The Grade 8 MCAS mathematics assessment is one of the most important benchmarks in a Massachusetts student’s academic journey. At this level, students are expected to work with linear functions, write and solve equations and systems, apply the Pythagorean theorem, understand geometric transformations, and analyze bivariate data. The practice problems in this post cover each of those domains at a level that reflects the rigor of the actual MCAS assessment.
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What MCAS Grade 8 Math Covers
The Massachusetts Curriculum Framework for Grade 8 Mathematics draws on the following domains:
- The Number System (8.NS): Irrational numbers, approximating square roots and cube roots, locating irrationals on a number line
- Expressions and Equations (8.EE): Integer exponents, scientific notation, proportional and non-proportional linear equations, linear systems
- Functions (8.F): Defining functions, comparing functions, modeling with linear functions, slope as rate of change
- Geometry (8.G): Transformations (translation, reflection, rotation, dilation), congruence and similarity, Pythagorean theorem, volume of cones, cylinders, and spheres
- Statistics and Probability (8.SP): Scatter plots, clustering and outliers, lines of best fit, two-way tables
16 MCAS-Style Grade 8 Practice Problems
Functions
Problem 1. The table below shows values for function f(x): when x = 0, f(x) = −2; when x = 1, f(x) = 1; when x = 2, f(x) = 4; when x = 3, f(x) = 7. What is the slope of this linear function? Write an equation in slope-intercept form.
Problem 2. Function A has the equation y = 3x + 1. Function B passes through (0, 2) and (4, 10). Which function has a greater rate of change? Explain.
Problem 3. A taxi company charges a $2.50 flat fee plus $1.75 per mile. Write a function C(m) for the total cost in dollars for a trip of m miles. What is the total cost for a 6-mile trip?
Expressions and Equations
Problem 4. Solve for x: 3(2x − 4) = 2(x + 5)
Problem 5. Solve the system of equations:
2x + 3y = 12
4x − y = 10
Problem 6. Write 0.0000487 in scientific notation.
Problem 7. The weight of a proton is approximately 1.67 × 10⁻²⁷ kilograms. The weight of an electron is approximately 9.11 × 10⁻³¹ kilograms. How many times heavier is a proton than an electron? Express your answer in scientific notation and round the coefficient to two decimal places.
Number System
Problem 8. Between which two consecutive integers does √55 lie? Which integer is it closer to?
Problem 9. A square garden has an area of 200 square feet. What is the length of each side to the nearest tenth of a foot?
Geometry
Problem 10. Triangle ABC has vertices at A(1, 2), B(4, 2), and C(4, 6). Triangle A’B’C’ is the image of triangle ABC after a reflection over the y-axis. What are the coordinates of A’, B’, and C’?
Problem 11. A right triangle has legs of length 7 cm and 24 cm. What is the length of the hypotenuse?
Problem 12. A ladder 13 feet long leans against a vertical wall. The base of the ladder is 5 feet from the wall. How high up the wall does the ladder reach?
Problem 13. A cone has a radius of 4 cm and a height of 9 cm. What is its volume? Use π ≈ 3.14 and round to the nearest tenth.
Problem 14. Figure ABCD is a square with side length 6. It is dilated by a scale factor of 1.5 centered at the origin. What is the perimeter of the resulting figure?
Statistics and Probability
Problem 15. A scatter plot shows a positive linear association between hours of study and test score. The line of best fit passes through (2, 65) and (8, 89). What is the slope of the line of best fit? What does this slope represent in context?
Problem 16. A survey asked 200 students whether they prefer reading or watching movies. The two-way table shows: Grade 7: 45 reading, 55 movies. Grade 8: 60 reading, 40 movies. What percentage of all Grade 8 students prefer reading?
Answer Key with Explanations
1. Slope = 3; y = 3x − 2. The output increases by 3 for each increase of 1 in x. At x = 0, y = −2, so the y-intercept is −2.
2. Function A has the greater rate of change. Rate for A = 3. Rate for B = (10 − 2)/(4 − 0) = 2. Since 3 > 2, Function A has the greater rate of change. Students should compute both rates before answering.
3. C(m) = 2.50 + 1.75m. For 6 miles: C(6) = 2.50 + 10.50 = $13.00.
4. x = 5.5. Distribute: 6x − 12 = 2x + 10 → 4x = 22 → x = 5.5. (Recheck: 6(5.5) − 12 = 33 − 12 = 21; 2(5.5) + 10 = 11 + 10 = 21. ✓)
5. x = 3, y = 2. Multiply equation 2 by 3: 12x − 3y = 30. Add to equation 1: 14x = 42 → x = 3. Substitute: 6 + 3y = 12 → y = 2.
6. 4.87 × 10⁻⁵.
7. ≈ 1.83 × 10³ times heavier. (1.67 × 10⁻²⁷) ÷ (9.11 × 10⁻³¹) = (1.67/9.11) × 10⁴ ≈ 0.1833 × 10⁴ = 1.83 × 10³.
8. Between 7 and 8; closer to 7. (7² = 49, 8² = 64; √55 ≈ 7.42.)
9. ≈ 14.1 feet. √200 ≈ 14.142.
10. A'(−1, 2), B'(−4, 2), C'(−4, 6). Reflecting over the y-axis negates the x-coordinate.
11. 25 cm. a² + b² = c² → 49 + 576 = 625 → c = 25.
12. 12 feet. 5² + h² = 13² → 25 + h² = 169 → h² = 144 → h = 12.
13. ≈ 150.7 cm³. V = (1/3)πr²h = (1/3)(3.14)(16)(9) = (1/3)(452.16) ≈ 150.7.
14. 36. New side length = 6 × 1.5 = 9. Perimeter = 4 × 9 = 36.
15. Slope = 4. (89 − 65)/(8 − 2) = 24/6 = 4. In context: for each additional hour of study, the predicted test score increases by 4 points.
16. 60%. Grade 8 total = 60 + 40 = 100. Reading = 60. 60/100 = 60%.
What to Study Next
If you missed several functions or equations problems, prioritize building fluency with slope-intercept form, rate of change, and solving systems using substitution and elimination. If geometry was the challenge, work through the Pythagorean theorem in multiple contexts — distance problems, ladder problems, and coordinate geometry — before moving to volume and transformations.
ViewMath offers comprehensive Grade 8 math practice books built to match the rigor and topic distribution of the Massachusetts MCAS. Browse the collection at viewmath.com/shop.
