Ratio, proportion and rates of change worksheet — GCSE Foundation

1.A map has a scale of 1 : 20 000. A different map of the same area has a scale of 1 : 80 000. A lake's shoreline is drawn 5 cm long on the first map. Work out the length of the same shoreline on the second map, in centimetres.

2.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.

3.Before a charity campaign, donations were £6400 per month. Donations grew by 8% in the first year after the campaign, and then fell by 3% in the second year as interest faded. Work out the amount donated per month at the end of the second year, to the nearest pound.

4.A straight line passes through the points (1, 20) and (5, 8). Work out the gradient of the line.

5.A car is bought for £9000. Its value decreases by 8% each year. Work out its value after 2 years.

6.Ffion is paid £11.20 per hour. She works 6 hours on Monday and 4.5 hours on Tuesday. Work out her total pay for the two days.

7.Last week Priya worked 5 shifts of 7 hours. This week she worked 4 shifts of 8 hours. Write the number of hours she worked last week as a fraction of the number of hours she worked this week.

8.A company's turnover was £128 000 in 2023 and £176 000 in 2024. Work out the multiplier that changes the 2023 turnover into the 2024 turnover.

9.Priya invests £750 in a savings account that pays simple interest. After 3 years, the account contains £840. Work out the annual rate of simple interest.

10.A delivery driver travels 45 km in the first 30 minutes of a journey, and then a further 75 km in the next 1 hour. Work out her average speed for the whole journey, in km/h.

11.A sculptor makes two mathematically similar statues. The smaller statue is 20 cm tall and 80 ml of varnish covers its surface. The larger statue is 50 cm tall. Work out how much varnish is needed to cover the surface of the larger statue.

12.Four graphs are described below. Each shows one quantity plotted against another. Write down the description of the graph that shows two quantities in direct proportion.

13.A runner's speed is 8 m/s. Given that there are 3600 seconds in an hour and 1000 metres in a kilometre, work out the runner's speed in km/h.

14.A laptop priced at £520 is first increased by 15%, and then the new price is decreased by 20%. Work out the final price of the laptop.

15.A population of penguins on an island is 2400. The population is predicted to grow by 7% each year. Work out the predicted population after 2 years, to the nearest whole number.