Seventh grade math across the five domains of Utah's RISE blueprint, from proportional reasoning to probability, with worked answers.
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Unofficial practice questions, not affiliated with the Utah State Board of Education. Bank checked October 13, 2026.
The real test: RISE mathematics, grade 7
Questions
50
Time limit
None
Domains, by share of the items
Ratio and Proportions 22 to 26%, Expressions and Equations 16 to 20%, The Number System 18 to 22%, Geometry 18 to 22%, Statistics and Probability 18 to 22%.
Depth of Knowledge
DOK 1: 12 to 24% of the items. DOK 2: 48 to 60%. DOK 3: 20 to 26%.
How it is given
On a computer, adaptive and not timed: the difficulty of the questions adjusts to the student.
Which test
Students take the RISE test of the course they are enrolled in.
Scores
A scale score and one of four proficiency levels: Below Proficient, Approaching Proficient, Proficient or Highly Proficient.
Results
The Individual Student Report usually arrives within three weeks of the school's testing window.
A chess club grows from 25 members to 32 members. By what percent did the membership increase?Utah Core State Standards for Mathematics, grade 7, Standard 7.RP.3 (RISE Mathematics Blueprint domain: Ratio and Proportions)
A faucet drips at a constant rate of 15 milliliters every 2 minutes. Which equation gives the milliliters w dripped in m minutes?Utah Core State Standards for Mathematics, grade 7, Standard 7.RP.2c (RISE Mathematics Blueprint domain: Ratio and Proportions)
A graph of a proportional relationship shows the cost y, in dollars, of x pounds of trail mix. The point (1, 6) is on the graph. What does this point mean?Utah Core State Standards for Mathematics, grade 7, Standard 7.RP.2d (RISE Mathematics Blueprint domain: Ratio and Proportions)
A jacket has a regular price of $80. It is marked down 25%, and then a 5% sales tax is added to the sale price. What is the final cost?Utah Core State Standards for Mathematics, grade 7, Standard 7.RP.3 (RISE Mathematics Blueprint domain: Ratio and Proportions)
Show all 50 questions (46 more)
Ratio and Proportions, continued
A painter covers 5/8 of a wall with 1/4 gallon of paint. At that rate, how many walls does 1 gallon cover?Utah Core State Standards for Mathematics, grade 7, Standard 7.RP.1 (RISE Mathematics Blueprint domain: Ratio and Proportions)
A table lists the cost of gasoline: 4 gallons for $14, 6 gallons for $21 and 10 gallons for $35. What is the constant of proportionality in dollars per gallon?Utah Core State Standards for Mathematics, grade 7, Standard 7.RP.2b (RISE Mathematics Blueprint domain: Ratio and Proportions)
Dev estimates that a rope is 60 feet long. Its actual length is 48 feet. What is the percent error of his estimate?Utah Core State Standards for Mathematics, grade 7, Standard 7.RP.3 (RISE Mathematics Blueprint domain: Ratio and Proportions)
Four tables pair x with y. In which one is y proportional to x?Utah Core State Standards for Mathematics, grade 7, Standard 7.RP.2a (RISE Mathematics Blueprint domain: Ratio and Proportions)
The graph of a relationship is a straight line that crosses the y-axis at (0, 3). Is the relationship proportional?Utah Core State Standards for Mathematics, grade 7, Standard 7.RP.2a (RISE Mathematics Blueprint domain: Ratio and Proportions)
Lena jogs 3/4 mile in 1/6 hour. What is her unit rate in miles per hour?Utah Core State Standards for Mathematics, grade 7, Standard 7.RP.1 (RISE Mathematics Blueprint domain: Ratio and Proportions)
Maya puts $450 in an account that pays 4% simple interest each year. How much interest does she earn in 5 years?Utah Core State Standards for Mathematics, grade 7, Standard 7.RP.3 (RISE Mathematics Blueprint domain: Ratio and Proportions)
Expressions and Equations 9
A coat is on sale for 35% off its regular price p. The sale price is p − 0.35p. Which expression is equivalent?Utah Core State Standards for Mathematics, grade 7, Standard 7.EE.2 (RISE Mathematics Blueprint domain: Expressions and Equations)
A plumber charges $45 for a visit plus $30 for each half hour of work. What is the charge for a job that takes 2 1/2 hours?Utah Core State Standards for Mathematics, grade 7, Standard 7.EE.3 (RISE Mathematics Blueprint domain: Expressions and Equations)
Five friends share the cost c of a pizza order equally. Each then uses a $2 coupon and pays $6.50. Which equation fits, and what is c?Utah Core State Standards for Mathematics, grade 7, Standard 7.EE.4a (RISE Mathematics Blueprint domain: Expressions and Equations)
Rosa has $50. She buys 3 shirts that cost $11.95 each. Rounding each price to $12, about how much money does she have left?Utah Core State Standards for Mathematics, grade 7, Standard 7.EE.3 (RISE Mathematics Blueprint domain: Expressions and Equations)
Simplify: (6x + 2) − (4x − 9)Utah Core State Standards for Mathematics, grade 7, Standard 7.EE.1 (RISE Mathematics Blueprint domain: Expressions and Equations)
Solve for x: 4x + 9 = −15Utah Core State Standards for Mathematics, grade 7, Standard 7.EE.4a (RISE Mathematics Blueprint domain: Expressions and Equations)
Tasha has $120 and saves $15 more each week. She wants to have more than $300. Which inequality gives the number of weeks w she needs?Utah Core State Standards for Mathematics, grade 7, Standard 7.EE.4b (RISE Mathematics Blueprint domain: Expressions and Equations)
Which expression is equivalent to 1/2 x + 3?Utah Core State Standards for Mathematics, grade 7, Standard 7.EE.1 (RISE Mathematics Blueprint domain: Expressions and Equations)
Which expression is equivalent to −6(3x − 4)?Utah Core State Standards for Mathematics, grade 7, Standard 7.EE.1 (RISE Mathematics Blueprint domain: Expressions and Equations)
The Number System 10
A submarine is at an elevation of −150 feet. It then descends 35 feet each minute for 4 minutes. What is its new elevation?Utah Core State Standards for Mathematics, grade 7, Standard 7.NS.3 (RISE Mathematics Blueprint domain: The Number System)
A team gains 8 yards on one play and loses 8 yards on the next. What is the total change in its position?Utah Core State Standards for Mathematics, grade 7, Standard 7.NS.1a (RISE Mathematics Blueprint domain: The Number System)
Find the product: −7/8 × 4/21Utah Core State Standards for Mathematics, grade 7, Standard 7.NS.2c (RISE Mathematics Blueprint domain: The Number System)
On a number line, how far apart are −12 and 7?Utah Core State Standards for Mathematics, grade 7, Standard 7.NS.1c (RISE Mathematics Blueprint domain: The Number System)
Start at −3 on a number line and add −8. Where do you land, and how did you move?Utah Core State Standards for Mathematics, grade 7, Standard 7.NS.1b (RISE Mathematics Blueprint domain: The Number System)
What is the value of (3/4) ÷ (−1/8)?Utah Core State Standards for Mathematics, grade 7, Standard 7.NS.3 (RISE Mathematics Blueprint domain: The Number System)
What is the value of (−2)(−5)(−3)?Utah Core State Standards for Mathematics, grade 7, Standard 7.NS.2a (RISE Mathematics Blueprint domain: The Number System)
What is −2.5 + 7.25 + 2.5?Utah Core State Standards for Mathematics, grade 7, Standard 7.NS.1d (RISE Mathematics Blueprint domain: The Number System)
Which expression has the same value as −(12/5)?Utah Core State Standards for Mathematics, grade 7, Standard 7.NS.2b (RISE Mathematics Blueprint domain: The Number System)
Which fraction has a decimal form that repeats instead of ending?Utah Core State Standards for Mathematics, grade 7, Standard 7.NS.2d (RISE Mathematics Blueprint domain: The Number System)
Geometry 11
A circular pond has a radius of 7 meters. Using 3.14 for π, what is its area?Utah Core State Standards for Mathematics, grade 7, Standard 7.G.4 (RISE Mathematics Blueprint domain: Geometry)
A plane slices a right rectangular pyramid parallel to its base, partway up. What two-dimensional figure is the slice?Utah Core State Standards for Mathematics, grade 7, Standard 7.G.3 (RISE Mathematics Blueprint domain: Geometry)
A rectangular prism is 4 meters long, 3 meters wide and 2.5 meters high. What is its surface area?Utah Core State Standards for Mathematics, grade 7, Standard 7.G.6 (RISE Mathematics Blueprint domain: Geometry)
A round table has a radius of 2.5 feet. Using 3.14 for π, what is its circumference?Utah Core State Standards for Mathematics, grade 7, Standard 7.G.4 (RISE Mathematics Blueprint domain: Geometry)
A scale drawing of a garden uses 1 centimeter for 3 meters. On the drawing the garden is a rectangle 4 centimeters by 5 centimeters. What is the area of the real garden?Utah Core State Standards for Mathematics, grade 7, Standard 7.G.1 (RISE Mathematics Blueprint domain: Geometry)
The base of a right prism is a right triangle with legs of 5 cm and 12 cm. The prism is 9 cm long. What is its volume?Utah Core State Standards for Mathematics, grade 7, Standard 7.G.6 (RISE Mathematics Blueprint domain: Geometry)
How many different triangles can be drawn with angles of 35°, 55° and 90°?Utah Core State Standards for Mathematics, grade 7, Standard 7.G.2 (RISE Mathematics Blueprint domain: Geometry)
On a scale drawing, 1 inch stands for 6 feet. A room is 3.5 inches long on the drawing. How long is the real room?Utah Core State Standards for Mathematics, grade 7, Standard 7.G.1 (RISE Mathematics Blueprint domain: Geometry)
Two angles are complementary. One measures (2x + 10)° and the other measures 40°. What is the value of x?Utah Core State Standards for Mathematics, grade 7, Standard 7.G.5 (RISE Mathematics Blueprint domain: Geometry)
Two straight lines cross and one of the four angles measures 65°. What are the measures of the other three angles?Utah Core State Standards for Mathematics, grade 7, Standard 7.G.5 (RISE Mathematics Blueprint domain: Geometry)
Which set of three side lengths cannot make a triangle?Utah Core State Standards for Mathematics, grade 7, Standard 7.G.2 (RISE Mathematics Blueprint domain: Geometry)
Statistics and Probability 9
A fair number cube with faces 1 to 6 is rolled twice. What is the probability that both rolls show a number less than 3?Utah Core State Standards for Mathematics, grade 7, Standard 7.SP.8a (RISE Mathematics Blueprint domain: Statistics and Probability)
A forecast gives a probability of 0.95 for snow tomorrow. Which word best describes the chance of snow?Utah Core State Standards for Mathematics, grade 7, Standard 7.SP.5 (RISE Mathematics Blueprint domain: Statistics and Probability)
A plastic spoon is dropped 75 times and lands with its bowl facing up 45 times. Based on these results, what is the probability that the spoon lands bowl up?Utah Core State Standards for Mathematics, grade 7, Standard 7.SP.7b (RISE Mathematics Blueprint domain: Statistics and Probability)
A school wants to learn which lunch its 600 students like best. Which sample is most likely to be representative?Utah Core State Standards for Mathematics, grade 7, Standard 7.SP.1 (RISE Mathematics Blueprint domain: Statistics and Probability)
A spinner lands on green with probability 0.35. About how many times should it land on green in 120 spins?Utah Core State Standards for Mathematics, grade 7, Standard 7.SP.6 (RISE Mathematics Blueprint domain: Statistics and Probability)
Ari picks one of 3 shirts, red, blue or green, and one of 4 hats lettered A to D. How many outcomes are in the sample space?Utah Core State Standards for Mathematics, grade 7, Standard 7.SP.8b (RISE Mathematics Blueprint domain: Statistics and Probability)
In a random sample of 40 students, 14 walk to school. The school has 520 students. About how many students in the school walk?Utah Core State Standards for Mathematics, grade 7, Standard 7.SP.2 (RISE Mathematics Blueprint domain: Statistics and Probability)
The mean height on team A is 62 inches and on team B is 68 inches. Each team has a mean absolute deviation of 2 inches. The difference between the means is how many times the mean absolute deviation?Utah Core State Standards for Mathematics, grade 7, Standard 7.SP.3 (RISE Mathematics Blueprint domain: Statistics and Probability)
Random samples of plants from two gardens are measured. Garden X has a median height of 30 cm and an interquartile range of 4 cm. Garden Y has a median of 30 cm and an interquartile range of 12 cm. Which inference do the samples support?Utah Core State Standards for Mathematics, grade 7, Standard 7.SP.4 (RISE Mathematics Blueprint domain: Statistics and Probability)
How this list was compiled: Outline: Utah RISE Mathematics Blueprint, grade 7 (50 operational items; minimum and maximum percent for each domain), the document Math Blueprints on the Utah RISE portal, https://utahrise.org/resources (https://utahrise.org/content/contentresources/en/Math%20Blueprints.pdf), read 2026-10-13. Each question names the standard it practices in the Utah Core State Standards for Mathematics, Middle/Junior High School Grades (6-8), grade 7, linked from the Utah State Board of Education's page Utah Mathematics Standards, https://schools.utah.gov/curr/mathematics/core, read 2026-10-13. Test facts: RISE Testing: A Guide for Utah Families (June 2026), Making Sense of RISE Scores (June 2026) and RISE Testing Overview (October 2025), linked from https://schools.utah.gov/assessment/assessments/rise, read 2026-10-13. Every calculation was worked out a second time from the numbers in the question. Licence: Own work. Questions, answer choices and explanations were written for this site. Nothing is copied or reworded from a RISE test, a released item, a training or sample test of the state or another practice test, and no example of the standards document is reused.
How it works
Unofficial practice with fifty of our own questions for Utah's grade 7 RISE mathematics test, shared among the blueprint's five domains. None comes from a RISE test or training test. Not affiliated with the Utah State Board of Education.
Read the full guide
What the grade 7 RISE math test covers
Grade 7 is the only grade from 3 to 8 whose blueprint has five domains: geometry and statistics each get their own. Ratio and Proportions is the largest, 22 to 26 percent of 50 operational items: unit rates with fractions, constants of proportionality, and percent problems such as tax, markdowns, simple interest and percent error. The Number System, Geometry, and Statistics and Probability take 18 to 22 percent each, and Expressions and Equations 16 to 20 percent.
More Depth of Knowledge 3 than grade 6
The blueprint sets Depth of Knowledge 3, the highest level it lists, at 20 to 26 percent of grade 7 items. In grade 6 the range is 8 to 20 percent.
Questions and answers
How many questions are on the 7th grade RISE math test?
50 operational items, by the RISE mathematics blueprint. Ratio and Proportions has the largest share, 22 to 26 percent. The shares are targets, because the adaptive test gives each student a different set.
Is the RISE math test timed in 7th grade?
No. RISE assessments are not timed, by the State Board's guide for families. The same guide tells students to take their time, and says that getting harder questions means a student is doing well.
What RISE tests do 7th graders take?
Mathematics, English language arts and science. The State Board lists RISE writing for grades 5 and 8 only, so seventh grade has no writing test.
What do the RISE proficiency levels mean?
There are four: Below Proficient, Approaching Proficient, Proficient and Highly Proficient. The State Board describes Proficient as a solid understanding of grade-level standards. Results also carry a scale score, and no percent to pass is published.
Where can I find Utah RISE training tests?
On the Utah RISE portal, at utahrise.org/training-tests.html. The State Board says to sign in as a guest. The training tests cover a range of grades, show the tools and question types, and give no scores.