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 8

← 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 paint mixture contains \(\frac{5}{6}\) gallon of white paint for every \(\frac{1}{2}\) gallon of red paint. How many gallons of white paint are used per gallon of red paint? (Express your answer as a decimal.)
2.
An ice-cream shop sells 12 scoops for $30 and 4 scoops for $10. There is a proportional relationship between scoops and cost. What is the constant of proportionality?
3.
On a map, a scale of 2 inches represents 50 miles. Two cities are 7 inches apart on the map. A train travels between them at an average speed of 70 miles per hour. How many hours does the trip take?
4.
A landscaper plants oak and pine trees in a ratio of 5 : 3. If she plants 145 oak trees, how many pine trees does she plant?

Percents

5.
A farm has 896 chickens, which is 12% more than it had last year. How many more chickens does the farm have than last year?
6.
When asked a yes/no question, 80% of those polled answered “yes.” If 51 people did NOT answer yes, what was the total number of people polled?
7.
By what percent did the price of a cup of coffee increase if its price rose from $1.25 to $1.40?
8.
In a certain state the sales-tax rate increased from 6.0% to 6.5%. What was the increase in sales tax on a $320 item?

The Number System

9.
Simplify: \(6.3 \div 0.09\)
10.
What is the greatest common factor (GCF) of 360 and 420?
11.
How many integers between 1 and 200 (inclusive) are divisible by 6 but not by 9?
12.
Evaluate: \(\dfrac{3}{4} - \dfrac{1}{2} \cdot \dfrac{2}{3} + \dfrac{5}{12}\)

Expressions & Equations

13.
If \(4(2x - 3) - 2(x + 5) = 3x + 2\), what is the value of \(x\)?
14.
A taxi charges a $4.00 base fare plus $2.50 per mile. A second taxi charges a $6.00 base fare plus $2.00 per mile. At how many miles do the two taxis cost the same?
15.
The sum of three consecutive odd integers is 9 more than twice the largest of the three. What is the smallest of the three?

Word Problems & Rates

16.
Dalia rented a truck for a one-time fee of $45 plus $1 per mile. She used a coupon for 20% off the total cost and paid $52 after the coupon. How many miles did she drive?
17.
Lian bought enough oranges to fill 4 bags, with each bag holding 8 oranges. The total cost was $11.52. At that rate, how much would Lian pay for 50 oranges?
18.
A water tank with a 600-gallon capacity already holds 90 gallons. Water is added at 6 gallons per minute. After 40 minutes, what percent of the tank's capacity is filled? (Assume no water is lost.)

Geometry

19.
Two parallel lines are cut by a transversal. One angle measures \((4x + 10)^\circ\) and its corresponding angle measures \((6x - 20)^\circ\). What is the measure of this angle?
20.
A rectangle has a perimeter of 80 cm. Its length is 4 cm more than twice its width. What is the area of the rectangle?
21.
A triangle has sides of length 8, 13, and \(x\). If \(x\) is an integer, how many possible values of \(x\) are there?
22.
A cylindrical tank has a radius of 4 feet and a height of 10 feet. Water flows in at 8 cubic feet per minute. To the nearest minute, how long does it take to fill the tank? (Use \(\pi \approx 3.14\).)

Statistics & Probability

23.
The mean of 6 test scores is 81. If five of the scores are 75, 84, 88, 79, and 90, what is the sixth score?
24.
A bag contains 5 red, 4 blue, and 6 green marbles. Two marbles are drawn at random without replacement. What is the probability that both are green?
25.
The table shows the number of children in each of 80 families. What is the median number of children?
CHILDREN PER FAMILY
Number of childrenNumber of families
012
118
228
314
48

Results