Updated
Below are 14 sample questions, two from each topic, with the answer and a step-by-step explanation under each one. Every question is an original PrepCAT practice item, not an official SHSAT question. Then practice all 76 questions with instant feedback; your accuracy by topic is saved to My Progress.
Rates, scale, proportions and percent change, including discounts, tax and percent increase. PrepCAT has 12 ratios & percents questions; here are 2. Practice all 12 →
A jacket costs $80. It is on sale for 25% off, and then a 5% sales tax is added to the sale price. What is the final cost of the jacket?
Answer: B. $63.00
Sale price: 80 × 0.75 = 60. With tax: 60 × 1.05 = 63. Choice C combines the percents first (20% off), which is not equivalent.
On a map, 1 inch represents 25 miles. Two towns are 3.2 inches apart on the map. What is the actual distance between them?
Answer: C. 80 miles
3.2 × 25 = 80 miles.
Equivalent expressions, equations, inequalities and word problems that need an equation. PrepCAT has 13 expressions & equations questions; here are 2. Practice all 13 →
Which inequality describes all solutions of −3x + 5 ≥ 20?
Answer: B. x ≤ −5
Subtract 5: −3x ≥ 15. Divide by −3 and reverse the sign: x ≤ −5.
The length of a rectangle is 3 inches more than twice its width. The perimeter is 54 inches. What is the width, in inches?
Typed answer: work it out, then check below.
Answer: 8
2(w + 2w + 3) = 54, so 6w + 6 = 54 and w = 8.
Negative numbers, fractions, decimals, exponents and distance on a number line. PrepCAT has 8 number system questions; here are 2. Practice all 8 →
What is the value of (−2)³ − (−3)²?
Answer: A. −17
(−2)³ = −8 and (−3)² = 9, so −8 − 9 = −17.
Point P is at −3.5 and point Q is at 4.25 on a number line. What is the distance between P and Q?
Answer: C. 7.75
Distance = |4.25 − (−3.5)| = 4.25 + 3.5 = 7.75. Choice A subtracts the absolute values.
Angles, triangles, circles, area and volume. The SHSAT does not give formulas, so students need them memorized. PrepCAT has 5 geometry questions; here are 2. Practice all 5 →
Two angles are complementary. The larger angle is 4 times the smaller angle. What is the measure of the smaller angle?
Answer: A. 18°
x + 4x = 90, so 5x = 90 and x = 18°. Choice C uses 180° instead of 90°.
A circle has a diameter of 10 centimeters. What is its area, in square centimeters?
Answer: C. 25π
The radius is 5, so the area is π × 5² = 25π. Choice D uses the diameter as the radius.
Mean and data sets, and the probability of simple and compound events. PrepCAT has 6 statistics & probability questions; here are 2. Practice all 6 →
The mean of 6 numbers is 20. After one number is removed, the mean of the remaining 5 numbers is 18. What number was removed?
Answer: D. 30
Total before: 6 × 20 = 120. Total after: 5 × 18 = 90. Removed: 120 − 90 = 30.
Two fair six-sided number cubes are rolled. What is the probability that the sum is 8?
Answer: B. 5/36
Sums of 8: (2,6), (3,5), (4,4), (5,3), (6,2), which is 5 of 36 outcomes.
Grammar, punctuation and combining sentences, in the style of Revising/Editing Part B. PrepCAT has 18 revising & editing questions; here are 2. Practice all 18 →
Which sentence is punctuated correctly?
Answer: C. My cousin, who lives in Queens, visits us every summer.
C is correct: a nonessential clause (“who lives in Queens”) needs a comma on both sides.
What is the best way to combine the sentences?
Answer: B. Mount Everest, which stands on the border between Nepal and China, is the highest mountain above sea level.
B is correct: it combines the ideas with a nonessential clause and keeps the meaning. A is a comma splice, C is ungrammatical, and D changes the meaning.
Questions about a passage: central idea, how a paragraph fits, and what the evidence shows. PrepCAT has 14 reading comprehension questions; here are 2. Practice all 14 →
1 An octopus resting on a coral reef can vanish in less than a second. Its skin shifts from pale cream to mottled brown, and small bumps rise to copy the texture of rock. For a predator scanning the reef, the octopus has simply disappeared.
2 The trick depends on thousands of tiny sacs of pigment in the skin called chromatophores. Each sac is surrounded by small muscles connected to nerves. When the muscles pull, the sac stretches wide and shows its color; when they relax, the sac shrinks to a dot that is almost invisible. Because nerves control the muscles directly, an octopus can change color far faster than animals that rely on slower chemical signals.
3 Color change is not only for hiding. Some octopuses flash dark colors when threatened, perhaps to startle an attacker, and scientists have observed color displays when two octopuses meet.
4 One puzzle remains. Most octopuses appear to have only one type of light-detecting cell in their eyes, which suggests that they cannot see color the way people do. How, then, do they match their surroundings so well? Researchers are testing several ideas, including the possibility that light-sensitive proteins in the skin play a role. For now, the octopus remains a master of disguise that keeps some of its own secrets.
Original passage written for PrepCAT.
Paragraph 2 mainly explains
Answer: A. how chromatophores produce changes in color.
A is correct: the paragraph describes the pigment sacs, the muscles around them, and how stretching or relaxing shows or hides color.
Why does the author point out that nerves control the muscles directly (paragraph 2)?
Answer: A. to explain why an octopus can change color so quickly
A is correct: the sentence contrasts direct nerve control with “slower chemical signals” to explain the speed.
Ready for the real format? Take PrepCAT’s 40-minute adaptive SHSAT practice test (21 questions, no sign-up), or the four official NYC practice tests. See what’s on the 2026 SHSAT for the full topic list.
Pick a topic, answer, and see why each choice is right or wrong. Your accuracy by topic is saved to My Progress.
All questions are original PrepCAT practice items aligned to New York State grade 6–7 standards, in the styles used on the SHSAT. They are not official SHSAT questions.