Math
What the section tests
The PSAT 10 Math section has two 35-minute modules with 22 questions each; a calculator is permitted on the entire section. Questions are multiple-choice or student-produced response (grid-in). The four domains are Algebra (linear equations, inequalities, systems, functions), Advanced Math (quadratic, exponential, polynomial, radical, and rational expressions), Problem-Solving and Data Analysis (ratios, percentages, rates, statistics, probability, tables and graphs), and Geometry and Trigonometry (angles, triangles, circles, area, volume, right-triangle ratios).
Core rules
- Linear models: identify slope as a rate and intercept as a starting value; parallel lines share slope, perpendicular slopes are negative reciprocals.
- Systems: solve by substitution or elimination; a system with no solution has the same slope but different intercepts.
- Quadratics: factored form gives zeros; vertex form gives the maximum or minimum; standard form connects to y-intercept.
- Exponential models: growth/decay factor is 1 ± r; repeated percent change multiplies factors.
- Data: percentages are not additive across successive changes. Use the multiplier product.
- Geometry: keep formulas on hand-area, circumference, Pythagorean theorem, special right triangles, volume-and watch units.
Worked example
A jacket is marked down 20%, then an additional 15% is taken off the sale price. The final price is $54.40. What was the original price? After 20% off, the price is 0.80x. The extra 15% off multiplies by 0.85: 0.80 × 0.85 = 0.68, so 0.68x = 54.40. Divide: x = 80. The original price was $80.
Traps
- Adding 20% + 15% and dividing by 0.65; successive discounts multiply, not add.
- Mixing up radius and diameter, or forgetting to convert units.
- Solving for x but answering a different quantity, such as the discounted price.
- Dropping the negative root of a quadratic when the context allows it, or keeping a root the context rules out.
- Grid-in answers must be entered exactly; no units or commas.