Ratio, proportion and rates of change worksheet — GCSE Foundation

1.A water tank has a capacity of 500 litres. It currently holds 350 litres of water. Write the amount of empty space in the tank as a fraction of the tank's capacity. Give your answer in its simplest form.

2.Two mathematically similar triangular flags have areas in the ratio 4 : 25. The height of the smaller flag is 6 cm. Work out the height of the larger flag.

3.A bottle contains 1.5 litres of juice. Given that 1 litre = 1000 ml, work out the capacity of the bottle in millilitres.

4.A straight-line graph shows the cost, C pounds, of hiring a small van for m miles driven. The line passes through the origin and the point (25, 20). Work out the gradient of the line.

5.y is directly proportional to x. When x = 2, y = 9. Which of these pairs of values is also consistent with this proportion?

6.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.

7.A blue ribbon is 45 cm long. A red ribbon is 30 cm long. Write the length of the blue ribbon as a fraction of the length of the red ribbon. Give your answer in its simplest form.

8.In a choir of 30 singers, 40% are altos and the rest are sopranos. Write the number of sopranos as a fraction of the number of altos. Give your answer in its simplest form.

9.A 1.5 kg bag of pasta costs £2.85 and a 2.4 kg bag of the same pasta costs £4.32. Work out which bag gives better value for money.

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

11.Two mathematically similar cylinders have volumes 64 cm³ and 216 cm³. Work out the ratio of the height of the smaller cylinder to the height of the larger cylinder, in simplest form.

12.Write 3/4 as a percentage.

13.A 5 kg bag of potatoes costs £4.50. Work out the cost per kilogram.

14.A hosepipe fills a paddling pool at a constant rate. The volume of water in the pool increases by 15 litres every 3 minutes. Write down the gradient of the graph of volume against time.

15.A recipe for 4 people needs 300 g of rice. Work out how much rice is needed for 6 people, assuming the amount is in direct proportion to the number of people.