• 45 questions

PSSA Math 8th Grade Practice Test

Grade 8 math in the shares of Pennsylvania's test design, from irrational numbers to scatter plots, every answer worked out.

Which number is rational?

Pick an answer, then press Check answer. Then you see Correct or Not quite, with the reason. Keys: A to D pick, Enter checks.

Print covers the next 43 questions. Share this set copies a link to the same questions in the same order.

Exam mode: 43 questions, no time limit.

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Unofficial practice questions, not affiliated with the Pennsylvania Department of Education. Bank checked October 9, 2026.

The real test: PSSA mathematics, grade 8

Questions
43
Core items
43, worth 52 points: 40 multiple-choice or technology-enhanced items worth 1 point each and 3 open-ended items worth 4 points each.
Items that do not count
Each form adds 8 multiple-choice or technology-enhanced items and 1 open-ended item for field testing and psychometric use.
Sections
Two. Each has 24 multiple-choice or technology-enhanced items and 2 open-ended items, with an estimated testing time of 78 minutes.
Reporting categories
Expressions and Equations 30 to 35% of the core; Functions 20 to 25%; Geometry 17 to 21%; The Number System and Statistics and Probability 14 to 17% each.
Calculator
In grades 4 to 8 just part of the test is non-calculator. Devices with wireless links or a computer algebra system are not permitted.
Results
Four performance levels: advanced, proficient, basic and below basic.

Checked October 9, 2026 against the PSSA Mathematics Test Design (2025), the Pennsylvania Calculator Policy and the PSSA page of the Pennsylvania Department of Education. Rules change, so confirm with the agency itself before your test.

The department's PSSA page, with its samplers and formula sheets

Next step PSSA science, grade 8More grade 8 math questions

All 45 questions

The Number System 7

  • The decimal form of 5/11 is 0.454545… with the digits 45 repeating forever. What does this show about 5/11? Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 8 (April 2014), eligible content M08.A-N.1.1.1
  • Which fraction is equal to 0.625? Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 8 (April 2014), eligible content M08.A-N.1.1.2
  • Which fraction is equal to the repeating decimal 0.363636…? Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 8 (April 2014), eligible content M08.A-N.1.1.2
  • Which list puts 3 1/8, π, √10 and 3.2 in order from least to greatest? Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 8 (April 2014), eligible content M08.A-N.1.1.4
  • Which number is closest to the place of √45 on a number line? Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 8 (April 2014), eligible content M08.A-N.1.1.5
  • Which number is rational? Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 8 (April 2014), eligible content M08.A-N.1.1.1
  • Without a calculator, where does √70 lie? Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 8 (April 2014), eligible content M08.A-N.1.1.3
Show all 45 questions (38 more)

Expressions and Equations 14

  • A cube has a volume of 27 cubic inches, so its edge length x fits the equation x³ = 27. What is x? Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 8 (April 2014), eligible content M08.B-E.1.1.2
  • A line crosses the y-axis at (0, −3) and has a slope of 2. What is its equation? Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 8 (April 2014), eligible content M08.B-E.2.1.3
  • A student rewrites (4³)³ ÷ 4⁷ as a single power of 4. Which power is correct? Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 8 (April 2014), eligible content M08.B-E.1.1.1
  • A student rewrites 6⁸ × 6⁻⁵ as a single power of 6. Which power is correct? Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 8 (April 2014), eligible content M08.B-E.1.1.1
  • A student simplifies a linear equation in one variable step by step and ends with 4 = 9. What does this show? Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 8 (April 2014), eligible content M08.B-E.3.1.1
  • Adult tickets cost $8 and child tickets cost $5. A family buys 7 tickets and pays $47. How many adult tickets does the family buy? Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 8 (April 2014), eligible content M08.B-E.3.1.5
  • The graph of a proportional relationship is a line through (0, 0) and (6, 21). What is the unit rate? Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 8 (April 2014), eligible content M08.B-E.2.1.1
  • The graphs of two linear equations cross at exactly one point, (2, −1). What does that point represent? Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 8 (April 2014), eligible content M08.B-E.3.1.3
  • How many solutions does the equation 2(3x + 5) = 6x + 10 have? Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 8 (April 2014), eligible content M08.B-E.3.1.1
  • One particle is 2 × 10⁻⁶ meter wide, and a second particle is 4 × 10⁻³ meter wide. About how many times as wide as the first particle is the second? Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 8 (April 2014), eligible content M08.B-E.1.1.3
  • What is (3 × 10⁴) × (2.5 × 10³) in scientific notation? Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 8 (April 2014), eligible content M08.B-E.1.1.4
  • What is the solution of 4(2x − 3) = 3x + 13? Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 8 (April 2014), eligible content M08.B-E.3.1.2
  • What is the solution of the system y = 3x − 2 and y = −2x + 13? Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 8 (April 2014), eligible content M08.B-E.3.1.4
  • Which choice gives every solution of the equation x² = 81? Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 8 (April 2014), eligible content M08.B-E.1.1.2

Functions 9

  • A hiker walks away from camp at a steady pace for 2 hours, rests for 1 hour, then walks back at a steady pace. Which describes a graph of the hiker's distance from camp over time? Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 8 (April 2014), eligible content M08.B-F.2.1.2
  • A plumber's bill is modeled by c = 65h + 40, where c is the cost in dollars and h is the number of hours worked. What does the 40 represent? Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 8 (April 2014), eligible content M08.B-F.2.1.1
  • A relation pairs each student in a class with that student's age in years. Is the relation a function? Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 8 (April 2014), eligible content M08.B-F.1.1.1
  • Function A is y = 2x + 9. Function B is given by a table that pairs x = 0, 2 and 4 with y = 1, 7 and 13. Which function changes at the greater rate? Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 8 (April 2014), eligible content M08.B-F.1.1.2
  • Function P is y = −2x + 10. Function Q is described in words: "start at 6 and add 1 for each increase of 1 in x." Which function has the greater initial value? Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 8 (April 2014), eligible content M08.B-F.1.1.2
  • The graph of a linear function passes through (3, 5) and (7, 25). What is the rate of change of the function? Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 8 (April 2014), eligible content M08.B-F.2.1.1
  • In which set of ordered pairs is one input paired with two outputs, so that the set is not a function? Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 8 (April 2014), eligible content M08.B-F.1.1.1
  • Which describes the graph of y = −3x + 4? Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 8 (April 2014), eligible content M08.B-F.1.1.3
  • Which of these equations has a graph that is not a straight line? Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 8 (April 2014), eligible content M08.B-F.1.1.3

Geometry 8

  • A cylinder has a radius of 3 centimeters and a height of 10 centimeters. What is its volume in terms of π? Use V = πr²h. Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 8 (April 2014), eligible content M08.C-G.3.1.1
  • A ramp rises 7 feet over a horizontal run of 24 feet. How long is the sloped surface of the ramp? Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 8 (April 2014), eligible content M08.C-G.2.1.2
  • A triangle is a right triangle when its side lengths fit a² + b² = c². Which set of side lengths does? Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 8 (April 2014), eligible content M08.C-G.2.1.1
  • A triangle with a vertex at (−8, 12) is dilated by a scale factor of 1/4 with its center at the origin. Where is the image of that vertex? Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 8 (April 2014), eligible content M08.C-G.1.1.3
  • Figure B is the image of figure A after a dilation by a scale factor of 3 followed by a reflection. Which describes the two figures? Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 8 (April 2014), eligible content M08.C-G.1.1.4
  • The point (3, −5) is translated 4 units left and 6 units up. What are the coordinates of its image? Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 8 (April 2014), eligible content M08.C-G.1.1.3
  • Triangle ABC is rotated 90° about the origin to make triangle A′B′C′. Which statement is true? Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 8 (April 2014), eligible content M08.C-G.1.1.1
  • What is the distance between the points (−3, 2) and (9, 7)? Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 8 (April 2014), eligible content M08.C-G.2.1.3

Statistics and Probability 7

  • A line of best fit for a class's data is s = 6h + 52, where s is a test score and h is the number of hours studied. What does the slope, 6, mean? Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 8 (April 2014), eligible content M08.D-S.1.1.3
  • A linear model for test scores is s = 6h + 52, where h is the number of hours studied. What score does the model predict for 4 hours of study? Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 8 (April 2014), eligible content M08.D-S.1.1.3
  • A scatter plot shows that as weekly hours of practice increase, the number of errors in a recital decreases. Which describes the association? Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 8 (April 2014), eligible content M08.D-S.1.1.1
  • A scatter plot suggests a linear association. Which line is the best fit? Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 8 (April 2014), eligible content M08.D-S.1.1.2
  • In a survey of 50 students, 30 play a sport, and 18 of those 30 also play an instrument. Of the 20 who do not play a sport, 6 play an instrument. What is the relative frequency of playing an instrument among the students who play a sport? Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 8 (April 2014), eligible content M08.D-S.1.2.1
  • Most of the points on a scatter plot are grouped closely around ages 10 to 12, with few points anywhere else. What is this grouping called? Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 8 (April 2014), eligible content M08.D-S.1.1.1
  • The points on a scatter plot rise steeply, then level off along a curve. Which describes the association? Pennsylvania Department of Education, Assessment Anchors and Eligible Content, Mathematics, Grade 8 (April 2014), eligible content M08.D-S.1.1.1

How this list was compiled: Outline: PSSA Mathematics Test Design (PCS PSSA Test Design, 2025), Pennsylvania Department of Education, https://www.pa.gov/content/dam/copapwp-pagov/en/education/documents/instruction/assessment-and-accountability/pssa/test-designs/pssa%20mathematics%20test%20design.pdf, linked from Pennsylvania System of School Assessment (PSSA), https://www.pa.gov/agencies/education/programs-and-services/instruction/elementary-and-secondary-education/assessment-and-accountability/pennsylvania-system-of-school-assessment-pssa, read 2026-10-09. Each question names the eligible content it practices in the department's Assessment Anchors and Eligible Content, Mathematics, Grade 8 (final, April 2014), https://www.pa.gov/content/dam/copapwp-pagov/en/education/documents/instruction/assessment-and-accountability/pssa/assessment-anchors/2014%20grade%208%20math%20aa.pdf, read 2026-10-09. The answers are arithmetic on the numbers in the question, worked out twice. Licence: Own work. Questions, answer choices and explanations were written for this site. Nothing is copied or reworded from a PSSA test, an item and scoring sampler, the examples printed in the assessment anchors or another practice test.

How it works

Unofficial practice for Pennsylvania's grade 8 PSSA mathematics test. The questions were written for this site from the grade 8 assessment anchors and eligible content, and none is taken from a test or a sampler. Not affiliated with the Pennsylvania Department of Education.

Read the full guide

What the PSSA math test covers in 8th grade

Five reporting categories make up the test design, and the questions here follow its shares. Expressions and Equations is about a third: exponents, scientific notation, linear equations and systems. Functions comes next: rate of change, initial value, linear against nonlinear. Geometry covers transformations, the Pythagorean theorem and the volume of cylinders, cones and spheres. The Number System is irrational numbers, and Statistics and Probability is scatter plots and two-way tables.

Reading the answers

Every answer shows its steps and its eligible content code, such as M08.B-F.2.1.1. Many wrong choices are the usual slips, such as multiplying exponents that should be added, and the explanation says where the slip comes from.

  • Square roots up to 144 and cube roots up to 125 are tested without a calculator, so learn those perfect squares and cubes.

Questions and answers

How many questions are on the 8th grade math PSSA?

43 core items: 40 multiple-choice or technology-enhanced items and 3 open-ended items worth four points each, 52 points in all. Field-test items sit beside them on each form. This page has 45 questions, all multiple choice.

What is on the 8th grade math PSSA?

Expressions and Equations, 30 to 35 percent of the core; Functions, 20 to 25; Geometry, 17 to 21; and The Number System and Statistics and Probability, 14 to 17 each.

Is a calculator allowed on the 8th grade PSSA math test?

Yes, except on a non-calculator portion: the test design says only a portion of the grade 8 test is non-calculator. Some eligible content, such as estimating an irrational number, is written to be done without one.

Do you get a formula sheet on the 8th grade math PSSA?

The anchors say that formulas for the volume of cones, cylinders and spheres will be provided, and the properties of exponents too. The department posts the grade 8 formula sheet on its PSSA page.

How long is the 8th grade math PSSA?

Two sections, each with 24 multiple-choice or technology-enhanced items and 2 open-ended items. The test design estimates 78 minutes of testing time for each section.

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