GCSE MATH 4

Question 1

Factorise fully: 6x² − 9x

Accepted Answer

3x(2x − 3)

Answer

The HCF of 6x² and 9x is 3x, giving 3x(2x − 3).

Question 2

In a right-angled triangle, the two shorter sides are 5 cm and 12 cm. What is the hypotenuse?

Accepted Answer

13 cm

Answer

By Pythagoras: c = √(5² + 12²) = √(25 + 144) = √169 = 13 cm.

Question 3

What is the median of the data set: 7, 3, 9, 1, 5, 8, 4?

Accepted Answer

5

Answer

Arranged in order: 1, 3, 4, 5, 7, 8, 9 — the middle value is 5.

Question 4

Write 0.00047 in standard form.

Accepted Answer

4.7 × 10⁻⁴

Answer

0.00047 = 4.7 × 10⁻⁴ because we move the decimal 4 places to the right.

Question 5

What is the area of a trapezoid with parallel sides 8 cm and 14 cm, and height 6 cm?

Accepted Answer

66 cm²

Answer

Area = ½ × (a + b) × h = ½ × (8 + 14) × 6 = ½ × 22 × 6 = 66 cm².

GCSE - General Certificate of Secondary Education Practice Test