Free Grade 8 Math Worksheets With Answers
Eighth grade is pre-algebra becoming algebra: linear functions, slope, exponents and the Pythagorean theorem. These free questions cover each of them, with the full working shown.
10 free questions · Answer keys included · No sign-up to practice
Skills covered in Grade 8
Aligned to Common Core Grade 8 domains: 8.NS, 8.EE expressions and equations, 8.F functions, 8.G geometry and the Pythagorean theorem, and 8.SP statistics.
- Solving multi-step linear equations
- Slope and rate of change
- Graphing linear functions
- Systems of two linear equations
- Laws of exponents and scientific notation
- The Pythagorean theorem
- Volume of cylinders, cones and spheres
- Transformations and congruence
Free Grade 8 practice questions with answers
Filter by topic or difficulty, or work straight through. Every answer opens to show the steps, so the page works as a worksheet and an answer key at the same time.
- Question 1easyLinear equations
Solve: 4x − 7 = 21
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Answer: x = 7
Add 7: 4x = 28. Divide by 4: x = 7.
- Question 2easyExponents
Simplify: 2³ × 2⁴
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Answer: 2⁷ = 128
Same base, so add the exponents: 3 + 4 = 7, giving 2⁷ = 128.
- Question 3easySlope
Find the slope through (1, 2) and (4, 11).
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Answer: 3
Slope = (11 − 2) ÷ (4 − 1) = 9 ÷ 3 = 3.
- Question 4easyPythagorean theorem
A right triangle has legs 3 and 4. Find the hypotenuse.
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Answer: 5
a² + b² = c², so 9 + 16 = 25 and c = √25 = 5.
- Question 5easyFunctions
If f(x) = 2x + 1, find f(5).
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Answer: 11
Substitute 5: 2 × 5 + 1 = 10 + 1 = 11.
- Question 6mediumLinear equations
Solve: 5x + 3 = 2x + 18
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Answer: x = 5
Subtract 2x: 3x + 3 = 18. Subtract 3: 3x = 15. Divide by 3: x = 5.
- Question 7mediumExponents
Write 45,000 in scientific notation.
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Answer: 4.5 × 10⁴
Move the decimal four places left to get 4.5, so the exponent is 4.
- Question 8mediumSlope
What is the y-intercept of y = −2x + 7?
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Answer: 7
In y = mx + b, the value of b is the y-intercept, which is 7.
- Question 9hardPythagorean theorem
A ladder 13 m long leans against a wall with its base 5 m out. How high does it reach?
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Answer: 12 m
13² − 5² = 169 − 25 = 144, and √144 = 12 m.
- Question 10hardVolume
Find the volume of a cylinder with radius 3 cm and height 10 cm. Use π ≈ 3.14.
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Answer: 282.6 cubic cm
V = πr²h = 3.14 × 9 × 10 = 282.6 cubic centimetres.
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What Grade 8 students are expected to master
Eighth grade is the last year before algebra is graded as algebra, and it front-loads the two ideas that Algebra 1 assumes: that a linear relationship can be written as an equation, drawn as a line, and read from a table, and that all three are the same object. Students who can move between the three representations find Algebra 1 mostly familiar. Students who can only do one arrive already behind.
Slope is the connective tissue. It is a rate of change in a table, a steepness on a graph, and the coefficient of x in an equation. Teaching it as three separate definitions is the most common reason students find functions harder than they need to be.
Where Grade 8 students most often lose marks
Exponent laws get over-applied. Students who correctly write 2³ × 2⁴ = 2⁷ will often then write 2³ + 2⁴ = 2⁷, because the pattern feels the same. The addition case has no shortcut at all: it is 8 + 16 = 24. Making students state which law they are using, and checking that the operation matches, catches this.
The second is the Pythagorean theorem applied to the wrong side. In the ladder problem, the 13 m ladder is the hypotenuse, so the working is a subtraction, not an addition. Students who always add squares will get 194 and a nonsensical answer. Identifying the hypotenuse as the side opposite the right angle before substituting is worth doing every single time.