After analyzing hundreds of SHSAT practice sessions from New York City students, the same pattern appears again and again.
It's not the hardest problems that separate high scorers from the rest on the Specialized High School Admissions Test. It's mastery of five very specific math topics that appear reliably across every version of the test. Students who have drilled these five topics correctly outscore equally capable students who haven't — by 30, 40, sometimes 60 points.
Here's what those topics are, why each one is hard, and what the actual error looks like.
1. Ratios and Proportions
Ratio problems appear on every version of the SHSAT. They show up in straightforward form ("the ratio of boys to girls is 3:5, there are 40 students — how many girls?") and in disguised form, embedded in multi-step word problems where the ratio relationship isn't obvious until you're halfway through.
The most common error: Setting up the ratio backwards. Students frequently invert the relationship — writing boys/girls when the problem calls for girls/boys — and get an answer that's in the answer choices (because the test anticipates this error) but wrong.
How to fix it: Practice ratio problems in two specific forms — direct ratio setup and cross-multiplication — until the setup step is automatic. Then practice identifying ratio relationships in word problems where the word "ratio" doesn't appear.
2. Percentages and Percent Change
Percent questions on the SHSAT range from basic ("what is 30% of 80?") to percent change, percent of a percent, and reverse percentage problems ("after a 20% increase, the price is $84 — what was the original price?").
The most common error: Applying a percentage to the wrong base. In percent change problems, students frequently calculate the percentage of the new value instead of the original value. This is a one-step error that's easy to make under time pressure and very hard to catch without specifically practicing it.
How to fix it: Practice reverse percentage problems until the instinct to identify "percent of what?" becomes automatic before doing any calculation.
3. Multi-Step Word Problems
The SHSAT math section includes word problems that require 3–5 separate steps to solve. Many of these problems look straightforward in the first sentence and reveal their complexity only midway through.
The most common error: Stopping at the intermediate answer. The test is designed to place intermediate values in the answer choices. A student who gets to "the answer is 12" and sees 12 as an option will frequently circle it — even if the question was asking for something that required one more step.
How to fix it: Practice reading the last sentence of every word problem before starting the calculation. The last sentence tells you what the final answer actually needs to be. This prevents the "stopped too early" error that accounts for a surprising number of lost points on the Specialized High School Admissions Test.
4. Probability and Statistics
Probability is one of the highest-frequency topics on the SHSAT that students are almost never prepared for. Most NYC middle schoolers haven't covered probability deeply in school by the time they take the Specialized High School Admissions Test.
The most common error: Confusing "probability of A and B" with "probability of A or B." These require different operations (multiply vs. add), and the difference is easy to miss when you're working quickly.
How to fix it: Practice probability problems in isolated sessions focused entirely on setting up the problem correctly before doing any arithmetic. The calculation is easy once the setup is right. The setup is where students lose points.
5. Grid-In and Digital Input Problems (Free Response)
The SHSAT math section includes free-response questions where students enter their own answer rather than selecting from multiple choice. On the paper version of the test, these were "grid-in" problems filled in on a numbered bubble grid. On the digital SHSAT that launched Fall 2025, these are now typed directly into an answer field.
The Fall 2026 adaptive format also introduces new Technology-Enhanced Item (TEI) math types: graphing questions where students plot points or lines on a coordinate plane, ordering questions where values must be dragged into sequence, and multipart problems where earlier answers feed into later parts.
The most common error on digital free-response: Students who only practiced paper-based grid-in problems are slow on the digital input — they're used to filling bubbles, not typing. Under time pressure, that hesitation costs real seconds per question. On TEI graphing questions, students who have never practiced on a screen frequently misclick the coordinate grid and submit wrong answers they would have gotten right on paper.
How to fix it: Practice free-response math on a screen, not just on paper. For the Fall 2026 adaptive test specifically, make sure your child has seen and practiced the graphing and ordering input formats before test day — because encountering them for the first time during the actual exam is an avoidable disadvantage.
The Common Thread
Each of these five topics has a specific, predictable error pattern. The students who score highest on the SHSAT aren't avoiding these topics — they're making the same mistakes everyone else makes during practice, then correcting them with enough repetition that the correct approach becomes automatic.
That's the whole game. Not finding new topics to study. Fixing the specific errors in the topics that matter most.
Focus your child's prep time on these five, drill each one until the error pattern stops repeating, and the SHSAT math score will reflect the work.