• 44 questions

SBAC Math Grade 8 Practice Test

Eighth grade math by the Smarter Balanced blueprint: equations, functions, geometry, reasoning and a six-part performance task.

A car uses 3 gallons of gas to travel 96 miles at a steady rate. On a graph of miles against gallons, what is the slope of the line?

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

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Unofficial practice questions, not affiliated with the Smarter Balanced Assessment Consortium. Bank checked October 9, 2026.

The real test: Smarter Balanced math, grade 8

Parts
A computer adaptive test and one performance task of 4 to 6 items, up to four of them scored by hand.
Items by claim
Concepts and Procedures 17 to 20; Problem Solving with Modeling and Data Analysis 8 to 10; Communicating Reasoning 8 to 10.
Grade 8 targets
Lines and linear equations 5 or 6 items; exponents, functions and congruence 5 or 6; function models and the Pythagorean Theorem 2 or 3.
Calculator
One section has an embedded online scientific calculator. The other section has none.
Time
Untimed. Estimate for grades 6 to 8 mathematics: 3 hours, of which 1 hour is the performance task.
Scores
Four achievement levels, no pass mark. In grade 8 mathematics, Level 3 runs from 2586 to 2652.

Checked October 9, 2026 against the Smarter Balanced Assessment Consortium's mathematics blueprint, estimated testing times, calculator rules and score levels. Rules change, so confirm with the agency itself before your test.

The consortium's own practice and training tests

Next step More SBAC math: grades 6 to 8Review: grade 7 math and English

All 44 questions

Concepts: Equations and Lines 6

  • A car uses 3 gallons of gas to travel 96 miles at a steady rate. On a graph of miles against gallons, what is the slope of the line? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 8, Claim 1 (Concepts and Procedures), target C: understand the connections between proportional relationships, lines, and linear equations
  • A line has a slope of 2/5 and crosses the y-axis at (0, −3). Which equation describes the line? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 8, Claim 1 (Concepts and Procedures), target C: understand the connections between proportional relationships, lines, and linear equations
  • Bike A travels by the equation d = 12t, with d in miles and t in hours. Bike B travels 28 miles in 2 hours and 42 miles in 3 hours. Which bike is faster, and by how much? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 8, Claim 1 (Concepts and Procedures), target C: understand the connections between proportional relationships, lines, and linear equations
  • How many solutions does the equation 2(x + 4) = 2x + 8 have? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 8, Claim 1 (Concepts and Procedures), target D: analyze and solve linear equations and pairs of simultaneous linear equations
  • What is the solution of 3(2x − 1) = 5x + 9? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 8, Claim 1 (Concepts and Procedures), target D: analyze and solve linear equations and pairs of simultaneous linear equations
  • What is the solution of the system y = 3x − 5 and 2x + y = 10? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 8, Claim 1 (Concepts and Procedures), target D: analyze and solve linear equations and pairs of simultaneous linear equations
Show all 44 questions (38 more)

Concepts: Functions 6

  • A function rule says: multiply the input by −2, then add 7. What is the output when the input is −3? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 8, Claim 1 (Concepts and Procedures), target E: define, evaluate, and compare functions
  • A graph shows a walker's distance from home over time. It rises, then stays flat, then falls. What does the flat part show? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 8, Claim 1 (Concepts and Procedures), target F: use functions to model relationships between quantities
  • A linear function has the values x = 2, 4, 6 and y = 11, 17, 23. What are its rate of change and its initial value? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 8, Claim 1 (Concepts and Procedures), target F: use functions to model relationships between quantities
  • Function A is y = 4x + 1. Function B is given by a table: x = 0, 1, 2 and y = 3, 8, 13. Which function has the greater rate of change? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 8, Claim 1 (Concepts and Procedures), target E: define, evaluate, and compare functions
  • The function y = −4x + 100 gives the liters of water, y, in a tub after x minutes. Which description fits the function? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 8, Claim 1 (Concepts and Procedures), target F: use functions to model relationships between quantities
  • Which of these rules is NOT a linear function of x? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 8, Claim 1 (Concepts and Procedures), target E: define, evaluate, and compare functions

Concepts: Geometry 5

  • A ball is a sphere with a radius of 6 inches. In terms of π, what is its volume? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 8, Claim 1 (Concepts and Procedures), target I: solve real-world and mathematical problems involving volume of cylinders, cones, and spheres
  • A ladder 17 feet long leans against a wall. Its base is 8 feet from the wall. How high up the wall does the ladder reach? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 8, Claim 1 (Concepts and Procedures), target H: understand and apply the Pythagorean Theorem
  • A paper cone has a radius of 9 centimeters and a height of 4 centimeters. In terms of π, what is its volume? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 8, Claim 1 (Concepts and Procedures), target I: solve real-world and mathematical problems involving volume of cylinders, cones, and spheres
  • Point P is at (2, −5). It is translated 4 units left and 3 units up. Where is its image? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 8, Claim 1 (Concepts and Procedures), target G: understand congruence and similarity using physical models, transparencies, or geometry software
  • Triangle A is dilated by a scale factor of 3 to make triangle B. Which statement is true? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 8, Claim 1 (Concepts and Procedures), target G: understand congruence and similarity using physical models, transparencies, or geometry software

Concepts: Numbers, Exponents and Data 5

  • The number √70 lies between which two whole numbers that are next to each other? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 8, Claim 1 (Concepts and Procedures), target A: know that there are numbers that are not rational, and approximate them by rational numbers
  • On a scatter plot of hours studied and test scores, the points rise from lower left to upper right and lie close to a line. What kind of association does the plot show? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 8, Claim 1 (Concepts and Procedures), target J: investigate patterns of association in bivariate data
  • What is (6 × 10⁵) ÷ (3 × 10²) in scientific notation? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 8, Claim 1 (Concepts and Procedures), target B: work with radicals and integer exponents
  • What is the value of (2³)² × 2⁻⁴? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 8, Claim 1 (Concepts and Procedures), target B: work with radicals and integer exponents
  • Which of these numbers is NOT rational? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 8, Claim 1 (Concepts and Procedures), target A: know that there are numbers that are not rational, and approximate them by rational numbers

Problem Solving and Modeling 8

  • A box is 12 centimeters long, 9 centimeters wide and 8 centimeters high. What is the length of the longest straight rod that fits inside, from one corner to the opposite corner? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 8, Claim 2 (Problem Solving), target A: apply mathematics to solve well-posed problems arising in everyday life, society, and the workplace
  • A model for a bowl of cooling soup is T = −3m + 85, where T is the temperature in degrees Celsius after m minutes. What does the number 85 stand for? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 8, Claim 4 (Modeling and Data Analysis), target D: interpret results in the context of a situation
  • A school needs buses for 215 students. Each bus holds 50 students, and 215 ÷ 50 = 4.3. How many buses should the school order? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 8, Claim 2 (Problem Solving), target C: interpret results in the context of a situation
  • A student models the points (1, 3), (2, 5), (3, 7) and (4, 9) with y = 2x. Which change makes the model fit all four points? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 8, Claim 4 (Modeling and Data Analysis), target E: analyze the adequacy of and make improvements to an existing model
  • A survey asks 200 students two things. Of the 120 who have a pet, 45 walk to school. Of the 80 with no pet, 20 walk to school. Which statement do the data support? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 8, Claim 4 (Modeling and Data Analysis), target F: identify important quantities in a practical situation and map their relationships
  • A theater sells adult tickets for $9 and child tickets for $6. It sells 40 tickets for $291. Which system of equations can be used to find the number of each kind? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 8, Claim 2 (Problem Solving), target D: identify important quantities in a practical situation and map their relationships
  • A town has 8,000 people and grows by about 250 people each year. If the growth stays steady, what will the population be in 12 years? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 8, Claim 4 (Modeling and Data Analysis), target A: apply mathematics to solve problems arising in everyday life, society, and the workplace
  • One print shop charges a $12 setup fee plus $0.30 a flyer. A second shop charges $0.45 a flyer with no fee. For which orders is the second shop cheaper? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 8, Claim 2 (Problem Solving), target A: apply mathematics to solve well-posed problems arising in everyday life, society, and the workplace

Communicating Reasoning 8

  • A figure is reflected across the x-axis and then translated 5 units right. Why is the final figure congruent to the first one? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 8, Claim 3 (Communicating Reasoning), target F: base arguments on concrete referents such as objects, drawings, diagrams, and actions
  • A garden has four sides. Two sides that meet at a corner are 6 meters and 8 meters long. Ray uses the Pythagorean Theorem and says the diagonal is 10 meters. What is he assuming? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 8, Claim 3 (Communicating Reasoning), target C: state logical assumptions being used
  • A line has a positive slope and a negative y-intercept. Why must it cross the x-axis at a positive value of x? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 8, Claim 3 (Communicating Reasoning), target B: construct chains of reasoning that will justify or refute propositions or conjectures
  • Ben says a triangle with sides 6, 8 and 11 is a right triangle because 6 + 8 is greater than 11. What is the flaw? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 8, Claim 3 (Communicating Reasoning), target E: distinguish correct logic or reasoning from that which is flawed and explain the flaw
  • Is x² always greater than x? Look at the cases. Smarter Balanced Mathematics Summative Assessment Blueprint, grade 8, Claim 3 (Communicating Reasoning), target D: use the technique of breaking an argument into cases
  • Kay finds the slope of the line through (1, 2) and (4, 8). She writes (4 − 1) ÷ (8 − 2) = 1/2. What is her error? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 8, Claim 3 (Communicating Reasoning), target E: distinguish correct logic or reasoning from that which is flawed and explain the flaw
  • Lee says, "The graph of y = mx + b is a straight line through the origin." For which lines is this true? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 8, Claim 3 (Communicating Reasoning), target G: determine conditions under which an argument does and does not apply
  • Tia claims, "A number raised to a negative power is always negative." Which example shows that she is wrong? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 8, Claim 3 (Communicating Reasoning), target A: test propositions or conjectures with specific examples

Performance Task: A Class Trip 6

  • Class trip, part 1. A museum is 36 miles from school, so the round trip is 72 miles. Bus company A charges $150 plus $2.50 a mile. What does company A charge for the trip? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 8, performance task, Claim 2 (Problem Solving), target A: apply mathematics to solve well-posed problems arising in everyday life, society, and the workplace
  • Class trip, part 2. For the 72-mile round trip, company A charges $330. Company B charges $4 a mile and no fee. Which company costs less, and by how much? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 8, performance task, Claim 2 (Problem Solving), target A: apply mathematics to solve well-posed problems arising in everyday life, society, and the workplace
  • Class trip, part 3. Company A charges $150 plus $2.50 a mile. Company B charges $4 a mile. For what trip length do the two companies charge the same? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 8, performance task, Claim 4 (Modeling and Data Analysis), target F: identify important quantities in a practical situation and map their relationships
  • Class trip, part 4. Museum tickets cost $9 for each of 28 students and $14 for each of 4 adults. Groups of 30 or more get 15% off. What does the class pay for tickets? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 8, performance task, Claim 4 (Modeling and Data Analysis), target A: apply mathematics to solve problems arising in everyday life, society, and the workplace
  • Class trip, part 5. Company A charges $150 plus $2.50 a mile, and company B charges $4 a mile. Both charge $400 for 100 miles. Why is company A cheaper for every longer trip? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 8, performance task, Claim 3 (Communicating Reasoning), target B: construct chains of reasoning that will justify or refute propositions or conjectures
  • Class trip, part 6. The bus costs $288 and the tickets cost $261.80. The 28 students share the whole cost equally. A student says $20 each is enough. Is that correct? Smarter Balanced Mathematics Summative Assessment Blueprint, grade 8, performance task, Claim 3 (Communicating Reasoning), target E: distinguish correct logic or reasoning from that which is flawed and explain the flaw

How this list was compiled: Outline: the Mathematics Summative Assessment Blueprint of the Smarter Balanced Assessment Consortium (as of the 2018-19 test administration), https://portal.smarterbalanced.org/library/en/mathematics-summative-assessment-blueprint.pdf, linked from https://contentexplorer.smarterbalanced.org/test-development, read 2026-10-09: the blueprint table for grades 6 to 8 and the two pages headed Target Sampling Mathematics Grade 8. Each question names the claim and the assessment target it practices. Every answer is arithmetic on the numbers in the question, worked out again. Licence: Own work. Questions, answer choices and explanations were written for this site. Nothing is copied or reworded from a Smarter Balanced test, practice test, training test, sample item, performance task or another practice test.

How it works

Unofficial grade 8 math practice for the Smarter Balanced (SBAC) test. Every question was written for this page to a target of the consortium's blueprint; none is from its practice test. Not affiliated with the Smarter Balanced Assessment Consortium.

Read the full guide

What the grade 8 blueprint counts

Concepts and Procedures is about half the test, 17 to 20 items. Two groups of targets carry 5 or 6 items each: proportional relationships, lines and linear equations; and exponents, functions and congruence. Problem Solving with Modeling and Data Analysis has 8 to 10 items, and so does Communicating Reasoning. Here the concepts questions sit in four topics, one of them functions.

The performance task (PT)

The real performance task is 4 to 6 items about one situation, some scored by hand. The Performance Task topic here is six questions about one class trip, where earlier answers feed later ones. They are multiple choice, so they practice the thinking, not the written explanation.

  • In the performance task, keep your earlier answers: later parts use them again.

Questions and answers

Is there an SBAC practice test math PT for 8th grade?

The Performance Task topic on this page is one: six linked questions about planning a class trip. The consortium's own practice and training tests are taken online, and the box under the questions links to them.

Which questions practice functions for the 8th grade math SBAC?

Under Start from, pick Concepts: Functions. Its six questions cover targets E and F: evaluating and comparing functions, and using functions to model relationships. Several problem-solving questions use linear functions too.

Is this the SBAC grade 8 math student practice test?

No. The consortium publishes its own practice tests for students. This page is separate, unofficial practice: 44 questions written to the same grade 8 claims and targets, each with its working.

Can 8th graders use a calculator on the SBAC math test?

On one section. The grade 8 test has a Calculator Available section with an embedded online scientific calculator and a Calculator Not Available section.

How long is the SBAC grade 8 mathematics test?

It is untimed. The consortium estimates 3 hours for mathematics in grades 6 to 8: 2 hours for the adaptive part and 1 hour for the performance task.

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