Mathematics: Arithmetic, Algebra, and Quantitative Reasoning
The Mathematics section tests arithmetic fluency, algebraic manipulation, ratio and proportion, percentages, geometry, and data interpretation under time pressure. Prioritize the high-frequency skills: solving linear equations and inequalities, factoring and expanding, working with exponents and roots, and translating word problems into equations. For percentages, remember that a percent increase then decrease of the same rate does not return to the original value. For ratios, set up a proportion with matching units and cross-multiply. In geometry, memorize area, circumference, and the Pythagorean theorem, and recognize similar triangles (equal angles → proportional sides).
Traps to watch
- Unit mismatches (minutes vs. hours, cm vs. m) - convert before computing.
- "Percent of" vs. "percent more than" - these differ.
- Average problems: the sum equals average × count; use this to find missing values.
- Inequalities: multiplying or dividing by a negative flips the sign.
Worked example
A shirt costs $80, is discounted 25%, then taxed 10%. Discounted price = 80 × 0.75 = $60. Final = 60 × 1.10 = $66. Rule of thumb: apply successive percent changes as multipliers (0.75 × 1.10 = 0.825), never by adding percentages.