Original practice set (not from a published test) — Authored to the NY State Next Generation Math Standards across the same SHSAT reporting categories. · Added Jun 6, 2026

Practice Test 3

← 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.

1. Ratios & Proportional Relationships (RP)

1.
A restaurant bill is $192.00 before tax. The tax rate is 7.5%, and the diners want to add a 22% tip calculated on the pre-tax amount. If 8 people split the total equally, how much does each person pay?
2.
A map uses a scale of 1.2 inches = 36 miles. Two cities are 5.6 inches apart on the map. A car drives between them averaging 48 mph. How many hours does the trip take?
3.
A coat is on sale for 40% off. A customer uses a coupon for an additional 10% off the sale price. After both discounts, the coat costs $43.20. What was the original price?
4.
Mix A is made with 5 cups of syrup and 8 cups of water. Mix B is made with 3 cups of syrup and 5 cups of water. Which mix has a higher syrup-to-water ratio, and by what fraction of a cup of syrup per cup of water is the ratio greater?
5.
A machine processes 8 pages every 18 seconds. At this rate, how many minutes will it take to process 320 pages?

2. The Number System (NS) — including divisibility & counting tricks

6.
How many integers between 1 and 360 (inclusive) are divisible by 6 but not by 9?
7.
What is the greatest common factor (GCF) of 648 and 1,080?
8.
The product of three consecutive positive integers is 4,080. What is the sum of these three integers?
9.
When a positive integer \(N\) is divided by 9, the remainder is 4. When \(N\) is divided by 7, the remainder is 2. What is the smallest possible value of \(N\) greater than 25?
10.
Evaluate: \(\dfrac{3}{4} - \dfrac{1}{2} \cdot \dfrac{5}{6} + \dfrac{2}{3}\)

3. Expressions & Equations (EE)

11.
If \(4(3x - 2) - 5(x + 1) = 7x + 3\), what is the value of \(x\)?
12.
A plumber charges a $40 service fee plus $35 per hour. Another plumber charges a $60 service fee plus $30 per hour. After how many hours do both plumbers cost the same?
13.
Simplify: \(\dfrac{9x^4 y^3}{6x^2 y} \cdot \dfrac{2y}{3x}\)
14.
The sum of three consecutive even integers is 24 more than twice the smallest of the three. What is the largest of the three integers?
15.
If \(4x - 3y = 18\) and \(x + y = 8\), what is the value of \(x - y\)?

4. Geometry (G)

16.
A rectangle has a perimeter of 72 cm. Its length is 6 cm more than twice its width. What is the area of the rectangle?
17.
Lines \(\ell\) and \(m\) are parallel and cut by a transversal. One angle measures \((5x + 8)°\), and its corresponding angle measures \((7x - 22)°\). What is the measure of either angle?
18.
A cylindrical tank has a radius of 6 feet and a height of 10 feet. If water flows in at 9 cubic feet per minute, how many minutes does it take to fill the tank, to the nearest minute? (Use π ≈ 3.14)
19.
A triangle has sides of length 8, 15, and \(x\). If \(x\) is an integer, how many possible values of \(x\) are there?
20.
A square is inscribed in a circle of radius 8. What is the area of the region inside the circle but outside the square? (Use π ≈ 3.14)

5. Statistics & Probability (SP)

21.
The mean of 7 test scores is 88. If 6 of the scores are 82, 85, 90, 91, 93, and 95, what is the seventh score?
22.
A bag contains 6 red marbles, 5 blue marbles, and 4 green marbles. Two marbles are drawn at random without replacement. What is the probability that both are green?
23.
An ice cream shop offers 5 flavors, 3 cone types, and 6 toppings. If a sundae must have exactly 2 different toppings (order doesn't matter), how many distinct sundaes are possible?
24.
The median of the data set {5, 9, 12, \(x\), 16, 21} is 14. What is the value of \(x\)?
25.
A spinner is divided into 10 equal sections numbered 1 through 10. If the spinner is spun twice, what is the probability that the sum of the two numbers is exactly 11?

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