AFOQT math practice: Arithmetic Reasoning and Math Knowledge

The AFOQT has two math subtests: Arithmetic Reasoning (25 word problems in 29 minutes) and Math Knowledge (25 algebra, geometry and number questions in 22 minutes), both without a calculator. Together they make the Quantitative composite, which needs at least the 10th percentile for a commission, and Math Knowledge also feeds the Pilot composite. The free drills below are 12 original questions each.

50
math items on the real test: No
calculator allowed: 10th
Quantitative percentile minimum: 2
free drills

Last checked 22 October 2026 · Counts and times from the Air Force AFOQT pamphlet; minimum from AFROTC detachment pages

Free math drills: 12 original AFOQT-style questions each, at the real subtest pace, then every answer worked out. No sign-up.

12
questions
13:55
time limit
Free
every answer explained

By the LifeScore Editorial Team · Updated 22 October 2026 · How we check facts · How this is scored

What is on AFOQT Arithmetic Reasoning?

Word problems you solve by hand: rates and distance, percents and interest, ratios and proportions, averages, work problems, and measurement.

The problem types that come up most, and the one line to write first
Type	Write this first
Distance, rate, time	distance = rate × time
Percent	part = percent × whole
Percent change	change ÷ original × 100
Ratio	total parts, then one part = total ÷ parts
Average	total = average × count
Work together	1/a + 1/b = 1/t
Simple interest	interest = principal × rate × time

With 29 minutes for 25 problems you have about 70 seconds each, which is enough if you write the equation before you calculate. Estimate first, so an answer ten times too big stands out.

What is on AFOQT Math Knowledge?

High-school algebra and geometry: solving equations and inequalities, exponents and roots, factoring, slope, angles, areas, volumes and the Pythagorean theorem.

Rules worth having on a card
Topic	Rule
Exponents	aᵐ × aⁿ = aᵐ⁺ⁿ; (aᵐ)ⁿ = aᵐⁿ; a⁰ = 1
Factoring	x² − y² = (x − y)(x + y)
Slope	(y₂ − y₁) ÷ (x₂ − x₁)
Right triangles	a² + b² = c²; 3-4-5 and 5-12-13 triangles
Circle	area = πr²; circumference = 2πr
Angles	a triangle's angles add to 180°; a straight line is 180°
Volume	box = l × w × h; cylinder = πr²h

Math Knowledge gives about 53 seconds a question. Most items are one rule applied cleanly, so the rule card is worth more than long practice sets.

What do AFOQT math questions look like?

Three examples follow: a fuel-and-reserve problem, a ratio and a linear equation. The first is worked in full.

AFOQT-style question 1 · Fuel and time
A training aircraft burns 12 gallons of fuel an hour and takes off with 78 gallons. It must land with at least 30 minutes of fuel in reserve. What is the longest it can fly?
1. A5.5 hours
2. B6 hours
3. C6.5 hours
4. D7 hours
5. E6.25 hours
Worked answer
B: 6 hours. Thirty minutes of reserve at 12 gallons an hour is 6 gallons, leaving 78 − 6 = 72 usable gallons, and 72 ÷ 12 = 6 hours.
1. Reserve: 0.5 hour × 12 = 6 gallons.
2. Usable: 78 − 6 = 72 gallons.
3. Time: 72 ÷ 12 = 6 hours.
The trap: 78 ÷ 12 = 6.5 hours ignores the reserve, which is the whole point of the question.
AFOQT-style question 2 · Ratio
A detachment of 48 cadets has pilot candidates and non-rated candidates in the ratio 5 to 3. How many are non-rated?
1. A16
2. B18
3. C24
4. D30
5. E15
Show the worked answer
B: 18. The ratio has 5 + 3 = 8 parts, so each part is 48 ÷ 8 = 6 cadets. Non-rated: 3 × 6 = 18.
1. Total parts: 5 + 3 = 8.
2. One part: 48 ÷ 8 = 6.
3. Non-rated: 3 parts × 6 = 18.
The trap: Answering 30, the pilot candidates. Check which side of the ratio the question asks for.
AFOQT-style question 3 · Linear equation
If 3(x − 4) = 2x + 5, what is x?
1. A1
2. B9
3. C17
4. D−7
5. E7
Show the worked answer
C: 17. Expand: 3x − 12 = 2x + 5. Subtract 2x: x − 12 = 5. Add 12: x = 17.
1. Distribute: 3x − 12 = 2x + 5.
2. Subtract 2x from both sides: x − 12 = 5.
3. Add 12: x = 17. Check: 3 × 13 = 39 and 2 × 17 + 5 = 39.
The trap: Distributing only to x (3x − 4) gives x = 9. Multiply every term inside the brackets.

Raise your Quantitative composite

Four drills for each math subtest and eight full mocks, every answer worked out by hand.

The AFOQT Pass Pack gives you 8 full mocks on the real clock, 32 drills of 12 questions for the sections that cost you points, and a predictor that turns your mocks into the odds of reaching your target. One payment, no subscription, and your free score stays free.

Prep courses for these tests usually cost $19 to $129. The AFOQT Pass Pack is US$39 (£29), once.

See the AFOQT Pass Pack How our questions are built and checked

8
timed mocks: 32
topic drills: 1
score predictor

How do I get fast at AFOQT math without a calculator?

Practise the hand skills the problems keep needing: fractions, percents as decimals, long division by small numbers, and squares up to 15.

Know the common fraction, decimal and percent equivalents: 1/8 = 0.125 = 12.5%, 3/8 = 37.5%, 2/3 ≈ 66.7%.
Turn a percent problem into a fraction when it is friendlier: 25% of 48 is 48 ÷ 4.
Cancel before you multiply: 36/48 × 8/9 becomes 3/4 × 8/9 = 2/3.
Use the options: plug one in when solving looks slow, starting with the middle value.
Memorize squares to 15² and the square roots that go with them.

Which AFOQT composites use the math subtests?

Quantitative (both), Academic Aptitude (both, with the verbal subtests), and Pilot and CSO (Math Knowledge). Math Knowledge is the subtest that touches the most composites.

AFOQT composites (Wikipedia and AFROTC sources)
Composite	Built from	Commonly published minimum
Quantitative	Arithmetic Reasoning, Math Knowledge	All officers: minimum 10
Academic Aptitude	The verbal and quantitative subtests together	Used by boards as a general measure
Pilot	Math Knowledge, Table Reading, Instrument Comprehension, Aviation Information	Pilot: minimum 25
Combat Systems Officer (CSO)	Includes Math Knowledge, Table Reading and Block Counting (sources differ on the rest)	CSO: minimum 25

If you want a rated job, Math Knowledge is the best-value subtest to improve, because it raises Pilot and CSO along with Quantitative. The AFOQT scores page explains the composites.

What are the most common AFOQT math mistakes?

Answering for the wrong quantity, skipping a step the problem builds in (a reserve, a discount, a return trip), distributing to one term only, and sign slips when moving terms across an equation.

Wrong quantity: a ratio question asks for one side; a percent question asks for the new price, not the discount. Underline what is asked.
Built-in steps: fuel reserves, round trips, tax on top of a price. The wrong options are what you get when you skip them.
Brackets: 3(x − 4) is 3x − 12, not 3x − 4.
Signs: moving a term across the equals sign changes its sign; subtracting a negative adds.
Units: minutes and hours, inches and feet. Convert before you calculate.
Percent change: divide by the original, not the new value.

Each of these is a habit, not a gap in knowledge, which is why the explanations in our drills name the slip behind each wrong option. When you review a miss, write down which of these it was, and after a week you will see your own pattern.

How should I study for AFOQT math?

Make the rule card, take the free drills, rework every miss by hand, and run a timed set every other day until 70 seconds for a word problem feels comfortable.

The full AFOQT practice test runs both math subtests on their real clocks. The ASVAB Math Knowledge and ASVAB Arithmetic Reasoning pages have extra free drills on the same skills, at a similar level.

Frequently asked questions

Can you use a calculator on the AFOQT?

No. Both math subtests are done by hand.

How many math questions are on the AFOQT?

50: 25 Arithmetic Reasoning in 29 minutes and 25 Math Knowledge in 22 minutes.

What level is AFOQT math?

High-school algebra and geometry, with word problems at a similar level to the ASVAB.

Which math subtest matters most for pilots?

Math Knowledge, which is part of the Pilot composite as well as Quantitative.

Is there a formula sheet on the AFOQT?

No. Learn the area, volume, slope and Pythagorean formulas before the test.

Make math the subtest you are sure of

Four drills per math subtest, eight full AFOQT-style mocks and every answer worked out, in one payment.