Free AFOQT Math Practice Test 2026 (With Answers & Solutions)
Free AFOQT Math Practice Test (With Answers & Step-by-Step Solutions)
Test your skills with 10 AFOQT-style math questions — each with a worked solution — then keep practicing with free worksheets and study books.
What’s on the AFOQT Math Test?
The AFOQT is required to become a U.S. Air Force or Space Force officer. Two of its subtests are math, and together they build your Quantitative composite.
Arithmetic Reasoning (AR) — 25 questions in 29 minutes — is all word problems testing ratios, proportions, percentages, rates, and basic algebra in context. Mathematics Knowledge (MK) — 25 questions in 22 minutes — tests algebra, geometry, exponents, and number properties directly.
A calculator is not allowed on either subtest, so sharpen your mental math and hand calculations.
Scoring: the AFOQT reports composite percentile scores rather than a raw total. Your AR and MK results feed the Quantitative composite, which is important for many officer career fields — aim as high as you can.
A Simple 4-Week AFOQT Math Study Plan
Free AFOQT Math Practice Test
Work through 10 AFOQT-style questions one at a time. Answer, tap Show answer, then press Next.
A car travels 180 miles in 3 hours. What is its average speed?
- A) 45 mph
- B) 54 mph
- C) 60 mph
- D) 90 mph
Show answer
Solve: 3x + 6 = 18.
- A) 3
- B) 4
- C) 5
- D) 6
Show answer
If 5 pencils cost $2.50, how much do 8 pencils cost?
- A) $3.20
- B) $4.00
- C) $4.50
- D) $5.00
Show answer
What is 3³?
- A) 9
- B) 18
- C) 27
- D) 81
Show answer
What is a 15% tip on a $40 bill?
- A) $4
- B) $6
- C) $8
- D) $10
Show answer
Area of a circle with radius 3?
- A) 6π
- B) 9π
- C) 12π
- D) 3π
Show answer
What is 3/4 of 60?
- A) 30
- B) 40
- C) 45
- D) 48
Show answer
Solve: x² − 16 = 0.
- A) 4 only
- B) −4 only
- C) 4 and −4
- D) 16
Show answer
Two numbers are in a 2 : 3 ratio and total 25. What is the smaller number?
- A) 8
- B) 10
- C) 12
- D) 15
Show answer
Simplify: (x³)².
- A) x⁵
- B) x⁶
- C) x⁹
- D) 2x³
Show answer
Nice work — you finished all 10!
Keep practicing with free math worksheets.
Practice by Topic
Find your weak spots, then drill each with our free math worksheets:
Free AFOQT Math Resources
Related AFOQT Math Books
Browse our AFOQT Math library — scroll for more, or see all books.
AFOQT Math Formulas You Should Know
- Percent: part = percent × whole.
- Distance: distance = rate × time.
- Quadratic formula: x = (−b ± √(b² − 4ac)) ÷ 2a.
- Area: circle = πr²; triangle = ½bh; rectangle = l × w.
- Pythagorean theorem: a² + b² = c².
- Exponent rules: xᵃ·xᵇ = xᵃ⁺ᵇ; (xᵃ)ᵇ = xᵃᵇ.
Tips to Boost Your AFOQT Math Score
- No calculator — practice arithmetic and estimation by hand.
- Watch the clock — MK gives barely a minute per question.
- Translate word problems into equations before solving.
- Memorize the core formulas — none are provided.