SAT Math · Passport to Advanced Math
Exponential expressions and radicals
Exponent rules, scientific notation, and exponential growth/decay.
What's tested in this subtopic
Items test the laws of exponents (product, quotient, power, negative, fractional), simplifying radicals, and modelling exponential growth and decay using y = a·b^t. Compound-interest and half-life problems are extremely common.
Tactics that actually move your score
Memorize the five exponent rules cold. For growth-versus-decay setup, ask whether the quantity is multiplying by something bigger than 1 (growth) or smaller than 1 (decay) per time period; the base b in y = a·b^t is exactly that multiplier. The single biggest leverage point on most subtopics isn't learning more math — it's recognizing the test's preferred surface forms quickly enough that you don't burn 30 seconds re-reading the question. The first time you see a particular phrasing it might take you a full minute. The tenth time you see it, you should be reaching for your method before you've finished the sentence. Repetition is what builds that recognition. Fifteen problems in a row of the same shape is more useful than fifty mixed.
Practice questions (14)
- Easy A town's population was 60 in 2020 and grew at a constant annual rate of 9% per year. Approximately what was the population 2 years later?
- Easy A town's population was 349 in 2020 and grew at a constant annual rate of 6% per year. Approximately what was the population 4 years later?
- Medium A town's population was 347 in 2020 and grew at a constant annual rate of 8% per year. Approximately what was the population 3 years later?
- Medium A town's population was 102 in 2020 and grew at a constant annual rate of 7% per year. Approximately what was the population 2 years later?
- Medium A town's population was 258 in 2020 and grew at a constant annual rate of 5% per year. Approximately what was the population 2 years later?
- Hard A town's population was 298 in 2020 and grew at a constant annual rate of 12% per year. Approximately what was the population 3 years later?
- Easy A town's population was 477 in 2020 and grew at a constant annual rate of 5% per year. Approximately what was the population 3 years later?
- Easy A town's population was 125 in 2020 and grew at a constant annual rate of 2% per year. Approximately what was the population 4 years later?
- Medium A town's population was 444 in 2020 and grew at a constant annual rate of 11% per year. Approximately what was the population 2 years later?
- Medium A town's population was 259 in 2020 and grew at a constant annual rate of 10% per year. Approximately what was the population 2 years later?
- Medium A town's population was 288 in 2020 and grew at a constant annual rate of 6% per year. Approximately what was the population 3 years later?
- Hard A town's population was 190 in 2020 and grew at a constant annual rate of 11% per year. Approximately what was the population 4 years later?
- Easy A town's population was 98 in 2020 and grew at a constant annual rate of 10% per year. Approximately what was the population 6 years later?
- Easy A town's population was 304 in 2020 and grew at a constant annual rate of 11% per year. Approximately what was the population 4 years later?
How to drill
Work through the questions above untimed. After each one, read the worked solution from start to finish — even when you got it right. Note which solution method you used, and which method we used; if they differ, ask yourself which would have been faster on test day. Speed in SAT math comes from shortening your method-selection step, not from doing arithmetic faster. Most fast students are doing the same arithmetic everyone else is — they're just spending less time deciding what to do.
Once you can clear the easy and medium items in this subtopic at 90% accuracy, attempt a timed mini-set of ten hard items at 75 seconds each. If you finish in time and score 7+ correct, you've effectively mastered the subtopic for test purposes and can move on.