Eighth grade math for Colorado's CMAS: exponents, linear equations and systems, functions, transformations and the Pythagorean theorem.
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Unofficial practice questions, not affiliated with the Colorado Department of Education. Bank checked October 13, 2026.
The real test: CMAS math, grade 8
Who takes it
Students enrolled in grade 8. CMAS math is given in grades 3 to 8.
Score points
50 to 51: major content 24, supporting content 7, reasoning 10 to 11, modeling 9.
Shares
Major content 47 to 48% of the points, supporting content 13 to 14%, reasoning 20 to 22%, modeling 18%.
Calculator
A scientific calculator on calculator sections, which carry 36 to 37 of the points. None on the other sections, and never a graphing calculator.
Reasoning and modeling
Reasoning tasks rest on constructing arguments and attending to precision; modeling tasks on modeling with mathematics. Both may draw on securely held grade 7 c
Scores
Scale scores from 650 to 850. In grade 8 math, Met Expectations is 750 to 800 and Exceeded Expectations is 801 to 850.
A cube has a volume of 512 cubic centimeters, so its edge length x satisfies x³ = 512. What is x?CMAS Grade 8 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim A: Major Content, evidence outcome 8.EE.A.2
A function uses the rule "multiply the input by 4, then subtract 1." What is the output when the input is 6?CMAS Grade 8 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim A: Major Content, evidence outcome 8.F.A.1
A graph shows the depth of water in a bathtub over time. The line rises steadily, then runs flat, then falls steadily to zero. What does the flat part show?CMAS Grade 8 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim A: Major Content, evidence outcome 8.F.B.5
A line crosses the y-axis at (0, 5) and has a slope of −3. Which equation describes the line?CMAS Grade 8 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim A: Major Content, evidence outcome 8.EE.B.6
A linear function contains the points (2, 11) and (5, 20). What is its rate of change?CMAS Grade 8 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim A: Major Content, evidence outcome 8.F.B.4
Show all 44 questions (39 more)
Major content, continued
A pool holds 900 gallons of water and drains at a steady 15 gallons each minute. Which function gives the gallons g left after t minutes?CMAS Grade 8 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim A: Major Content, evidence outcome 8.F.B.4
A town has about 3 × 10⁴ people. A country has about 9 × 10⁷ people. About how many times as many people does the country have?CMAS Grade 8 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim A: Major Content, evidence outcome 8.EE.A.3
Function A is y = 3x + 1. Function B is linear and its table holds the points (0, 2), (1, 6) and (2, 10). Which function has the greater rate of change?CMAS Grade 8 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim A: Major Content, evidence outcome 8.F.A.2
The point (−2, 5) is dilated by a scale factor of 3 with the origin as center. What are the coordinates of its image?CMAS Grade 8 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim A: Major Content, evidence outcome 8.G.A.3
Rectangle A is 2 units by 3 units. Which rectangle is similar to rectangle A?CMAS Grade 8 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim A: Major Content, evidence outcome 8.G.A.4
Solve 3(x − 4) = x + 6.CMAS Grade 8 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim A: Major Content, evidence outcome 8.EE.C.7b
Train A travels d = 65t, where d is miles and t is hours. Train B travels 280 miles in 4 hours at a steady speed. Which train is faster?CMAS Grade 8 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim A: Major Content, evidence outcome 8.EE.B.5
Two angles of a triangle measure 39° and 74°. What is the measure of the third angle?CMAS Grade 8 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim A: Major Content, evidence outcome 8.G.A.5
What is (6 × 10⁸) ÷ (3 × 10²) in scientific notation?CMAS Grade 8 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim A: Major Content, evidence outcome 8.EE.A.4
What is the distance between the points (−2, 1) and (3, 13)?CMAS Grade 8 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim A: Major Content, evidence outcome 8.G.B.8
What is the solution of the system x + y = 13 and x − y = 5?CMAS Grade 8 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim A: Major Content, evidence outcome 8.EE.C.8b
What is the solution of the system y = 3x and x + y = 12?CMAS Grade 8 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim A: Major Content, evidence outcome 8.EE.C.8b
What is the value of 10⁻³?CMAS Grade 8 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim A: Major Content, evidence outcome 8.EE.A.1
Which equation defines a linear function?CMAS Grade 8 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim A: Major Content, evidence outcome 8.F.A.3
Which equation has no solution?CMAS Grade 8 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim A: Major Content, evidence outcome 8.EE.C.7a
Which expression is equal to (2³)⁴?CMAS Grade 8 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim A: Major Content, evidence outcome 8.EE.A.1
Supporting content 6
A line fitted to class data is s = 6h + 62, where s is a test score and h is hours studied. What score does the model predict for 4 hours of study?CMAS Grade 8 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim B: Supporting Content, evidence outcome 8.SP.A.3
A sphere has a radius of 3 centimeters. What is its volume, in terms of π?CMAS Grade 8 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim B: Supporting Content, evidence outcome 8.G.C.9
A two-way table shows 40 students with a pet, of whom 30 do chores, and 60 students with no pet, of whom 30 do chores. Which statement do the relative frequencies support?CMAS Grade 8 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim B: Supporting Content, evidence outcome 8.SP.A.4
Between which two whole numbers does √75 lie?CMAS Grade 8 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim B: Supporting Content, evidence outcome 8.NS.A.2
On a scatter plot, the points fall from upper left to lower right: as hours of practice go up, the number of mistakes goes down. Which pattern is this?CMAS Grade 8 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim B: Supporting Content, evidence outcome 8.SP.A.1
Which fraction is equal to 0.444…, where the 4 repeats forever?CMAS Grade 8 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim B: Supporting Content, evidence outcome 8.NS.A.1
Reasoning 9
A shirt is marked 20% off. Later the sale price is raised by 20%. Jon says the shirt is back at its original price. Which reasoning is correct?CMAS Grade 8 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim C: Expressing Mathematical Reasoning, content scope 7.RP.A
A student solves 4(x − 2) = 20. Step 1: 4x − 2 = 20. Step 2: 4x = 22. Step 3: x = 5.5. Where is the first error?CMAS Grade 8 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim C: Expressing Mathematical Reasoning, content scope 8.EE.7b
A triangle has sides of 6, 8 and 11 units. Ana says it is a right triangle. Which check shows whether she is correct?CMAS Grade 8 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim C: Expressing Mathematical Reasoning, content scope 8.G.B
Figure B is made from figure A by a dilation with scale factor 3 followed by a reflection. Which statement is true?CMAS Grade 8 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim C: Expressing Mathematical Reasoning, content scope 8.G.4
For which value of a does 3x + a = 3x + 6 have infinitely many solutions?CMAS Grade 8 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim C: Expressing Mathematical Reasoning, content scope 8.EE.7a
For x = 0, 1, 2 and 3, four functions give these outputs. Which function is not linear?CMAS Grade 8 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim C: Expressing Mathematical Reasoning, content scope 8.F.3
Tara says the point (4, 9) is on the line y = 2x + 3. Which check settles the question?CMAS Grade 8 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim C: Expressing Mathematical Reasoning, content scope 8.EE.6
Triangle ABC has vertices A(1, 1), B(4, 1) and C(1, 5). Triangle A'B'C' has vertices (−1, 1), (−4, 1) and (−1, 5). Which single transformation shows the triangles are congruent?CMAS Grade 8 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim C: Expressing Mathematical Reasoning, content scope 8.G.2
Two parallel lines are cut by a transversal. One angle measures 110°. Li says its alternate interior angle measures 70°. Is Li correct?CMAS Grade 8 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim C: Expressing Mathematical Reasoning, content scope 8.G.5
Modeling 8
A bike helmet costs $40. It is marked 15% off, and then a 5% sales tax is added to the sale price. What is the final cost?CMAS Grade 8 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim D: Modeling and Application, content scope 7.RP.A
A circular garden has a diameter of 10 meters. Fence costs $6 for each meter. Using 3.14 for π, what does it cost to fence the garden?CMAS Grade 8 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim D: Modeling and Application, content scope 7.G
A hiker starts 250 feet below sea level, at −250 feet, and climbs 40 feet each minute. After how many minutes is the hiker 150 feet above sea level?CMAS Grade 8 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim D: Modeling and Application, content scope 7.NS.3
A machine prints 4 × 10³ labels each hour. How many labels does it print in 2.5 × 10² hours?CMAS Grade 8 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim D: Modeling and Application, content scope 8.EE.A.4
A rectangular field is 30 meters wide and 40 meters long. How much shorter is the walk straight across the diagonal than the walk along two sides?CMAS Grade 8 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim D: Modeling and Application, content scope 8.G.B.7
A tank is filled at a steady rate. It holds 120 liters after 2 minutes and 210 liters after 5 minutes. How much water was in the tank at the start?CMAS Grade 8 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim D: Modeling and Application, content scope 8.F.B.4
Adult tickets cost $9 and child tickets cost $5. A group of 12 people pays $80 in all. How many adults are in the group?CMAS Grade 8 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim D: Modeling and Application, content scope 8.EE.C.8c
The players on team A have a mean height of 150 centimeters and those on team B have a mean of 158 centimeters. Each team's mean absolute deviation is 4 centimeters. How many mean absolute deviations apart are the two means?CMAS Grade 8 Mathematics Frameworks (Colorado Department of Education, 2020), Subclaim D: Modeling and Application, content scope 7.SP.B
How this list was compiled: Outline and standards: CMAS Grade 8 Mathematics Frameworks (Colorado Department of Education, 2020), https://ed.cde.state.co.us/fs/resource-manager/view/675d177c-a695-4d01-945c-0a2467050ca3, linked from the department's page CMAS Test Design, https://ed.cde.state.co.us/assessment/cmas-testdesign, read 2026-10-13. The framework lists the evidence outcomes of the Colorado Academic Standards that the grade 8 test may ask, the content scope of its reasoning and modeling tasks and the score points of each reporting category; each question names the outcome or content scope it practices. Every numeric answer is arithmetic or algebra on the numbers in the question, worked a second time. Licence: Own work. Questions, answer choices and explanations were written for this site. Nothing is copied or reworded from a CMAS test, a released item or practice resource of the department, or another practice test. No released item was read.
How it works
Forty-four eighth grade math questions for Colorado's CMAS, the Colorado Measures of Academic Success. The practice is unofficial: each question is our own, built on the state's grade 8 framework. It is not affiliated with the Colorado Department of Education, which owns the test.
Read the full guide
What 8th grade CMAS math covers
Nearly half of the grade 8 points are major content, so 21 of these 44 questions are too: exponents and scientific notation, slope, linear equations and systems, functions, transformations, angle sums and the Pythagorean theorem. Six are supporting content: irrational numbers, scatter plots, two-way tables and the volume of a sphere. Nine test reasoning by asking which argument holds or where worked steps go wrong, and eight are multistep modeling problems.
Grade 7 content comes back
Reasoning and modeling tasks may reach back to grade 7, the framework says, so percents, circles and signed numbers appear in a few questions.
Grade 8 is the only CMAS math test that allows a scientific calculator, yet 13 to 14 of its points are earned without one.
Questions and answers
How many points is the 8th grade CMAS math test worth?
50 to 51 score points. Major content carries 24 of them, supporting content 7, expressing mathematical reasoning 10 or 11, and modeling and application 9. Colorado's framework counts points, not questions, and states no time limit.
Which calculator is allowed on 8th grade CMAS math?
A scientific calculator, on calculator sections only; those sections carry 36 to 37 of the points. Graphing calculators, calculators with a computer algebra system and phone or tablet calculators are barred, and students may not share one.
What score meets expectations on 8th grade CMAS math?
A scale score of 750 to 800 is Met Expectations in grade 8 math, and 801 to 850 is Exceeded Expectations. No other grade from 3 to 8 has so wide a Met band.
Does Colorado publish its own 8th grade CMAS math practice?
Yes. The department's CMAS Practice Resources are built from released CMAS content and are, in its words, the only state-sanctioned ones. Nothing here is taken from them.