• 64 questions

8th Grade Math Practice Test

Linear equations, functions, the Pythagorean Theorem and scatter plots, with every step shown and a paper copy to print.

Which of these four numbers is irrational, so it cannot be written as a fraction of two whole numbers?

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 25 questions. Share this set copies a link to the same questions in the same order.

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Unofficial practice questions, not affiliated with any school, district, state or test publisher. Bank checked October 10, 2026.

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All 64 questions

The Number System 6

  • The square root of 130 lies between which two whole numbers? Common Core State Standards for Mathematics, 8.NS.A.2: rational approximations of irrational numbers
  • Which fraction equals the repeating decimal 0.272727…? Common Core State Standards for Mathematics, 8.NS.A.1: converting a repeating decimal into a rational number
  • Which fraction equals the repeating decimal 0.777…? Common Core State Standards for Mathematics, 8.NS.A.1: converting a repeating decimal into a rational number
  • Which list shows √5, 2.5, π and √10 in order from least to greatest? Common Core State Standards for Mathematics, 8.NS.A.2: comparing the size of irrational numbers
  • Which number is closest to √40? Common Core State Standards for Mathematics, 8.NS.A.2: rational approximations of irrational numbers
  • Which of these four numbers is irrational, so it cannot be written as a fraction of two whole numbers? Common Core State Standards for Mathematics, 8.NS.A.1: numbers that are not rational are irrational
Show all 64 questions (58 more)

Expressions and Equations 21

  • A grain of sand is about 0.0006 meter wide. How is that written as a single digit times a power of 10? Common Core State Standards for Mathematics, 8.EE.A.3: a single digit times an integer power of 10
  • A graph of pay against hours worked is a straight line through (0, 0) and (4, 58). What is the unit rate in dollars per hour? Common Core State Standards for Mathematics, 8.EE.B.5: the unit rate as the slope of a proportional graph
  • A line has a slope of −3 and crosses the y-axis at (0, 5). Which equation describes it? Common Core State Standards for Mathematics, 8.EE.B.6: the slope between any two points on a line; y = mx + b
  • Adult tickets cost $9 and child tickets cost $5. A family buys 7 tickets for $47. How many adult tickets did the family buy? Common Core State Standards for Mathematics, 8.EE.C.8.c: real-world problems that lead to two linear equations
  • The graphs of two linear equations cross at the point (−2, 5) and nowhere else. What does that point represent? Common Core State Standards for Mathematics, 8.EE.C.8.a: solutions of a system as points where the graphs intersect
  • How many solutions does the equation 4(x + 3) = 4x + 12 have? Common Core State Standards for Mathematics, 8.EE.C.7.a: equations with one solution, infinitely many solutions or no solution
  • How many solutions does the equation 5x − 4 = 5x + 9 have? Common Core State Standards for Mathematics, 8.EE.C.7.a: equations with one solution, infinitely many solutions or no solution
  • One city has about 8 × 10⁶ people and a town has about 4 × 10⁴ people. About how many times as large is the city? Common Core State Standards for Mathematics, 8.EE.A.3: how many times as much one quantity is than another
  • Pump A fills a tank by the equation g = 7.5m, with g in gallons and m in minutes. Pump B fills 42 gallons in 6 minutes at a steady rate. Which pump is faster? Common Core State Standards for Mathematics, 8.EE.B.5: comparing two proportional relationships shown in different ways
  • The volume of a cube is 216 cubic centimeters. How long is one edge? Common Core State Standards for Mathematics, 8.EE.A.2: square roots and cube roots as solutions of equations
  • What are the solutions of x² = 169? Common Core State Standards for Mathematics, 8.EE.A.2: square roots and cube roots as solutions of equations
  • What is (3 × 10⁵) × (2.5 × 10³) in scientific notation? Common Core State Standards for Mathematics, 8.EE.A.4: operations with numbers in scientific notation
  • What is (8.4 × 10⁷) ÷ (2 × 10²) in scientific notation? Common Core State Standards for Mathematics, 8.EE.A.4: operations with numbers in scientific notation
  • What is 5.2 × 10⁴ + 3 × 10³ in scientific notation? Common Core State Standards for Mathematics, 8.EE.A.4: operations with numbers in scientific notation
  • What is the slope of the line through (1, 4) and (5, 16)? Common Core State Standards for Mathematics, 8.EE.B.6: the slope between any two points on a line; y = mx + b
  • What is the solution of (3/4)x − 5 = 7? Common Core State Standards for Mathematics, 8.EE.C.7.b: linear equations with rational number coefficients
  • What is the solution of 4(x − 3) = 2x + 10? Common Core State Standards for Mathematics, 8.EE.C.7.b: linear equations that need the distributive property and like terms
  • What is the solution of the system x + y = 12 and x − y = 4? Common Core State Standards for Mathematics, 8.EE.C.8.b: solving a system of two linear equations algebraically
  • What is the solution of the system y = 2x + 1 and y = −x + 10? Common Core State Standards for Mathematics, 8.EE.C.8.b: solving a system of two linear equations algebraically
  • Which is equal to (3²)⁵? Common Core State Standards for Mathematics, 8.EE.A.1: properties of integer exponents
  • Which is equal to 4³ × 4⁻⁵? Common Core State Standards for Mathematics, 8.EE.A.1: properties of integer exponents

Functions 12

  • A candle's height is h = 20 − 1.5t, with h in centimeters and t in hours burned. What does the −1.5 mean? Common Core State Standards for Mathematics, 8.F.B.4: interpreting the rate of change and initial value in a situation
  • A graph shows a hiker's distance from camp over time. The line rises steadily, stays flat for a while, then falls back to zero. What is the hiker doing during the flat part? Common Core State Standards for Mathematics, 8.F.B.5: describing a functional relationship from its graph
  • A gym charges a $25 joining fee plus $18 each month. Which function gives the total cost C, in dollars, after m months? Common Core State Standards for Mathematics, 8.F.B.4: constructing a function to model a linear relationship
  • A line passes through (1, 7) and (3, 13). What is its y-intercept? Common Core State Standards for Mathematics, 8.F.B.4: the rate of change and initial value of a linear function
  • A linear function has the table x = 2, 4, 6 and y = 9, 15, 21. What is its rate of change? Common Core State Standards for Mathematics, 8.F.B.4: the rate of change and initial value of a linear function
  • A rule gives each input x the output 3x − 2. What is the output for an input of 6? Common Core State Standards for Mathematics, 8.F.A.1: a function assigns to each input exactly one output
  • A taxi ride costs $3.50 to start plus $2.25 for each mile. How much does a 6-mile ride cost? Common Core State Standards for Mathematics, 8.F.B.4: constructing a function to model a linear relationship
  • Function A is y = 4x + 1. Function B has the table x = 0, 1, 2 and y = 3, 8, 13. Which function has the greater rate of change? Common Core State Standards for Mathematics, 8.F.A.2: comparing two functions represented in different ways
  • In which set of ordered pairs does every input have exactly one output, making the set a function? Common Core State Standards for Mathematics, 8.F.A.1: a function assigns to each input exactly one output
  • The points (1, 2), (2, 5) and (3, 10) lie on the graph of y = x² + 1. Why is this function not linear? Common Core State Standards for Mathematics, 8.F.A.3: y = mx + b defines a linear function; functions that are not linear
  • Which of these equations has a graph that is a straight line? Common Core State Standards for Mathematics, 8.F.A.3: y = mx + b defines a linear function; functions that are not linear
  • Which words describe the function y = −2x + 8 as x increases? Common Core State Standards for Mathematics, 8.F.B.5: describing a functional relationship from its graph

Geometry 17

  • A 25-foot ladder leans against a wall. Its base is 7 feet from the wall. How high up the wall does the ladder reach? Common Core State Standards for Mathematics, 8.G.B.7: unknown side lengths in right triangles
  • A cone has a radius of 6 inches and a height of 5 inches. What is its volume in terms of π? Common Core State Standards for Mathematics, 8.G.C.9: volumes of cones, cylinders and spheres
  • A cylinder has a radius of 3 centimeters and a height of 10 centimeters. What is its volume in terms of π? Common Core State Standards for Mathematics, 8.G.C.9: volumes of cones, cylinders and spheres
  • A line segment 7 units long is reflected across a line. How long is its image? Common Core State Standards for Mathematics, 8.G.A.1.a: rotations, reflections and translations take segments to segments of the same length
  • A right triangle has legs of 8 inches and 15 inches. How long is its hypotenuse? Common Core State Standards for Mathematics, 8.G.B.7: unknown side lengths in right triangles
  • A sphere has a radius of 6 meters. What is its volume in terms of π? Common Core State Standards for Mathematics, 8.G.C.9: volumes of cones, cylinders and spheres
  • A triangle has a vertex at (6, −9). The triangle is dilated by a scale factor of 1/3 centered at the origin. Where is the image of that vertex? Common Core State Standards for Mathematics, 8.G.A.3: the effect of dilations on figures, using coordinates
  • An exterior angle of a triangle measures 130°. One of the two interior angles that are not next to it measures 55°. What is the other one? Common Core State Standards for Mathematics, 8.G.A.5: the angle sum and exterior angle of triangles
  • On a coordinate grid, a park is at (−3, 2) and a library is at (9, 7). What is the straight-line distance between them? Common Core State Standards for Mathematics, 8.G.B.8: the distance between two points in a coordinate system
  • Point P(3, −2) is translated 5 units left and 4 units up. What are the coordinates of its image? Common Core State Standards for Mathematics, 8.G.A.3: the effect of transformations on figures, using coordinates
  • Point Q(−4, 6) is reflected across the y-axis. What are the coordinates of its image? Common Core State Standards for Mathematics, 8.G.A.3: the effect of transformations on figures, using coordinates
  • Point R(2, 5) is rotated 90° counterclockwise about the origin. What are the coordinates of its image? Common Core State Standards for Mathematics, 8.G.A.3: the effect of transformations on figures, using coordinates
  • Rectangle A is 4 units by 6 units. Rectangle B is 10 units by 15 units. Which statement is true? Common Core State Standards for Mathematics, 8.G.A.4: similarity through rotations, reflections, translations and dilations
  • Three sticks are joined at their ends to make a triangle. Which set of lengths makes a right triangle? Common Core State Standards for Mathematics, 8.G.B.6: the Pythagorean Theorem and its converse
  • Triangle ABC is translated 4 units right and then reflected across the x-axis to make triangle DEF. Which statement is true? Common Core State Standards for Mathematics, 8.G.A.2: congruence through a sequence of rotations, reflections and translations
  • Two angles of a triangle measure 38° and 77°. What is the measure of the third angle? Common Core State Standards for Mathematics, 8.G.A.5: the angle sum and exterior angle of triangles
  • Two parallel lines are cut by a transversal. One of the angles formed measures 112°. What is the measure of its alternate interior angle? Common Core State Standards for Mathematics, 8.G.A.5: angles made when parallel lines are cut by a transversal

Statistics and Probability 8

  • A model for a plant's height is h = 2.5w + 4, with h in centimeters and w in weeks. What height does the model predict at 6 weeks? Common Core State Standards for Mathematics, 8.SP.A.3: using the equation of a linear model; interpreting slope and intercept
  • A model for the money in a savings jar is s = 15w + 40, with s in dollars and w in weeks. What does the 40 mean? Common Core State Standards for Mathematics, 8.SP.A.3: using the equation of a linear model; interpreting slope and intercept
  • A scatter plot compares hours of practice with free throws made. One point lies far away from all the others. What is that point called? Common Core State Standards for Mathematics, 8.SP.A.1: patterns of association in scatter plots
  • A scatter plot suggests a linear association. Which straight line fits the data best? Common Core State Standards for Mathematics, 8.SP.A.2: fitting a straight line to a scatter plot and judging the fit
  • A two-way table shows that 25 of 40 eighth graders and 15 of 60 sixth graders walk to school. What is the relative frequency of walkers among the eighth graders? Common Core State Standards for Mathematics, 8.SP.A.4: two-way tables and relative frequencies
  • In a survey of 80 students, 30 play a sport and have a pet, 20 play a sport and have no pet, 18 have a pet and play no sport, and 12 do neither. What fraction of the students who play a sport have a pet? Common Core State Standards for Mathematics, 8.SP.A.4: two-way tables and relative frequencies
  • In the model c = 0.75m + 12, c is the cost in dollars of a phone plan with m minutes of calls. What does the 0.75 mean? Common Core State Standards for Mathematics, 8.SP.A.3: using the equation of a linear model; interpreting slope and intercept
  • On a scatter plot, the points rise from the lower left to the upper right and lie close to a straight line. What kind of association is this? Common Core State Standards for Mathematics, 8.SP.A.1: patterns of association in scatter plots

How this list was compiled: Our own questions. Outline: the Common Core State Standards for Mathematics, grade 8, https://www.thecorestandards.org/Math/Content/8/introduction/, with the five domain pages (The Number System, Expressions and Equations, Functions, Geometry, Statistics and Probability) and the glossary, https://www.thecorestandards.org/Math/Content/mathematics-glossary/glossary/, read 2026-10-10. Each question names the standard it practices and links to that domain page. Every answer is arithmetic or algebra on the numbers the question prints, and each one was worked out again on 2026-10-10. Licence: Own work. Questions, answer choices and explanations were written for this site. Nothing is copied or reworded from a state test, a released form, a sample item, a textbook or another practice test.

How it works

Unofficial eighth grade math practice: 64 questions written for this page to the five domains of the Common Core grade 8 standards. No state's test is copied or followed, so no test length or pass mark is implied.

Read the full guide

What the 64 questions cover

Expressions and Equations has 21 questions, Geometry 17, Functions 12, Statistics and Probability 8, and The Number System 6.

Graphs and figures are in words

Each question is text only. A line is given by two of its points, a table by its rows, a scatter plot by its pattern, a triangle by its sides. Sketching the picture on paper first is part of the practice.

  • Slope is the change in y divided by the change in x. Subtract in the same order on top and bottom.
  • After you solve an equation, put the answer back into both sides.
  • In a right triangle, the hypotenuse is the side across from the right angle, and it is the longest.

Questions and answers

Is there a printable grade 8 math practice test PDF?

The questions print as a paper test, with an answer key if you want one. Choose Save as PDF in the print window to keep the file.

Is this an 8th grade Common Core math practice test PDF?

Each question names the Common Core grade 8 standard it practices, such as 8.EE.C.7 for linear equations or 8.G.B.7 for right triangles, and the printed paper saves as a PDF. The questions are our own, not the standards' authors'.

Is this 8th grade math standardized test practice?

It practices the grade 8 standards without following one test. For a single test's own design, try the STAAR, Smarter Balanced or PSSA grade 8 math pages.

What math do 8th graders learn?

By the Common Core: linear equations and systems of two equations, functions, and geometry with transformations, similarity and the Pythagorean Theorem. Irrational numbers, integer exponents, scientific notation, volume and scatter plots are taught as well.

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