Ratio, proportion and rates of change worksheet — GCSE Foundation

1.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.

2.A metal cylinder has a mass of 356.5 g and a volume of 47 cm³. Work out the density of the cylinder, in g/cm³, to 1 decimal place.

3.A cyclist travels 18 km in 45 minutes. Work out the average speed, in km/h.

4.Two mathematically similar logos are printed on a poster. They have areas 20 cm² and 45 cm². Nadia says that the length scale factor from the smaller logo to the larger logo is 45 ÷ 20 = 2.25. Give a reason why Nadia is incorrect, and work out the correct length scale factor.

5.A 750 g box of cereal costs £2.70. A 500 g box of the same cereal costs £1.95. Work out which box is better value, and its cost per 100 g.

6.Two mathematically similar jugs have heights 8 cm and 12 cm. The smaller jug holds 200 ml when it is full. Work out how much the larger jug holds when it is full.

7.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.

8.Map A has a scale of 1 : 25000 and Map B has a scale of 1 : 50000, both showing the same area. A real distance of 10 km is measured on each map. On which map does this distance appear as the longer length, and how long is it on that map, in centimetres?

9.The mass of a length of copper pipe is proportional to its length. A pipe of length 4.5 m has a mass of 12.6 kg. Work out the mass of a pipe of the same type of length 9.5 m.

10.Two taxi firms show their charges on straight-line graphs, with the cost in pounds on the vertical axis and the distance in miles on the horizontal axis. Firm A's line passes through (0, 4) and (5, 14). Firm B's line passes through (0, 6) and (5, 21). Work out which firm charges more per mile.

11.Given that 1 mile ≈ 1.6 km, work out a speed of 55 mph in km/h.

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

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 scale model of a shipping container is built at a scale of 1 : 30, using material with the same density as the real container. The model has a mass of 400 g. Work out the mass of the real container, giving your answer in kilograms.

15.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.