Year 8 Maths Test is a free online practice test with 15 questions on algebra, fractions, percentages, percentage change, proportion, pythagoras, circles, polygons, sequences, indices and probability. The questions use algebra, percentages and percentage change, proportion, Pythagoras’ theorem, circles, polygon angles, index laws and probability. The test scores itself, and it shows the correct answer and an explanation for every question you miss.
Take it in test mode to see your score and answers at the end, or in practice mode to check each answer straight away. A printable version and an answer key are included, and the test takes about 30 minutes.
This test needs JavaScript. The questions and the answer key are also listed further down the page.
Year 8 Maths Test
Name: ______________________ Date: ______________
Find the value of 3x² − 2x when x = 4.
Answer: ______________
Solve for x: 7x − 9 = 4x + 12.
Answer: ______________
Solve for x: (x + 5) ÷ 3 = 8.
Answer: ______________
What is 5/8 of 96?
Answer: ______________
A coat costs £120 and is reduced by 35%. What is the sale price in pounds?
Answer: ______________
A price goes from £40 to £46. What is the percentage increase? Enter the number only.
Answer: ______________
8 workers build a wall in 12 days. How many days would 6 workers take at the same rate?
Answer: ______________
A right-angled triangle has shorter sides of 9 cm and 12 cm. What is the length of the hypotenuse in centimetres?
Answer: ______________
A circle has radius 7 cm. What is its circumference in centimetres? Use 22/7 for pi.
Answer: ______________
What is the area of a circle with radius 10 cm? Use 3.14 for pi.
Answer: ______________
Each interior angle of a regular polygon is 135°. How many sides does it have?
Answer: ______________
What is the 20th term of the sequence 3, 8, 13, 18, ...?
Answer: ______________
What is 2⁵ × 2³ written as a single number?
Answer: ______________
A fair coin is flipped twice. What is the probability of two heads? Write a fraction.
Answer: ______________
Expand 3(x + 4).
A. 3x + 4 B. 3x + 12 C. x + 12 D. 3x + 7
Answer key: Year 8 Maths Test
- 40
- 7
- 19
- 60
- 78
- 15
- 16
- 15
- 44
- 314
- 8
- 98
- 256
- 1/4
- 3x + 12
What this test covers
- Algebra (4 questions)
- Fractions (1 question)
- Percentages (1 question)
- Percentage change (1 question)
- Proportion (1 question)
- Pythagoras (1 question)
- Circles (2 questions)
- Polygons (1 question)
- Sequences (1 question)
- Indices (1 question)
- Probability (1 question)
How the test works
Test mode and practice mode
In test mode you answer every question first and see your score, the time you took and the answers at the end. In practice mode you press Check after each answer to see right away whether it is correct, with the explanation.
How answers are scored
For questions with a number as the answer, you can type a whole number, a decimal such as 2.5, or a fraction such as 3/4. A pound sign is ignored, and a fraction and its decimal value count as the same answer. Multiple choice questions have one correct choice.
Printing the test and the answer key
Use Print the test for a paper copy with a space for each answer, and Print the answer key for the matching answers. Both print without the rest of the page.
Questions and answer key
The questions
- Find the value of 3x² − 2x when x = 4.
- Solve for x: 7x − 9 = 4x + 12.
- Solve for x: (x + 5) ÷ 3 = 8.
- What is 5/8 of 96?
- A coat costs £120 and is reduced by 35%. What is the sale price in pounds?
- A price goes from £40 to £46. What is the percentage increase? Enter the number only.
- 8 workers build a wall in 12 days. How many days would 6 workers take at the same rate?
- A right-angled triangle has shorter sides of 9 cm and 12 cm. What is the length of the hypotenuse in centimetres?
- A circle has radius 7 cm. What is its circumference in centimetres? Use 22/7 for pi.
- What is the area of a circle with radius 10 cm? Use 3.14 for pi.
- Each interior angle of a regular polygon is 135°. How many sides does it have?
- What is the 20th term of the sequence 3, 8, 13, 18, …?
- What is 2⁵ × 2³ written as a single number?
- A fair coin is flipped twice. What is the probability of two heads? Write a fraction.
- Expand 3(x + 4). (A. 3x + 4; B. 3x + 12; C. x + 12; D. 3x + 7)
Answers and explanations
| Question | Answer | Explanation |
|---|---|---|
| 1 | 40 | x² = 16, so 3 × 16 = 48. Then 48 − 8 = 40. |
| 2 | 7 | Subtract 4x from both sides to get 3x − 9 = 12, then add 9 to get 3x = 21, so x = 7. |
| 3 | 19 | Multiply both sides by 3 to get x + 5 = 24, then subtract 5: x = 19. |
| 4 | 60 | One eighth of 96 is 12, so five eighths is 60. |
| 5 | 78 | 35% of 120 is 42. 120 − 42 = 78. |
| 6 | 15 | The increase is £6. 6 ÷ 40 = 0.15, which is 15%. |
| 7 | 16 | The job is 8 × 12 = 96 worker-days. With 6 workers it takes 96 ÷ 6 = 16 days. |
| 8 | 15 | 9² + 12² = 81 + 144 = 225, and the square root of 225 is 15. |
| 9 | 44 | Circumference = 2 × π × r = 2 × 22/7 × 7 = 44. |
| 10 | 314 | Area = π × r² = 3.14 × 100 = 314. |
| 11 | 8 | Each exterior angle is 180 − 135 = 45°. Exterior angles add up to 360°, so the number of sides is 360 ÷ 45 = 8. |
| 12 | 98 | The sequence goes up by 5, so the nth term is 5n − 2. The 20th term is 5 × 20 − 2 = 98. |
| 13 | 256 | Add the powers: 2⁵ × 2³ = 2⁸ = 256. |
| 14 | 1/4 | There are 4 equally likely outcomes and one of them is two heads, so 1/4. |
| 15 | 3x + 12 | Multiply both terms inside the bracket by 3: 3 × x = 3x and 3 × 4 = 12. |
Tips for Year 8 maths
- Solve equations by doing the same thing to both sides, and collect the x terms on one side first.
- For percentage change, divide the change by the original amount.
- In Pythagoras questions, square the two shorter sides and add them before taking the square root.
Frequently asked questions
How many questions are on this test?
There are 15 questions. Most students need about 30 minutes, but there is no time limit.
Can I print this test?
Yes. Use the Print the test button for the questions and Print the answer key for the answers. The full question list and answer key are also on this page.
Does the test show the answers?
Yes. At the end you see the correct answer and an explanation for every question, and in practice mode you see them after each question.
Do I need an account?
No. There is no sign-up. Your best score is kept only in your own browser.
Is a maths test the same as a math test?
Yes. Maths is the UK spelling and math is the US spelling of the same subject. This test uses pounds and metric units and is written for UK school years.
What should I do if I miss questions?
Look at the skills table on your result page, read the explanations for the questions you missed, and take the test again. If a step in your working looks wrong, the answer checker on this site can help you find the slip.