How Math Knowledge works
Where Arithmetic Reasoning wraps maths in a story, Math Knowledge asks it directly: solve this equation, find this angle, simplify this expression. The Air Force describes it as knowledge of mathematical terms and principles.
Topics include fraction arithmetic, simultaneous equations, factoring, exponents and roots, order of operations, absolute values, proportions, graphs, triangle facts and the Pythagorean theorem. Some questions come with a figure.
It counts towards Quantitative, Academic Aptitude, Pilot, Combat Systems Officer and Air Battle Manager. That makes it the single subtest most worth improving, whatever role you are applying for.
How to approach Math Knowledge questions
There is no formula sheet, so the method starts before test day:
- Know by heart the area and perimeter of rectangles, triangles and circles, the angle sum of a triangle and the Pythagorean theorem.
- For an equation, do the same thing to both sides one step at a time on paper, rather than in your head.
- Check a solved equation by putting the answer back in. It takes five seconds and catches sign errors.
- For a quadratic, look for two numbers that multiply to the constant and add to the middle coefficient.
- Read figures for what they label, not how they look. Work from the numbers given.
Worked examples
“If x² − 5x + 6 = 0 and x > 2, what is x? (A) 1 (B) 2 (C) 3 (D) 5 (E) 6.” Two numbers that multiply to 6 and add to −5 are −2 and −3, so (x − 2)(x − 3) = 0 and x is 2 or 3. Only 3 is greater than 2: C.
“A right triangle has legs of 6 and 8 inches. How long is the hypotenuse? (A) 7 (B) 10 (C) 12 (D) 14 (E) 48.” 6² + 8² = 36 + 64 = 100, and the square root of 100 is 10: B. Option D adds the legs, and E is twice the area.
Tips for the real subtest
- Revise from a high school algebra and geometry book, not just practice questions. The subtest tests principles, so gaps in the basics show.
- Learn the perfect squares to 15² and the primes to 50.
- Practise exponent rules: multiplying powers of the same base adds the exponents, and a negative exponent means a reciprocal.
- Answer every question. There is no penalty, and you cannot get results with a blank.
Practise Math Knowledge on CogniPrep
Our Math Knowledge game gives you 25 questions in 22 minutes with five options each, no calculator and no formula sheet, mixing number theory, fractions and exponents, algebra, geometry with figures, and probability. You can move back and change answers until time runs out. Your result is the number right, with the topics you missed and a comparison with other CogniPrep users, not an AFOQT percentile.