NYC SHSAT Sample Test, Form A (2024) — Original variations modeled on the math question types in the 2024 Form A (questions 58–114). Numbers and contexts are new — problems are not copied verbatim. · Added Jun 14, 2026

Practice Test 7

← All teststarget ~37:30 (90s/question, SHSAT pace)00:000 / 25 answered

The SHSAT runs about 90 seconds per question. This 25-question set ≈ 38 min — the timer counts up so you can track your pace.

Ratios & Proportional Relationships

1.
A trail-mix recipe uses \(\frac{3}{4}\) cup of raisins for every \(\frac{2}{5}\) cup of almonds. How many cups of raisins are used per cup of almonds? (Express your answer as a decimal.)
2.
A print shop charges a proportional rate: 5 pages cost $0.40 and 20 pages cost $1.60. What is the constant of proportionality for this relationship?
3.
A rectangular garden has an area of 720 square feet. In a scale drawing, 1 inch represents 12 feet. If the length of the garden is 5 inches in the drawing, what is the width of the garden in the drawing?
4.
Lin bought 5 crates of apples; each crate holds 9 apples. The total cost was $16.20. At that rate, how much would 30 apples cost?

Percents

5.
A library has 660 books in its new-arrivals section, which is 20% more than it had last month. How many more books does it have now than last month?
6.
In a survey, 65% of the people polled answered “yes.” If 84 people did NOT answer yes, what was the total number of people polled?
7.
The price of a notebook increased from $2.40 to $2.76. What was the percent increase in price?
8.
Carla deposits $480 in an account that earns 6% simple interest each year. How much will be in the account after 1 year, with no withdrawals?

The Number System

9.
Simplify: \(4.8 \div 0.012\)
10.
How many integers are in the list of consecutive integers from −7 to 18, inclusive?
11.
The reciprocal of 4 is added to the reciprocal of 6. What is the reciprocal of this sum?
12.
Each number in a sequence is formed by doubling the previous number and then subtracting 3. If the 5th number is 35, what is the 6th number minus the 3rd number?

Expressions & Equations

13.
Simplify: \(\dfrac{8x^3 y^2}{6xy} \cdot \dfrac{3y}{4x^2}\)
14.
A bike-rental shop charges a flat $25 fee plus $0.50 per mile. Sam used a coupon for 20% off the total and then paid $28. How many miles did Sam ride?
15.
A 12-foot board is cut into two pieces of different lengths. The shorter piece has length \(x\) feet. Which inequality expresses all possible values of \(x\)?

Word Problems & Rates

16.
On Friday a bakery made 120 more muffins than it made on Thursday. On Saturday it made 30 fewer muffins than on Thursday. If the total for the three days was 480 muffins, how many were made on Friday?
17.
Mara's plant grows 1.5 inches every 2 weeks. Every 2 weeks she also trims 0.5 inch off the top. If the plant starts at 4 inches tall, how tall is it after 8 weeks?
18.
A factory makes 144 widgets in 6 hours at a constant rate. How many widgets does it make in a 15-hour shift?

Geometry

19.
Angle A and angle B are supplementary. The measure of angle B is 4 times the measure of angle A. What is the measure of angle B, in degrees?
20.
One square has a side length of 14 inches and another has a side length of 16 inches. What is the difference, in square inches, between their areas?
21.
What is the area, in square feet, of the parallelogram shown below?
25 ft18 ft
22.
Raquel makes a square pyramid from a square base with side 10 inches and 4 identical triangular faces. Each triangular face has a base of 10 inches and a slant height (the triangle's height) of 12 inches. What is the total surface area, in square inches, including the base?
10 in12 in

Statistics & Probability

23.
The table shows the number of pets in each of 50 households. What is the median number of pets?
PETS PER HOUSEHOLD
Number of petsNumber of households
018
114
210
35
43
24.
At a diving competition, seven judges each give a score. The highest and lowest scores are discarded, and the mean of the remaining five is reported. A diver received the scores 7.8, 8.4, 8.0, 8.6, 8.2, 9.0, and 7.6. What is the diver's reported score?
25.
A bag of 30 candies has a \(\frac{2}{5}\) probability of drawing a red candy at random. After 6 red candies are removed from the bag, what is the probability of randomly drawing a red candy?

Results