GCSE Maths practice questions
Ten GCSE Maths questions covering percentages, algebra, prime factors, sequences, circles, ratio, straight lines and probability. Useful for Foundation and Higher tier revision, each with a worked solution.
Original questions written by Studoli tutors in the style of the GCSE exam. They are not official past questions.
Topic: Percentages
1. Work out 15% of 240.
Solution
B. 36
- 10% of 240 = 24 and 5% = 12.
- 15% = 24 + 12 = 36.
Topic: Algebra
2. Simplify 6a + 3b − 2a + b.
Solution
A. 4a + 4b
- Collect the a terms: 6a − 2a = 4a.
- Collect the b terms: 3b + b = 4b.
Topic: Equations
3. Solve 4(x − 2) = 20.
Solution
C. x = 7
- Divide both sides by 4: x − 2 = 5.
- Add 2: x = 7.
Topic: Number
4. Write 72 as a product of its prime factors.
Solution
B. 2³ × 3²
- 72 = 2 × 36 = 2 × 2 × 18 = 2 × 2 × 2 × 9 = 2 × 2 × 2 × 3 × 3.
- In index form: 2³ × 3².
Topic: Sequences
5. Find the nth term of the sequence 5, 8, 11, 14, ...
Solution
B. 3n + 2
- The sequence goes up by 3, so it starts with 3n.
- When n = 1, 3n = 3, but the first term is 5, so add 2: 3n + 2.
Topic: Geometry
6. Find the area of a circle with radius 3 cm, to 1 decimal place.
Solution
C. 28.3 cm²
- Area = πr² = π × 3² = 9π.
- 9π = 28.27..., which is 28.3 cm² to 1 decimal place.
Topic: Ratio
7. Share £60 in the ratio 2 : 3.
Solution
B. £24 and £36
- Total parts: 2 + 3 = 5, so one part is £60 ÷ 5 = £12.
- 2 × 12 = £24 and 3 × 12 = £36.
Topic: Graphs
8. What is the gradient of the line y = 4x − 1?
Solution
C. 4
- In y = mx + c, m is the gradient.
- Here m = 4.
Topic: Algebra
9. Expand and simplify (x + 4)(x − 2).
Solution
B. x² + 2x − 8
- x × x = x², x × (−2) = −2x, 4 × x = 4x, 4 × (−2) = −8.
- Collect terms: x² + 2x − 8.
Topic: Probability
10. The probability of picking a red counter is 0.35. What is the probability of not picking a red counter?
Solution
B. 0.65
- Probabilities of an event and its opposite add up to 1.
- 1 − 0.35 = 0.65.
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