at 24.

  88. What is the greatest common factor of 18 and 24?
    1. 6
    2. 8
    3. 12
    4. 18
    Answer and explanation

    Answer: A. The largest number that divides both 18 and 24 is 6.

  89. Write 2 1/3 as an improper fraction.
    1. 5/3
    2. 6/3
    3. 8/3
    4. 7/3
    Answer and explanation

    Answer: D. 2 1/3 = (2 × 3 + 1)/3 = 7/3.

  90. Write 11/4 as a mixed number.
    1. 2 1/4
    2. 2 1/2
    3. 2 3/4
    4. 3 1/4
    Answer and explanation

    Answer: C. 11 ÷ 4 = 2 remainder 3, so 11/4 = 2 3/4.

  91. Solve 2x + 3 = 11.
    1. 3
    2. 4
    3. 5
    4. 7
    Answer and explanation

    Answer: B. Subtract 3 to get 2x=8, then divide by 2 to get x=4.

  92. Evaluate 4a - b when a=3 and b=5.
    1. 7
    2. 9
    3. 12
    4. 17
    Answer and explanation

    Answer: A. Substitute values: 4(3)-5=12-5=7.

  93. Solve 2y + 6 = 0.
    1. 3
    2. -6
    3. -3
    4. 0
    Answer and explanation

    Answer: C. Subtract 6 to get 2y=-6, then divide by 2 to get y=-3.

  94. If x=-2, evaluate x2 + 3.
    1. -1
    2. 1
    3. 5
    4. 7
    Answer and explanation

    Answer: D. (-2)2 = 4, and 4+3=7.

  95. In the expression 7m + 5, what is the coefficient of m?
    1. 5
    2. 7
    3. 12
    4. m
    Answer and explanation

    Answer: B. The coefficient is the number multiplying the variable, which is 7.

  96. In the expression 3x + 9, what is the constant term?
    1. 9
    2. 3
    3. x
    4. 12
    Answer and explanation

    Answer: A. The constant is the term without a variable, which is 9.

  97. What is the next number in the sequence 2, 5, 8, ...?
    1. 9
    2. 10
    3. 11
    4. 13
    Answer and explanation

    Answer: C. The pattern adds 3 each time, so the next number is 11.

  98. What is the next number in the sequence 3, 6, 12, ...?
    1. 15
    2. 18
    3. 21
    4. 24
    Answer and explanation

    Answer: D. The pattern multiplies by 2, so the next number is 24.

  99. A triangle has angles of 90 degrees and 30 degrees. What is the third angle?
    1. 30
    2. 60
    3. 90
    4. 120
    Answer and explanation

    Answer: B. Triangle angles total 180 degrees, so 180-90-30=60.

  100. Which is the best estimate of 198 × 5?
    1. 1,000
    2. 500
    3. 200
    4. 2,000
    Answer and explanation

    Answer: A. Round 198 to 200, then 200 × 5 = 1,000.

What Your Practice Result Means

This practice test does not produce an official ASVAB score. Official ASVAB scores use standard-score procedures, and AFQT is computed from official standard scores for Arithmetic Reasoning, Mathematics Knowledge, Paragraph Comprehension, and Word Knowledge. Use this page as a topic diagnostic. If your misses cluster in fractions or algebra, do not keep retaking random sets. Fix that topic directly, then return to mixed practice.

Practice score out of 100MeaningNext step
85-100Strong practice readinessMove to timed 15-question and 25-question mixed MK sets.
70-84Good foundation with several fixable gapsReview missed items by topic and retake only those topics after 24 hours.
50-69Basic math is forming, but accuracy is inconsistentWork untimed by category before using official-style timing.
Below 50Start with arithmetic, fractions, and one-step equationsUse the beginner review and explanations as lessons before scoring yourself.

Official Sources Used

The ASVAB structure, Mathematics Knowledge description, timing, calculator context, CAT-ASVAB behavior, and AFQT relationship in this page were checked against official ASVAB and ASVAB CEP sources. The 100 practice questions are original NUM8ERS study questions.

Official ASVAB: Mathematics Knowledge sample page Official ASVAB: Sample Questions Official ASVAB: Subtests Official ASVAB: CAT-ASVAB Official ASVAB Fact Sheet PDF Official ASVAB: What to Expect Official ASVAB: Preparing for the ASVAB Official ASVAB: Understanding ASVAB Scores Official ASVAB FAQs

ASVAB Mathematics Knowledge Practice Test FAQs

Are these real ASVAB Mathematics Knowledge questions?

No. They are original practice questions written for study. They are based on the official public MK skill description, not copied from official test forms or official sample questions.

What does Mathematics Knowledge test?

Official ASVAB materials describe Mathematics Knowledge as knowledge of high school mathematics principles.

Does Mathematics Knowledge count toward AFQT?

Yes. Official score guidance lists Mathematics Knowledge as one of the four subtests used to compute AFQT, along with Arithmetic Reasoning, Word Knowledge, and Paragraph Comprehension.

Can I use a calculator on ASVAB Mathematics Knowledge?

Official ASVAB FAQs explain that calculators are not allowed because the test assesses ability to do basic calculations without one.

How many Mathematics Knowledge questions are on the real ASVAB?

Official CAT-ASVAB information lists 15 scored Mathematics Knowledge questions. Official paper-and-pencil timing tables list 25 Mathematics Knowledge questions.

What To Study After Mathematics Knowledge Practice

Mathematics Knowledge checks math principles without calculator support. Your next move depends on whether the weak point is a rule, a formula, or applying math inside a word problem.

Use the ASVAB Study Guide for exam format and retake planning, not for extra MK drills.