Chapter 4 of 813% of exam

Mathematics Knowledge

Mathematics Knowledge tests your understanding of mathematical concepts and principles, including algebra and geometry. Unlike Arithmetic Reasoning, these questions focus on the math itself rather than word problems. This subtest also contributes to the AFQT score. Mastering formulas, algebraic manipulation, and geometric relationships is the path to a strong score.

Number Properties and Operations

A solid grasp of how numbers behave underlies all higher math. This includes order of operations, exponents, roots, and factors.

Follow order of operations

Evaluate parentheses, then exponents, then multiplication and division, then addition and subtraction.

Use exponents correctly

An exponent tells how many times to multiply the base by itself, so 3 cubed is 3 times 3 times 3.

Understand square roots

The square root of a number is the value that multiplied by itself gives that number.

Know factors and multiples

A factor divides a number evenly, while a multiple is the product of that number and a whole number.

Algebraic Expressions and Equations

Algebra uses letters to stand for unknown values. Solving equations means isolating the variable using inverse operations.

Combine like terms

Add or subtract only terms that share the same variable, so 3x plus 2x equals 5x.

Isolate the variable

Perform the same inverse operation on both sides to get the variable alone.

Check by substitution

Put your solution back into the original equation to confirm it is correct.

Handle negative numbers

Track signs carefully, remembering that subtracting a negative is the same as adding.

Geometry Basics

Geometry questions cover shapes, angles, area, perimeter, and volume. Knowing the key formulas and angle rules is essential.

Sum of triangle angles

The interior angles of any triangle always add up to 180 degrees.

Area of a triangle

Area equals one half times base times height, so remember the one-half factor.

Circle formulas

Circumference equals 2 times pi times the radius, and area equals pi times the radius squared.

Perimeter and volume

Perimeter is the distance around a shape, while volume of a cube is the edge length cubed.

Working with Formulas

Many questions simply require plugging values into a known formula. Memorizing and applying formulas accurately saves time.

Memorize core formulas

Know the common area, perimeter, and volume formulas cold so you can apply them quickly.

Substitute carefully

Replace each variable with its given value, keeping units and signs correct.

Rearrange when needed

Solve a formula for a different variable by applying inverse operations.

Estimate the result

Judge whether your computed answer is reasonable for the size of the shape or numbers involved.

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Last updated: November 2026

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