SAT Math — percentage points, compound growth and multi-step percents

Percentages are their own skill in the SAT Math domain of Problem-Solving and Data Analysis. College Board's description asks students to use percentages in many contexts, including discounts, interest, taxes and tips, and increases and decreases of many kinds, and to understand the link between a percent change and a growth factor (5 percent and 1.05), including percentages of 100 percent or more. Single discounts and simple reverse percents are the easy end of that list. This material works on the multi-step end, the kind of problem that often appears as a student-produced response, where no answer choices hint at the method.

The first questions separate two ideas that are easy to blur. A tax rate of 5 percent raised by 20 percent becomes 6 percent, not 25 percent: a percent change is not a change in percentage points. Two schools of different sizes with 42 and 36 percent support do not average to 39 percent; the counts have to be combined. Then come relations stated purely in percents, such as 30 percent of x equals 45 percent of y, and an increase of 150 percent, where the new amount is two and a half times the old one.

The middle of the set is about repeated percent change, which is exponential growth and decay in disguise. You compound interest for three years, find what share of a van's value remains after four years of 15 percent losses, turn a monthly growth rate of 2 percent into a yearly one, and read the two-year change in an exponential model. In each case the wrong answers come from adding percents instead of multiplying factors, and the explanations show how large that error becomes.

The last questions chain several steps in everyday money settings, with amounts written in words as the test does in context: the decrease that undoes a 30 percent increase, a restaurant bill with tax and a tip on the pre-tax amount, a jacket marked up 60 percent and then sold at 25 percent off, and a city that grew from 12,000 to 14,520 residents in two years at a constant rate.

The flashcards collect the tools behind all of this: percent change, percentage points, growth and decay factors, multiplying successive changes, undoing an increase, compound growth, combining groups and solving for a constant rate.

A calculator is welcome, as it is throughout the digital SAT Math section. The material offers a quiz and flashcards. It is independent practice; the situations are invented and no question is taken from any published test.

• Distinguish a percent change from a change in percentage points
• Combine percents from groups of different sizes by converting them to counts
• Use growth and decay factors, including increases of 100 percent or more
• Compute compound growth and decay over several periods and convert a monthly rate to a yearly one
• Find the percent decrease that undoes an increase and chain several percent changes
• Solve for a constant percent rate from two values and relate p percent of x to q percent of y

Practice material written by Zestly, based on the SAT Math skill "Percentages" in the Problem-Solving and Data Analysis domain, as described in College Board's Assessment Framework for the Digital SAT Suite (version 3.01, August 2024, Appendix B). All data sets and situations are invented. Zestly is not affiliated with College Board.