SHSAT Math in 2026: The Complete Topic Breakdown and Study Strategy

SHSAT math prep doesn't have to feel overwhelming. The math section tests specific, predictable topics — and with the right study strategy, any motivated student can improve significantly. Whether you're starting from scratch or fine-tuning for test day, this guide gives you the complete SHSAT math topics 2026 breakdown, the most-tested concepts, and a week-by-week study plan to follow.

The SHSAT Math Section at a Glance

The math section of the 2026 SHSAT has 57 questions total:

• 47 multiple-choice questions (4 answer choices each)
• 5 grid-in questions (you write in a numeric answer)
• 5 unscored field-test items (you won't know which ones)

You get 180 minutes total for both ELA and Math, and you manage your own time. There's no calculator allowed. Every correct answer earns 1 point, and there's no penalty for guessing — so never leave a question blank.

With the 2026 adaptive format, questions adjust in difficulty based on your performance. This means strong math students will face harder questions as the test progresses, and accuracy on early questions matters more than ever.

SHSAT Math Topics 2026: The Full Breakdown

Here's what the math section covers and approximately how much of the test each area represents:

Arithmetic & Number Sense (~20%)

This is your foundation. About 1 in 5 math questions tests basic number skills:

• Fractions (adding, subtracting, multiplying, dividing)
• Decimals and place value
• Percentages (finding percents, percent of a number, percent change)
• Ratios and proportions
• Unit conversions
• Order of operations (PEMDAS)
• Absolute value

These aren't "easy" questions — the SHSAT tests arithmetic in tricky, multi-step contexts. A question might ask you to find 15% of a number, then use that result in a ratio.

Algebra (~30%)

Algebra is the biggest chunk of the SHSAT math section. Expect questions on:

• Simplifying and evaluating expressions
• Solving linear equations (one variable and two variables)
• Inequalities (solving and graphing on a number line)
• Systems of equations
• Exponent rules (multiplying, dividing, negative exponents)
• Patterns and sequences (arithmetic and geometric)
• Algebraic word problems (translating English into equations)

If you're going to focus extra time on one area, this is it. Algebra questions appear more than any other type, and they range from straightforward equation solving to complex multi-step word problems.

Geometry (~25%)

Geometry is the second-largest topic area. Key concepts include:

• Perimeter and area (rectangles, triangles, circles, composite shapes)
• Volume (rectangular prisms, cylinders)
• Angle relationships (complementary, supplementary, vertical angles)
• Triangle properties (angle sum, isosceles/equilateral rules, exterior angles)
• Parallel lines cut by a transversal (alternate interior, corresponding angles)
• Coordinate geometry (distance, midpoint, slope)
• Transformations (translations, reflections, rotations)
• Pythagorean theorem
• Circle properties (circumference, area, arc length)

Geometry questions often combine multiple concepts — like finding the area of a shape using the Pythagorean theorem first to calculate a missing side.

Statistics & Probability (~10%)

A smaller but important section:

• Mean, median, mode, and range
• Basic probability (single events, compound events)
• Data interpretation (reading bar graphs, tables, line graphs)

These questions tend to be more straightforward, making them great opportunities to pick up points. Don't skip studying this section just because it's small.

Word Problems (~15%)

Multi-step word problems deserve their own category because they blend multiple skills:

• Rate, distance, and time problems
• Ratio and proportion scenarios
• Percent change (increase/decrease)
• Combined work problems ("If Maria can paint a room in 3 hours and Alex can paint it in 5 hours...")
• Age problems

The challenge with word problems isn't usually the math — it's translating the English into equations. Practice this translation skill specifically.

The 5 Grid-In Questions: What They Are and How to Prepare

Grid-in questions don't give you answer choices. Instead, you type in a numeric answer — an integer, decimal, or fraction.

Why Grid-Ins Matter

Without answer choices, you can't use process of elimination or work backward from the options. You need to solve the problem completely and get the exact right answer.

How to Prepare for Grid-Ins

1. Practice solving without looking at answer choices. Cover up the options on multiple-choice questions and solve them as if they were grid-ins.
2. Check your work. Without options to sanity-check against, careless errors are more costly.
3. Know the input format. Practice entering fractions, decimals, and negative numbers in the digital grid-in interface.
4. Simplify fractions. If the answer is 6/8, enter 3/4. Grid-ins may require simplified form.

Grid-in questions can come from any topic area, but they frequently test algebra and arithmetic.

No Calculator: Mental Math Strategies That Win

The no-calculator policy is one of the biggest challenges of SHSAT math. Here are strategies to build your mental math muscles:

Memorize Key Facts

• Times tables through 15×15 — know these cold
• Perfect squares up to 20² (400)
• Common fraction-decimal-percent conversions (1/8 = 0.125 = 12.5%, 1/3 ≈ 0.333, 3/4 = 0.75 = 75%)
• Powers of 2 (2, 4, 8, 16, 32, 64, 128, 256)

Use Estimation

Before calculating an exact answer, estimate. If the answer choices are 42, 78, 156, and 312, and your estimate is "around 150," you can focus your work on confirming whether it's 156.

Break Down Complex Calculations

• Multiply by breaking apart: 47 × 6 = (50 × 6) − (3 × 6) = 300 − 18 = 282
• Percentage shortcut: 15% of 80 = 10% of 80 + 5% of 80 = 8 + 4 = 12
• Fraction operations: Find common denominators mentally by identifying the LCM quickly

Practice Daily

Spend 5 minutes every day doing mental math drills. Calculate tips at restaurants, estimate grocery totals, or use mental math apps. Speed and accuracy with numbers is a skill that improves with consistent practice.

Top 10 Most-Tested SHSAT Math Concepts

Based on analysis of SHSAT question patterns, these concepts appear most frequently:

1. Solving Linear Equations

Single-variable equations like 3x + 7 = 22. Master isolating the variable, handling fractions in equations, and checking your answer by substituting back.

2. Ratios and Proportions

Setting up and solving proportions (a/b = c/d), including cross-multiplication. Often appears in word problem form.

3. Percent Problems

Finding the percent of a number, calculating percent increase/decrease, and "what percent is X of Y?" questions.

4. Area and Perimeter

Calculating area of triangles, rectangles, circles, and composite (irregular) shapes. Know the formulas cold.

5. Angle Relationships

Complementary (90°), supplementary (180°), vertical angles, and angles formed by parallel lines and transversals.

6. Algebraic Expressions

Simplifying expressions, combining like terms, and using the distributive property. Often the first step in a larger problem.

7. Exponent Rules

Multiplying powers (add exponents), dividing powers (subtract exponents), power of a power (multiply exponents), and negative exponents.

8. Coordinate Geometry

Plotting points, finding slope (rise/run), calculating distance between points, and identifying equations of lines.

9. Mean/Median/Mode

Calculating averages, finding the median in sorted data sets, and understanding how adding/removing data points affects these measures.

10. Multi-Step Word Problems

Translating a real-world scenario into mathematical operations and solving in multiple steps. The #1 skill separator on the SHSAT.

Common Mistakes and How to Avoid Them

Sign Errors

Forgetting to distribute a negative sign is the most common algebra mistake. When you see −(3x − 5), it becomes −3x + 5, not −3x − 5. Fix: Circle negative signs and handle them one at a time.

Order of Operations (PEMDAS) Violations

Students frequently multiply before handling parentheses, or add before multiplying. Fix: Write out each step on a separate line. Don't skip steps to save time — skipping steps costs time when you get the wrong answer.

Misreading Word Problems

The question asks "how many MORE apples does John have" and students just calculate how many John has. Fix: Underline exactly what the question is asking before you start solving.

Unit Conversion Errors

Mixing up inches and feet, minutes and hours, or forgetting to convert units mid-problem. Fix: Write units next to every number in your work. If units don't cancel correctly, something's wrong.

Fraction Fumbles

Adding fractions without finding a common denominator, or forgetting to flip the second fraction when dividing. Fix: For addition/subtraction, always find the LCD first. For division, remember "keep, change, flip."

Not Checking Grid-In Answers

On multiple-choice questions, a wrong answer is just a wrong bubble. On grid-ins, a careless calculation error means zero points with no safety net. Fix: Always re-read the question and verify your grid-in answer makes sense in context.

The 8-Week SHSAT Math Study Plan

This week-by-week framework assumes 45–60 minutes of math practice per day, 5–6 days a week.

Weeks 1–2: Foundations

• Review arithmetic: fractions, decimals, percentages, ratios
• Memorize key facts (times tables, perfect squares, conversions)
• Daily mental math drills (10 minutes)
• Practice 15–20 questions per day (easy to medium difficulty)

Weeks 3–4: Core Algebra & Geometry

• Linear equations, expressions, inequalities
• Exponent rules and patterns
• Perimeter, area, volume basics
• Angle relationships
• Practice 20–25 questions per day (medium difficulty)

Weeks 5–6: Advanced Topics & Word Problems

• Systems of equations
• Coordinate geometry and transformations
• Pythagorean theorem and circle properties
• Multi-step word problems (rate/distance, percent change, combined work)
• Practice 25–30 questions per day (medium to hard difficulty)
• Introduce grid-in practice

Weeks 7–8: Test Simulation & Review

• Take 2 full-length timed practice tests
• Review every wrong answer — categorize by topic
• Focus extra time on your 2–3 weakest areas
• Practice under adaptive conditions (no going back)
• Maintain 20 questions per day with mixed topics
• Final week: light review only, no cramming

How Many Questions Per Day?

Aim for 20–30 practice questions daily during active prep. Quality matters more than quantity — spend time understanding why you got a question wrong, not just doing more questions. A student who does 20 questions and reviews all mistakes will improve faster than one who does 50 questions and never looks back.

Frequently Asked Questions

Is SHSAT math harder than school math?

It depends on your school, but generally: SHSAT math covers 8th-grade-level content, which many students learn in school. The difference is the difficulty of application. School math might ask you to solve 2x + 3 = 11. SHSAT math might wrap that same equation in a three-sentence word problem with an extra step. The concepts are the same — the presentation is trickier.

What grade level is SHSAT math?

The SHSAT math section is aligned to 8th-grade Common Core math standards. However, some questions require deeper problem-solving skills that go beyond what's typically covered in a standard 8th-grade curriculum. Students in advanced math classes may find the content more familiar.

Should I memorize formulas?

Yes — but only the ones that actually appear on the test. Key formulas to know:

• Area of triangle: ½ × base × height
• Area of circle: πr²
• Circumference: 2πr
• Volume of rectangular prism: length × width × height
• Pythagorean theorem: a² + b² = c²
• Slope: (y₂ − y₁) / (x₂ − x₁)
• Distance formula: √[(x₂−x₁)² + (y₂−y₁)²]

The SHSAT does not provide a formula sheet, so these need to be memorized.

How do grid-in questions work on the digital test?

On the digital SHSAT, grid-in questions provide an input field where you type your numeric answer. You can enter integers, decimals, or fractions. There are no answer choices — you must calculate the exact answer. There are 5 grid-in questions on the math section, and they can cover any math topic.

Build a Study System That Works

The students who succeed on SHSAT math aren't necessarily the ones who are "naturally good at math." They're the ones who practice consistently, learn from mistakes, and build skills systematically across all topic areas.

The 2026 adaptive format adds another layer: questions get harder as you get them right, which means you need deep preparation across difficulty levels — not just surface-level familiarity. Tools designed for the 2026 format, like SHS Prep, offer structured practice with difficulty-adapted questions that mirror the real adaptive test experience, tracking your progress by topic so you always know where to focus next.

Start your 8-week plan today. Future you will be grateful.