Mathematics: Percents, Algebra, Geometry, and Data
Number and operation fluency
Expect fractions, decimals, percents, ratios, proportions, and signed-number arithmetic, often embedded in word problems. Convert everything to one form before computing. A percent is a fraction over 100, 'of' means multiply, and percent change is (new − old) ÷ old - dividing by the original rather than the new value is the most common error. Consecutive percent changes do not add: a 20% increase followed by a 20% decrease leaves 96% of the original, not 100%.
Algebra and geometry
Solve linear equations by undoing operations in reverse order, and distribute carefully - a minus sign before parentheses flips every interior sign. Know slope as rise over run, slope–intercept form, and how to substitute a point to check an equation. Keep geometry formulas straight: area versus perimeter, triangle area = ½bh, circle area = πr² versus circumference = 2πr, and the Pythagorean theorem for right triangles only. Watch units: convert before computing, then label the answer.
Data and probability
Know mean, median, mode, and range, and read graphs by checking axis labels and scale. Probability of a single event is favorable outcomes over total outcomes; for independent events, multiply the probabilities.
Worked example
A jacket is marked down 25%, then the sale price is reduced another 10%. Final price = 0.75 × 0.90 = 0.675 of the original, a 32.5% total discount, not 35%. Rule of thumb: chain percent changes by multiplying multipliers.