SHSAT guide

SHSAT Math Practice: Topics, Questions & Worked Solutions

Updated October 13, 2026

SHSAT Math tests middle-school content, but rarely in a straightforward way. A single question might combine a ratio, a percent, and a careful reading of what is being asked. Students who score well have made the core skills automatic and have practiced enough real problems to recognize the traps.

This page brings that practice together in one place: what the Math section covers, the kinds of questions to expect, ten original practice problems with full explanations, and how to pace yourself on the computer-adaptive test.

SHSAT Math topics at a glance

The Math section has 50 questions drawn from content most students see in 6th through 8th grade. Calculators are not allowed, so accurate arithmetic matters as much as knowing the concept.

Number sense: fractions, decimals, percents, exponents, factors, and multiples.
Ratios, rates, and proportional reasoning, including percent change and unit rates.
Expressions, linear equations, inequalities, and simple systems.
Geometry and measurement: angles, triangles, the Pythagorean theorem, area, perimeter, and volume.
Probability, statistics, and reading data from tables and graphs.
Multi-step word problems that combine several of the topics above.
For a detailed review list, see our SHSAT Math topics checklist.

Common SHSAT Math question types

On the Fall 2026 computer-adaptive SHSAT, Math questions appear in a few formats. Knowing each one ahead of time keeps test-day surprises to a minimum.

Multiple choice

Most questions offer four answer choices. Wrong choices are often the result of a predictable mistake, such as adding percents that should be multiplied or answering for the wrong quantity. Estimating first helps rule out choices that cannot be right.

Fill-in-the-blank

Some questions ask students to type a numerical answer with no choices to check against. Plugging the answer back into the problem is the best protection, because Math questions cannot be revisited after advancing.

Technology-enhanced items

These questions use the computer interface in ways a paper test cannot, for example asking students to select more than one correct answer. The Student Readiness Tool on the NYC SHSAT Portal (opens in a new tab) is the best way to see these formats before test day.

Multi-step word problems

Word problems appear in every format. The challenge is usually translating the words into math, not the calculation itself. Before solving, write down what the question asks for in a few words.

SHSAT Math practice questions

Try each problem on scratch paper without a calculator before opening the explanation. Time yourself: on test day, most students have a little under two minutes per Math question.

Question 1 · Percents
A $40 jacket is marked up 15%. The store then offers 15% off the new price. What is the final price?
1. Choice A: $40.00
2. Choice B: $39.10
3. Choice C: $38.50
4. Choice D: $34.00
Show answer and explanation
Answer: B. $39.10
The markup gives 40 × 1.15 = $46. The discount is taken from $46, not $40: 46 × 0.85 = $39.10.
Trap: choosing $40.00 because +15% and −15% seem to cancel. They do not, because each percent is applied to a different amount.
Question 2 · Ratios
A recipe uses flour and sugar in a ratio of 5:2. If the recipe uses 21 cups of flour and sugar combined, how many more cups of flour than sugar does it use?
1. Choice A: 3
2. Choice B: 6
3. Choice C: 9
4. Choice D: 15
Show answer and explanation
Answer: C. 9
The ratio has 5 + 2 = 7 parts, so each part is 21 ÷ 7 = 3 cups. Flour is 5 × 3 = 15 cups and sugar is 2 × 3 = 6 cups. The difference is 15 − 6 = 9 cups.
Trap: answering 15 or 6, which are the amounts of each ingredient rather than the difference the question asks for.
Question 3 · Rates
Maya walks 3 miles to the library at 4 miles per hour and returns the same way at 6 miles per hour. What is her average speed for the whole trip, in miles per hour?
1. Choice A: 4.8
2. Choice B: 5
3. Choice C: 5.2
4. Choice D: 5.5
Show answer and explanation
Answer: A. 4.8
Average speed is total distance divided by total time. The trip there takes 3 ÷ 4 = 0.75 hours and the trip back takes 3 ÷ 6 = 0.5 hours, for 1.25 hours total. Total distance is 6 miles, so the average speed is 6 ÷ 1.25 = 4.8 mph.
Trap: averaging the two speeds to get 5. She spends more time at the slower speed, so the average is pulled below 5.
Question 4 · Linear equations (fill-in-the-blank)
If 4(x − 3) = 2x + 10, what is the value of x?
Fill in the blank: no answer choices.
Show answer and explanation
Answer: 11
Distribute: 4x − 12 = 2x + 10. Subtract 2x from both sides: 2x − 12 = 10. Add 12: 2x = 22, so x = 11.
Check before advancing: 4(11 − 3) = 32 and 2(11) + 10 = 32. Both sides match.
Question 5 · Inequalities
What is the greatest integer n that satisfies −3n + 5 > 17?
1. Choice A: −3
2. Choice B: −4
3. Choice C: −5
4. Choice D: −6
Show answer and explanation
Answer: C. −5
Subtract 5 from both sides: −3n > 12. Divide by −3 and flip the inequality sign: n < −4. The greatest integer less than −4 is −5.
Traps: forgetting to flip the sign when dividing by a negative, or choosing −4, which is not included because the inequality is strict.
Question 6 · Geometry: right triangles
A right triangle has legs of length 9 and 12. What is its perimeter?
1. Choice A: 21
2. Choice B: 30
3. Choice C: 36
4. Choice D: 54
Show answer and explanation
Answer: C. 36
By the Pythagorean theorem, the hypotenuse is √(9² + 12²) = √(81 + 144) = √225 = 15. The perimeter is 9 + 12 + 15 = 36.
Recognizing 9-12-15 as a multiple of the 3-4-5 triangle saves time. Trap: 54 is the area, not the perimeter.
Question 7 · Geometry: angles
Two parallel lines are cut by a transversal. Two same-side interior angles measure (3x + 10)° and (2x + 20)°. What is the measure of the larger angle?
1. Choice A: 30°
2. Choice B: 80°
3. Choice C: 100°
4. Choice D: 110°
Show answer and explanation
Answer: C. 100°
Same-side interior angles are supplementary, so (3x + 10) + (2x + 20) = 180. That gives 5x + 30 = 180, so x = 30. The angles are 3(30) + 10 = 100° and 2(30) + 20 = 80°. The larger angle is 100°.
Trap: stopping at x = 30. The question asks for an angle, not for x.
Question 8 · Statistics (fill-in-the-blank)
The mean of Dev's first five test scores is 84. What score does he need on his sixth test to raise his mean to 86?
Fill in the blank: no answer choices.
Show answer and explanation
Answer: 96
Work with totals instead of averages. Five tests at a mean of 84 total 5 × 84 = 420 points. Six tests at a mean of 86 total 6 × 86 = 516 points. He needs 516 − 420 = 96.
Question 9 · Probability
A bag holds 4 red marbles and 6 blue marbles. Two marbles are drawn at random without replacement. What is the probability that both are red?
1. Choice A: 4/25
2. Choice B: 2/15
3. Choice C: 1/5
4. Choice D: 2/5
Show answer and explanation
Answer: B. 2/15
The first draw is red with probability 4/10. With one red marble gone, the second draw is red with probability 3/9. Multiply: (4/10) × (3/9) = 12/90 = 2/15.
Trap: 4/25 is the answer if the first marble were put back. "Without replacement" changes the second fraction.
Question 10 · Number sense: multiples
One bus leaves a station every 12 minutes and another leaves every 18 minutes. Both leave at 8:00 a.m. When is the next time they leave together?
1. Choice A: 8:30 a.m.
2. Choice B: 8:36 a.m.
3. Choice C: 8:54 a.m.
4. Choice D: 9:12 a.m.
Show answer and explanation
Answer: B. 8:36 a.m.
The buses leave together at multiples of both 12 and 18. The least common multiple is 36 (12 = 2² × 3 and 18 = 2 × 3², so the LCM is 2² × 3² = 36). They next leave together 36 minutes after 8:00, at 8:36 a.m.

Pacing SHSAT Math on the digital test

Students get 180 minutes for both subjects and decide how to split the time. A common starting point is about 90 minutes for Math, which works out to just under two minutes per question. The right split depends on the student, so test it on full-length practice exams before test day.

Because Math questions cannot be revisited after advancing, the familiar paper-test strategy of skipping a hard problem and coming back later does not apply. Pacing has to happen one question at a time.

Set a personal time ceiling, such as three minutes. If a problem is still unsolved, eliminate what you can, choose the best remaining answer, and advance.
Use checkpoints. For example, aim to be around question 25 by the 45-minute mark of your Math time.
Spend the seconds you save on easier questions checking fill-in-the-blank answers, where there are no choices to catch a mistake.
Practice the full 180 minutes in one sitting so the second subject does not suffer from fatigue.

Common SHSAT Math mistakes and how to fix them

Answering a different question: solving for x when the question asks for 2x, or for one part of a ratio when it asks for the difference. Fix: underline the final ask before calculating.
Adding percents that should be multiplied: successive discounts or markups apply to a new amount each time.
Averaging rates directly: average speed is total distance over total time.
Sign errors with inequalities: flip the sign when multiplying or dividing by a negative number.
Arithmetic slips without a calculator: write each step on scratch paper instead of doing it in your head.
Spending too long on one problem: since you cannot return, a stuck question costs time on every question after it.
Not checking fill-in answers: substitute your answer back into the original problem before advancing.

How to keep practicing SHSAT Math

Practice is most effective when it targets the topics where a student actually loses points. A short error log, reviewed weekly, shows those patterns quickly. Pair focused topic practice with periodic full-length tests, and review each test as carefully as you took it. Our guide on how to use SHSAT practice tests walks through a review routine.

If you would like an outside view of where your child stands, our free SHSAT diagnostic in Astoria identifies the Math and ELA skills that will move the score most. Students can also join the free Sunday SHSAT class, where we work through problems like these live. For structured, week-by-week preparation, see our SHSAT prep program.

Preparing for the other half of the test? Continue with our SHSAT ELA practice guide.

Need help preparing for the SHSAT?

AhmedPrep is based in Astoria, Queens, and helps students across NYC prepare for the SHSAT. A free diagnostic is the clearest first step: it shows your child's strengths, gaps, and a realistic plan for the time remaining.

BOOK A FREE DIAGNOSTIC VIEW SHSAT PREP FREE SUNDAY SHSAT CLASS

Questions? Call or text 347-479-5020

Next steps for SHSAT students

All free tools