GCSE GCSE Mathematics 5

Question 1

What is the gradient of a line segment from (1, 2) to (4, 8)?

Accepted Answer

2

Answer

Gradient = (change in y) ÷ (change in x) = (8 − 2) ÷ (4 − 1) = 6 ÷ 3 = 2.

Question 2

What is a vector in mathematics?

Accepted Answer

A quantity with both magnitude and direction

Answer

A vector has both magnitude (size) and direction. Velocity is a vector (e.g., 60 km/h north) whereas speed is a scalar (just magnitude, no direction). Vectors are written as arrows or column vectors.

Question 3

Solve: x² − 9 = 0

Accepted Answer

x = 3 or x = −3

Answer

x² = 9, so x = ±√9 = ±3. Both x = 3 and x = −3 satisfy the equation because both squared give 9.

Question 4

What does the discriminant (b² − 4ac) tell you about a quadratic equation ax² + bx + c = 0?

Accepted Answer

The number of real solutions the equation has

Answer

If b² − 4ac > 0, there are two distinct real solutions; if = 0, one repeated solution; if < 0, no real solutions. The discriminant determines the nature of the roots without solving fully.

Question 5

A shape is enlarged by scale factor 3. The original area is 12 cm². What is the new area?

Accepted Answer

108 cm²

Answer

When a shape is enlarged by scale factor k, areas scale by k². Scale factor 3 means area scales by 3² = 9. New area = 12 × 9 = 108 cm².

GCSE Revision Practice Test

GCSE Revision Practice Test

GCSE GCSE Mathematics 5