What Kind of Math Is on the ASVAB Test?

Why there are two mathematics parts, not one

They test different things. Arithmetic reasoning is about reading a situation and turning it into a calculation — the arithmetic itself is easy, and nearly every lost point comes from setting the problem up wrong. Mathematics knowledge is about knowing the rule — once you recognize which rule applies, the work takes seconds.

That difference decides how you study. Reasoning improves by doing many word problems and noticing the shapes that repeat. Knowledge improves by learning a short, finite list of rules — which is why it is the part that moves fastest when a test date is close.

Arithmetic Reasoning: what actually comes up

• Rates. Distance, speed and time; work per hour; cost per unit. Two of the three are given and the third is one step away.
• Percentages. Discounts, markups, tax, increase and decrease. The usual trap is working from the wrong starting figure.
• Ratios and proportions. Recipes, mixtures, parts of a whole, scaling a quantity up or down.
• Money in several steps. A few purchases, a total, then change — easy arithmetic with several places to drop a digit.
• Averages. Mean of a short list, and finding a missing value when the average is given.

Worked example. A jacket costs $24 after a 20% discount — what was the original price? Adding 20% back gives $28.80, and that is wrong. The $24 is 80% of the original, so 24 ÷ 0.8 = $30. Percent questions are about identifying the base, every time.

Mathematics Knowledge: the list is short

• Linear equations. Solve for x; do the same thing to both sides.
• Exponents and roots. Multiplying adds the powers, dividing subtracts them, anything to the power zero is 1.
• Factoring. The difference of two squares, and simple quadratics.
• Order of operations. Parentheses, exponents, multiply and divide, then add and subtract.
• Fractions, decimals and percents. Converting between them quickly and without a calculator.
• Angles. A triangle is 180 degrees, a quadrilateral 360; complementary pairs make 90, supplementary pairs 180.
• Area, perimeter and volume. Rectangle, triangle, circle, cube, cylinder.
• The Pythagorean theorem. And the 3-4-5 and 5-12-13 triangles, which appear constantly.
• Basic statistics. Mean and median of a short list.

Worked example. A right triangle has legs of 6 and 8 — how long is the hypotenuse? 6² + 8² = 100, so the answer is 10. That is the 3-4-5 triangle doubled; recognizing it removes the arithmetic entirely.

How far does it go?

The ASVAB program describes mathematics knowledge as "knowledge of high school mathematics principles" and arithmetic reasoning as the ability to solve basic arithmetic word problems. It does not publish a topic-by-topic syllabus, so nobody — this site included — can hand you a definitive list of what is excluded.

What we can tell you is what this bank contains: the topics above, nothing past them, and every question written to close by hand. If a prep site is drilling you on something far outside that range for the ASVAB, ask it where the syllabus came from.

Do the mathematics parts count toward getting in?

Yes, and heavily: two of the four parts that make up the AFQT score are mathematics. The AFQT is what decides whether you can enlist at all, so of the four things that decide it, half are the two described here.

Where to start if mathematics is your weak part

Mathematics knowledge first, because it is a list of rules rather than a skill, and a fortnight of work on it shows up in the score. Then arithmetic reasoning, slowly at first — set the problem up on paper before touching a number, until doing so is automatic. Only then practice against the clock.

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