Math: Problem Solving, Algebra, and Quantitative Reasoning
PSAT 8/9 Math emphasizes linear relationships, proportional reasoning, data interpretation, and multi-step word problems, with some geometry and basic statistics. Most errors come from setup, not arithmetic, so translate words into equations deliberately.
For word problems, define the variable in writing (for example, let x = number of adult tickets) and identify the fixed amount versus the rate. A common trap is confusing a one-time fee with a per-unit cost, or reversing the slope and intercept. In linear models, slope is the change per unit and the intercept is the starting value when the input is zero.
For proportions and percents, set up a ratio with matching units in the same positions. Percent change is (new - old) / old; a 20% increase followed by a 20% decrease does not return to the original value. When a question asks for a rate, check whether the answer needs units per one item.
Data questions often show a table or described set. Distinguish mean from median: the mean is sensitive to outliers, while the median is the middle value of an ordered list. For probability, count favorable outcomes over total outcomes, and remember that probabilities of complementary events sum to 1.
Geometry questions usually need area, perimeter, volume, or angle relationships. Know that angles on a straight line sum to 180 degrees and that vertical angles are equal.
Worked example: A gym charges a $30 joining fee plus $15 per month. The total cost after m months is 30 + 15m. After 6 months: 30 + 90 = $120. If a question instead gives the total and asks for months, subtract the fee first, then divide: (120 - 30) / 15 = 6.