ASVAB Mathematics Knowledge practice

Work through grouping symbols, exponents, multiplication/division, then addition/subtraction. Operations at the same level are processed from left to right.

A negative sign outside a power differs from a negative base inside parentheses: −3² = −9, while (−3)² = 9. For fractions, a common denominator is needed for addition, not for multiplication.

Distribute carefully, combine like terms and perform the same operation on both sides. Substitute your result into the original equation to check it.

For inequalities, reverse the inequality sign when multiplying or dividing both sides by a negative number. When clearing denominators, remember any values the original expression excludes.

For the same nonzero base, multiplying powers adds exponents and dividing powers subtracts them. Raising a power to another power multiplies the exponents.

Factor out a common factor before trying more complicated patterns. The difference of squares is a² − b² = (a − b)(a + b). When a product equals zero, at least one factor must equal zero.

Rectangle area = length × width. Triangle area = 1/2 × base × perpendicular height. Circle area = πr² and circumference = 2πr. The perpendicular height of a triangle need not be one of its sloping sides.

For a right triangle, a² + b² = c², with c opposite the right angle. A rectangular prism has volume length × width × height; a cylinder has volume πr²h. Area uses square units; volume uses cubic units.

On a coordinate plane, slope is change in y divided by change in x. A positive slope rises from left to right; a horizontal line has slope zero. Distinguish a point’s coordinates from a line’s intercepts.

For equally likely outcomes, probability = favorable outcomes ÷ total possible outcomes. Check whether a selection is replaced before a second draw; without replacement, both the counts and the denominator can change.