The Math/Science Problem-Solving Essay (PSE) is a writing exam where applicants write a response to a Math or Science problem, typically a multi-step word problem, in essay format. Apart from the Student Portrait Sheet (SPS), this is a major component in the admissions process.
Format
- Number of prompts: 1 problem-solving prompt
- Character limit: Maximum of 3,700 characters
- Total time: 30 minutes
- Test format: Computerized exam (typed, not hand-written)
Real Sample Question from the 2021 Admissions Exam
Here is the actual question that appeared on the 2021 TJ Admissions exam:
2021 PSE Problem
You and two friends want to meet up at a location equally distant from each of your homes. One of your friends lives 4 miles north of your home and the other lives 4 miles east.
Determine the best place to meet such that you each travel the same distance to that point.
A third friend will ride her bicycle to your meeting point from her home 4 miles northwest of your home. Assume that you and your first two friends walk at 4 miles per hour.
What speed should the third friend ride to meet the group?
This type of problem tests your ability to:
- Apply geometric concepts (distance, midpoints, coordinate geometry)
- Break down a multi-part problem into logical steps
- Communicate your mathematical reasoning clearly in essay format
What Graders Are Looking For
This essay is intended to help demonstrate your ability to both problem-solve and communicate complex ideas in STEM in a thorough, clear, and concise manner. Your paragraphs should detail:
- Mathematical steps you took
- Assumptions you made and why
- Reasoning that supports your final answer
Critical Insight: The PSE is not all about stating the correct answer. There is a much bigger emphasis on how you explain your steps. A student with a strong explanation but a wrong answer is more likely to be admitted than a student with a correct answer but a weak explanation.
Common Math Topics That Appear
Starting in 2016, TJ introduced the problem-solving essay. Topics have included:
- Pythagorean theorem
- Percent change and ratios
- Midpoint and distance formulas
- Triangle properties
- Rate, time, and distance problems
- Basic algebra and equation solving
In 2021, TJ added "Science" to the name, but the problems have remained fundamentally math-based.
How to Write a Strong PSE Response
- Start with your approach — Briefly explain how you plan to tackle the problem
- Show your work step-by-step — Walk the reader through each calculation
- State your assumptions — If you make any simplifying assumptions, explain them
- Connect steps logically — Use transition phrases like "therefore," "using this result," etc.
- End with a clear answer — Restate your final answer and briefly summarize your reasoning
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