Top 10 7th Grade PSSA Math Practice Questions
TL;DR: If your seventh grader is prepping for PSSA Math in Pennsylvania, these 10 practice questions cover what the test leans on hardest at this level: proportional reasoning, integer and rational operations, two-step equations, and geometry. Each one comes with a full worked solution, so when something gets missed you can review the reasoning together step by step. A solid quick gut-check before test day to find the topics that still need a little more time.
Key takeaways:
- PSSA Grade 7 math is given each spring in Pennsylvania.
- All 10 practice questions come with step-by-step worked solutions.
- Aligned with the Pennsylvania Core Standards for Math grade 7.
- Includes multiple choice and open-ended items – both count.
- Open-ended items reward clear, labeled steps for partial credit.
Help your students start their PSSA Math test prep journey right now with these sample 7th Grade PSSA Math questions.
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1- Two concentric circles are drawn. The larger circle has a radius of \(8\) cm and the smaller circle has a radius of \(5\) cm. What is the area of the region between the two circles?
A. \(25\pi \space cm^2\)
B. \(36\pi \space cm^2\)
C. \(39\pi \space cm^2\)
D. \(64\pi \space cm^2\)
2- William ate \(\frac{1}{4}\) of his pizza and Ella ate \(\frac{1}{2}\) of her pizza. What part of the two pizzas was left?
A. \(\frac{1}{2}\)
B. \(\frac{1}{3}\)
C. \(\frac{3}{8}\)
D. \(\frac{5}{8}\)
3- Simplify \(6x^2 y^3 (2x^2 y)^3\).
A. \( 12x^4 y^6\)
B. \( 12x^8 y^6\)
C. \( 48x^4 y^6\)
D. \( 48x^8 y^6\)
4- Right triangle ABC has two legs of lengths 6 cm (AB) and 8 cm (AC). What is the length of the third side (BC)?
A. 4 cm
B. 6 cm
C. 8 cm
D. 10 cm
5- The marked price of a computer is D dollar. Its price decreased by \(20\%\) in January and later increased by \(10\%\) in February. What is the final price of the computer in D dollars?
A. 0.80 D
B. 0.88 D
C. 0.90 D
D. 1.20 D
6- \([6 × (–24) + 8] – (–4) + [4 × 5] ÷ 2 =\) ?
A. \(-122\)
B. \(-112\)
C. \(-102\)
D. \(-92\)
7- The area of a circle is \(64 π\). What is the circumference of the circle?
A. \(8 π\)
B. \(16 π\)
C. \(32 π\)
D. \(64 π\)
8- A $40 shirt now selling for $28 is discounted by what percent?
A. \(20 \%\)
B. \(30 \%\)
C. \(40 \%\)
D. \(60 \%\)
9- From last year, the price of gasoline has increased from $1.25 per gallon to $1.75 per gallon. The new price is what percent of the original price?
A. \(72 \%\)
B. \(120 \%\)
C. \(140 \%\)
D. \(160 \%\)
10- If \(40 \%\) of a class are girls, and \(25 \%\) of girls play tennis, what fraction of the class play tennis?
A. \(10 \%\)
B. \(15 \%\)
C. \(20 \%\)
D. \(40 \%\)
Best 7th Grade PSSA Math Prep Resource for 2026
Answers:
1- C
In this case, to find the area of the shaded region, subtract the area of two circles. (S1: the area of the big circle. S2: the area of a little circle)
Use the area of a circle formula.
S = \(π\)r\(^2\)
\(S_{1} – S_{2}= π( 5 + 3 cm)^2 – π(5 cm)^2\) ⇒ \(S_{1} – S_{2} = π64 cm^2 – π25 cm^2\) ⇒ \(S_{1} – S_{2} = 39π cm^2\)
2- D
William ate \(\frac{1}{4}\) of 8 parts of his pizza that it means 2 parts out of 8 parts ( \(\frac{1}{4}\) of 8 parts = x ⇒ x = 2) and left 6 parts.
Ella ate \(\frac{1}{2}\) of 8 parts of her pizza that it means 4 parts out of 8 parts ( \(\frac{1}{2}\) of 8 parts = x ⇒ x = 4) and left 4 parts.
Therefore, they ate \((4 + 2)\) parts out of\( (8 + 8)\) parts of their pizza and left \((6 + 4)\) parts out of \((8 + 8)\) parts of their pizza that it means: \(\frac{10}{16}\)
After simplification we have: \(\frac{5}{8}\)
3- D
Simplify.
\(6x^2 y^3 (2x^2 y)^3= 6x^2 y^3 (8x^6 y^3 ) = 48x^8 y^6\)
4- D
Use Pythagorean Theorem: \(a^2 + b^2 = c^2\)
\(62 + 82 = c^2 ⇒ 100 = c^2 ⇒ c = 10\)
5- B
To find the discount, multiply the number by (\(100\%\) – rate of discount).
Therefore, for the first discount we get:
\((D) (100\% – 20\%) = (D) (0.80) = 0.80 D\)
For increase of \(10 \%\):
\((0.80 D) (100\% + 10\%) = (0.85 D) (1.10) = 0.88 D = 88\% D\)
6- A
Use PEMDAS (order of operation):
\([6 × (– 24) + 8] – (– 4) + [4 × 5] ÷ 2 = [– 144 + 8] – (– 4) + [20] ÷ 2 = [– 144 + 8] – (– 4) + 10 =\)
\([– 136] – (– 4) + 10 = [– 136] + 4 + 10 = – 122\)
7- B
Use the formula of areas of circles.
Area =\( πr^2 ⇒ 64 π = πr^2 ⇒ 64 = r^2 ⇒ r = 8\)
The radius of the circle is 8. Now, use the circumference formula:
Circumference = \(2πr = 2π (8) = 16 π\)
8- B
Use the formula for Percent of Change
\(\frac{New Value-Old Value}{Old Value}× 100 \%\)
\(\frac{28-40}{40}× 100 \% = – 30 \% \)
(negative sign here means that the new price is less than old price).
9- C
The question is this: 1.75 is what percent of 1.25?
Use percent formula:
part =\( \frac{percent}{100}× whole\)
\(\frac{percent}{100}× 1.25\) ⇒ \(1.75 = \frac{percent ×1.25}{100}⇒175 =\) percent \(×1.25\) ⇒ percent \(= \frac{175}{1.25}= 140\)
10- A
Let x be the amount of students in the class.
\(40 \%\) of \(x =\) girls
\(25 \%\) of girls = tennis player
Input \(40\%\) of a class instead of girls in second formula. Therefore, \(25\%\) of \(40\%\) of a class = tennis player
tennis player = \(10\%\)
Looking for the best resource to help you succeed on the 7th Grade PSSA Math test?
The Best Books to Ace the 7th Grade PSSA Math Test
Recommended EffortlessMath Books
For a workbook that pairs with these practice questions, Mastering Grade 7 Math walks through every seventh-grade topic with clear examples and practice sets. If proportional reasoning, integers, or equation-solving are giving you trouble, Pre-Algebra for Beginners rebuilds those skills with worked examples.
Frequently Asked Questions
What does the PSSA Grade 7 math test cover?
PSSA Grade 7 math covers Numbers and Operations, Algebraic Concepts (two-step equations and inequalities, proportional reasoning), Geometry (scale, circles, surface area, volume), Measurement, and Data Analysis / Probability. At grade 7, the heaviest content strands are proportional reasoning, integer and rational operations, percent change, two-step equations and inequalities, and circle geometry. The 10 practice questions on this page sample across those strands so you can see where your skills are strong and where you need a few more reps.
How long is the PSSA math test for 7th-grade students?
PSSA Grade 7 math runs across three sessions over multiple days, with about 60-70 items total – mostly multiple choice with some open-ended. Plan to pace yourself – skip a problem and come back rather than burning five minutes on one tough question. The 10 practice items here are short enough to do in one sitting (about 20-25 minutes) and they mirror the kinds of items you’ll see on the real test.
Are these 7th-grade practice questions free?
Yes – every practice question on this page is free, with a worked solution. No login, no email, no paywall. Print the page or work through it on screen. If you find these helpful, share the link with a classmate or your teacher – it’s the best free way to sample the test format.
What’s the best way to study for the PSSA Grade 7 math test?
For PSSA specifically, the open-ended items are scored on a rubric that rewards showing every step. Even if you’re not sure of the final answer, write down what you tried – it usually earns at least one point. The general rule for middle school: 20-30 minutes a day, four or five days a week, beats a weekend cram. Mix topic practice (one skill at a time) with mixed practice (random topics in one sitting). The mixed sets are closer to how the real test feels.
What if I can’t solve some of these practice questions?
That’s normal – one of the points of practice is finding gaps. When you miss a question, read the worked solution slowly. Then redo the problem on a fresh sheet without looking. If a whole topic feels hard, drop back to the basics first – it’s faster to fill a gap than to push through frustration. The Related Lessons below cover the 7th-grade skills students miss most.
Are calculators allowed on the PSSA math test?
For most state 7th-grade math tests, a calculator is allowed on part of the test but not on the section that tests basic computation. Check your state’s policy on the official PSSA page. The 10 questions here can be solved with pencil and paper – we recommend practicing both with and without a calculator so you’re ready either way.
How many questions are on the real PSSA Grade 7 math test?
It varies by state and year, but most 7th-grade state tests have 40-60 math questions total, often split across two sessions. The 10 sample questions here are a representative slice – if you’re getting 8 or more right and showing solid work, you’re tracking well for the real test.
What item types appear on PSSA Grade 7 math?
Multiple choice is most common, but you’ll also see multi-select (“choose all that apply”), fill-in-the-blank, drag-and-drop, equation builders, and short open-response items where you show work. The practice questions on this page mostly use multiple choice, but the underlying math is the same across item types.
How can parents help a 7th-grade student prepare in Pennsylvania?
Two things matter most: steady practice (not last-minute cramming) and going through wrong answers together. Ask your child to explain each step out loud – hearing themselves explain often catches the slip. Don’t drill speed at the expense of accuracy; accuracy with reasonable pace is what the test rewards.
Where do I get more 7th-grade math practice?
EffortlessMath has full-length practice tests, topic-by-topic worksheets, and step-by-step lessons for every 7th-grade math skill. The Related Lessons below cover the topics students miss most on PSSA. For a complete workbook, the Mastering Grade 7 Math book walks through every standard with worked examples and answer keys.
Related EffortlessMath Lessons
If a topic on this page feels rusty, these short lessons go deeper:
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