Worried about the Math or Science Problem-Solving Essay? Study these topics:

Starting in 2016, TJ introduced a problem-solving essay. Every year, this has been primarily math-based on topics ranging from the Pythagorean theorem and percent change to midpoint/distance and triangles. In 2021, they added "Science" to the name, but the problem given was still fundamentally math-based. A common question we get from students and parents is: what topics should I study?

Often, school instruction on the conceptual material needed to succeed is insufficient. Typically, schools emphasize memorization of formulas and numeric answers, instead of application and word problems—which is exactly what the PSE tests.

Math Topics to Master

Based on our analysis of past PSE problems, here are the math concepts you should be comfortable with:

High Priority (Appeared Frequently)

• Percentage and Percentage change — rate increases, discounts, etc.
• Speed, Time, Distance problems — the 2021 PSE was based on this
• Ratios, rates, and proportions
• Coordinate geometry — distance formula, midpoint formula
• Pythagorean theorem and right triangle properties

Medium Priority

• Fractions and operations with fractions
• Exponents and radical operations
• Arithmetic sequences and series (finding sums, patterns)
• Geometric sequences
• Population growth or decline (exponential reasoning)
• Simple and compound interest

Good to Know

• Number theory and set theory
• Direct and inverse proportionality
• Work problems (two people completing a task at different rates)
• Mixture problems
• Permutations and combinations
• Basic probability (coin problems, deck of cards, marbles in a bag)

Science Topics to Review

While science-based PSE problems have been less common, the 2022 exam featured a science problem. Be prepared for:

• Experimental Design — the scientific method, hypothesis formation
• Variables — identifying independent, dependent, and control variables
• Data Analysis — reading and interpreting charts, graphs, histograms, scatterplots
• Drawing Conclusions — determining which conclusion is supported by given data
• Interpolating and Extrapolating — predicting values from trends
• Experimental Modifications — understanding how to improve or extend experiments

How to Study These Topics

Don't just review the formulas—practice applying them:

1. Work through word problems — find practice problems that require you to set up the equation, not just solve it
2. Practice explaining your reasoning — write out your solution steps as if teaching someone else
3. Time yourself — the PSE gives you 30 minutes, so practice under realistic time constraints
4. Get feedback on your writing — the PSE is graded on communication, not just correctness

Pro Tip: After solving a problem, ask yourself: "Could I explain this solution to someone who has never seen the problem?" If the answer is no, practice writing it out more clearly.