100+ Free SBAC Math Grade 7 Practice Questions

Pass your Smarter Balanced Mathematics Summative Assessment, Grade 7 exam on the first try — instant access, no signup required.

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A class of 25 students has 15 girls. A student is chosen at random. What is the probability the student is a boy?

2/3

3/5

1/5

2/5

to track

2026 Statistics

Key Facts: SBAC Math Grade 7 Exam

SBAC Grade 7 Mathematics is a free, Common Core-aligned online assessment measuring four claims (Concepts and Procedures, Problem Solving, Communicating Reasoning, and Modeling and Data Analysis) across proportional relationships, rational numbers, expressions and equations, geometry, and statistics and probability.

Sample SBAC Math Grade 7 Practice Questions

Try these sample questions to test your SBAC Math Grade 7 exam readiness. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1A recipe uses 3 cups of flour for every 2 cups of sugar. What is the unit rate of flour to sugar in cups of flour per cup of sugar?

A.1.5 cups of flour per cup of sugar

B.0.67 cups of flour per cup of sugar

C.6 cups of flour per cup of sugar

D.2.5 cups of flour per cup of sugar

Explanation: A unit rate of flour to sugar is the number of cups of flour for 1 cup of sugar. Divide 3 by 2 to get 1.5 cups of flour per cup of sugar. The unit rate is the constant of proportionality for this relationship.

2A person walks 1/2 mile in 1/4 hour at a steady pace. What is the walking speed in miles per hour?

A.1/8 mile per hour

B.4 miles per hour

C.2 miles per hour

D.1 mile per hour

Explanation: Speed equals distance divided by time: (1/2) divided by (1/4). Dividing by 1/4 is the same as multiplying by 4, so (1/2)(4) = 2 miles per hour. This is a unit rate computed from a complex fraction.

3The table shows a proportional relationship between x and y: when x = 4, y = 10; when x = 6, y = 15. What is the constant of proportionality (y = kx)?

A.0.4

B.2.5

C.6

D.40

Explanation: In a proportional relationship y = kx, the constant k equals y divided by x. Using 10/4 = 2.5, and checking 15/6 = 2.5 confirms it. The constant of proportionality is 2.5.

4Which equation represents a proportional relationship between x and y?

A.y = 3x + 2

B.y = x^2

C.y = 3/x

D.y = 3x

Explanation: A proportional relationship has the form y = kx, a straight line through the origin with constant ratio y to x. y = 3x fits this form with k = 3. The graph passes through (0, 0).

5A map has a scale of 1 inch = 25 miles. Two cities are 3.5 inches apart on the map. How far apart are the actual cities?

A.28.5 miles

B.87.5 miles

C.7.14 miles

D.71.4 miles

Explanation: Multiply the map distance by the scale: 3.5 inches times 25 miles per inch = 87.5 miles. Scale drawings use proportional reasoning to convert map measurements to real distances.

6A shirt originally costs $40 and is on sale for 25% off. What is the sale price?

A.$30

B.$15

C.$35

D.$10

Explanation: A 25% discount removes 0.25 times $40 = $10 from the price. The sale price is $40 minus $10 = $30. You can also multiply $40 by 0.75 to get $30 directly.

7A meal costs $60 before tax. With a 7% sales tax, what is the total amount paid?

A.$67.00

B.$60.07

C.$62.20

D.$64.20

Explanation: The tax is 0.07 times $60 = $4.20. Add it to the original cost: $60 + $4.20 = $64.20. Equivalently, multiply $60 by 1.07 to get $64.20.

8An investment of $500 earns 4% simple interest per year. How much interest is earned in 3 years?

A.$20

B.$600

C.$60

D.$56

Explanation: Simple interest is principal times rate times time: 500 times 0.04 times 3 = $60. The interest grows by $20 each year for 3 years, totaling $60.

9A population of birds increases from 80 to 100. What is the percent increase?

A.20%

B.25%

C.80%

D.125%

Explanation: Percent increase equals the change divided by the original amount: (100 - 80)/80 = 20/80 = 0.25 = 25%. The increase is measured relative to the starting value of 80.

10After a 20% decrease, a price is $48. What was the original price?

A.$57.60

B.$38.40

C.$68

D.$60

Explanation: A 20% decrease means $48 is 80% of the original. Divide $48 by 0.80 to get $60. Check: 20% of $60 is $12, and $60 minus $12 equals $48.

About the SBAC Math Grade 7 Exam

The Smarter Balanced (SBAC) Mathematics Summative Assessment for Grade 7 is a standards-based test aligned to the Common Core State Standards and administered by member states such as California, Washington, Oregon, and others. It measures four claims: Concepts and Procedures (Claim 1), Problem Solving (Claim 2), Communicating Reasoning (Claim 3), and Modeling and Data Analysis (Claim 4). The Grade 7 content focuses on proportional relationships, operations with rational numbers, linear expressions and equations and inequalities, geometry involving scale drawings, angles, area, surface area and volume, and statistics and probability. The test is delivered online as a computer-adaptive section plus a performance task, using item types such as multiple-choice, multiple-select, technology-enhanced, and constructed-response. Results are reported on a vertical scale with four achievement levels, where Levels 3 and 4 indicate students are on track for college and career readiness. There is no fee for students, as states and districts fund administration.

Questions

100 scored questions

Time Limit

Untimed; states estimate about 2 to 2.5 hours total for the Grade 7 Mathematics computer-adaptive test and performance task, usually across multiple sessions.

Passing Score

Four achievement levels are reported. For Grade 7 Mathematics, Level 3 (Standard Met) starts at 2567 and Level 4 (Standard Exceeded) starts at 2635; Levels 3 and 4 show on-track college and career readiness.

Exam Fee

Free to students; the assessment is funded by Smarter Balanced member states and local districts. (Smarter Balanced Assessment Consortium, administered through member states and their testing vendors)

SBAC Math Grade 7 Exam Content Outline

22%

Ratios & Proportional Relationships (7.RP)

Unit rates with fractions, the constant of proportionality, identifying proportional relationships, scale drawings, and percent problems including tax, tip, discount, simple interest, and percent change.

20%

The Number System (7.NS)

Operations with rational numbers (integers, fractions, decimals), absolute value, order of operations, and converting between fractions and decimals.

20%

Expressions & Equations (7.EE)

Equivalent expressions, the distributive property, combining like terms, factoring linear expressions, and solving two-step equations and inequalities in context.

20%

Geometry (7.G)

Scale drawings, angle relationships, circle area and circumference, composite-figure area, surface area and volume of prisms, cross-sections, and triangle angle sums.

18%

Statistics & Probability (7.SP)

Random sampling and population inferences, comparing populations, simple and compound probability, experimental versus theoretical probability, and predicting outcomes.

How to Pass the SBAC Math Grade 7 Exam

What You Need to Know

Passing score: Four achievement levels are reported. For Grade 7 Mathematics, Level 3 (Standard Met) starts at 2567 and Level 4 (Standard Exceeded) starts at 2635; Levels 3 and 4 show on-track college and career readiness.
Exam length: 100 questions
Time limit: Untimed; states estimate about 2 to 2.5 hours total for the Grade 7 Mathematics computer-adaptive test and performance task, usually across multiple sessions.
Exam fee: Free to students; the assessment is funded by Smarter Balanced member states and local districts.

Keys to Passing

Complete 500+ practice questions
Score 80%+ consistently before scheduling
Focus on highest-weighted sections
Use our AI tutor for tough concepts

SBAC Math Grade 7 Study Tips from Top Performers

1Master proportional reasoning first, since unit rates, the constant of proportionality, percents, and scale drawings appear throughout the test.

2Practice operations with rational numbers, especially integer and fraction rules for signs, until sign errors disappear.

3Learn to solve two-step equations and inequalities, and remember to flip the inequality when multiplying or dividing by a negative.

4Memorize key geometry formulas: circle area and circumference, triangle and trapezoid area, prism volume, and angle relationships.

5Use the performance task to show full reasoning; explain each step clearly because Claim 3 rewards communicating mathematical arguments.

6Work multi-step word problems under untimed but focused conditions, checking each answer by substituting back into the original situation.

Frequently Asked Questions

What is the SBAC Grade 7 Mathematics assessment?

It is the Smarter Balanced summative mathematics test for seventh grade, aligned to the Common Core State Standards and administered by member states such as California, Washington, and Oregon. It is delivered online as a computer-adaptive test plus a performance task.

What math topics are tested in Grade 7?

Grade 7 covers proportional relationships, operations with rational numbers, linear expressions and equations and inequalities, geometry (scale drawings, angles, area, surface area, volume), and statistics and probability, all at the seventh-grade level.

What are the four SBAC math claims?

The four claims are Claim 1 Concepts and Procedures, Claim 2 Problem Solving, Claim 3 Communicating Reasoning, and Claim 4 Modeling and Data Analysis. Claim 1 carries the most items, while Claims 2, 3, and 4 are combined for subscore reporting.

How is the SBAC Grade 7 math test scored?

Scores are reported on a vertical scale with four achievement levels. For Grade 7 mathematics, Level 3 (Standard Met) begins at 2567 and Level 4 (Standard Exceeded) begins at 2635, with Levels 3 and 4 showing on-track readiness.

Is the SBAC Grade 7 math test timed?

No, the test is untimed by design, though states estimate about 2 to 2.5 hours of total testing time for Grade 7 mathematics, usually split across the computer-adaptive section and the performance task over multiple sessions.

Does the SBAC Grade 7 math test cost anything?

No. The assessment is free for students and families because Smarter Balanced member states and local school districts fund the administration of the test.