Ratio, proportion and rates of change worksheet — GCSE Foundation

1.y is directly proportional to x. When x = 8, y = 20. Work out the value of y when x = 12.

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

3.Write 3/4 as a percentage.

4.A map has a scale of 2 cm : 5 km. A footpath measures 8 cm on the map. Work out the real length of the footpath, in kilometres.

5.A science technician mixes 400 g of a salt solution of concentration 5% with 100 g of a salt solution of concentration 25%. Work out the concentration of the mixture.

6.A scale model of a bus is built so that 5 cm on the model represents 60 cm on the real bus. Write the ratio of the length of the model to the length of the real bus, in its simplest form.

7.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.

8.40% of a number is 12 more than 25% of the same number. Work out the number.

9.A car is bought for £12000. Its value falls by 15% in the first year and by 10% in each year after that. Work out the value of the car 3 years after it was bought.

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

11.In a test, Amelia answered 18 of the 24 questions correctly. Work out the percentage of the questions she answered correctly.

12.A car uses 6 litres of petrol to travel 90 km. Write the ratio of the distance travelled in km to the amount of petrol used in litres, in its simplest form.

13.Write the ratio 5 : 8 in the form 1 : n.

14.The number of members of a running club increases from 45 to 54. Work out the percentage increase.

15.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.