Top 10 7th Grade PSSA Math Practice Questions

Help your students start their PSSA Math test prep journey right now with these sample 7th Grade PSSA Math questions.

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PSSA Math Exercise Book for Grade 7 Student Workbook and Two Realistic PSSA Math Tests

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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. \(40 \%\)

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Answers:

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 = \(10\%\)

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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 grades take the PSSA in PA?

Pennsylvania students take the PSSA in English language arts and math every spring in grades 3 through 8, and science in grades 4 and 8. So a 7th grader sits both the ELA and math PSSA. High school students take the Keystone Exams instead. Your school will share the exact testing dates, which usually fall in April and May.

Is there a PSSA grade 7 math formula sheet?

Yes. The Pennsylvania Department of Education publishes a grade 7 PSSA math formula sheet that students receive on test day. It includes formulas such as the area and circumference of a circle and volume of prisms. Have your 7th grader practice with a printed copy, for example using A = πr² to find that a circle with radius 5 cm has area 25π cm².

What is the PSSA grade 7 math item sampler?

The item sampler is a free booklet from the Pennsylvania Department of Education with released PSSA questions, answer keys and scoring guides for open-ended items. It shows exactly how grade 7 questions are worded and how partial credit is earned. Working through it after a shorter set like this one gives your child a clear picture of the real test.

Is there a 7th grade math PSSA practice test?

Yes. The state’s item samplers act as official practice, and ten-question sets like this one with worked solutions are good for quick checks. Mix in a few problems with negative numbers, such as [6 × (−24) + 8] − (−4) + 20 ÷ 2 = −136 + 4 + 10 = −122, since integer operations trip up many Pennsylvania 7th graders.

Are there 7th grade PSSA math practice worksheets?

Yes, and topic worksheets pair well with the PSSA because the grade 7 test spans proportions, rational numbers, equations, geometry and probability. Pick one worksheet per weak topic, such as percent change or two-step equations, and do 10 to 15 problems at a time. For open-ended practice, have your child write every step, since PSSA scorers give partial credit for clear work.

Related EffortlessMath Lessons

If a topic on this page feels rusty, these short lessons go deeper:

• How to add and subtract integers
• How to solve proportional ratios
• How to solve percent of change
• How to solve one-step equations
• How to solve multi-step word problems