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 2

← 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 $176.00 before tax. The tax rate is 8.5%, and the diners want to add an 18% tip calculated on the pre-tax amount. If 5 people split the total equally, how much does each person pay?
2.
A map uses a scale of 2.4 inches = 54 miles. Two towns are 6.8 inches apart on the map. A bus travels between them averaging 51 mph. How many hours does the trip take?
3.
A jacket is on sale for 25% off. A customer uses a coupon for an additional 20% off the sale price. After both discounts, the jacket costs $54. What was the original price?
4.
Drink A is made with 4 cups of juice and 7 cups of water. Drink B is made with 5 cups of juice and 9 cups of water. Which drink has a higher juice-to-water ratio, and by what fraction of a cup of juice per cup of water is the ratio greater?
5.
A scanner processes 9 pages every 15 seconds. At this rate, how many minutes will it take to process 324 pages?

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

6.
How many integers between 1 and 400 (inclusive) are divisible by 5 but not by 8?
7.
What is the greatest common factor (GCF) of 756 and 1,134?
8.
The product of three consecutive positive integers is 2,730. What is the sum of these three integers?
9.
When a positive integer \(N\) is divided by 8, the remainder is 5. When \(N\) is divided by 6, the remainder is 3. What is the smallest possible value of \(N\) greater than 30?
10.
Evaluate: \(\dfrac{5}{6} - \dfrac{2}{3} \cdot \dfrac{3}{8} + \dfrac{7}{12}\)

3. Expressions & Equations (EE)

11.
If \(5(2x - 3) - 4 = 10x - 19\), what is the value of \(x\)?
12.
A bike rental shop charges a $12 starting fee plus $5 per hour. Another shop charges a $20 starting fee plus $3 per hour. After how many hours do both rentals cost the same?
13.
Simplify: \(\dfrac{8x^3y^2}{6xy} \cdot \dfrac{3y}{4x}\)
14.
The sum of three consecutive odd integers is 15 more than twice the smallest of the three. What is the largest of the three integers?
15.
If \(3x - 2y = 16\) and \(x + y = 7\), what is the value of \(x - y\)?

4. Geometry (G)

16.
A rectangle has a perimeter of 88 cm. Its length is 8 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 \((4x + 7)°\), and its corresponding angle measures \((6x - 19)°\). What is the measure of either angle?
18.
A cylindrical tank has a radius of 4 feet and a height of 15 feet. If water flows in at 12 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 9, 14, 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 5. 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 6 test scores is 79. If 5 of the scores are 74, 76, 81, 83, and 85, what is the sixth score?
22.
A bag contains 5 red marbles, 7 blue marbles, and 4 green marbles. Two marbles are drawn at random without replacement. What is the probability that both are red?
23.
A sandwich shop offers 4 types of bread, 3 types of cheese, and 7 fillings. If a sandwich must have exactly 2 different fillings (order doesn't matter), how many distinct sandwiches are possible?
24.
The median of the data set {4, 8, 11, \(x\), 17, 20} is 13. What is the value of \(x\)?
25.
A standard six-sided number cube is rolled twice. What is the probability that the sum of the two rolls is exactly 8?

Results