Grade 8 math on the Georgia Milestones End-of-Grade (EOG) assessment is the most demanding of the K–8 assessments. Students encounter formal function notation, the Pythagorean theorem, multi-step linear equations, transformational geometry, and statistics for the first time in a testing context — all within a single exam. The content is also the direct predecessor to Algebra 1, so mastering it gives students a significant advantage in high school.
This page provides original practice problems with detailed solutions for the three largest Georgia Grade 8 domains, along with a realistic 3-week prep plan.
ViewMath is not affiliated with or endorsed by the Georgia Department of Education. For official test information, visit gadoe.org.
Georgia Milestones Grade 8 Math: Domain Overview
- Expressions and Equations: Integer exponents, scientific notation, square roots, cube roots, multi-step linear equations (including equations with no solution or infinitely many solutions), systems of linear equations
- Functions: Defining, interpreting, and comparing functions (rules, tables, graphs, equations); linear vs. non-linear functions; analyzing rate of change
- Geometry: Transformations (translations, reflections, rotations, dilations), congruence and similarity, Pythagorean theorem and its converse, distance in the coordinate plane, volume of cylinders/cones/spheres
- Statistics and Probability: Scatter plots, line of best fit, two-way tables, bivariate data patterns
Practice Problems: Functions
1. A function is defined by the equation y = 3x − 5. Complete the table of values for x = −2, 0, 1, 4. Is this function linear or non-linear?
x = −2: y = 3(−2) − 5 = −11. x = 0: y = −5. x = 1: y = −2. x = 4: y = 7. The rate of change is constant (3 for every unit increase in x), so the function is linear.
2. The table below shows a relationship between x and y: x: 1, 2, 3, 4 / y: 2, 4, 8, 16. Is this a linear or non-linear function? How can you tell?
The differences between consecutive y-values are 2, 4, 8 — not constant. The rate of change is not constant, so the function is non-linear (it is exponential).
3. Function A is described by the equation y = 2x + 1. Function B passes through the points (0, 3) and (2, 7). Which function has the greater rate of change?
Function A: slope = 2. Function B: slope = (7 − 3)/(2 − 0) = 4/2 = 2. The rates of change are equal.
4. A bicycle rental shop charges a flat fee of $5 plus $3 per hour. Write a function rule. What does the y-intercept represent in this context?
y = 3x + 5, where x = hours. The y-intercept (5) represents the flat fee paid even when renting for zero hours — it’s the starting cost.
Practice Problems: Linear Equations and Systems
5. Solve for x: 4(2x − 3) = 2(3x + 1)
8x − 12 = 6x + 2 → 2x = 14 → x = 7.
6. Solve: 5x + 2 = 5x − 9
Subtract 5x from both sides: 2 = −9. This is false — the equation has no solution. The lines are parallel.
7. Solve: 3(x + 4) = 3x + 12
3x + 12 = 3x + 12. Both sides are identical — the equation is true for all values of x. Infinitely many solutions.
8. Solve the system: y = 2x + 1 and y = −x + 7
Set equal: 2x + 1 = −x + 7 → 3x = 6 → x = 2. y = 2(2) + 1 = 5. Solution: (2, 5).
9. Use elimination to solve: 3x + 2y = 16 and 3x − y = 4
Subtract the second equation from the first: 3y = 12 → y = 4. Substitute: 3x + 8 = 16 → x = 8/3. (Or: 3x − 4 = 4 → 3x = 8 → x = 8/3.) Solution: (8/3, 4).
Practice Problems: Pythagorean Theorem and Geometry
10. A right triangle has legs of length 9 and 12. What is the length of the hypotenuse?
c² = 9² + 12² = 81 + 144 = 225 → c = 15.
11. A ladder 17 feet long leans against a wall. The base of the ladder is 8 feet from the wall. How high up the wall does the ladder reach?
8² + h² = 17² → 64 + h² = 289 → h² = 225 → h = 15 feet.
12. A right triangle has a hypotenuse of 10 and one leg of 6. What is the other leg? Is (6, 8, 10) a Pythagorean triple?
6² + b² = 10² → 36 + b² = 100 → b² = 64 → b = 8. Yes, (6, 8, 10) is a Pythagorean triple (it’s a scaled version of 3-4-5).
13. Find the distance between the points (1, 2) and (5, 5).
d = √[(5−1)² + (5−2)²] = √[16 + 9] = √25 = 5.
14. Triangle ABC has vertices A(0, 0), B(4, 0), and C(4, 3). Describe the effect of a reflection across the x-axis on the coordinates of each vertex.
Reflecting across x-axis: (x, y) → (x, −y). A(0,0)→(0,0), B(4,0)→(4,0), C(4,3)→(4,−3). The shape and size are preserved (congruent); only the vertical orientation flips.
15. A cylinder has a radius of 5 cm and height of 10 cm. What is its volume? (Use π ≈ 3.14)
V = πr²h = 3.14 × 25 × 10 = 785 cm³.
Practice Problems: Scientific Notation
16. Write 0.00000045 in scientific notation.
4.5 × 10⁻⁷
17. Compute: (3 × 10⁴) × (2 × 10⁻²)
= 6 × 10² = 600
18. The mass of an electron is approximately 9.11 × 10⁻³¹ kg. The mass of a proton is approximately 1.67 × 10⁻²⁷ kg. How many times heavier is the proton than the electron?
(1.67 × 10⁻²⁷) ÷ (9.11 × 10⁻³¹) ≈ 0.183 × 10⁴ = 1,833 times heavier.
Common Georgia Grade 8 Milestones Mistakes
- Confusing equations with no solution and infinitely many solutions: No solution produces a false constant equation (2 = −9). Infinite solutions produce a true constant equation (12 = 12). Practice identifying both forms until they’re automatic.
- Applying the Pythagorean theorem when the triangle is not a right triangle: The theorem works only for right triangles. If no right angle is given or implied, you cannot use a² + b² = c².
- Applying dilations additively instead of multiplicatively: A dilation with scale factor 3 multiplies all coordinates by 3 — it does not add 3 to each coordinate.
- Moving the decimal in the wrong direction for scientific notation: Numbers less than 1 use negative exponents. A systematic rule: the exponent tells you how many places the decimal moves, and its sign tells you which direction.
3-Week Georgia Grade 8 Milestones Prep Plan
Week 1: Equations, Exponents, and Scientific Notation
Work through multi-step equations including no-solution and infinite-solution cases. Spend two days on exponent rules (product, quotient, power, zero, and negative exponents). Finish the week with scientific notation operations and comparison problems.
Week 2: Functions and Systems
Build fluency with function tables, rules, and graphs. Distinguish linear from non-linear functions using rate of change. Solve systems by graphing, substitution, and elimination. Focus on the meaning of the intersection point in word problem contexts.
Week 3: Geometry, Statistics, and Mixed Review
Practice the Pythagorean theorem and its converse across contexts (shortest path, screen diagonal, missing leg). Work through volume problems for cylinders, cones, and spheres. Review transformations and congruence/similarity reasoning. Finish with scatter plot/two-way table problems, then a 20-question full practice test.
Georgia Grade 8 Math Resources
ViewMath publishes Grade 8 math workbooks, practice test books, and study guides that cover all Georgia Grade 8 domains. Browse the full Grade 8 catalog using the sidebar.
ViewMath is an independent publisher. Our materials are not official Georgia Milestones test items and are not produced by or affiliated with the Georgia Department of Education.
