SHSAT Math Topics 2026: Complete Breakdown & Study Guide

TL;DR: The SHSAT math section covers 50 questions across four domains: Number Sense & Operations, Algebra & Functions, Geometry & Measurement, and Statistics & Probability. No calculator is allowed, no formulas are provided, and the test is now computer-adaptive starting fall 2026. Algebra makes up roughly 30% of the questions, making it the highest-value domain, while ratios and proportions are the single most frequently tested topic family.

The Specialized High School Admissions Test determines admission to New York City’s eight specialized high schools, including Stuyvesant, Bronx Science, and Brooklyn Tech. If you’re an 8th grader (or a parent helping one), knowing exactly which SHSAT math topics appear on the test is the first step toward a focused study plan.

This glossary breaks down every topic, defines it in plain language, flags common mistakes, and tells you how often each area actually shows up. Everything here reflects the 2026 computer-adaptive format confirmed by NYC Public Schools on June 4, 2026.

Before you read further, consider taking a diagnostic test to pinpoint which of these topics you already know and which need work.

How the 2026 SHSAT Math Section Works

The math section contains 50 scored questions. You share 180 minutes between ELA and Math, and you decide how to split that time. Older prep books and some websites still reference 57 questions per section, but that was the pre-2026 paper format.

Starting fall 2026, the SHSAT is a computer-adaptive test (CAT). The test adjusts question difficulty based on your answers in real time. Everyone answers 50 math questions, but the difficulty path differs from student to student. Navigation is forward-only, meaning you cannot go back to a previous question after submitting it.

Three critical rules to internalize right now:

1. No calculator. Not on any question. Students who rely on calculators for routine arithmetic at school will feel this immediately.
2. No formula sheet. Every formula in this glossary must be memorized.
3. No penalty for guessing. Never leave a question blank.

Beyond standard multiple-choice and grid-in questions, the computer format introduces Technology-Enhanced Items (TEI): drag-and-drop, inline dropdowns, multi-select, and click-to-place. These test the same math skills in a different interaction format, so practicing on a computer matters.

Number Sense & Operations (~20% of Questions)

This domain covers the foundational arithmetic that underlies every other SHSAT math topic. Expect roughly 10 questions on the 50-question format.

Fractions

A fraction represents a part of a whole. On the SHSAT, you’ll add, subtract, multiply, and divide fractions without a calculator. Converting between improper fractions and mixed numbers is essential.

Watch out: The most common error is forgetting to find a common denominator before adding or subtracting. The test places the “wrong denominator” answer in the choices deliberately.

Decimals

Decimal operations (addition, subtraction, multiplication, division) appear frequently, often embedded in word problems. Know how to convert between decimals and fractions quickly.

Percents

“What is 35% of 240?” is a standard SHSAT question, but the test goes further. You’ll encounter percent increase, percent decrease, and occasionally percent of a percent (e.g., “a price drops 20%, then drops another 15%”).

Formula — Percent Change: (new − old) / old × 100

Watch out: A 20% decrease followed by a 20% increase does not return you to the original value. The test exploits this misunderstanding regularly.

Ratios and Proportions

Ratios compare two quantities. Proportions set two ratios equal. According to topic-frequency analysis from SHSATlab, ratios, proportions, and rates are the single highest-frequency topic family on the SHSAT, appearing in 5 to 8 questions per test.

Watch out: Setting up the ratio backwards is the #1 mistake. If a problem says “the ratio of boys to girls is 3:5,” make sure boys are in the numerator, not girls.

Unit Conversions

These problems ask you to convert between units (minutes to hours, inches to feet, etc.) using multiplication or division. They often appear inside larger word problems rather than as standalone questions.

Absolute Value

The absolute value of a number is its distance from zero on a number line. |−7| = 7 and |7| = 7. The SHSAT tests this concept inside equations, such as |x − 3| = 5, which has two solutions.

PEMDAS (Order of Operations)

PEMDAS stands for Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right). Without a calculator enforcing order for you, getting this wrong cascades through the entire problem.

Factors, Multiples, and Prime Factorization

A factor divides evenly into a number. A multiple is the product of a number and any integer. Prime factorization breaks a number into its prime components (e.g., 60 = 2² × 3 × 5). These concepts appear in GCF/LCM problems and in questions about divisibility.

Exponents and Square Roots

Know the rules: x^a × x^b = x^(a+b), (x^a)^b = x^(ab), x^0 = 1. For square roots, understand that √(a × b) = √a × √b. The SHSAT expects you to recognize perfect squares up to at least 15² = 225.

Algebra & Functions (~30% of Questions)

Algebra is the largest SHSAT math domain, accounting for roughly 15 questions. Practitioners on Reddit and prep forums consistently identify this as the area where focused practice yields the biggest score gains. If you’re building a study plan, this study plan generator can help you prioritize topics based on your diagnostic results.

Evaluating and Simplifying Expressions

You’ll substitute values into expressions and simplify using the distributive property, combining like terms, and factoring. Example: If x = 3, evaluate 2x² − 5x + 1.

Solving Linear Equations

Single-variable equations like 3x + 7 = 22 are bread-and-butter SHSAT questions. They get harder when variables appear on both sides or when the equation involves fractions.

Inequalities

Inequalities work like equations with one crucial difference: multiplying or dividing by a negative number flips the inequality sign. The test loves to check whether you remember this rule.

Systems of Equations

Two equations with two unknowns. Solve by substitution or elimination. Example: x + y = 10 and 2x − y = 5 gives x = 5, y = 5. These problems carry medium difficulty and are essential for students targeting Stuyvesant-range scores (the 2026 cutoff was 561).

Translating Word Problems into Equations

This is the single most important algebra skill on the SHSAT. One NYC-based prep center (Khan’s Tutorial) emphasizes that students must practice this daily. The test describes a situation in words and expects you to write an equation, then solve it.

Watch out: Multi-step word problems are designed so that intermediate answers appear among the answer choices. If a problem requires three steps and you stop after two, the test has already placed your premature answer as a trap.

Slope

Slope measures how steep a line is.

Formula — Slope: (y₂ − y₁) / (x₂ − x₁)

Know that parallel lines have equal slopes and perpendicular lines have slopes that are negative reciprocals of each other.

Linear Functions

A linear function has the form y = mx + b, where m is the slope and b is the y-intercept. The SHSAT tests your ability to identify slope and intercept from a graph, a table, or an equation.

Arithmetic Sequences

An arithmetic sequence adds a constant difference between terms: 3, 7, 11, 15, … (common difference = 4). The nth term = first term + (n − 1) × common difference.

Geometric Sequences

A geometric sequence multiplies by a constant ratio: 2, 6, 18, 54, … (common ratio = 3). These appear less frequently than arithmetic sequences but can trip students who confuse the two types.

Substitution and Backsolving

Backsolving means plugging answer choices into the problem to see which one works. This is a legitimate and often faster strategy on multiple-choice questions. On grid-in questions, you can’t backsolveyou need to work through the algebra.

Geometry & Measurement (~25% of Questions)

Geometry accounts for roughly 11 to 13 questions. Practitioners from Khan’s Tutorial note that “geometry questions tend to be the hardest thing for most students. Not only is it a topic from 10th grade, you also have to know a lot of formulas.” Analysis from School of Math (Manhattan) adds that the hardest SHSAT items typically combine two domains, such as a percent problem layered onto a coordinate geometry setup.

If you want to practice coordinate geometry concepts with interactive tools, graphing resources here can build that fluency.

Perimeter and Area

Perimeter is the total distance around a shape. Area is the space inside it.

• Rectangle: Perimeter = 2(l + w), Area = l × w
• Triangle: Area = ½ × base × height
• Circle: Area = πr², Circumference = 2πr

Composite Shapes

A composite shape is made of two or more basic shapes combined. To find its area, break it into recognizable pieces, calculate each area, and add (or subtract) as needed.

Volume

Formula — Rectangular Prism: l × w × h
Formula — Cylinder: πr²h

Volume questions are straightforward if you know the formulas. Without a formula sheet, though, blanking on πr²h is a real risk.

Angle Relationships

• Complementary angles add to 90°
• Supplementary angles add to 180°
• Vertical angles are equal

These definitions power many geometry problems and often appear early in the section as accessible questions worth getting right.

Parallel Lines Cut by a Transversal

When a line crosses two parallel lines, it creates eight angles with predictable relationships. Alternate interior angles are equal. Corresponding angles are equal. Same-side interior angles are supplementary.

Triangle Properties

The angles in any triangle sum to 180°. Isosceles triangles have two equal sides and two equal angles. Equilateral triangles have all sides and angles equal (60° each). The exterior angle of a triangle equals the sum of the two non-adjacent interior angles.

Pythagorean Theorem

Formula: a² + b² = c² (where c is the hypotenuse of a right triangle)

Memorize common Pythagorean triples: 3-4-5, 5-12-13, 8-15-17, and their multiples (6-8-10, etc.). Recognizing these instantly saves valuable time.

Coordinate Geometry

This subtopic tests distance, midpoint, and slope on the coordinate plane.

Formula — Distance: √[(x₂ − x₁)² + (y₂ − y₁)²]
Formula — Midpoint: ((x₁ + x₂)/2, (y₁ + y₂)/2)

Transformations

Translations (slides), reflections (flips), and rotations (turns). Know how each transformation changes coordinates. For example, reflecting a point (x, y) over the x-axis gives (x, −y).

Circle Properties: Arc Length and Sector Area

SHSATlab’s frequency analysis of the newest 50-question practice test (Practice Test C) showed circle problems jumping from 0 to 3 questions, a significant increase. Prep instructors consistently flag these as disproportionately hard.

Formula — Arc Length: (central angle / 360) × 2πr
Formula — Sector Area: (central angle / 360) × πr²

Watch out: Set up a proportion using the central angle. If the central angle is 90°, the arc is 90/360 = ¼ of the circumference.

Statistics & Probability (~10% of Questions)

Statistics and probability yield roughly 5 to 8 questions. This may seem small, but SHSAT prep specialists point out that probability is one of the highest-frequency topics that students are almost never prepared for. Most NYC middle schoolers haven’t covered probability deeply by test day.

Mean (Average)

Formula: Sum of values ÷ number of values

The SHSAT often asks what happens to the mean when a value is added or removed. Think of it as adjusting the sum and the count, then recalculating.

Median

The middle value when data is arranged in order. For an even number of values, the median is the average of the two middle numbers. The test sometimes lists values out of order to see if you’ll sort them first.

Mode and Range

Mode is the most frequent value. Range is the difference between the largest and smallest values. These are quick to calculate but easy to rush through carelessly.

Weighted Average

Formula: Σ(value × weight) / Σ(weights)

Weighted average questions describe situations where different groups contribute different amounts to the total. Example: 20 students scored 80 and 30 students scored 90. The class average is not 85, it’s (20×80 + 30×90) / 50 = 86.

Probability

Formula: Favorable outcomes / total outcomes

The SHSAT tests single-event probability (“what is the chance of drawing a red marble?”) and compound probability (“what is the chance of drawing two red marbles in a row without replacement?”). On Practice Test C, probability and counting problems rose from 4 to 6 questions.

Charts, Tables, and Graphs

You’ll read bar graphs, line graphs, tables, and occasionally pie charts to extract data. The math itself is usually simple. The challenge is reading carefully and not misidentifying which data point the question asks about.

Test Format Terms You Need to Know

Grid-In Questions

Grid-in questions require you to type a numerical answer rather than select from choices. There is no partial credit. The SHSAT typically includes around 5 grid-in questions per section. Because you can’t backsolveyou can’t test answer choices when there are no choicesthese questions reward students who are confident in their algebra.

Multiple-Select Questions

As Kaplan’s SHSAT guide explains, multiple-select questions are similar to multiple-choice except that more than one answer is correct. You must select all correct answers and no incorrect answers to receive credit. The question tells you how many to select.

Technology-Enhanced Items (TEI)

New to the 2026 format, TEI questions include graphing (plotting points or lines on a coordinate plane), ordering (dragging values into sequence), and multipart problems where earlier answers feed into later parts. The underlying math is the same; only the way you input your answer changes.

Computer-Adaptive Testing (CAT)

The adaptive algorithm adjusts difficulty based on your responses. Get a question right, and the next one may be harder (and worth more toward your score). Get one wrong, and the difficulty may decrease. This means accuracy on the first 10 to 15 questions carries more strategic weight than ever before. To understand how adaptive study paths mirror this format, see our methodology.

Scaled Score

Your raw number of correct answers is converted to a scaled score. The scaled score accounts for question difficulty. Cutoff scores for 2026 admissions were approximately 561 for Stuyvesant, 525 for Bronx Science, and 506 for Brooklyn Tech. For a deeper breakdown, read about SHSAT cutoff scores by school.

Field-Test Items

Some questions on the SHSAT are unscored experimental questions being tested for future exams. You won’t know which ones they are, so treat every question as if it counts.

What to Study First: The SHSAT Math Priority Map

Not all SHSAT math topics deserve equal study time. Based on frequency data from SHSATlab’s practice test analysis and insights from NYC prep centers, here’s how to prioritize:

Priority	Topic Cluster	Why	Approx. Questions
1	Ratios, proportions, percent change	Highest frequency, fastest to improve	6 to 8
2	Linear equations and algebraic word problems	Largest domain, highest total point value	~15
3	Circles, triangles, angle relationships	Disproportionately hard, high error rate	3 to 5
4	Weighted averages and probability	Under-taught in school, surprise difficulty	3 to 5
5	Systems of equations and sequences	Medium difficulty, essential for top scores	3 to 4

SHSATlab’s analysis puts it bluntly: “It’s not the hardest problems that separate high scorers from the rest. It’s mastery of five very specific math topics that appear reliably across every version of the test.” Students who drill these core areas outscore equally capable students who scatter their preparation, sometimes by 30 to 60 points.

Start with Priority 1 and 2. They cover over half the test. Then work through Priority 3 and 4, which catch students off guard. Priority 5 matters most for students chasing Stuyvesant-level scores.

For a detailed study approach tailored to your timeline, our guide on how to study for the SHSAT walks through week-by-week planning.

Essential Formulas to Memorize

Since the SHSAT provides no formula sheet, you must commit these to memory. As the SHSAT Buddy study guide warns: “Formulas and definitions of mathematical terms and symbols are not provided.”

Formula	Expression
Percent Change	(new − old) / old × 100
Mean	sum of values ÷ number of values
Weighted Mean	Σ(value × weight) / Σ(weights)
Probability	favorable outcomes / total outcomes
Area of a Circle	πr²
Circumference	2πr
Pythagorean Theorem	a² + b² = c²
Slope	(y₂ − y₁) / (x₂ − x₁)
Distance Formula	√[(x₂ − x₁)² + (y₂ − y₁)²]
Volume (Rectangular Prism)	l × w × h
Volume (Cylinder)	πr²h
Arc Length	(central angle / 360) × 2πr

Write each formula on a flashcard. Quiz yourself until you can reproduce them all from memory in under two minutes.

Practice Under Real Conditions

Knowing the SHSAT math topics is different from performing under test conditions. The no-calculator, forward-only, timed environment creates pressure that casual studying doesn’t replicate. IvyTP’s 2026 tips article emphasizes that “students must apply concepts rather than recall formulas alone,” which means multi-step problem solving under time pressure is the real skill.

To build that skill, practice with full-length tests that simulate real timing and format constraints.

Frequently Asked Questions

Is SHSAT math harder than regular school math?

Yes, for most students. The SHSAT pulls from topics across 7th, 8th, and even some 9th/10th grade curricula (particularly geometry). The difficulty comes not from any single concept but from multi-step problems, the no-calculator policy, and the time pressure. School math also rarely covers probability and weighted averages at the depth the SHSAT tests them.

What grade level is SHSAT math?

The content spans roughly 7th through early 10th grade. Arithmetic and basic algebra align with 7th and 8th grade standards. Geometry topics like the Pythagorean theorem, transformations, and circle properties push into 9th and 10th grade material.

Can you use a calculator on the SHSAT?

No. Calculators are not permitted on any part of the SHSAT. This means you need strong mental math skills and comfort with hand calculations. School of Math (Manhattan) notes that “students who use calculators at school for routine arithmetic struggle on the no-calculator SHSAT.”

What are grid-in questions on the SHSAT?

Grid-in questions require you to produce and type a numerical answer rather than selecting from multiple-choice options. There are approximately 5 per math section. You cannot backsolveyou must work through the problem and arrive at the answer independently.

How many SHSAT math questions are actually scored?

All 50 math questions on the 2026 adaptive test are presented, but some may be unscored field-test items. You will not know which questions are experimental, so answer every one. There is no penalty for wrong answers. For help estimating what your performance might translate to, our score calculator can give you a rough projection.

What changed about SHSAT math in 2026?

The format shifted from a 57-question paper test to a 50-question computer-adaptive test. The math content and standards stayed the same. New question types (TEI) were added, including drag-and-drop and graphing interactions. Navigation is now forward-only. The adaptive engine adjusts difficulty in real time based on your answers.

Do I need to memorize formulas for the SHSAT?

Absolutely. No formulas, definitions, or mathematical symbols are provided during the test. Every formula listed in this glossary, from percent change to arc length, must be memorized before test day.

What are the most important SHSAT math topics to study first?

Ratios, proportions, and percent change are the highest-frequency topics and the fastest to improve. Linear equations and word-problem translation follow close behind as the largest scoring domain. After those, focus on circles, triangles, probability, and weighted averages, which catch students off guard due to limited school coverage.