Ratio, proportion and rates of change worksheet — GCSE Foundation

1.A cyclist travels 45 km in 3 hours at a constant speed. Work out the cyclist's average speed, in km/h.

2.Write the ratio 2/3 : 1/2 as a ratio of whole numbers, in its simplest form.

3.A metal alloy is made from copper and tin in the ratio 9:1. Write the mass of tin as a fraction of the mass of copper, in its simplest form.

4.A shop sells ribbon by the metre. 2 m costs £3.00, 4 m costs £6.00, and 7 m costs £10.50. Does this data show that the cost is directly proportional to the length of ribbon bought? Choose the correct verdict and reason.

5.y is inversely proportional to x. When x = 5, y = 8. Work out the value of y when x = 10.

6.The rent on a flat increases by 10% one year and by a further 10% the following year. Work out the overall percentage increase over the two years.

7.The exchange rate is £1 = €1.15. Convert £200 to euros.

8.Write 350 ml : 1.4 l as a ratio in its simplest form.

9.Two printers' running costs are shown on separate straight-line graphs of total cost against number of pages printed. Printer A's graph has gradient £0.04 per page. Printer B's graph has gradient £0.05 per page. Work out how much cheaper it is to print 200 pages on Printer A than on Printer B, based on these running costs alone.

10.A rectangle has its height and its width in the ratio 3:2. The height of the rectangle is 18 cm. Work out the width of the rectangle.

11.A garden plan is enlarged by a scale factor of 3. A flower bed on the original plan is 5 cm long. Work out the length of the flower bed on the enlarged plan, in centimetres.

12.Two quantities x and y are inversely proportional. When x = 2, the value of y is 15. Work out the value of y when x = 5.

13.A post 2 metres tall casts a shadow 3 metres long. At the same time a nearby tree casts a shadow 12 metres long. Work out the height of the tree.

14.In one batch of shortbread, a bakery uses 240 g of butter and 160 g of sugar. Another batch, made in the same ratio, uses 90 g of sugar. Work out how much butter is needed for the second batch.

15.Maya buys a vintage car for £15000. Its value is expected to increase by 4% each year for 2 years. She then plans to sell the car and use £2000 of the money from the sale to buy a trailer. Work out how much money she will have left after selling the car and buying the trailer.