A student sorts four numbers into rational and irrational. Which one belongs with the irrational numbers?Wisconsin Department of Public Instruction, Forward Exam Mathematics Blueprint, Grade 8, The Number System; Wisconsin Standards for Mathematics (2021), M.8.NS.A.1
The decimal 0.444... repeats forever. Which fraction is equal to it?Wisconsin Department of Public Instruction, Forward Exam Mathematics Blueprint, Grade 8, The Number System; Wisconsin Standards for Mathematics (2021), M.8.NS.A.1
The square root of 50 is not a whole number. Which two consecutive whole numbers is it between?Wisconsin Department of Public Instruction, Forward Exam Mathematics Blueprint, Grade 8, The Number System; Wisconsin Standards for Mathematics (2021), M.8.NS.A.2
Which list shows √17, 4.5 and 13/3 in order from least to greatest?Wisconsin Department of Public Instruction, Forward Exam Mathematics Blueprint, Grade 8, The Number System; Wisconsin Standards for Mathematics (2021), M.8.NS.A.2
Which number is the best estimate of √45 to the nearest tenth?Wisconsin Department of Public Instruction, Forward Exam Mathematics Blueprint, Grade 8, The Number System; Wisconsin Standards for Mathematics (2021), M.8.NS.A.2
Show all 42 questions (37 more)
Expressions and Equations 12
A calculator multiplies 2.5 × 10⁴ by 2 × 10³. What is the product in scientific notation?Wisconsin Department of Public Instruction, Forward Exam Mathematics Blueprint, Grade 8, Expressions and Equations; Wisconsin Standards for Mathematics (2021), M.8.EE.A.4
A line crosses the y-axis at 4 and rises 2 units for every 1 unit it moves to the right. Which equation describes the line?Wisconsin Department of Public Instruction, Forward Exam Mathematics Blueprint, Grade 8, Expressions and Equations; Wisconsin Standards for Mathematics (2021), M.8.EE.B.6
A school play sells adult tickets for $8 and student tickets for $5. It sells 40 tickets and takes in $245. How many adult tickets are sold?Wisconsin Department of Public Instruction, Forward Exam Mathematics Blueprint, Grade 8, Expressions and Equations; Wisconsin Standards for Mathematics (2021), M.8.EE.C.8c
Car A travels 220 miles in 4 hours at a steady speed. The distance of Car B is given by d = 50t, where t is time in hours. Which car is faster, and by how much?Wisconsin Department of Public Instruction, Forward Exam Mathematics Blueprint, Grade 8, Expressions and Equations; Wisconsin Standards for Mathematics (2021), M.8.EE.B.5
The lines y = 2x + 1 and y = −x + 7 are graphed on one coordinate plane. At which point do they cross?Wisconsin Department of Public Instruction, Forward Exam Mathematics Blueprint, Grade 8, Expressions and Equations; Wisconsin Standards for Mathematics (2021), M.8.EE.C.8b
One city has about 6 × 10⁸ dollars in its budget and a town has about 3 × 10⁵ dollars. About how many times as large is the budget of the city?Wisconsin Department of Public Instruction, Forward Exam Mathematics Blueprint, Grade 8, Expressions and Equations; Wisconsin Standards for Mathematics (2021), M.8.EE.A.3
What is the solution of 3(x − 4) = 2x + 5?Wisconsin Department of Public Instruction, Forward Exam Mathematics Blueprint, Grade 8, Expressions and Equations; Wisconsin Standards for Mathematics (2021), M.8.EE.C.7b
Which equation is false for every value of x?Wisconsin Department of Public Instruction, Forward Exam Mathematics Blueprint, Grade 8, Expressions and Equations; Wisconsin Standards for Mathematics (2021), M.8.EE.C.7a
Which expression is equal to 4⁵ × 4⁻²?Wisconsin Department of Public Instruction, Forward Exam Mathematics Blueprint, Grade 8, Expressions and Equations; Wisconsin Standards for Mathematics (2021), M.8.EE.A.1
Which fraction has the same value as 6⁻²?Wisconsin Department of Public Instruction, Forward Exam Mathematics Blueprint, Grade 8, Expressions and Equations; Wisconsin Standards for Mathematics (2021), M.8.EE.A.1
Which two values of x satisfy x² = 121?Wisconsin Department of Public Instruction, Forward Exam Mathematics Blueprint, Grade 8, Expressions and Equations; Wisconsin Standards for Mathematics (2021), M.8.EE.A.2
Which value of x makes x³ = 125 true?Wisconsin Department of Public Instruction, Forward Exam Mathematics Blueprint, Grade 8, Expressions and Equations; Wisconsin Standards for Mathematics (2021), M.8.EE.A.2
Functions 10
A bathtub fills at a steady rate, sits full for a while, and then drains at a steady rate. Which description fits a graph of water level against time?Wisconsin Department of Public Instruction, Forward Exam Mathematics Blueprint, Grade 8, Functions; Wisconsin Standards for Mathematics (2021), M.8.F.B.5
A candle is 20 centimeters tall and burns down 2 centimeters each hour. Which function gives its height h after t hours?Wisconsin Department of Public Instruction, Forward Exam Mathematics Blueprint, Grade 8, Functions; Wisconsin Standards for Mathematics (2021), M.8.F.B.4
A linear function contains the points (2, 11) and (6, 23). What is its rate of change?Wisconsin Department of Public Instruction, Forward Exam Mathematics Blueprint, Grade 8, Functions; Wisconsin Standards for Mathematics (2021), M.8.F.B.4
A plumber charges a fixed fee for a visit plus an hourly rate. A 2-hour job costs $130 and a 5-hour job costs $250. What is the fixed fee?Wisconsin Department of Public Instruction, Forward Exam Mathematics Blueprint, Grade 8, Functions; Wisconsin Standards for Mathematics (2021), M.8.F.B.4
A rule multiplies each input by 4 and then subtracts 3. What is the output for an input of 6?Wisconsin Department of Public Instruction, Forward Exam Mathematics Blueprint, Grade 8, Functions; Wisconsin Standards for Mathematics (2021), M.8.F.A.1
Function A is y = 3x + 2. Function B is linear and contains the points (0, 1), (2, 9) and (4, 17). Which function changes at the greater rate?Wisconsin Department of Public Instruction, Forward Exam Mathematics Blueprint, Grade 8, Functions; Wisconsin Standards for Mathematics (2021), M.8.F.A.2
The graph of y = −4x + 6 is a line. What are its slope and its y-intercept?Wisconsin Department of Public Instruction, Forward Exam Mathematics Blueprint, Grade 8, Functions; Wisconsin Standards for Mathematics (2021), M.8.F.A.3
In which set of ordered pairs does every input have exactly one output?Wisconsin Department of Public Instruction, Forward Exam Mathematics Blueprint, Grade 8, Functions; Wisconsin Standards for Mathematics (2021), M.8.F.A.1
One of these equations has a graph that is not a straight line. Which one?Wisconsin Department of Public Instruction, Forward Exam Mathematics Blueprint, Grade 8, Functions; Wisconsin Standards for Mathematics (2021), M.8.F.A.3
The total cost in dollars of a set of music lessons after x lessons is y = 22x + 35. What does the 35 stand for?Wisconsin Department of Public Instruction, Forward Exam Mathematics Blueprint, Grade 8, Functions; Wisconsin Standards for Mathematics (2021), M.8.F.B.4
Geometry 9
A cone and a cylinder have the same radius and the same height. The volume of the cylinder is 60π cubic inches. What is the volume of the cone?Wisconsin Department of Public Instruction, Forward Exam Mathematics Blueprint, Grade 8, Geometry; Wisconsin Standards for Mathematics (2021), M.8.G.C.9
A ramp, the ground and a wall form a right triangle. The two legs are 9 feet and 12 feet long. How long is the ramp, the sloped side?Wisconsin Department of Public Instruction, Forward Exam Mathematics Blueprint, Grade 8, Geometry; Wisconsin Standards for Mathematics (2021), M.8.G.B.7
A triangle is rotated and then reflected. Which statement about the image is true?Wisconsin Department of Public Instruction, Forward Exam Mathematics Blueprint, Grade 8, Geometry; Wisconsin Standards for Mathematics (2021), M.8.G.A.1
A triangular sign has angles of 48° and 67° at two of its corners. What is the angle at the third corner?Wisconsin Department of Public Instruction, Forward Exam Mathematics Blueprint, Grade 8, Geometry; Wisconsin Standards for Mathematics (2021), M.8.G.A.5
On a coordinate map, a school is at (1, 2) and a library is at (7, 10). What is the straight-line distance between them?Wisconsin Department of Public Instruction, Forward Exam Mathematics Blueprint, Grade 8, Geometry; Wisconsin Standards for Mathematics (2021), M.8.G.B.8
The point (3, −2) is translated 5 units left and 4 units up. What are the coordinates of its image?Wisconsin Department of Public Instruction, Forward Exam Mathematics Blueprint, Grade 8, Geometry; Wisconsin Standards for Mathematics (2021), M.8.G.A.3
The point (4, −7) is reflected across the x-axis. What are the coordinates of its image?Wisconsin Department of Public Instruction, Forward Exam Mathematics Blueprint, Grade 8, Geometry; Wisconsin Standards for Mathematics (2021), M.8.G.A.3
The point (−4, 6) is dilated by a scale factor of 1/2 with the origin as center. What are the coordinates of its image?Wisconsin Department of Public Instruction, Forward Exam Mathematics Blueprint, Grade 8, Geometry; Wisconsin Standards for Mathematics (2021), M.8.G.A.3
Triangle ABC is dilated by a scale factor of 2 and then translated to make triangle DEF. How are the two triangles related?Wisconsin Department of Public Instruction, Forward Exam Mathematics Blueprint, Grade 8, Geometry; Wisconsin Standards for Mathematics (2021), M.8.G.A.4
Statistics and Probability 6
A line of fit for daily sales at an ice cream stand is y = 8x − 150, where x is the high temperature in °F and y is the number of cones sold. How many cones does the model predict for a day with a high of 85°F?Wisconsin Department of Public Instruction, Forward Exam Mathematics Blueprint, Grade 8, Statistics and Probability; Wisconsin Standards for Mathematics (2021), M.8.SP.A.3
A line of fit relates the age of the trees in a park, x years, to the width of their trunks, y centimeters: y = 1.2x + 3. What does the 1.2 mean?Wisconsin Department of Public Instruction, Forward Exam Mathematics Blueprint, Grade 8, Statistics and Probability; Wisconsin Standards for Mathematics (2021), M.8.SP.A.3
A scatter plot shows hours of practice and free throws made for 20 players. As the hours increase, the number of free throws made tends to increase. What kind of association is this?Wisconsin Department of Public Instruction, Forward Exam Mathematics Blueprint, Grade 8, Statistics and Probability; Wisconsin Standards for Mathematics (2021), M.8.SP.A.1
A two-way table shows 100 students. Of the 50 students who play a sport, 30 also play an instrument. Of the 50 who play no sport, 20 play an instrument. What is the relative frequency of playing an instrument among the students who play a sport?Wisconsin Department of Public Instruction, Forward Exam Mathematics Blueprint, Grade 8, Statistics and Probability; Wisconsin Standards for Mathematics (2021), M.8.SP.A.4
Four students each draw a straight line on the same scatter plot to model the data. Which line fits best?Wisconsin Department of Public Instruction, Forward Exam Mathematics Blueprint, Grade 8, Statistics and Probability; Wisconsin Standards for Mathematics (2021), M.8.SP.A.2
On a scatter plot of height and shoe size, most points lie close to a rising line. One point lies far below the others. What is that point called?Wisconsin Department of Public Instruction, Forward Exam Mathematics Blueprint, Grade 8, Statistics and Probability; Wisconsin Standards for Mathematics (2021), M.8.SP.A.1
How this list was compiled: Outline: Forward Exam Mathematics Blueprints, Grades 3-8, Mathematics Blueprint Grade 8, Wisconsin Department of Public Instruction, https://dpi.wi.gov/media/26847/download?inline, and Wisconsin Forward Exam 2026 Test Designs, https://dpi.wi.gov/media/26486/download?inline, both linked from Forward Exam Resources, https://dpi.wi.gov/assessment/forward/resources, read 2026-10-10: the reporting categories, their cluster statements and possible points, and the number of questions. Each question names the standard it practices in the Wisconsin Standards for Mathematics (2021), https://dpi.wi.gov/media/27134/download?inline, read 2026-10-10. The answers are arithmetic, algebra and geometry on the numbers in the question, each worked a second time. Licence: Own work. Questions, answer choices and explanations were written for this site. Nothing is copied or reworded from a Forward Exam, the department's practice test, a sample item or another practice test. The department's grade 8 mathematics practice test was not read.
How it works
Unofficial practice for the grade 8 mathematics section of the Wisconsin Forward Exam. Its 42 questions match the number that are scored on the real test. Not affiliated with the Wisconsin Department of Public Instruction.
Read the full guide
What a Wisconsin Forward Exam practice test for math in 8th grade covers
The state blueprint spreads 48 points over five reporting categories. Expressions and Equations has the most, 13 to 15: exponents, roots, scientific notation, slope, linear equations and systems. Functions and Geometry have 10 to 12 each: rules, rates of change and graphs, then transformations, angle facts, the Pythagorean Theorem and volume. Statistics and Probability has 6 to 8, on scatter plots and two-way tables, and The Number System 4 to 6, on irrational numbers.
Where each answer can be checked
Each explanation shows the steps and names its standard, such as M.8.EE.C.7, in the Wisconsin Standards for Mathematics (2021). Every answer was worked out a second time from the numbers in the question.
The first session, 9 questions, allows no calculator. Work some of the exponent and equation questions here by hand.
Questions and answers
Is there a Wisconsin Forward practice test for eighth grade math from the state?
Yes. The Department of Public Instruction posts its own grade 8 mathematics practice test on its Forward Exam practice test page, linked in the box under the questions. This page is separate and unofficial, and its questions are different ones.
How many questions are on the 8th grade Forward Exam math test?
50 in three sessions: 42 scored questions worth 48 points and 8 field test questions. Session 1 has 9 questions with no calculator. Sessions 2 and 3 have 21 and 20 questions with the test's built-in calculator.
Is the Wisconsin Forward Exam timed?
No. The department calls it an untimed test. Its suggested times for grade 8 mathematics, meant for scheduling only, are 25 minutes for session 1 and 45 minutes each for sessions 2 and 3.
How is the 8th grade Forward math test scored?
Results are reported on a four-digit scale in four performance levels: Developing, Approaching, Meeting and Advanced. In grade 8 mathematics the scale runs from 1440 to 1860, and Meeting begins at 1653. A percent here is practice only.