How the Mathematics Knowledge subtest works
Mathematics Knowledge is the fifth subtest. The CAT-ASVAB gives you 15 scored questions in 31 minutes, a little over 2 minutes each. Unlike Arithmetic Reasoning, most questions are set out as maths rather than as stories: solve an equation, simplify an expression, find an angle, an area or a volume, or work out a probability. Some show a figure.
The official topic list is number theory, numeration, algebraic operations and equations, geometry and measurement, and probability, all at high school level.
It is adaptive and you cannot go back. Besides counting towards your AFQT, it feeds job composites such as the Air Force Administrative score, the Navy BEE composite, where it counts twice, and the Army Clerical line score.
How to solve a Mathematics Knowledge question
Start by working out which kind of question it is, then use its standard move:
- Equation: do the same thing to both sides until the unknown stands alone, then check by putting your answer back in.
- Slow to solve? Test the options instead. Start with a middle value and see whether it is too big or too small.
- Geometry: write down the formula before you put in any numbers, and use the measurements given on the figure.
- Number facts: simplify fractions, powers and roots fully before you compare with the options.
- Probability: favourable outcomes divided by total outcomes. Count both carefully.
Worked example
“A rectangle has a perimeter of 30 inches and a length of 9 inches. What is its area?” A. 54 square inches, B. 81 square inches, C. 108 square inches, D. 189 square inches.
Write the formula first: perimeter = 2 × (length + width). So 30 = 2 × (9 + width), which gives 9 + width = 15 and a width of 6 inches. Area = length × width = 9 × 6 = 54 square inches, option A.
The other options come from common slips. Taking both lengths off the perimeter but forgetting to halve gives a width of 12 and an area of 108. Taking off only one length gives 21 and 189. Treating the shape as a square gives 81.
Tips for the real Mathematics Knowledge subtest
- Learn the core formulas by heart: area and perimeter of rectangles, triangles and circles, the volume of a box and a cylinder, and the Pythagorean theorem.
- Practise fractions, exponents and square roots by hand until they are automatic.
- Know the angle facts: angles on a straight line and in a triangle add up to 180 degrees, and in a four-sided shape to 360.
- Pace at about 2 minutes a question. If one is taking far longer, test the options rather than solving from scratch.
- Treat Mathematics Knowledge and Arithmetic Reasoning as one block of revision: both count towards the AFQT, and both are done by hand.
Practise Mathematics Knowledge on CogniPrep
Our Mathematics Knowledge game gives you 15 adaptive questions with the real 31-minute clock and no calculator, covering number facts, algebra, geometry with figures and probability. Difficulty starts at medium and follows your answers, and anything unanswered when time runs out is scored as a random guess. You see a standard score, where 50 is the average for US 18 to 23 year olds, and the AFQT you would reach if your other three AFQT subtests matched it. The questions and their difficulty are our own, so read the score as a guide.