SHSAT · Math practice

SHSAT math questions and practice test: 10 problems with explanations

By Trieu Ly · Updated

Try 10 SHSAT-style math questions. We wrote them for this site and reviewed each one before publishing, so they are not questions from NYC Public Schools. Most are multiple choice, and the fill-in-the-blank ones ask you to type an answer (fractions like 3/4 work). Use scrap paper and no calculator, since you can’t bring one to the real test.

SHSAT Practice Test is independent and not affiliated with NYC (where our facts come from).

SHSAT math practice questions

  1. Question 1 of 10 What is the value of 0.4 − 1.3?

    Explanation

    1.3 is larger than 0.4 by 0.9, so subtracting 1.3 from 0.4 goes below zero: 0.4 − 1.3 = −0.9. −1.7 and 1.7 come from adding 0.4 and 1.3. 0.9 forgets the negative sign.

  2. Question 2 of 10 A park crew planted 72 trees, all maples or oaks. The ratio of maples to oaks is 7 : 2. How many oaks did the crew plant?

    Explanation

    The whole is 7 + 2 = 9 parts, so one part is 72 ÷ 9 = 8 trees. Oaks are 2 parts: 2 × 8 = 16. Check: 56 maples + 16 oaks = 72. 56 is tempting: that is the maples.

  3. Question 3 of 10 If p = (q + r)/s and s is not zero, what is q in terms of p, r and s?

    Explanation

    Multiply both sides by s first: ps = q + r. Then subtract r: q = ps − r. Check p = 3, r = 2, s = 4: q = 10, and (10 + 2)/4 = 3. (p − r)s is tempting: it subtracts r first, but r is inside the group divided by s.

  4. Question 4 of 10 Ms. Alvarez draws a straight line on the board and a ray from point O on the line, as shown. What is the measure of angle COB?
    Points A, O and B lie on a straight line. Ray OC goes up and to the right from O. Angle AOC is marked 132 degrees. Angle COB is marked with a question mark.132°?ABOC

    Explanation

    Angles AOC and COB lie along a straight line, so they add to 180°. Angle COB = 180° − 132° = 48°. 42° comes from 132° − 90°, which treats the line like a right angle. 132° repeats the given angle. 138° comes from first finding 42° and then subtracting it from 180°.

  5. Question 5 of 10 A pitcher's records show that 2 out of every 9 pitches she throws are curveballs. In her next game she throws 126 pitches. Based on her records, about how many of these pitches should be curveballs?

    Explanation

    Curveballs are 2/9 of all pitches. 126 ÷ 9 = 14, and 2 × 14 = 28. Check: 28 curveballs + 98 other pitches = 126, and 28 out of 126 is 2 out of 9. The tempting 14 finds one ninth of the pitches and forgets to multiply by 2.

  6. Question 6 of 10 A school art class paints a mural made of 25 equal square tiles in a 5-by-5 grid. The figure shows the tiles that are painted (dark). What percent of the mural is painted?
    A 5 by 5 grid of square tiles. Row 1 has 5 dark tiles, row 2 has 4, row 3 has 3, row 4 has 2, and row 5 has none.

    Explanation

    Count the painted tiles: 5 + 4 + 3 + 2 + 0 = 14 out of 25. 14/25 = 56/100 = 56%. An answer of 14 is just the count of painted tiles, and 44 is the percent of the mural that is not painted (11/25).

  7. Question 7 of 10 What is the unit rate for 45 meters in 6 seconds?

    Explanation

    Unit rate = meters ÷ seconds = 45 ÷ 6 = 7.5 meters per second. Check: 7.5 × 6 = 45. 2/15 divides 6 by 45 (that is seconds per meter); 7.3 writes the remainder 3 as a decimal; 75 drops the decimal point.

  8. Question 8 of 10 −(3/5)x = 12
    What is the value of x?

    Explanation

    Multiply both sides by −5/3, the reciprocal of −3/5: x = 12 × (−5/3) = −20. Check: −(3/5)(−20) = 12. The tempting 20 uses the right reciprocal but drops the negative sign.

  9. Question 9 of 10 A craft box is a rectangular prism, as shown. Marco fills it with wooden cubes that are 2 inches on each edge. How many cubes fit in the box with no gaps?
    A rectangular box. The front is 12 inches wide and 6 inches tall, and the box is 8 inches deep.12 in6 in8 in

    Explanation

    Along the 12-inch side, 12 ÷ 2 = 6 cubes fit. Along the 8-inch side, 4 cubes fit. Along the 6-inch side, 3 cubes fit. Number of cubes = 6 × 4 × 3 = 72. (Check: the box holds 12 × 8 × 6 = 576 cubic inches, and each cube is 2 × 2 × 2 = 8 cubic inches, so 576 ÷ 8 = 72.) 288 divides the box volume by 2, the edge of a cube, instead of by 8, its volume. 13 adds the counts along the three edges (6 + 4 + 3). 576 is the volume of the box, which counts 1-inch cubes.

  10. Question 10 of 10 A train line has 120 stations, numbered 1 through 120. Express train A stops at every station whose number is a multiple of 6. Express train B stops at every station whose number is a multiple of 9. How many stations are served by exactly one of the two express trains?

    Explanation

    Multiples of 6 up to 120: 120 ÷ 6 = 20. Multiples of 9: 120 ÷ 9 = 13 remainder 3, so 13. A station is a multiple of both 6 and 9 when it is a multiple of 18: 120 ÷ 18 = 6 remainder 12, so 6. Only train A: 20 − 6 = 14. Only train B: 13 − 6 = 7. Exactly one train: 14 + 7 = 21.

Take a full SHSAT math practice test

For a full SHSAT math practice test, take Practice Test 1. It is a full-length test we wrote, and this button opens it on the 50-question math section. The whole test has 50 math and 50 ELA questions in 3 hours. It ends with an estimated score range and an explanation for every question, and you do not need to sign up.

Ready for all 50 math questions under test conditions?

Start the SHSAT math practice test

How to use this set

What the SHSAT math section covers

NYC lists six math areas: ratios and proportional relationships, the number system and expressions, equations, inequalities, statistics and probability, and geometry. The math section of the Specialized High Schools Admissions Test (SHSAT) has 50 questions, both word problems and computation. The 8th-grade test covers New York State math standards through grade 7. The 9th-grade test covers standards through grade 8, so 9th graders should use our SHSAT 9th grade practice test page.

The short descriptions in this table are our own:

NYC’s six SHSAT math domains, with our short descriptions
NYC domainWhat a question can ask
Ratios and proportional relationshipsUnit rates, proportions, percent problems, scale
Number system and expressionsFractions, decimals and negative numbers; simplifying expressions
EquationsSolve for a missing value in one or more steps
InequalitiesSolve an inequality and show it on a number line
Statistics and probabilityMean and median, samples, the chance of an outcome
GeometryAngles, area, perimeter, circles, volume, surface area

Sources: NYC’s SHSAT page and the NYC Guide to the SHSAT for 2027 Admissions (PDF, pages 20 and 21), checked November 2, 2026.

Does SHSAT math include Algebra I or trigonometry?

No, not as NYC describes it. NYC tests 8th graders on New York State learning standards through grade 7, and 9th graders on standards through grade 8. NYC’s SHSAT pages and the 2027 guide do not mention Algebra I, trigonometry or the SAT anywhere. On the adaptive test, every test taker gets the same grade-level standards, content areas and question types.

What this means for practice:

Formulas to know (they are not given)

NYC does not give formulas on the test. It says students should know perimeter, area, volume and surface area formulas for 2D and 3D shapes. Our questions also include circle and mean formulas, among others. The last two rows are worth knowing.

Formulas to know for SHSAT math
Shape or topicFormulaWhy it is here
RectanglePerimeter = 2 × length + 2 × width; area = length × widthNYC lists perimeter and area
TriangleArea = 1/2 × base × heightNYC lists area
Rectangular prism (box)Volume = length × width × height; surface area = the sum of the areas of all 6 facesNYC lists volume and surface area
CircleArea = π × radius²; circumference = 2 × π × radiusIn our questions
MeanSum of the values ÷ number of valuesIn our questions
Right trianglea² + b² = c² (Pythagorean theorem)For 9th graders (grade 8 topic)
Percent change(new − original) ÷ original × 100Worth knowing

Working without a calculator

Calculators are not allowed on the SHSAT. NYC does not say whether the test software has an on-screen calculator, so practice without one. You get scrap paper, but only the answers you enter on screen count.

Common traps to watch for: mixing up a percent of a number with the new total, unit conversions, graph scales, and negative signs.

Next steps

Common questions

Does this practice adapt like the real test?

No. Our sets do not change based on your answers. NYC’s four practice tests do not adapt either. We opened all four on October 14, 2026, and each was a fixed list of 100 questions. The real SHSAT does adapt, so after each answer the next question can get harder or easier.

What answer formats are on the real test?

Multiple choice, fill in the blank, and technology-enhanced items. Examples include picking more than one answer or typing into an equation editor. Our set has multiple choice and typed grid-ins. For every item type and the full format, see SHSAT item types and format.

Is SAT math good practice for the SHSAT?

Only as extra skill work, if at all. SAT math goes well past the SHSAT’s scope, so it can waste time on topics the test does not use. Practice with the material on this page instead.