Ratio, proportion and rates of change worksheet — GCSE Foundation

1.Write 2 m : 150 cm : 50 cm as a ratio of whole numbers in its simplest form.

2.Line P passes through the origin and the point (3, 21). Line Q passes through the origin and the point (5, 45). Both lines represent the distance, in metres, run by an athlete against the time, in seconds. Work out the gradient of the steeper line.

3.A jug holds 2 litres. Given that 1 litre = 1000 cm³, work out the capacity of the jug in cm³.

4.3 kg of apples cost £6. Work out the cost of 5 kg of the same apples.

5.The same jumper is sold at two shops. Shop A charges £40 and Shop B charges £50. Write down the price at Shop A as a percentage of the price at Shop B.

6.A car travels 180 miles in 3 hours. A lorry travels 160 miles in 4 hours. Write the car's average speed as a fraction of the lorry's average speed, giving your answer in its simplest form.

7.A garden centre has 90 rose bushes in stock. It receives a delivery that increases its stock of rose bushes by 20%. In the same week it sells 150 lavender bushes. Work out the new number of rose bushes, then write it as a fraction of the number of lavender bushes sold, giving your answer in its simplest form.

8.A ribbon of length 90 cm is cut into two pieces in the ratio 4:5. Work out the length of the shorter piece.

9.A graph shows two quantities, x and y, in direct proportion. Write down which statement about the graph must be true.

10.Two numbers are in the ratio 5 : 8. The larger number is 40. Work out the smaller number.

11.A shop sells fruit juice concentrate that must be diluted with water in the ratio 2 : 5 (concentrate : water) to make squash. Priya has 8 litres of concentrate. Work out how much water she needs to keep the same ratio.

12.An acid solution has a concentration of 20%. The solution contains 40 g of acid, and the rest of the solution is water. Work out the mass of water in the solution.

13.A table shows three pairs of values: when x = 2, y = 6; when x = 5, y = 15; when x = 8, y = 24. In every pair the ratio y : x is the same. Write down a formula for y in terms of x.

14.Two mathematically similar circles have radii 4 cm and 20 cm. Write the ratio of the area of the smaller circle to the area of the larger circle in its simplest form.

15.A map has a scale of 1 : 50 000. Two villages are 4 cm apart on the map. Work out the real distance between the villages, in kilometres.