ASVAB Math Practice: Arithmetic Reasoning and Math Knowledge
The math you need for the ASVAB, the formulas worth memorizing, and 8 practice questions with step-by-step answers.
Two math subtests, both in the AFQT
- Arithmetic Reasoning (AR): 15 word problems in 55 minutes. The math is usually simple; reading the problem carefully is the hard part.
- Mathematics Knowledge (MK): 15 questions in 31 minutes on number rules, algebra and geometry.
You can't use a calculator, but you get scratch paper.
Formulas worth memorizing
| Topic | Formula |
|---|---|
| Percent of a number | part = percent × whole (20% of 80 = 0.20 × 80 = 16) |
| Distance | distance = rate × time |
| Simple interest | I = P × r × t |
| Average | sum ÷ how many |
| Rectangle | area = length × width; perimeter = 2L + 2W |
| Triangle | area = ½ × base × height; angles add to 180° |
| Circle | area = πr²; circumference = 2πr |
| Right triangle | a² + b² = c² |
Strategies
- Read the last sentence first so you know exactly what they ask.
- Estimate to eliminate impossible answers.
- Try the answers in the problem when setting up an equation is hard.
- Watch the units: minutes vs. hours, inches vs. feet.
Practice questions
1. A car travels 240 miles on 8 gallons of gas. How many miles does it travel per gallon?
- 32
- 30
- 20
- 1,920
Show answer
Answer: 30. 240 ÷ 8 = 30 miles per gallon.
2. A $60 shirt is 25% off. What is the sale price?
- $45
- $35
- $15
- $50
Show answer
Answer: $45. 25% of $60 is $15. $60 − $15 = $45.
3. Three friends earn $36, $48 and $60. What is their average pay?
- $50
- $48
- $144
- $36
Show answer
Answer: $48. (36 + 48 + 60) ÷ 3 = 144 ÷ 3 = 48.
4. Solve: 4x + 6 = 30
- x = 4
- x = 24
- x = 6
- x = 9
Show answer
Answer: x = 6. Subtract 6: 4x = 24. Divide by 4: x = 6.
5. What is the area of a circle with a radius of 3? (Use π = 3.14.)
- 18.84
- 28.26
- 9.42
- 113.04
Show answer
Answer: 28.26. A = πr² = 3.14 × 9 = 28.26.
6. What is 2⁵?
- 10
- 32
- 16
- 25
Show answer
Answer: 32. 2 × 2 × 2 × 2 × 2 = 32.
7. Two angles of a triangle are 45° and 65°. What is the third angle?
- 60°
- 80°
- 70°
- 110°
Show answer
Answer: 70°. 180 − 45 − 65 = 70°.
8. A worker earns $15 an hour and $22.50 an hour for overtime. How much does she earn for 40 regular hours and 4 overtime hours?
- $750
- $600
- $660
- $690
Show answer
Answer: $690. 40 × $15 = $600. 4 × $22.50 = $90. $600 + $90 = $690.