Free Year 10 Maths Practice Test (10 Questions)

1. Solve x² − 5x + 6 = 0

x = −2 or x = −3 x = 2 or x = 3 x = 1 or x = 6 x = 5 or x = 6

Answer: Factorise: (x − 2)(x − 3) = 0, so x = 2 or x = 3.

2. £2,000 is invested at 3% compound interest per year. How much is it worth after 2 years?

£2,060.00 £2,120.00 £2,121.80 £2,180.00

Answer: £2,000 × 1.03² = £2,000 × 1.0609 = £2,121.80.

3. Solve x + y = 10 and x − y = 4

x = 6, y = 4 x = 7, y = 3 x = 5, y = 5 x = 8, y = 2

Answer: Add the equations: 2x = 14, so x = 7, and y = 10 − 7 = 3: x = 7, y = 3.

4. Simplify √50

5√2 2√5 25√2 10√5

Answer: √50 = √(25 × 2) = 5√2.

5. y is directly proportional to x, and y = 12 when x = 3. Find y when x = 5.

15 17 20 36

Answer: y = 4x (since 12 = 4 × 3), so y = 4 × 5 = 20.

6. A and B are independent, with P(A) = 0.5 and P(B) = 0.4. What is P(A and B)?

0.1 0.2 0.9 0.45

Answer: Multiply: 0.5 × 0.4 = 0.2.

7. What is the exterior angle of a regular octagon?

36° 45° 60° 135°

Answer: 360° ÷ 8 = 45°.

8. cos 60° =

0 ½ √3⁄2 1

Answer: cos 60° = ½ (and sin 30° = ½ too).

9. Make r the subject of A = πr²

r = A ÷ π r = √(A ÷ π) r = √A ÷ π r = (A ÷ π)²

Answer: Divide by π, then square root: r = √(A ÷ π).

10. 7.3 has been rounded to 1 decimal place. What is its upper bound?

7.30 7.34 7.35 7.4

Answer: Anything up to (but not including) 7.35 rounds to 7.3, so the upper bound is 7.35.

About this test

Year 10 covers much of the GCSE specification: quadratic equations, simultaneous equations, compound interest, surds and trigonometry. Steady weekly practice now leaves Year 11 free for exam technique.

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