GCSE Mathematics Foundation and Higher 2

Question 1

A car travels 150 miles in 2.5 hours. What is its average speed?

Accepted Answer

60 mph

Answer

Average speed = distance ÷ time = 150 ÷ 2.5 = 60 mph. The speed-distance-time triangle is a key tool for these calculations.

Question 2

Factorise the expression x² + 7x + 12.

Accepted Answer

(x + 3)(x + 4)

Answer

Find two numbers that multiply to 12 and add to 7. Those numbers are 3 and 4 (3 × 4 = 12, 3 + 4 = 7). So x² + 7x + 12 = (x + 3)(x + 4).

Question 3

Convert 0.375 to a fraction in its simplest form.

Accepted Answer

3/8

Answer

0.375 = 375/1000. Divide numerator and denominator by 125: 375 ÷ 125 = 3, 1000 ÷ 125 = 8. So 0.375 = 3/8.

Question 4

The exterior angle of a regular polygon is 40°. How many sides does the polygon have?

Accepted Answer

9

Answer

The sum of exterior angles of any polygon is 360°. For a regular polygon, each exterior angle is equal, so the number of sides = 360° ÷ 40° = 9.

Question 5

If y is directly proportional to x and y = 15 when x = 3, what is y when x = 7?

Accepted Answer

35

Answer

y = kx where k is the constant of proportionality. When y = 15 and x = 3: 15 = 3k, so k = 5. When x = 7: y = 5 × 7 = 35.

GCSE Revision Practice Test