SHSAT Math Practice Questions NYC – With Answers

Practice SHSAT Math with real-style questions, detailed explanations, and strategies designed for NYC students preparing for the digital and adaptive SHSAT.

Preparing for the SHSAT Math section requires more than just understanding basic concepts. Students must solve multi-step problems, apply logic, and work efficiently under time pressure.

At Tariq’s Class, students prepare using the Sigma digital platform, which provides full-length SHSAT practice tests, timed sections, and realistic question formats aligned with the current digital exam and the adaptive SHSAT beginning in 2026.

Students can begin practicing full-length SHSAT Math tests using the Sigma platform here:
https://www.tariqsclass.com/products/courses/shsat-sigma

What Is Covered on SHSAT Math?

The SHSAT Math section tests middle school math concepts at a higher level of difficulty. Questions often combine multiple skills in one problem.

Topics include:

  • Algebra and expressions
  • Word problems and multi-step reasoning
  • Ratios and proportions
  • Percentages
  • Geometry (area, volume, angles)
  • Probability

Success on SHSAT Math requires both strong fundamentals and the ability to apply concepts quickly and accurately.

SHSAT Math Practice Questions

Below are realistic SHSAT-style questions with detailed explanations.

Question 1 (Combinatorics)

A teacher wants to create a schedule for Friday. There are five subjects: Math, Art, Sports, History, and English. The only condition is that Math cannot go immediately after Sports.

How many different schedules are possible?

Answer: 96

Explanation:

Total arrangements of 5 subjects:
5! = 120

Invalid cases (Sports followed immediately by Math):

Treat (Sports-Math) as one block → now 4 items

Arrangements:
4! = 24

Valid schedules:
120 − 24 = 96

Question 2 (Age Problem)

Isaac is 34 years old now. Six years ago, his brother was as old as Isaac was three years ago. How old will Isaac’s brother be in 3 years?

A. 31
B. 37
C. 40
D. 43

Answer: C (40)

Explanation:

Isaac now = 34

Isaac 3 years ago:
34 − 3 = 31

Brother 6 years ago = 31

Brother now:
31 + 6 = 37

In 3 years:
37 + 3 = 40

Question 3 (Rates)

It took Ralph 8 days to read a 360-page book. Diana reads at a rate of 50 pages per day. How many more days will it take Ralph than Diana to read a 450-page book?

E. 1
F. 2
G. 3
H. 4

Answer: E (1)

Explanation:

Ralph’s rate:
360 ÷ 8 = 45 pages/day

Time for Ralph:
450 ÷ 45 = 10 days

Time for Diana:
450 ÷ 50 = 9 days

Difference:
10 − 9 = 1

Question 4 (Probability)

Mr. Bertram has two boxes of candy.

Box 1:
4 dark, 6 milk

Box 2:
3 dark, 7 milk

One candy is chosen from each box. What is the probability that one is milk chocolate and the other is dark chocolate?

E. 0.46
F. 0.36
G. 0.28
H. 0.18

Answer: E (0.46)

Explanation:

Milk (Box 1) × Dark (Box 2):
(6/10)(3/10) = 18/100

Dark (Box 1) × Milk (Box 2):
(4/10)(7/10) = 28/100

Total:
18/100 + 28/100 = 46/100 = 0.46

Question 5 (Percent & Algebra)

There are 45 people in a café. The number of 28% of adults is equal to 35% of the children. How many children are there?

E. 18
F. 20
G. 24
H. 25

Answer: F (20)

Explanation:

Let:
Adults = A
Children = C

A + C = 45

Given:
0.28A = 0.35C

A/C = 5/4

So:
A = (5/4)C

Substitute:
(5/4)C + C = 45

(9/4)C = 45

C = 20

Question 6 (Algebraic Expression)

Simplify:

(2/a)(2a/b − b/2a)

A. 4a²/b − b
B. 4/b − b/a²
C. 4a/b − b/a
D. 4a − b/a²

Answer: B

Explanation:

Distribute:

(2/a)(2a/b) = 4/b

(2/a)(b/2a) = b/a²

Final:
4/b − b/a²

Why Practice Questions Are Important

Practicing SHSAT Math questions helps students:

  • Improve problem-solving skills
  • Identify weak areas
  • Build confidence
  • Increase speed and accuracy

Students who practice consistently perform better on the actual exam.

SHSAT Math Strategy Tips

1. Work Step-by-Step

Avoid mental math for complex problems.

2. Manage Time Carefully

Do not spend too long on one question.

3. Check Your Work

Review calculations if time allows.

4. Practice Digitally

The SHSAT is now computer-based, so screen practice is essential.

Digital and Adaptive SHSAT Preparation

With the SHSAT now digital and transitioning to adaptive format in 2026, students must prepare differently.

They should practice:

  • On a computer
  • Under timed conditions
  • Without skipping questions
  • With realistic test simulations

At Tariq’s Class, the Sigma platform is designed to match these conditions.

Start Practicing SHSAT Math

Students preparing for the SHSAT need structured, realistic practice.

The Sigma platform provides:

  • Full-length SHSAT Math tests
  • Timed digital practice
  • Real exam simulation
  • Performance tracking

Start practicing here:
https://www.tariqsclass.com/products/courses/shsat-sigma