SHSAT Math: The 22 Topics Actually Tested, Ranked by Frequency

The SHSAT math section has 57 questions. Not all topics carry equal weight. Some appear on every test. Others show up once or twice. If you study everything equally, you are wasting time on low-frequency topics while under-preparing for the ones that actually determine your score.

We analyzed over 1,100 mock exam questions across 10 full-length practice tests and mapped them against the DOE's published content specifications. Here is exactly what is tested, how often it appears, and what difficulty level to expect.

In 2025, 25,933 students sat for the SHSAT and only 4,023 earned offers - a 15.5% acceptance rate. The math section is where most students have the greatest opportunity to gain points quickly, because math skills respond to targeted practice faster than reading comprehension does.

What Are the 22 Math Subtopics on the SHSAT?

The SHSAT math section covers 22 subtopics organized into six domains. Here is the complete list:

Number System (5 subtopics)

1. Fractions and Decimals
2. Integers and Absolute Value
3. Order of Operations
4. Number Properties (primes, factors, multiples)
5. Exponents and Roots

Algebra (6 subtopics)

1. Linear Equations (one variable)
2. Linear Equations (two variables)
3. Inequalities
4. Systems of Equations
5. Expressions and Simplification
6. Patterns and Sequences

Geometry (4 subtopics)

1. Angles and Lines
2. Triangles
3. Circles
4. Area, Perimeter, and Volume

Ratios and Proportions (4 subtopics)

1. Ratios
2. Proportions
3. Rates
4. Percents

Statistics and Probability (4 subtopics)

1. Data Interpretation (tables, charts, graphs)
2. Mean, Median, Mode
3. Probability and Counting

Word Problems

Word problems are not a separate domain on the DOE content spec. They cut across every domain above. But they deserve special attention because they represent the single most common question format on the test. A "word problem" in SHSAT terms means any question where you translate a real-world scenario into math before solving. These include arithmetic word problems, algebraic word problems, and rate/ratio word problems.

Which Topics Appear Most Often?

Based on our analysis of mock exam data and historical test patterns, here is how the 22 topics rank by frequency:

| Priority | Topic | Approximate Frequency | Domain | |---|---|---|---| | High | Word Problems (arithmetic) | Very High | Cross-domain | | High | Word Problems (algebraic) | Very High | Cross-domain | | High | Linear Equations (one variable) | High | Algebra | | High | Fractions and Decimals | High | Number System | | High | Ratios and Proportions | High | Ratios | | High | Percents | High | Ratios | | High | Data Interpretation | High | Statistics | | Medium | Expressions and Simplification | Medium | Algebra | | Medium | Area, Perimeter, and Volume | Medium | Geometry | | Medium | Angles and Lines | Medium | Geometry | | Medium | Rates | Medium | Ratios | | Medium | Inequalities | Medium | Algebra | | Medium | Integers and Absolute Value | Medium | Number System | | Medium | Triangles | Medium | Geometry | | Medium | Mean, Median, Mode | Medium | Statistics | | Low | Linear Equations (two variables) | Low-Medium | Algebra | | Low | Systems of Equations | Low | Algebra | | Low | Exponents and Roots | Low | Number System | | Low | Circles | Low | Geometry | | Low | Probability and Counting | Low | Statistics | | Low | Number Properties | Low | Number System | | Low | Patterns and Sequences | Low | Algebra | | Low | Order of Operations | Low | Number System |

The takeaway: word problems, linear equations, fractions/decimals, and ratios/percents make up the bulk of the test. Master those four areas and you have covered more than half of the 57 questions.

What Does the Difficulty Breakdown Look Like?

From our database of 1,140 math mock exam questions, here is how difficulty distributes:

| Difficulty Level | Question Count | Percentage | Description | |---|---|---|---| | Level 2 (Standard) | 396 | 35% | Core skills, straightforward application | | Level 3 (Challenging) | 644 | 57% | Multi-step problems, requires strategy | | Level 4 (Advanced) | 100 | 9% | Complex reasoning, highest difficulty |

Most of the test falls in the "challenging" range: problems that require two or three steps and some strategic thinking. Only about 9% of questions hit the advanced tier. This means the test rewards solid fundamentals applied carefully, not obscure mathematical knowledge.

Students who nail Level 2 and most of Level 3 are scoring in the range needed for Brooklyn Tech (505 cutoff) or Bronx Science (518 cutoff). Stuyvesant's 556 cutoff demands consistency across all levels, including most Level 4 questions.

What Is the 80/20 Rule for SHSAT Math?

If you are short on study time, focus on these five areas:

1. Word Problems (all types): The single largest category. If you can translate English into equations, you gain more points than from any other skill.
2. Linear Equations: Appears in pure algebra form and embedded within word problems. Being fast and accurate with one-variable equations is non-negotiable.
3. Fractions and Decimals: Operations with fractions show up in their own questions and within nearly every other topic. Weak fraction skills create errors everywhere.
4. Ratios, Proportions, and Percents: These three subtopics are closely related and collectively represent a large portion of the test. Ratio tables and cross-multiplication are essential tools.
5. Data Interpretation: Reading tables, bar graphs, and line charts accurately. These questions test whether you can extract the right number before doing any math.

Mastering these five areas covers approximately 60% of the math section. That is the 80/20 rule in action: focused effort on high-frequency topics yields disproportionate score gains.

How Do Grid-In Questions Differ from Multiple Choice?

The SHSAT includes approximately 5 grid-in questions per math section. These require you to type a numerical answer rather than selecting from options.

Grid-ins are disproportionately important for two reasons:

First, there are no answer choices to sanity-check against. On a multiple-choice question, if your answer does not match any option, you know to re-solve. Grid-ins offer no such safety net. You compute an answer, type it in, and move on. If you made an arithmetic error, nothing flags it.

Second, grid-ins tend to cover specific topics. They frequently involve:

• Computing a specific numerical value from a word problem
• Solving an equation for a variable
• Calculating area, perimeter, or volume
• Finding a mean, median, or probability expressed as a decimal

The fix is simple but requires discipline: after solving a grid-in, re-read the question and verify you answered what was actually asked. The most common grid-in error is solving for x when the question asks for x + 5, or finding the area when the question asks for the perimeter.

What Are the Most Common Math Traps on the SHSAT?

Experienced test-takers lose points not because they lack knowledge but because they fall for predictable traps. Here are the ones that show up repeatedly:

The "Solve for the Wrong Thing" Trap

The question asks: "What is the value of 3x - 2 if x = 4?" You solve and get x = 4, then select 4 as your answer. The actual answer is 3(4) - 2 = 10. This trap is especially deadly on grid-in questions.

The Graph Scale Trap

A bar graph shows sales data, but the y-axis starts at 50 instead of 0. Students who glance at bar heights without reading the axis labels misread the actual values. Always check where the axis starts and what each grid line represents.

The Unit Trap

"If a train travels 180 miles in 3 hours, what is its speed in miles per minute?" Students calculate 60 mph and select it, missing the "per minute" specification. The answer is 1 mile per minute. Always circle the unit the question asks for.

The Percent Trap

"The price increased by 20%, then decreased by 20%. Is the final price the same as the original?" No. A 20% increase on $100 gives $120. A 20% decrease on $120 gives $96. Students who think "up 20, down 20 = no change" lose this point every time.

The "Not" and "Except" Trap

"Which of the following is NOT a solution?" Your brain finds a solution and selects it. Re-read questions with negative qualifiers. Underline "NOT" or "EXCEPT" to keep yourself honest.

How Should You Build a Study Plan by Topic?

Here is a practical framework based on the priority table above:

Weeks 1-4: High-Priority Foundation

• Word problems: 30 minutes daily
• Linear equations: practice until solving feels automatic
• Fractions and decimals: operations, conversions, comparison
• Ratios and percents: cross-multiplication, percent change

Weeks 5-8: Medium-Priority Expansion

• Geometry basics: angle relationships, triangle properties, area formulas
• Data interpretation: practice reading complex tables and graphs
• Expressions and inequalities: simplification, solving, graphing on number lines
• Statistics: mean, median, mode calculations

Weeks 9-12: Low-Priority and Review

• Systems of equations: substitution and elimination methods
• Circles, probability, patterns: cover the basics, do not over-invest
• Full-length mock exams: simulate test conditions
• Targeted review: go back to any topic where mock exam accuracy is below 70%

This is a 12-week plan, but even 6 weeks of focused work on high-priority topics produces meaningful score improvement.

You can practice each of these 22 topics individually on SHS Prep's targeted question bank, which organizes all 3,178 practice questions by subtopic and difficulty level.

Does the Math Section Differ Between 8th and 9th Grade Tests?

The 8th grade and 9th grade SHSAT tests cover the same content domains, but the 9th grade test includes questions that assume completion of 8th grade math. In practice, this means the 9th grade test may include slightly more advanced algebra (basic quadratic concepts, more complex systems) and geometry (coordinate geometry, transformations).

For 8th graders: everything above applies directly. For 9th graders: add coordinate geometry and basic quadratic expressions to your study plan.

The cutoff scores also differ by grade level. The 2025 8th grade cutoffs ranged from 496 (Brooklyn Latin) to 556 (Stuyvesant). Ninth grade cutoffs are typically higher because fewer seats are available.

How Does Math Scoring Affect Your Overall Strategy?

The SHSAT composite score combines math and ELA. But here is what most families miss: the scoring is nonlinear. Improving from 50% accuracy to 70% accuracy in math yields more scaled points than improving from 70% to 90% in ELA, because the middle range of the scoring curve has the steepest scaling.

This means a targeted investment in math topics you currently get wrong has the highest return on study time. If you can move from missing 20 math questions to missing 10, that jump alone could push your composite score above the Brooklyn Tech cutoff of 505.

We will cover the full scoring mechanics in our SHSAT scoring strategy guide, but the short version is: math improvement is the fastest path to a higher score for most students.

What Is the Best Way to Practice SHSAT Math?

Generic math practice is not enough. The SHSAT tests specific skills in specific ways. Here is what effective practice looks like:

1. Topic-isolated practice: Work through one subtopic at a time until accuracy exceeds 80%.
2. Mixed practice: Once individual topics are solid, do mixed-topic sets to build the skill of identifying which approach a question requires.
3. Timed practice: Start untimed, then add time pressure. Target 1.5 minutes per question (57 questions in roughly 85-90 minutes of your total 180).
4. Error analysis: After every practice session, categorize your mistakes. Was it a knowledge gap, a careless error, or a time pressure issue? Each requires a different fix.
5. Full mock exams: Take at least 3-4 complete practice tests under real conditions. This builds stamina and reveals your weakest topics under pressure.

Ready to start? Try a free full-length mock exam to see exactly where you stand across all 22 math topics. The diagnostic breakdown shows your accuracy by subtopic, so you know precisely where to focus your study time.