While there might be open-ended questions on other sections of the PCAT, the math section is entirely in multiple-choice format. On the SAT, however, some questions are multiple choice, but others are in a response format, where students write out their answer to a question. In total, the math section of the SAT takes 70 minutes, including one 20-minute section and two 25-minute sections. In total, students answer 44 multiple choice questions and 10 open responses. The PCAT allows 40 minutes for students to complete 48 multiple-choice math questions.
The SAT and the PCAT are very similar in their focus on algebra. Students should have a thorough understanding of rational numbers, quadratic equations, inequalities, and radicals in equations. While the PCAT does not include a section on geometry, basic geometry concepts may be useful for answering algebra and calculus questions. For the SAT, however, students should know extensive geometry, like the calculation of areas, the Pythagorean Theorem, slopes and volumes.
Both the SAT and the PCAT include a significant amount of content about probability and statistics. In general, the statistical content in the two exams is similar, though the PCAT goes above and beyond what is covered by the SAT. Both, for example, require an understanding of central tendencies -- mean, median and mode -- graphs, tables, and probability. While the SAT does not test variation, the PCAT does include this topic.
Not all high school students take precalculus and the SAT does not include any content on this subject. The PCAT, however, devotes an entire section to precalculus. PCAT test-takers should understand logarithmic and exponential functions. Students should also have a close understanding of complex numbers and how to add vectors graphically and algebraically.
The SAT does not include calculus, but the PCAT devotes an entire section to it. Students should be prepared to calculate limits and show knowledge of continuous and discontinuous functions. Most importantly, PCAT students should be able to fluently use the properties of both derivatives and integrals. For derivatives, students should know how to use the sum and product rule, the power rule and the mean value theorem. For integrals, students should understand antiderivatives and how to use sigma notation.