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 slapped the term "science" on it as well. However, the problem given was still fundamentally math-based. A common question we get from students and parents is how to practice the conceptual material behind this.

Often times, 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. In order to best prepare, we recommend reviewing the following concepts and word problems:

Math Topics:

  • Number theory, Set Theory

  • Fractions, ratios, rates proportions,

  • Percentage and Percentage change

  • Exponents and radical operations

  • Arithmetic Series and Sequences (e.g. finding the sum)

  • Geometric sequence (e.g. finding the sum)

  • Population growth or decline

  • Simple and compound interest

  • Direct inverse proportionality

  • Work Problems

  • Speed Time Distance

  • Mixture problems

  • Permutations and combinations

  • Probability (coin problems, deck of cards, marbles in bag)

Science Topics:

  • Experimental Design Diagram and the Scientific Method

  • Identifying variables, controls

  • Compare, extend, modify experiments

  • Reading charts and graphs: histograms, pie charts, scatterplots, etc

  • Translating data into graphs

  • Interpolating and Extrapolating

  • Determining which conclusion is supported by data given

We will be posting good resources and examples for these topics in future blog post. Let us know what you'd like to see next! Email us at

Check out our SPS/Essay course at

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