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 9

← 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 smoothie uses \(\frac{7}{8}\) cup of yogurt for every \(\frac{1}{4}\) cup of honey. How many cups of yogurt are used per cup of honey? (Express your answer as a decimal.)
2.
A graph shows a proportional relationship between gallons of gas, \(x\), and miles driven, \(y\). The point \((3, 84)\) is on the graph. What does this point tell you about the relationship?
3.
The table shows cups of red and blue paint used to make a purple mixture, where the amounts are proportional. What is the value of \(y\)?
PURPLE PAINT
Cups of red paintCups of blue paint
11.5
46
11y
4.
A hiker plans to hike 24 miles over 3 days at a constant rate. Which equation describes the relationship between the number of days hiked, \(x\), and the number of miles traveled, \(y\)?

Percents

5.
Mr. Jones has 660 goats, which is 10% more than Mr. King has. How many more goats does Mr. Jones have than Mr. King?
6.
On a quiz, 75% of the students answered question 5 correctly. If 42 students did NOT answer it correctly, how many students took the quiz?
7.
The price of a sandwich was raised from $6.25 to $6.75. What was the percent increase in the price?
8.
Devin invests $750 in an account that earns 4% simple interest per year. How much interest does the account earn in 2 years, with no withdrawals?

The Number System

9.
Simplify: \(0.56 \div 0.007\)
10.
The product of three consecutive positive integers is 2,730. What is the sum of these three integers?
11.
When a positive integer \(N\) is divided by 8 the remainder is 5, and when \(N\) is divided by 6 the remainder is 1. What is the smallest value of \(N\) greater than 10?
12.
The reciprocal of 6 is added to the reciprocal of 2. What is the reciprocal of this sum?

Expressions & Equations

13.
If \(2x - 5y = 4\) and \(x + y = 9\), what is the value of \(x - y\)?
14.
If \(5(x - 2) - 3(2x + 1) = -x - 13\), how many values of \(x\) satisfy the equation?
15.
A cab company charges a $3.00 base fare plus $2.75 per mile. Another charges $5.50 base plus $2.25 per mile. At how many miles do the two cost the same?

Word Problems & Rates

16.
On Tuesday a print shop produced 80 more flyers than it did on Monday. On Wednesday it produced 40 fewer flyers than on Monday. If the three-day total was 400 flyers, how many flyers were produced on Tuesday?
17.
A printer prints 9 pages every 15 seconds. At this rate, how many minutes will it take to print a 360-page document?
18.
Misha needs ribbon for 2 backpack straps. Ribbon costs $4.00 per yard, and each strap requires \(1\frac{1}{4}\) yards. How much will Misha pay for the ribbon (not including tax)?

Geometry

19.
Angle M and angle R are supplementary. The measure of angle R is 5 times the measure of angle M. What is the measure of angle R, in degrees?
20.
A square is inscribed in a circle of radius 5. What is the area of the region inside the circle but outside the square? (Use \(\pi \approx 3.14\).)
21.
What is the area, in square feet, of the parallelogram shown below?
16 ft15 ft
22.
A triangle has sides of length 6, 9, and \(x\). If \(x\) is an integer, how many possible values of \(x\) are there?

Statistics & Probability

23.
Terrell played 5 video games and earned a mean score of 9 points per game. If his mean score for the first 4 games was 8 points per game, what was his score in the fifth game?
24.
A spinner is divided into 6 equal sections numbered 1 through 6. If the spinner is spun twice, what is the probability that the sum of the two numbers is exactly 7?
25.
The table shows the quiz scores in a class. What is the mean quiz score?
QUIZ SCORES
Quiz scoreNumber of students
6010
706
804
904
1001

Results