GCSE GCSE Mathematics 6

Question 1

What is direct proportion?

Accepted Answer

As one quantity increases, the other increases at the same rate, so y = kx

Answer

Direct proportion means two quantities increase at the same rate. If y is directly proportional to x, then y = kx for some constant k. Doubling x doubles y; the graph is a straight line through the origin.

Question 2

What is the area of a trapezium with parallel sides of 6 cm and 10 cm, and a height of 4 cm?

Accepted Answer

32 cm²

Answer

Area of a trapezium = ½(a + b) × h = ½(6 + 10) × 4 = ½ × 16 × 4 = 32 cm².

Question 3

Express 180 as a product of its prime factors.

Accepted Answer

2² × 3² × 5

Answer

180 = 2 × 90 = 2 × 2 × 45 = 2 × 2 × 9 × 5 = 2² × 3² × 5. Use a factor tree to break 180 into prime factors systematically.

Question 4

What is the range of the data set: 3, 7, 2, 14, 9, 5?

Accepted Answer

12

Answer

Range = maximum − minimum = 14 − 2 = 12. The range measures the spread of the data.

Question 5

Rearrange y = 3x + 6 to make x the subject.

Accepted Answer

x = (y − 6)/3

Answer

Subtract 6 from both sides: y − 6 = 3x. Divide both sides by 3: x = (y − 6)/3.

GCSE Revision Practice Test

GCSE Revision Practice Test

GCSE GCSE Mathematics 6