هذه المجموعة متاحة بلغتها الأصلية.
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.
أسئلة أصلية كتبها مدرّسو Studoli بأسلوب امتحان GCSE. ليست أسئلة رسمية.
الموضوع: Percentages
1. Work out 15% of 240.
الحل
B. 36
- 10% of 240 = 24 and 5% = 12.
- 15% = 24 + 12 = 36.
الموضوع: Algebra
2. Simplify 6a + 3b − 2a + b.
الحل
A. 4a + 4b
- Collect the a terms: 6a − 2a = 4a.
- Collect the b terms: 3b + b = 4b.
الموضوع: Equations
3. Solve 4(x − 2) = 20.
الحل
C. x = 7
- Divide both sides by 4: x − 2 = 5.
- Add 2: x = 7.
الموضوع: Number
4. Write 72 as a product of its prime factors.
الحل
B. 2³ × 3²
- 72 = 2 × 36 = 2 × 2 × 18 = 2 × 2 × 2 × 9 = 2 × 2 × 2 × 3 × 3.
- In index form: 2³ × 3².
الموضوع: Sequences
5. Find the nth term of the sequence 5, 8, 11, 14, ...
الحل
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.
الموضوع: Geometry
6. Find the area of a circle with radius 3 cm, to 1 decimal place.
الحل
C. 28.3 cm²
- Area = πr² = π × 3² = 9π.
- 9π = 28.27..., which is 28.3 cm² to 1 decimal place.
الموضوع: Ratio
7. Share £60 in the ratio 2 : 3.
الحل
B. £24 and £36
- Total parts: 2 + 3 = 5, so one part is £60 ÷ 5 = £12.
- 2 × 12 = £24 and 3 × 12 = £36.
الموضوع: Graphs
8. What is the gradient of the line y = 4x − 1?
الحل
C. 4
- In y = mx + c, m is the gradient.
- Here m = 4.
الموضوع: Algebra
9. Expand and simplify (x + 4)(x − 2).
الحل
B. x² + 2x − 8
- x × x = x², x × (−2) = −2x, 4 × x = 4x, 4 × (−2) = −8.
- Collect terms: x² + 2x − 8.
الموضوع: Probability
10. The probability of picking a red counter is 0.35. What is the probability of not picking a red counter?
الحل
B. 0.65
- Probabilities of an event and its opposite add up to 1.
- 1 − 0.35 = 0.65.
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