FREE SHSAT Math Practice Test

What changes for the fall 2026 SHSAT?

NYC Public Schools describes a computer-adaptive SHSAT beginning in fall 2026, for 2027 admissions. It has 50 Math questions and 50 ELA questions, with 180 minutes of standard testing time shared between the sections. Items include multiple-choice, fill-in-the-blank, and technology-enhanced questions. In Math, you must answer before advancing and cannot return to a previous question.

Use the official NYC Public Schools SHSAT guidance for current rules and links to digital practice. The NYC SHSAT Portal provides full-length digital samples and grade-specific preparation, including Grade 9 sample questions. Students taking the test as ninth graders should use those additional materials rather than treating this general review set as a complete Grade 9 diagnostic.

The questions on this page review fractions, percents, equations, geometry, averages, and counting. They retain some broader algebra and geometry practice, including polynomial simplification and a special right triangle; use them for skill review rather than as a topic-weighting guide. No official past-exam origin is claimed.

20 SHSAT Math review questions

1- Out of 55,000 voters in a city, 2,500 voted for a particular candidate. What fraction of voters voted for this candidate?

A. \(\frac{1}{22}\)

B. \(\frac{1}{20}\)

C. \(\frac{1}{18}\)

D. \(\frac{1}{15}\)

2- What is the value of \(4 \div \frac{1}{6} \)?

A. \(\frac{2}{3}\)

B. 6

C. 18

D. 24

3- Simplify \((6x^3-8x^2+2x^4 )-(4x^2-2x^4+2x^3 )\).

A. \(2x^4+4x^3-4x^2\)

B. \(4x^4+4x^3-12x^2\)

C. \(4x^4-4x^3-12x^2\)

D. \(8x^4+8x^3-12x^2\)

4- The population of a city increased by \(15\%\) in the first year and by \(20\%\) in the second year. What is the total percent increase in population over the two years?

A. \(35\%\)

B. \(37\%\)

C. \(38\%\)

D. \(40\%\)

5- What is the surface area of a cylinder with a diameter of 6 inches and a height of 8 inches?

A. \(48\pi \space in^2\)

B. \(54\pi \space in^2\)

C. \(66\pi \space in^2\)

D. \(132\pi \space in^2\)

6- A cruise line ship left Port A and traveled 80 miles due west and then 150 miles due north. At this point, what is the shortest distance from the cruise to port A in miles? ____________

7- A shirt costing $200 is discounted \(15\%\). After a month, the shirt is discounted another \(15\%\). Which of the following expressions can be used to find the selling price of the shirt?

A. \((200) (0.70)\)

B. \((200) \mathbin{-} 200 (0.30)\)

C. \((200) (0.15) \mathbin{-} (200) (0.15)\)

D. \((200) (0.85) (0.85)\)

8- \(5 + 8 \times (- 2) \mathbin{-} [4 + 22 \times 5] \div 6 = ? \)

A. \(-30\)

B. \(-20\)

C. \(-10\)

D. 0

9- Which of the following points lies on the line \(x+2y=4\)?

A. \((-2, 3)\)

B. \((1, 2)\)

C. \((-1, 3)\)

D. \((-3, 4)\)

10- 5 less than twice a positive integer is 83. What is the integer?

A. 39

B. 41

C. 42

D. 44

11- 11 yards 6 feet and 4 inches equal to how many inches?

A. 388

B. 468

C. 472

D. 476

12- Mr. Carlos’s family is choosing a menu for their reception. They have 3 choices of appetizers, 5 choices of entrees, and 4 choices of cake. If they choose one appetizer, one entree, and one cake, how many different menus are possible?

A. 12

B. 32

C. 60

D. 120

13- The average of five consecutive integers is 38. What is the smallest number?

A. 38

B. 36

C. 34

D. 12

14- What is the difference between the smallest positive 4-digit integer and the largest 4-digit integer?

A. 6666

B. 6789

C. 8888

D. 8999

15- How many tiles of 8 cm\(^2 \) are needed to cover a floor of dimension 6 cm by 24 cm?

A. 6

B. 12

C. 18

D. 24

16- A ladder leans against a wall forming a \(60^ \circ \) angle between the ground and the ladder. If the bottom of the ladder is 30 feet away from the wall, how long is the ladder?

A. 30 feet

B. 40 feet

C. 50 feet

D. 60 feet

17- The average weight of 18 girls in a class is 60 kg, and the average weight of 32 boys in the same class is 62 kg. What is the average weight of all the 50 students in that class?

A. 60

B. 61.28

C. 61.68

D. 62.90

18- An angle is equal to one-fifth of its supplement. What is the measure of that angle?

A. 20

B. 30

C. 45

D. 60

19- In a stadium, the ratio of home fans to visiting fans in a crowd is 5:7. Which of the following could be the total number of fans in the stadium?

A. 12,324

B. 42,326

C. 44,566

D. 66,812

20- If \(40\%\) of a class are girls, and \(25\%\) of girls play tennis, what percent of the class are girls who play tennis?

A. \(10\%\)

B. \(15\%\)

C. \(20\%\)

D. \(40\%\)

Answers and explanations

2- D
\(4 \div \frac{1}{6} = 24 \)

3- B
Distribute the subtraction across the second group, then combine matching powers.
Fourth powers: \(2x^4+2x^4=4x^4\).
Cubes: \(6x^3-2x^3=4x^3\).
Squares: \(-8x^2-4x^2=-12x^2\).
Result: \(4x^4+4x^3-12x^2\).

4- C
the population is increased by \(15\%\) and \(20\%\).
\(15\%\) increase changes the population to \(115\%\) of original population.
For the second increase, multiply the result by \(120\%\).
\((1.15) \times (1.20) = 1.38 = 138\%\)
38 percent of the population is increased after two years.

5- C
Surface Area of a cylinder \(= 2\pi\) r (r + h),
The radius of the cylinder is \(3(6 \div 2)\) inches and its height is 8 inches. Therefore,
Surface Area of a cylinder \(= 2\pi (3) (3 + 8) = 66\pi\)

6- 170
The westward and northward distances form perpendicular legs of a right triangle. The direct route is its hypotenuse.
\(c^2=80^2+150^2\).
\(c^2=6400+22500=28900\).
Taking the positive square root gives \(c=170\) miles.

7- D
To find the price after a discount, multiply the original price by (\(100{\%} – \)Rate of discount).
Therefore, for the first discount we get: \((200) (100{\%} \mathbin{-} 15{\%}) = (200) (0.85) = 170\)
For the next \(15{\%}\) discount: \((200) (0.85) (0.85)\)

8- A
Multiply inside the brackets first: \(4+22\times5=114\).
Then \(114\div6=19\) and \(8\times(-2)=-16\).
Finally, \(5-16-19=-30\).

9- A
Substitute each point into \(x+2y\). For A: \(-2+2(3)=4\). For B, C, and D the results are 5, 5, and 5, respectively. Only A satisfies \(x+2y=4\).

10- D
Let \(x\) be the integer. Then:
\(2x – 5 = 83\)
Add 5 both sides: \(2x = 88\)
Divide both sides by \(2: x = 44\)

11- C
\(11 \times 36 + 6 \times 12 + 4 = 472\)

12- C
To find the number of possible menu combinations, multiply the number of options for each factor:
\(3 \times 5 \times 4 = 60\)

13- B
The average of five consecutive integers is the middle integer. The five numbers are 36, 37, 38, 39, and 40, so the smallest is 36. Check: their sum is 190, and \(190\div5=38\).

14- D
The smallest 4, digit number is 1000, and the biggest 4, digit number is 9999. The difference is: 8999

15- C
The area of the floor is: 6 cm \(\times\) 24 cm = 144 cm\(^2 \)
The number of tiles needed \(= 144 \div 8 = 18\)

16- D
The ladder, wall, and ground form a right triangle. The angle between the ladder and ground is 60 degrees, so the other acute angle is 30 degrees. In a 30-60-90 triangle, the side opposite 30 degrees is half the hypotenuse. The 30-foot base is that shorter leg, so the ladder is \(2 \times 30 = 60\) feet long.

17- B
average \(= \frac{sum of terms}{number of terms}\)
The sum of the weight of all girls is: \(18 \times 60 = 1080\) kg
The sum of the weight of all boys is:\( 32 \times 62 = 1984\) kg
The sum of the weight of all students is: \(1080 + 1984 = 3064\) kg
average \(= \frac{3064}{50}=61.28 \)

18- B
The sum of supplement angles is 180. Let \(x\) be that angle. Therefore,
\(x + 5x = 180\)
\(6x = 180\), divide both sides by 6: \(x = 30\)

19- A
In the stadium the ratio of home fans to visiting fans in a crowd is \(5:7\). Therefore, total number of fans must be divisible by \(12: 5 + 7 = 12.\)
Let’s review the choices:
A. \(12,324: 12,324 \div 12 = 1027\)
B. \(42,326: 42,326 \div 12 = 3,527.166\)
C. \(44,566: 44,566 \div 12 = 3,713.833\)
D. \(66,812: 66,812 \div 12 = 5,567.666\)
Only choice A when divided by 12 results in a whole number.

20- A
The percentage of the whole class who are girls playing tennis is:
\(40 \% \times 25\% = 0.40 \times 0.25 = 0.10 = 10\%\)

Turn missed questions into focused review

Work on paper and record your answer before reading its explanation. For this short set, track your time to find slow skills; a score out of 20 cannot predict an official adaptive SHSAT score or a school offer.

Separate a calculation error from a setup error. For Questions 4, 7, and 20, identify the quantity each percentage applies to. For Question 6, sketch the perpendicular legs before using the Pythagorean theorem. For Question 17, find the total weight before dividing by the total number of students.

Use the SHSAT Math Online Center to choose a matching topic lesson or worksheet, then retry the missed question without the solution. For practice with the actual digital navigation and item types, return to the official portal above.

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Practice questions answered

Is this a full-length SHSAT Math test?

No. This page contains 20 independent mixed-skill practice questions and worked solutions. It does not reproduce the current adaptive exam or provide an official score prediction.

Where can I find official digital and Grade 9 SHSAT practice?

Use the NYC SHSAT Portal linked above for official digital sample tests and specific Grade 9 sample questions. This general review set is not a complete Grade 9 diagnostic.

How should I check my work?

Attempt the questions first, then compare your steps with the explanations. Review the skill behind each error and retry the question without looking at the solution.