See What the Test Looks Like
Sample questions from our AFOQT Math Knowledge practice tests. Each question comes with a detailed explanation so you understand the reasoning, not just the answer.
25 questions in 22 minutes. Master math concepts and boost your Quantitative, Pilot, CSO, and Academic Aptitude composite scores.
The Math Knowledge subtest presents 25 pure math concept questions in 22 minutes (~53 seconds each). Unlike Arithmetic Reasoning, there are no word problems — questions test algebra, geometry, and number theory directly. It feeds into four composites: Quantitative, Pilot, CSO, and Academic Aptitude, making it one of the highest-impact AFOQT subtests.
Sample questions from our AFOQT Math Knowledge practice tests. Each question comes with a detailed explanation so you understand the reasoning, not just the answer.
Math Knowledge tests your understanding of mathematical concepts, principles, and formulas. Questions are presented as straightforward math problems rather than real-world word problems. You'll solve equations, calculate geometric properties, and apply number theory.
The difficulty ranges from basic algebra to intermediate topics. You need to recall formulas from memory since no reference sheet is provided. The test rewards candidates who have a solid foundation in high school math.
This subtest is especially important because it contributes to four composites, including the Pilot composite, the CSO composite, the Quantitative composite, and the Academic Aptitude composite.
| Questions | 25 |
| Time Limit | 22 minutes |
| Time per Question | ~53 seconds |
| Format | Paper-based, multiple choice (5 options) |
| Calculator | Not allowed |
| Composite Scores | Quantitative, Pilot, CSO, Academic Aptitude |
The AFOQT Math Knowledge subtest covers these core areas.
Solving linear and quadratic equations, inequalities, systems of equations, exponent rules, radicals, factoring polynomials, and functions.
Area, perimeter, and volume of shapes. Angle relationships, parallel lines, triangles (including Pythagorean theorem), circles, and coordinate geometry.
Factors, multiples, prime numbers, greatest common factor (GCF), least common multiple (LCM), order of operations, and absolute value.
Operations with fractions, converting between fractions/decimals/percentages, comparing fractions, and mixed numbers.
Basic probability calculations, permutations, combinations, mean/median/mode, and interpreting data sets.
Arithmetic and geometric sequences, finding the nth term, and recognizing number patterns.
Pilot Composite: Math Knowledge + Table Reading + Instrument Comprehension + Aviation Information
CSO Composite: Math Knowledge + Table Reading + Block Counting + Word Knowledge + Reading Comprehension
Quantitative Composite: Arithmetic Reasoning + Math Knowledge
Academic Aptitude Composite: Verbal Analogies + Arithmetic Reasoning + Word Knowledge + Math Knowledge + Reading Comprehension + Physical Science
Math Knowledge is one of the most impactful subtests on the AFOQT. See the full composite breakdown on the AFOQT guide.
No formula sheet is provided. Commit area, volume, Pythagorean theorem, quadratic formula, and common conversions to memory before test day.
Plug answer choices back into the equation to see which one works. This is often faster than solving complex equations from scratch, especially with quadratics.
Exponent questions appear frequently. Master rules like x^a × x^b = x^(a+b), (x^a)^b = x^(ab), and x^0 = 1. Same for square root simplification.
Sketch the shape described in the question. Label the given measurements. Visual representation makes it much easier to identify the right formula and solve.
At 53 seconds per question, many problems are designed to be solved in under a minute. If you find yourself doing extensive multi-step work, reconsider your approach.
Math Knowledge is one of 12 AFOQT subtests. You have 25 questions and 22 minutes to solve math concept problems covering algebra, geometry, number theory, and probability. It contributes to four composite scores: Quantitative, Pilot, CSO, and Academic Aptitude.
With 25 questions in 22 minutes, you have approximately 53 seconds per question. The questions are more direct than Arithmetic Reasoning word problems, but you still need to work efficiently without a calculator.
Yes. Math Knowledge is one of the four subtests in the Pilot composite, along with Table Reading, Instrument Comprehension, and Aviation Information. It also contributes to Quantitative, CSO, and Academic Aptitude composites.
Review high school algebra (equations, inequalities, exponents) and geometry (area, volume, angles, Pythagorean theorem). Memorize key formulas since no reference sheet is provided. Practice solving problems without a calculator.
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