Mathematics Knowledge is described by the ASVAB program as knowledge of high school mathematics principles. On the computer form it is 15 scored questions in 31 minutes — about two minutes each, and most questions take well under that once the rule is known.
The list is short
- Solving linear equations — isolate the variable; do the same thing to both sides.
- Exponents — multiplying adds the powers, dividing subtracts them, a power of a power multiplies them, anything to the zero is 1.
- Factoring — the difference of two squares and simple quadratics cover nearly all of it.
- Order of operations — parentheses, exponents, multiply and divide, then add and subtract.
- 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 that appear again and again.
Ten worked examples
1. If 3x + 7 = 22, what is x?
Subtract 7: 3x = 15. Divide by 3: x = 5.
2. Simplify 5(x + 3) − 2x.
Distribute before combining: 5x + 15 − 2x = 3x + 15. The 15 is not touched by the −2x.
3. What is the area of a circle of radius 5?
Area is pi times the radius squared: pi × 25 = 25 pi. Square the radius, not the whole expression.
4. Simplify (x^3)(x^4).
Same base, multiplication, so add the exponents: x^7. Not x^12 — that is what happens when a power is raised to a power.
5. A right triangle has legs of 6 and 8. How long is the hypotenuse?
6² + 8² = 36 + 64 = 100, and the square root of 100 is 10. This is the 3-4-5 triangle doubled; recognizing it saves the arithmetic.
6. Factor x² − 9.
A difference of two squares: (x − 3)(x + 3). Whenever you see a square minus a square, this is the answer shape.
7. Two angles are supplementary and one is 110 degrees. What is the other?
180 − 110 = 70 degrees. Supplementary makes a straight line; complementary makes a right angle.
8. Simplify 4 + 3 × (8 − 6).
Parentheses first: 8 − 6 = 2. Then multiply: 3 × 2 = 6. Then add: 10. Working strictly left to right gives 14 and is the single most common slip on this subtest.
9. The radius of a circle is doubled. What happens to the area?
Area depends on the radius squared, so it becomes four times as large. Doubling a linear measure multiplies area by 4 and volume by 8.
10. Solve x² − 5x + 6 = 0.
Find two numbers that multiply to 6 and add to −5: −2 and −3. So (x − 2)(x − 3) = 0 and x is 2 or 3.
This is where a fortnight of work shows up in the score. Vocabulary takes months to move and reading comprehension is largely a habit, but the list above is finite — and every question on the subtest is an application of something on it.
How the questions are written here
Everything is in plain text: fractions as 3/4, powers as x^2, roots spelled out. That is deliberate — the same question has to read correctly in the practice test, the study guide and the timed exam. Ninety questions, each with the working shown rather than just the answer.
Ninety mathematics knowledge questions
Each with the rule it tests and the working written out. First five free, no account.