Ready for the PSE? A genuine guide to acing the Problem-Solving Essay

TJ-Prep Team
Nov 14
4 min read

No gimmicks. No “write this many fancy words.” Just preparation that works.

What the PSE really is

The PSE is not a typical essay about your life or your opinions. According to preparation guides, it’s a timed writing task in which the student is given a math/science/logic word problem, must reason through multiple steps, show assumptions, explain their thought process, and communicate clearly.

Example prompts have included:

A helicopter-boat problem (fuel, speed, distance) from 2016.
A 2022 genetics/Punnett-square prompt.
A 2024 prompt about driving speed, kilometers-to-miles conversion, and risk assessment.

What emerges from these is a consistent pattern:

Multi-step problem requiring combinations of rates, conversions, geometry, or combinatorics, or scientific reasoning.
Emphasis on the explanation of reasoning, not just the correct numeric answer. (“A strong explanation but a wrong answer” may beat “correct answer but weak explanation.”)
Strict time limit (often ~30 minutes) and typed format, meaning clarity and structure are crucial.

Hence, you must prepare content knowledge + problem-solving mindset + writing clarity under time pressure.

What types of problems to expect — the problem pool

Here are categories you’ll want to train in, based on past prompts and prep-course outlines:

Rates, distance, time, fuel/consumption
– e.g., helicopter problem, driver speed/stop problems.
Sequences / growth / decay / population models
– e.g., penguin population prompt.
Geometry / stairs / rise / tread / measurement constraints
– e.g., stairway design problem 2018.
Conversions / units / multi-step realism
– e.g., miles ↔ kilometers, time breaks, thresholds.
Probability / statistics / data interpretation (less common)
– e.g., probability of genetic trait inheritance)
Scientific reasoning / physics / chemistry / biology
– The 2022 genetics prompt; other modules list “Physical Science: chemistry, physics, earth science, astronomy” as practice sets.

Bottom Line: Preparation must span algebraic reasoning, logic & explanation, geometric/spatial reasoning, conversions/units, and clear communication.

How to prepare: Four-phase structure

Phase 1: Build your reasoning toolbox

Review key math and science topics: rates, work problems, geometry, conversions, sequences, basic statistics.
Use problems outside TJ context (e.g., math competition-style) to strengthen reasoning, not for essay writing yet.
Make sure you understand the steps, not just memorize formulae. Because the essay asks for an explanation of “how you thought,” not just “what you got.”

Phase 2: Practice explanation & structure

Pick practice prompts (retired ones help) and write the entire response in essay form, under timed conditions (30 minutes).
Focus on: (1) clearly stating assumptions, (2) showing reasoning steps, (3) explaining decisions (“why I chose this route”), (4) concluding with insight (“Given this, the best strategy is ___ because ___”).
Example: The 2024 prompt included a “Do you think this method of monitoring driving is effective? Why or why not? Explain.” That extra question demands analysis, not just calculation.

Phase 3: Simulate the test environment

Use a device (typed exam format) with no calculator or minimal assistance—as many prep guides say the PSE is “computerized exam (typed, not hand-written).”
Set exactly 30 minutes or whatever the official time is for your application cycle.
After each timed attempt, review: Did you start by restating the problem? Did you include a diagram or model (if helpful)? Did you visibly show your reasoning? Did you check units, conversions, and assumptions?

Phase 4: Feedback and refinement

Get a mentor, teacher, or peer to read your essay with a lens: “Does the reasoning flow? Are assumptions stated? Is the explanation clear?”
Track common weaknesses: skipping explanation, leaps in logic, vague assumptions, unit mistakes, or weak concluding insight.
Keep a log of “my errors” across 5-10 timed essays and aim to reduce those.

Time-limit strategy: 30-minute game plan

Minute 0-2: Read prompt twice. Underline keywords (“distance,” “fuel,” “rate,” “conversion,” “assess effectiveness”).

Minute 2-5: Sketch model/diagram (optional but helpful). Define variables. Write assumptions.

Minute 5-20: Do calculations/reasoning. Write an explanation alongside each step (e.g., “Assume the helicopter travels at full speed because…”).

Minute 20-25: Write the essay response formally:

Introduction (problem restatement + plan)
Body (step-by-step reasoning, with clear headings if needed)
Conclusion (numeric answer + justification + insight)

Minute 25-28: Review: Check units, label conversions, ensure every step has an explanation

Minute 28-30: Final polish: Remove dangling sentences, fix grammar, and make sure it reads clearly.

What they’re really evaluating

Clarity of thought: Can the student explain how they got there, not just what they got? (Emphasized in prep sources.) ,
Reasoning depth: Assumptions, alternatives, and why one path was chosen.
Communication: Flow, readability, correct units/formats, minimal ambiguity.
Scientific/mathematical accuracy: At a competent level—not necessarily competition-grade complexity—but correct logic.
Reflection in conclusion: It’s a math/science problem plus “so what?” Why does your answer matter or how realistic is it? Several prompts include evaluation questions.

Final word to parents

The PSE isn’t about being a math wizard; it’s about being a clear thinker who can reason, explain, and reflect within a time constraint. If you hear a program selling “tricks to get the answer in 10 seconds,” beware—it often ignores the explanation step, which is what TJHSST weighs heavily.

Help your child build the thinking muscle first, then practice the writing structure. Over time, they’ll move from “I know the math” → “I can explain what I did” → “I can do it under time pressure and write it clearly.” That is how you turn the PSE from a hurdle into a bridge.