ASVAB Math Practice Questions with Answers: 15 Problems to Try First

Try 15 ASVAB math practice questions with answers and explanations for Arithmetic Reasoning and Mathematics Knowledge.

ASVAB math practice should cover both Arithmetic Reasoning and Mathematics Knowledge. Arithmetic Reasoning asks you to solve word problems. Mathematics Knowledge asks more direct high-school math questions involving number properties, algebra, geometry, and formulas.

The official ASVAB site provides sample questions for Arithmetic Reasoning and Mathematics Knowledge and describes the CAT-ASVAB subtest structure. Its CAT-ASVAB page lists 15 scored Arithmetic Reasoning questions with a 55-minute time limit without tryout questions, and 15 scored Mathematics Knowledge questions with a 31-minute time limit without tryout questions. A 2026 official ASVAB calculator note states that the current calculator policy remains in place, so students should prepare to calculate without a calculator. ViewMath is independent and is not affiliated with or endorsed by the Department of Defense, MEPCOM, or any military branch. Use officialasvab.com for current details.

How to Use These Questions

Try the 15 questions without a calculator. Write your work on paper. After grading, divide missed questions into two groups: setup errors and calculation errors. Setup errors mean you chose the wrong operation or formula. Calculation errors mean you chose correctly but made an arithmetic slip. The fix is different for each type.

Arithmetic Reasoning Practice

  1. A truck travels 210 miles in 5 hours. What is its average speed?
  2. A shirt costs $36 and is discounted by 20%. What is the sale price?
  3. A recipe uses 4 cups of rice for 10 servings. How many cups are needed for 25 servings?
  4. A tank holds 48 gallons of water. If 3/8 of the water is used, how many gallons remain?
  5. A worker earns $16 per hour for 35 hours. How much does the worker earn?
  6. A box contains 18 red parts, 12 blue parts, and 10 green parts. What fraction of the parts are blue?
  7. A rectangular floor is 15 feet by 12 feet. Tiles cover 3 square feet each. How many tiles are needed?
  8. One machine makes 45 parts in 9 minutes. At the same rate, how many parts does it make in 30 minutes?

Mathematics Knowledge Practice

  1. Simplify: 4^2 + sqrt(81).
  2. Solve: 3x – 8 = 19.
  3. Factor: x^2 + 5x + 6.
  4. Find the perimeter of a square with side length 7.
  5. A right triangle has legs 9 and 12. Find the hypotenuse.
  6. What is the greatest common factor of 24 and 36?
  7. Simplify the ratio 42:56.

Answers and Explanations

  1. 42 mph. Divide distance by time: 210 / 5 = 42.
  2. $28.80. Twenty percent of 36 is 7.20; 36 – 7.20 = 28.80.
  3. 10 cups. 25 servings is 2.5 times 10 servings; 4 x 2.5 = 10.
  4. 30 gallons remain. 3/8 of 48 is 18; 48 – 18 = 30.
  5. $560. 16 x 35 = 560.
  6. 3/10. Total parts = 40; blue = 12; 12/40 = 3/10.
  7. 60 tiles. Area = 15 x 12 = 180 square feet; 180 / 3 = 60.
  8. 150 parts. Rate = 45 / 9 = 5 parts per minute; 5 x 30 = 150.
  9. 25. 4^2 = 16 and sqrt(81) = 9; 16 + 9 = 25.
  10. x = 9. Add 8 to get 3x = 27; divide by 3.
  11. (x + 2)(x + 3).
  12. 28. Perimeter = 4 x 7.
  13. 15. 9^2 + 12^2 = 81 + 144 = 225; sqrt(225) = 15.
  14. 12.
  15. 3:4. Divide both terms by 14.

What Your Score Means

If you missed 0-3 questions, move into timed mixed practice and focus on speed. If you missed 4-7, identify the topic pattern and spend one week on weak areas. If you missed 8 or more, rebuild foundations first: fractions, percents, ratios, basic equations, and geometry formulas.

ASVAB Math Study Checklist

  • Can you multiply and divide without a calculator?
  • Can you convert fractions, decimals, and percents?
  • Can you set up rate, distance, time, and unit-rate problems?
  • Can you solve one-variable equations quickly?
  • Can you use area, perimeter, volume, and Pythagorean theorem formulas?
  • Can you simplify ratios and work with factors, multiples, roots, and exponents?

Three-Day Fix Plan After This Practice Set

Day 1: Review every missed Arithmetic Reasoning question. Rewrite each word problem as a short equation or proportion. If the setup was wrong, solve two similar problems before moving on.

Day 2: Review Mathematics Knowledge facts: exponents, square roots, factoring, ratios, perimeter, area, and Pythagorean theorem. Make a short formula card, then solve without looking.

Day 3: Complete a timed mixed set with no calculator. Do not rush the first half. Accuracy matters more than speed until your setup is reliable. After grading, compare mistakes with Day 1 and Day 2. Repeated mistakes become the next study target.

Topic Fixes

  • Rates: Write units beside every number. Miles per hour, dollars per hour, and parts per minute all require division first.
  • Percents: Convert to decimals before multiplying. Twenty percent is 0.20, not 20.
  • Fractions: Simplify only after multiplying or dividing unless simplification makes the calculation easier.
  • Geometry: Sketch the shape and label dimensions before choosing a formula.

When to Retest Yourself

Do not retake a full practice set immediately after reading the answer key. Wait until you have solved at least five similar problems without help. Then take another timed set. This prevents false confidence from short-term memory of the solution and shows whether the method has actually improved.

If you are working with a recruiter-provided timeline, plan backward from the test date. Leave the final two days for light review, sleep, and no-calculator arithmetic warm-ups.

ViewMath does not need to be official to be useful. Use math practice resources that give full explanations, then train under no-calculator conditions so test-day arithmetic feels routine.

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