7th Grade PSSA Math FREE Sample Practice Questions
TL;DR: If your 7th grader is taking Pennsylvania’s PSSA, the math test pulls from proportional relationships, rational-number operations, two-step equations and inequalities, geometry (circles and prisms), and probability. That’s a lot of ground. These free sample questions show the actual format and difficulty Pennsylvania 7th graders see on test day, so you can sit together at home, spot the weak topics, and turn them into study sessions.
Key takeaways:
- PSSA is Pennsylvania’s annual state test for grades 3-8 in math and ELA.
- Aligned to the Pennsylvania Core Standards (closely tied to Common Core).
- Mix of multiple-choice, multi-select, and constructed-response items.
- Calculator policy splits: non-calculator section first, then sessions with the on-screen calculator.
- Performance levels: Below Basic, Basic, Proficient, Advanced.
If your student has studied the material well for the 7th Grade PSSA Math test, now is the time to focus more on practicing. The more students practice, the more material they will review. You can use the 7th Grade PSSA Math free sample questions to practice more for your 7th Grade student. In this article, our experts have prepared the most valuable practice questions for the 7th Grade PSSA Math test.
Start preparing your 7th-grade student for the 2026 PSSA Math test with our free sample practice questions. Also, make sure to follow some of the related links at the bottom of this post to get a better idea of what kind of mathematics questions students need to practice.
10 Sample 7th Grade PSSA Math Practice Questions
1- A chemical solution contains \(4\%\) alcohol. If there is 24 ml of alcohol, what is the volume of the solution?
A. 240 ml
B. 480 ml
C. 600 ml
D. 1200 ml
2- The price of a laptop is decreased by \(10\%\) to $360. What is its original price?
A. 320
B. 380
C. 400
D. 450
3- What is the median of these numbers? \(4, 9, 13, 8, 15, 18, 5\)
A. 8
B. 9
C. 13
D. 15
4- Three times the price of a laptop is equal to five times the price of a computer. If the price of the laptop is $200 more than a computer, what is the price of the computer?
A. 300
B. 500
C. 800
D. 1500
5- What is the perimeter of a square that has an area of 595.36 feet?
6- Jason is 9 miles ahead of Joe, running at 5.5 miles per hour, and Joe is running at the speed of 7 miles per hour. How long does it take Joe to catch Jason?
A. 3 hours
B. 4 hours
C. 6 hours
D. 8 hours
7- 55 students took an exam, and 11 of them failed. What percent of the students passed the exam?
A. \(20 \%\)
B. \(40 \%\)
C. \(60 \%\)
D. \(80 \%\)
8- Jason needs an \(75\%\) average in his writing class to pass. On his first 4 exams, he earned scores of \(68\%, 72\%, 85\%,\) and \(90\%\). What is the minimum score Jason can earn on his fifth and final test to pass?
9- A bank is offering \(3.5\%\) simple interest on a savings account. If you deposit $12,000, how much interest will you earn in two years?
A. $420
B. $840
C. $4200
D. $8400
10- 5 less than twice a positive integer is 83. What is the integer?
A. 39
B. 41
C. 42
D. 44
Best 7th Grade PSSA Math Workbook Resource for 2027
Answers:
1- C
\(4\%\) of the volume of the solution is alcohol. Let \(x\) be the volume of the solution.
Then: \(4\% \space\) of \(\space x = 24 \space \)ml\( ⇒ 0.04 x = 24 ⇒ x = 24 ÷ 0.04 = 600\)
2- C
Let \(x\) be the original price.
If the price of a laptop is decreased by \(10\%\) to $360, then:
\(90 \%\)of \(x=360 ⇒ 0.90x=360 ⇒ x=360÷0.90=400\)
3- B
Write the numbers in order:
\(4, 5, 8, 9, 13, 15, 18\)
Since we have 7 numbers (7 is odd), then the median is the number in the middle, which is 9.
4- A
Let L be the price of laptop and C be the price of computer.
\(3\)(L) \(=5\)(C) \(\space\) and \(\space\) L \(= $200 +\) C
Therefore, \(3($200 +\) C\()=5\)C \(⇒ $600 + 3\)C \(= 5\)C \(⇒\) C\(=$300\)
5- 97.6
Use the area of square formula.
\(S = a^2 ⇒ 595.36 = a^2 ⇒ a = 24.4\)
Use the perimeter of a square formula.
\(P = 4a ⇒ P=4(24.4) ⇒ P = 97.6\)
6- C
The distance between Jason and Joe is 9 miles. Jason is running at 5.5 miles per hour, and Joe is running at the speed of 7 miles per hour. Therefore, every hour, the distance is 1.5 miles less.
\(9 ÷ 1.5 = 6\)
7- D
The failing rate is 11 out of \(55 = \frac{11}{55}\).
Change the fraction to a percent:
\(\frac{11}{55} ×100\%=20\%\)
20 percent of students failed. Therefore, 80 percent of students passed the exam.
8- 60
Jason needs an \(75\%\) average to pass for five exams. Therefore, the sum of 5 exams must be at lease \(5 × 75 = 375\)
The sum of 4 exams is:
\(68 + 72 + 85 + 90 = 315\)
The minimum score Jason can earn on his fifth and final test to pass is:
\(375 – 315 = 60\)
9- B
Use the simple interest formula:
I=prt
(I = interest, p = principal, r = rate, t = time)
I\(=(12000)(0.035)(2)=840\)
10- D
Let \(x\) be the integer. Then:
\(2x – 5 = 83\)
Add 5 both sides: \(2x = 88\)
Divide both sides by \(2: x = 44\)
Looking for the best resource to help you succeed on the PSSA Grade 7 Math test?
The Best Books to Ace 7th Grade PSSA Math Test
Common Core Math Exercise Book for Grade 7 Student Workbook and Two Realistic Common Core Math Tests
Frequently Asked Questions
What is in the PSSA grade 7 math sampler?
The grade 7 PSSA math Item and Scoring Sampler from the Pennsylvania Department of Education contains retired test questions with answer keys and sample scored student responses. It is the clearest way to see how open-ended items are graded. Have your 7th grader try the open-ended problems first, then compare their work with the scoring guide to see what earns full credit.
Does the PSSA grade 7 math test have a formula sheet?
Yes, Pennsylvania provides a grade 7 mathematics formula sheet with formulas for area, circumference, volume and more. Knowing when to use each formula is the real skill. For example, a circle with diameter 10 has radius 5, so its circumference is 2 × π × 5 = 10π, about 31.4 units. Print the official sheet from PDE so your child practices with the same one.
Is there a PSSA 7th grade math practice test?
Yes. Free 7th grade PSSA math sample questions and practice tests help your child get used to the format: multiple choice plus open-ended problems that require shown work. A typical item: a solution is 4% alcohol and contains 24 ml of alcohol, so the full solution is 24 ÷ 0.04 = 600 ml. Time each practice session and review mistakes together.
What are the PSSA 7th grade math standards?
PSSA grade 7 math follows the Pennsylvania Core Standards, tested through Assessment Anchors and Eligible Content. Key skills include proportional relationships, operations with positive and negative rational numbers, two-step equations and inequalities, circles, scale drawings, volume of prisms, and probability. For instance, if y = 3.5x, the constant of proportionality is 3.5, the same for every x and y pair.
Related Lessons You May Like
- 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
If you want a workbook that pairs with these questions, Mastering Grade 7 Math covers every Grade 7 standard. For more word-problem practice, Mastering Grade 7 Math Word Problems is a great companion.
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