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

Practice Test 1

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

The SHSAT runs about 90 seconds per question. This 25-question set β‰ˆ 38 min β€” the timer counts up so you can track your pace.

1. Ratios & Proportional Relationships (RP)

1.
A restaurant bill is $148.50 before tax. The tax rate is 8.875%, and the diners want to add a 20% tip calculated on the pre-tax amount. If 6 people split the total equally, how much does each person pay?
2.
A map uses a scale of 1.5 inches = 40 miles. Two cities are 5.25 inches apart on the map. A car drives between them averaging 56 mph. How many hours does the trip take?
3.
A shirt is on sale for 30% off. Maria has a coupon for an additional 15% off the sale price. After both discounts, she pays $35.70 (no tax). What was the original price?
4.
Recipe A calls for 3 cups of flour and 2 cups of sugar. Recipe B calls for 5 cups of flour and 3 cups of sugar. Which recipe is sweeter (has a higher sugar-to-flour ratio), and by what fraction of a cup of sugar per cup of flour is it sweeter?
5.
A printer prints 7 pages every 12 seconds. At this rate, how many minutes will it take to print a 245-page document?

2. The Number System (NS) β€” including divisibility & counting tricks

6.
How many integers between 1 and 300 (inclusive) are divisible by 4 but not by 6?
7.
What is the greatest common factor (GCF) of 504 and 672?
8.
The product of three consecutive positive integers is 1,716. What is the sum of these three integers?
9.
When a positive integer N is divided by 7, the remainder is 3. When N is divided by 5, the remainder is 2. What is the smallest possible value of N greater than 20?
10.
Evaluate: \(\dfrac{2}{3} - \dfrac{1}{4} \cdot \dfrac{8}{9} + \dfrac{5}{6}\)

3. Expressions & Equations (EE)

11.
If \(3(2x - 5) - 4(x + 1) = 2x + 7\), what is the value of \(x\)?
12.
A taxi charges a $3.50 base fare plus $2.25 per mile. A second taxi charges a $5.00 base fare plus $1.75 per mile. At how many miles do both taxis cost the same?
13.
Simplify: \(\dfrac{6x^2 y^3}{4xy} \cdot \dfrac{2y}{3x}\)
14.
The sum of three consecutive even integers is 6 more than twice the smallest of the three. What is the largest of the three?
15.
If \(2x - 3y = 11\) and \(x + y = 3\), what is the value of \(x - y\)?

4. Geometry (G)

16.
A rectangle has a perimeter of 84 cm. Its length is 6 cm more than twice its width. What is the area of the rectangle?
17.
In the figure below, lines \(\ell\) and \(m\) are parallel, cut by a transversal. One angle measures \((3x + 20)Β°\) and the corresponding angle measures \((5x - 10)Β°\). What is the measure of the smaller angle?
18.
A cylindrical water tank has a radius of 5 feet and a height of 12 feet. If water flows in at 10 cubic feet per minute, how many minutes (to the nearest minute) does it take to fill the tank? (Use Ο€ β‰ˆ 3.14)
19.
A triangle has sides of length 7, 10, 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 6. What is the area of the region inside the circle but outside the square? (Use Ο€ β‰ˆ 3.14)

5. Statistics & Probability (SP)

21.
The mean of 5 test scores is 84. If 4 of the scores are 78, 82, 88, and 90, what is the fifth score?
22.
A bag contains 4 red marbles, 6 blue marbles, and 5 green marbles. Two marbles are drawn at random without replacement. What is the probability that both are blue?
23.
A pizza place offers 3 sizes, 2 crust types, and 8 toppings. If a pizza must have exactly 3 different toppings (order doesn't matter), how many distinct pizzas are possible?
24.
The median of the data set {3, 7, 9, \(x\), 15, 18} is 11. What is the value of \(x\)?
25.
A spinner is divided into 8 equal sections numbered 1 through 8. If the spinner is spun twice, what is the probability that the sum of the two numbers is exactly 9?

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