GCSE GCSE Mathematics 4 — Questions and Answers
Question 1: What is the formula for the volume of a cone?
- πr²h
- ⅓πr²h (Correct answer)
- ½πr²h
- ⅔πr³
Correct answer: ⅓πr²h
Volume of a cone = ⅓πr²h, where r is the radius of the base and h is the perpendicular height. A cone has exactly one-third the volume of a cylinder with the same base and height.
Question 2: Simplify: (x³)²
- x⁵
- x⁶ (Correct answer)
- x⁹
- 2x³
Correct answer: x⁶
When raising a power to another power, multiply the indices: (x³)² = x^(3×2) = x⁶.
Question 3: Find the nth term of the sequence: 5, 8, 11, 14, ...
- 3n + 2 (Correct answer)
- n + 3
- 3n − 1
- 4n + 1
Correct answer: 3n + 2
The sequence increases by 3 each time, so the nth term starts with 3n. For n = 1: 3(1) = 3, but we need 5, so add 2. Check: 3n + 2 gives 5, 8, 11, 14 ✓.
Question 4: Two angles in a triangle are 47° and 68°. What is the third angle?
- 55°
- 65° (Correct answer)
- 75°
- 85°
Correct answer: 65°
Angles in a triangle sum to 180°. 47° + 68° = 115°. 180° − 115° = 65°.
Question 5: What is 40% written as a fraction in its simplest form?
- 40/100
- 2/5 (Correct answer)
- 4/10
- 8/20
Correct answer: 2/5
40% = 40/100. Simplify by dividing both by 20: 40/100 = 2/5.
Question 6: Calculate the compound interest on £2,000 at 5% per year for 2 years.
- £200
- £205
- £210.50 (Correct answer)
- £205.00
Correct answer: £210.50
Year 1: £2,000 × 1.05 = £2,100. Year 2: £2,100 × 1.05 = £2,205. Interest = £2,205 − £2,000 = £205. Wait — £2,100 × 0.05 = £105; total interest = £100 + £105 = £205. Actually the final value is £2,205, and the interest is £205. Re-checking: the answer choices show £210.50 for option C but the calculation gives £205. Let me restate: interest = £205, so the closest correct answer in the list is actually £205. The answer is B (£205).
Question 7: A bag contains 3 red, 5 blue, and 2 green balls. What is the probability of picking a blue ball at random?
- 5/8
- 1/2 (Correct answer)
- 5/10
- 5/12
Correct answer: 1/2
Total balls = 3 + 5 + 2 = 10. Probability of blue = 5/10 = 1/2.
GCSE GCSE Mathematics 4
What is the formula for the volume of a cone?