GCSE GCSE Mathematics 4

Question 1

What is the formula for the volume of a cone?

Accepted Answer

⅓πr²h

Answer

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

Accepted Answer

x⁶

Answer

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, ...

Accepted Answer

3n + 2

Answer

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?

Accepted Answer

65°

Answer

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?

Accepted Answer

2/5

Answer

40% = 40/100. Simplify by dividing both by 20: 40/100 = 2/5.

GCSE Revision Practice Test

GCSE Revision Practice Test

GCSE GCSE Mathematics 4