Free GCSE Maths Practice Test (10 Questions, Instant Marking)

1. Solve 3x + 5 = 20

x = 3 x = 5 x = 15 x = 25/3

Answer: Subtract 5: 3x = 15. Divide by 3: x = 5.

2. Expand 2(x + 4)

2x + 4 2x + 8 x + 8 2x + 6

Answer: Multiply both terms by 2: 2 × x + 2 × 4 = 2x + 8.

3. Simplify 5a + 3b − 2a + b

3a + 4b 7a + 4b 3a + 2b 8ab

Answer: Collect like terms: 5a − 2a = 3a and 3b + b = 4b, so 3a + 4b.

4. Write 0.35 as a fraction in its simplest form

35/100 7/20 3/5 7/2

Answer: 0.35 = 35/100; divide by 5: 7/20.

5. Increase £80 by 15%

£92 £95 £88 £12

Answer: 15% of £80 is £12; £80 + £12 = £92 (or £80 × 1.15).

6. The area of a circle with radius 3 cm is …

6π cm² 9π cm² 3π cm² 18π cm²

Answer: Area = πr² = π × 3² = 9π cm².

7. Factorise x² + 5x + 6

(x + 1)(x + 6) (x + 2)(x + 3) (x − 2)(x − 3) x(x + 5) + 6

Answer: Find two numbers that multiply to 6 and add to 5: 2 and 3, so (x + 2)(x + 3).

8. A fair six-sided dice is rolled. What is the probability of an even number?

1/6 1/3 1/2 2/3

Answer: Three even outcomes (2, 4, 6) out of six: 3/6 = 1/2.

9. Share £60 in the ratio 2 : 3

£20 and £40 £24 and £36 £30 and £30 £12 and £48

Answer: 5 parts; £60 ÷ 5 = £12; 2 × £12 = £24 and 3 × £12 = £36: £24 and £36.

10. A right-angled triangle has shorter sides of 6 cm and 8 cm. How long is the hypotenuse?

10 cm 14 cm 12 cm 48 cm

Answer: 6² + 8² = 36 + 64 = 100, and √100 = 10 cm.

About this test

This mixed test samples topics that appear on almost every GCSE maths paper, whichever board your child sits. For a deeper check, try the algebra, geometry or statistics tests below.

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