Grade 8 is one of the most demanding years in K–8 math, and the Ohio State Test (OST) reflects that. For the first time, students work formally with functions, graph and interpret linear equations using slope-intercept form, apply the Pythagorean theorem in multi-step problems, and connect transformations to congruence and similarity. All of these topics require a level of algebraic reasoning that is noticeably higher than Grade 7.
This guide covers the major content areas on the Ohio Grade 8 OST, describes the problem types students encounter, and includes practice problems with answers.
ViewMath is not affiliated with or endorsed by the Ohio Department of Education and Workforce. For official OST information, visit education.ohio.gov.
Ohio Grade 8 OST Math: Content Domains
The Ohio State Test for Grade 8 math is aligned to Ohio’s Learning Standards, which are based on the Common Core State Standards. The major content domains are:
Expressions, Equations, and the Number System
Students work with radicals and integer exponents, simplify expressions using properties of exponents, and evaluate square roots and cube roots. They express very large and very small numbers in scientific notation and use scientific notation in calculations. Students also solve multi-step linear equations with rational number coefficients — equations that may have one solution, no solution, or infinitely many solutions — and solve systems of two linear equations using graphing and substitution.
Functions
Functions is a new major domain at Grade 8. Students define a function as a rule that assigns each input exactly one output, use function notation, and compare functions presented in different ways (table, graph, equation, verbal description). They analyze linear functions to determine rate of change (slope) and initial value (y-intercept), and they distinguish between linear and non-linear functions.
Geometry: Transformations
Students work with transformations — translations, reflections, rotations, and dilations — on the coordinate plane. They understand that rigid motions (translations, reflections, rotations) produce congruent figures, and that dilations produce similar figures. They describe a sequence of transformations that takes one figure to another.
Geometry: Pythagorean Theorem and Volume
Students prove and apply the Pythagorean theorem (a² + b² = c²) to find missing side lengths in right triangles and to find distances between points on the coordinate plane. They also find the volume of cylinders, cones, and spheres using the standard formulas.
Statistics and Probability
Students construct and interpret scatter plots, use lines of best fit to model bivariate data, describe patterns such as clustering and outliers, and interpret the slope and y-intercept of a trend line in context. They also work with two-way tables to describe associations between two categorical variables.
Grade 8 OST Practice Problems
Functions
1. The equation y = 3x − 4 represents a linear function. What is the slope and y-intercept? What does each represent in the context of a car that starts 4 miles from home and drives away at 3 miles per hour?
Slope = 3 (miles per hour, rate of change). Y-intercept = −4… wait, let me rewrite: y = 3x + 4 starts 4 miles from home. For y = 3x − 4: y-intercept is −4 (not meaningful in that context). Let’s use: A car is currently 4 miles from school and drives away at 3 mph. Answer: slope = 3 (rate, mph), y-intercept = 4 (starting distance). So y = 3x + 4.
1 (revised). A car is 4 miles from school and drives away from school at a constant speed of 3 miles per hour. Write a linear function for the distance d from school after t hours, then find the distance after 2.5 hours.
Answer: d = 3t + 4. At t = 2.5: d = 3(2.5) + 4 = 7.5 + 4 = 11.5 miles.
2. Which of the following tables represents a function? Table A: (1,3), (2,5), (3,3), (4,7). Table B: (1,2), (2,4), (1,6), (3,8).
Answer: Table A is a function — each input maps to exactly one output. Table B is not — input 1 maps to both 2 and 6.
3. Two functions are given: f(x) = 2x + 1 (equation) and g(x) shown as a table: (0, −3), (1, 0), (2, 3), (3, 6). Which function has the greater slope?
f(x) has slope 2. g(x): slope = (0 − (−3))/(1 − 0) = 3. g(x) has the greater slope.
Pythagorean Theorem
4. A ladder 15 feet long leans against a wall. The base of the ladder is 9 feet from the wall. How far up the wall does the ladder reach?
Answer: 12 feet. (9² + b² = 15² → 81 + b² = 225 → b² = 144 → b = 12)
5. Find the distance between points (−2, 3) and (4, 11).
Answer: 10 units. (d = √[(4−(−2))² + (11−3)²] = √[36 + 64] = √100 = 10)
6. A rectangular field is 24 m long and 10 m wide. What is the length of the diagonal?
Answer: 26 m. (24² + 10² = 576 + 100 = 676; √676 = 26)
Geometry: Volume
7. Find the volume of a cone with radius 6 cm and height 14 cm. Use π ≈ 3.14.
Answer: 527.52 cm³. (V = (1/3)πr²h = (1/3)(3.14)(36)(14) ≈ 527.52)
8. A sphere has a radius of 9 inches. Find its volume. Use π ≈ 3.14.
Answer: 3052.08 in³. (V = (4/3)πr³ = (4/3)(3.14)(729) ≈ 3052.08)
Linear Equations and Systems
9. Solve: 5x − 3 = 2x + 12
Answer: x = 5. (3x = 15 → x = 5)
10. Solve the system by substitution: y = 2x − 3 and 3x + y = 17
Answer: x = 4, y = 5. (3x + 2x − 3 = 17 → 5x = 20 → x = 4; y = 2(4) − 3 = 5)
Statistics: Scatter Plots
11. A scatter plot for hours of TV watched per week (x) and GPA (y) shows a negative linear relationship. The trend line equation is y = −0.12x + 4.0. Predict the GPA of a student who watches 15 hours of TV per week.
Answer: y = −0.12(15) + 4.0 = −1.8 + 4.0 = 2.2
12. In the context above, what does the slope −0.12 mean?
For each additional hour of TV per week, GPA is predicted to decrease by 0.12 points.
Common OST Grade 8 Math Mistakes
- Confusing congruence and similarity: Rigid transformations (translations, reflections, rotations) produce congruent figures with the same size and shape. Dilations produce similar figures with the same shape but different size. Students often mix these up.
- Misidentifying functions from tables: Always check whether any x-value repeats with a different y-value. If it does, the table does not represent a function.
- Applying the Pythagorean theorem to non-right triangles: a² + b² = c² only works for right triangles, where c is the hypotenuse (the side opposite the right angle).
- Forgetting the cube root for sphere volume: V = (4/3)πr³ requires cubing the radius, not squaring. This is an easy keypad error on a calculator.
4-Week OST Grade 8 Prep Plan
Week 1: Exponents, Scientific Notation, Radicals
Practice the exponent rules (product, quotient, power, zero, negative). Convert numbers to and from scientific notation. Evaluate √ and ∛ of perfect squares and cubes.
Week 2: Functions and Linear Equations
Define and identify functions. Graph linear functions using slope and y-intercept. Solve multi-step equations and systems of two equations.
Week 3: Geometry (Transformations, Pythagorean Theorem, Volume)
Practice the four transformations on graph paper. Apply the Pythagorean theorem to triangles and coordinate problems. Calculate volumes of cylinders, cones, and spheres.
Week 4: Statistics and Mixed Review
Interpret scatter plots, trend lines, and two-way tables. Take a full mixed-topic practice test and review every error by domain.
Ohio Grade 8 Math Resources
ViewMath publishes Grade 8 math study guides, workbooks, and practice test books aligned to Ohio’s Learning Standards. Use the sidebar to explore the full Grade 8 catalog.
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