Ratio, proportion and rates of change worksheet — GCSE Higher

1.A car travels 180 miles in 3 hours. A lorry travels 160 miles in 4 hours. Write the car's average speed as a fraction of the lorry's average speed, giving your answer in its simplest form.

2.Write £3.60 : £2.40 as a ratio in its simplest form.

3.Two quantities x and y are in direct proportion. When x = 8, the value of y is 20. Work out the value of y when x = 14.

4.A worker is paid £13.20 per hour. Work out this rate of pay in pence per minute.

5.A candidate wants to estimate the instantaneous rate of change of a reservoir's water level, in metres, at t = 5 days after heavy rain began. The reservoir's water level is plotted against time, in days, since the rain began. The candidate uses the chord joining the points at t = 0 days and t = 20 days to estimate the rate of change at t = 5 days. Give a reason why this is likely to be a poor estimate.

6.Two mathematically similar polygons have perimeters in the ratio 2 : 5. Write the ratio of their areas in its simplest form.

7.An adult cinema ticket costs £15 and a child ticket costs £9. Write the ratio of the adult price to the child price in its simplest form.

8.Which of these ratios is equivalent to 6 : 10 : 14?

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 kettle uses 2.1 kWh of energy. A toaster uses 0.9 kWh of energy. Write the energy used by the kettle as a fraction of the energy used by the toaster, giving your answer in its simplest form.

11.A recipe for 6 muffins needs 150 g of flour. Aisha wants to make 15 muffins using the same recipe. Work out how much flour she needs.

12.The width, the length and the height of a box are in the ratio 3:4:5. The length of the box is 16 cm. Work out the height of the box.

13.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.

14.Simplify the ratio 45 : 30 : 75 to its simplest form.

15.A recipe needs 1.2 kg of flour. Dan has 750 g of flour in his cupboard. Write the mass of flour the recipe needs as a fraction of the mass of flour Dan has. Give your answer in its simplest form.