Grade 8 Math quiz

Grade 8 Math Quiz

Practice Grade 8 math questions about linear equations, exponents, square roots, functions, slope, geometry, the Pythagorean theorem, scientific notation, and data interpretation. Use hints when needed, choose an answer, and review the explanation after each question.

1 Question 1 of 10
Not answered

Solve for x: 4x - 7 = 21

Hint: First add 7 to both sides, then divide by 4.
Explanation: Add 7 to both sides: 4x = 28. Divide by 4, so x = 7.
2 Question 2 of 10
Not answered

Simplify: 2³ × 2⁴

Hint: When multiplying powers with the same base, add the exponents.
Explanation: 2³ × 2⁴ = 2^(3+4) = 2⁷.
3 Question 3 of 10
Not answered

What is √144?

Hint: Find the number that multiplied by itself gives 144.
Explanation: 12 × 12 = 144, so √144 = 12.
4 Question 4 of 10
Not answered

Find the slope of a line that passes through (2, 3) and (6, 11).

Hint: Use slope = change in y divided by change in x.
Explanation: The change in y is 11 - 3 = 8. The change in x is 6 - 2 = 4. The slope is 8/4 = 2.
5 Question 5 of 10
Not answered

If y = 3x - 2, what is y when x = 5?

Hint: Substitute 5 for x in the function.
Explanation: y = 3x - 2. Substitute x = 5: y = 3(5) - 2 = 15 - 2 = 13.
6 Question 6 of 10
Not answered

A right triangle has legs 9 and 12. What is the hypotenuse?

Hint: Use the Pythagorean theorem: a² + b² = c².
Explanation: 9² + 12² = 81 + 144 = 225. Therefore c = √225 = 15.
7 Question 7 of 10
Not answered

Write 0.00056 in scientific notation.

Hint: Move the decimal until the number is between 1 and 10.
Explanation: 0.00056 becomes 5.6 when the decimal moves 4 places to the right. So the scientific notation is 5.6 × 10⁻⁴.
8 Question 8 of 10
Not answered

Solve the system: x + y = 12 and x - y = 4. What is x?

Hint: Add the two equations together to eliminate y.
Explanation: Add the equations: (x + y) + (x - y) = 12 + 4. This gives 2x = 16, so x = 8.
9 Question 9 of 10
Not answered

What is the volume of a cube with side length 5?

Hint: Volume of a cube = side³.
Explanation: The volume is 5³ = 5 × 5 × 5 = 125.
10 Question 10 of 10
Not answered

The data set is 6, 8, 10, 12, 14. What is the mean?

Hint: Add all values and divide by the number of values.
Explanation: 6 + 8 + 10 + 12 + 14 = 50. There are 5 values, so the mean is 50 ÷ 5 = 10.

Your result

You answered 0 out of 10 questions correctly.

Grade 8 control panel

Grade 8 math shifts from isolated calculations to models, rules, and representations

The 10 questions on this page cover linear equations, exponent rules, square roots, slope, functions, the Pythagorean theorem, scientific notation, systems, volume, and mean. At this level, the important skill is often recognizing which representation makes the problem easiest.

Linear equationsExponentsRootsSlope FunctionsPythagorean theoremScientific notationSystems
Exponent ladder

Same base means the exponent records repeated multiplication

The quiz asks for 2³ × 2⁴. Instead of multiplying 8 × 16 first, preserve the common base and combine the counts of factors.

2³ = 2·2·2
2⁴ = 2·2·2·2
2⁷
Why the exponents add Multiplying the two powers gives seven total factors of 2: 2³ × 2⁴ = 2³⁺⁴ = 2⁷.
Coordinate lab

Slope measures how much y changes for each unit of x

The points (2, 3) and (6, 11) define the same slope no matter which point you start from, as long as numerator and denominator use the same direction.

Δy = 11 − 3 = 8
Δx = 6 − 2 = 4
m = Δy / Δx = 8/4 = 2
Function machine

A function turns an input into an output according to a rule

For y = 3x − 2, substituting x = 5 means the function applies “multiply by 3, then subtract 2.”

input x5
rule×3, then −2
output y13
5 → 15 → 13, so the point (5, 13) lies on the line y = 3x − 2.
Pythagorean check

The theorem connects the three sides of a right triangle through squares

The current triangle has legs 9 and 12. The hypotenuse must be longer than either leg, and the square relationship identifies it exactly.

9² + 12² = c²
81 + 144 = 225
c = √225 = 15
Scientific-notation scale

Scientific notation separates the size of a number from its significant digits

To rewrite 0.00056, move the decimal until the leading factor is between 1 and 10. Moving four places to the right requires a power of 10⁻⁴.

0.00056
0.0056
0.056
0.56
5.6
0.00056 = 5.6 × 10⁻⁴
System intersection

Two equations describe two conditions that must be true at the same time

In x + y = 12 and x − y = 4, the y-terms are already opposites. That makes elimination the shortest route.

Add the equations

x + y = 12
x − y = 4
2x = 16

Finish and check

x = 8
8 + y = 12 → y = 4
8 − 4 = 4 ✓
solution point: (8, 4)
Skill diagnostic

Use the quiz result to identify the representation that needs practice

Instead of treating the score as one number, group mistakes by the kind of mathematics involved.

Algebraequations, systems
Powersexponents, roots, scientific notation
Functionsslope, substitution, coordinates
GeometryPythagorean theorem, volume
Datamean and interpretation