ASVAB guideSkills
ASVAB Mathematics Knowledge: Algebra and Geometry Explained
Mathematics Knowledge is the high-school math subtest, not the word-problem subtest. Work fractions, signs, order of operations, equations, exponents, and area.
Short answer
Mathematics Knowledge tests high-school math principles. Arithmetic Reasoning tests word problems. Start here with fractions, signed numbers, order of operations, two-step equations, exponents, and the difference between area and perimeter. No official page checked for this guide lists how often each topic appears, so this is a foundation set, not a frequency ranking.
A different job from word problems
The what-to-expect page calls Mathematics Knowledge “knowledge of high school mathematics principles” and Arithmetic Reasoning “ability to solve arithmetic word problems.” If the sentence is the hard part, use Arithmetic Reasoning. If you already know what to find and the fraction or the equation breaks, stay here. The formula reference is the short lookup. You still cannot bring it, or a calculator, into the test.
From a rule to a new example
Signed numbers. The rule: subtracting a negative is adding. Familiar case: 5 − (−2) = 7. New case: −6 − (−4). Rewrite as −6 + 4 = −2. The common wrong answer is −10, from adding the absolute values and keeping the minus.
Fractions. The rule: to add, use a common denominator. Familiar case: 1/4 + 1/4 = 1/2. New case: 1/3 + 1/6. The common denominator is 6. 1/3 = 2/6, so 2/6 + 1/6 = 3/6 = 1/2. Adding the tops and the bottoms to get 2/9 uses a rule that does not exist.
Order of operations. Multiplication and division run left to right before addition. 6 + 8 ÷ 2 × 3 = 6 + 4 × 3 = 6 + 12 = 18. Doing 8 ÷ (2 × 3) first invents parentheses and gets 6 + 8/6, which is not this expression.
Equations. Solve 2(x + 5) = 18. Divide by 2: x + 5 = 9, so x = 4. Check: 2(4 + 5) = 18. The wrong step x + 5 = 18 forgets the factor of 2 and gives x = 13. Then 2(13 + 5) = 36, which is not 18.
Exponents. 2^3 means 2 × 2 × 2 = 8, not 2 × 3 = 6. A square is the exponent 2. 5^2 = 25.
Area and perimeter. A rectangle 7 by 3 has area 7 × 3 = 21 square units and perimeter 2 × (7 + 3) = 20 units. If the question says “area” and you answer 20, you walked the outside instead of covering the inside.
A small repair table
| If the miss looks like this | Work this next |
|---|---|
| The sign flips the wrong way | Three signed additions and subtractions, including a minus-negative |
| The fraction answer is larger than both parts you added | Rebuild the common denominator |
| The equation checks out to the wrong total | Undo the multiplier before the added term, then substitute |
| Area and perimeter trade places | Say the unit out loud: square units or a length |
Practice one clean Mathematics Knowledge item after the repair, with numbers that are not on this page. Do not treat a single item as a topic frequency.
Trust the source
Official sources
Exam policies can change. Use these primary sources for the most current details.