10 Most Common SHSAT Math Questions

Preparing for the SHSAT Math test? Want a preview of the most common mathematics questions on the SHSAT Math test? If so, then you are in the right place.

The SHSAT changed for fall 2026: it is now computer-adaptive, with 50 math questions and no calculator. See SHSAT 2026 changes: the new adaptive test, explained before you practice.

The mathematics section of SHSAT can be a challenging area for many test-takers, but with enough patience, it can be easy and even enjoyable!

Preparing for the SHSAT Math test can be a nerve-wracking experience. Learning more about what you’re going to see when you take the SHSAT can help reduce those pre-test jitters. Here’s your chance to review the 10 most common SHSAT Math questions to help you know what to expect and what to practice most. Try these 10 most common SHSAT Math questions to hone your mathematical skills and to see if your math skills are up to date on what’s being asked on the exam or if you still need more practice.

Make sure to follow some of the related links at the bottom of this post to get a better idea of what kind of mathematics questions you need to practice.

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Practice Quiz: 10 Most Common SHSAT Math Questions

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Harder SHSAT-Style Problems, Solved

Once the ten questions below feel easy, try these. Each one takes more than one step.

1. Percent change twice

A jacket costs $50. The price goes up 20%, then the new price is cut by 20%. What is the final price? After the increase, 50 × 1.2 = $60. After the cut, 60 × 0.8 = $48. The jacket ends $2 cheaper, a 4% drop.

2. Working together

Pipe A fills a tank in 6 hours. Pipe B fills it in 3 hours. How long do they take together? Each hour, A fills 1/6 and B fills 1/3 of the tank. Together that is 1/6 + 2/6 = 3/6 = 1/2 per hour, so the tank fills in 2 hours.

3. Changing a ratio

A class of 40 has boys and girls in a 3 : 5 ratio. How many girls must join so the ratio becomes 1 : 2? There are 15 boys and 25 girls. For 1 : 2 you need 30 girls, so 5 girls must join.

4. A shaded region

A square has sides of 10 cm. A quarter circle with radius 10 cm is drawn from one corner. What area of the square is outside the quarter circle? The square is 100 cm². The quarter circle is ¼ × π × 10² = 25π ≈ 78.5 cm². The answer is 100 − 25π ≈ 21.5 cm².

Why These Questions Feel Hard

• Hidden second step. The first number you find is often not the answer.
• Percent of what? Each percent change applies to the newest amount, not the original.
• Ratios are parts, not totals. Turn a ratio into real counts before changing it.
• Figures may not be drawn to scale. Trust the given numbers, not how the picture looks.
• Answer choices are built from mistakes. If you stop one step early, the wrong number you found is often sitting in the choices.

A good check is to reread the last sentence of the question before you pick an answer. Ask yourself whether your number is the thing it asks for, in the right units. That habit alone catches many of the mistakes on hard problems.

Frequently Asked Questions

What are the hardest SHSAT math questions?

The hardest SHSAT math questions are usually multi-step word problems, not advanced topics. Percent change, changing ratios, probability with two events and shaded-area geometry catch many students. For example, if a price drops 25% and then rises 25%, it does not return to where it started: 0.75 × 1.25 = 0.9375, so it ends 6.25% lower.

What kind of math questions are on the SHSAT?

The SHSAT math section covers middle school math: number sense, fractions and decimals, ratios and percents, expressions and equations, geometry, and probability and statistics, with many word problems. Most questions are multiple choice, and some are grid-in questions where you fill in your own answer. Calculators are not allowed, so mental math and clean written work matter.

Where can I find SHSAT sample questions?

The New York City Department of Education publishes the Specialized High Schools Student Handbook each year, and it includes official sample SHSAT tests with answer explanations. Use those to learn the format, then practice with SHSAT-style sets like the 10 questions here. Redo every missed problem a few days later without looking at the solution.

What are common SHSAT math problems?

Ratio and proportion problems come up often. For example, if the ratio of boys to girls in a class of 40 is 3:5, there are 3 + 5 = 8 parts, each part is 40 ÷ 8 = 5 students, so there are 15 boys and 25 girls. Other common types include percent of a number, solving linear equations, area and perimeter, and simple probability.

How should I practice for SHSAT math?

Mix short topic drills with timed practice tests. Start by finding weak areas from a full sample test, then practice those topics in small sets without a calculator, since none is allowed on test day. Keep an error log that records why you missed each question, and take a timed full practice test every week or two to build pacing.