SAT Problem-Solving and Data Analysis: what your AP classes already cover

Rates, ratios and percentages, plus data, probability and inference. AP Statistics covers most of the data skills in more depth than the SAT asks for; the percent and rate questions reward careful reading more than new math.

Each row is one SAT Problem-Solving and Data Analysis skill and the AP units on this site where you already practice it. Revisit those notes, then work through the two examples below before opening the answers.

Problem-Solving and Data Analysis skills, matched to AP units

SAT skill	Where it comes up in AP	Why it carries over
Ratios, rates, proportional relationships, and units	AP Calculus AB, Unit 4	Units and rates in context: the same habit as stating units for a derivative in a related-rates answer.
Percentages	AP Precalculus, Unit 2	Percent increase and decrease as a growth factor, the basis of exponential models.
One-variable data: distributions and measures of center and spread	AP Statistics, Unit 1	Center, spread, shape and outliers of one-variable data.
Two-variable data: models and scatterplots	AP Statistics, Unit 5	Scatterplots, lines of best fit and what a model predicts.
Probability and conditional probability	AP Statistics, Unit 2	Two-way tables and conditional probability.
Inference from sample statistics and margin of error	AP Statistics, Unit 3 AP Statistics, Unit 4	What a margin of error means, from confidence intervals for proportions and means.
Evaluating statistical claims: observational studies and experiments	AP Statistics, Unit 1	Random sampling versus random assignment, and which conclusions each one supports.

Worked example 1: Probability and conditional probability

Of the 30 students in a class, 18 take AP Statistics, and 12 of those 18 also take AP Calculus. One student who takes AP Statistics is chosen at random. What is the probability that this student also takes AP Calculus?

Show the answer and working

Answer: \(\frac{2}{3}\)

The condition narrows the group to the 18 AP Statistics students, so the probability is \(\frac{12}{18}=\frac23\). The 30 is not the denominator: that is the most common slip on conditional questions.

Worked example 2: Percentages

A price rises by 20% and then the new price falls by 20%. What is the overall percent change from the original price?

Show the answer and working

Answer: A decrease of 4%

Multiply the factors: \(1.2\times0.8=0.96\), so the final price is \(96\%\) of the original, a \(4\%\) decrease. The two changes do not cancel because the second \(20\%\) is taken of a larger amount.