Printable · GCSE Foundation · ages 14-16
Ratio, proportion and rates of change worksheet — GCSE Foundation
Fifteen questions across the ratio, proportion and rates of change statements at Foundation tier. Choose the non-calculator filter to rehearse Paper 1, which counts for a third of the marks.
Ratio, proportion and rates of change worksheet — GCSE Foundation
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- 1.A toy manufacturer makes a model aircraft that is mathematically similar to the real aircraft, at a scale of 1 : 48. The wingspan of the model is 15 cm. Work out the wingspan of the real aircraft, giving your answer in metres.
- 2.A machine fills bottles at a constant rate. It fills 18 bottles in 3 minutes. Working at the same rate, work out how many bottles the machine fills in 8 minutes.
- 3.A lorry is carrying a load of mass m tonnes. Given that 1 tonne = 1000 kg, write down an expression for the mass of the load in kilograms.
- 4.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.
- 5.Work out the difference between 45% of 70 and 35% of 80.
- 6.A jar contains 24 green sweets and 16 orange sweets. Write the ratio of green sweets to orange sweets in its simplest form.
- 7.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.
- 8.A cyclist rides at an average speed of 24 km/h for 1 hour 15 minutes. Work out the distance travelled, in km.
- 9.A box holds 80 chocolates. 75% of them are milk chocolates. Work out how many milk chocolates are in the box.
- 10.A map has a scale of 1 : 1000. A road is 300 m long in real life. Work out the length of the road on the map, in centimetres.
- 11.On a straight-line graph the volume of water, V litres, in a tank is plotted on the vertical axis and the time, t minutes, on the horizontal axis. The line passes through (2, 50) and (6, 130). Work out the gradient of the line and give its units.
- 12.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.
- 13.A conversion graph between kilometres and miles passes through the origin and the point (50, 31), with the number of kilometres on the horizontal axis and the number of miles on the vertical axis. Work out the number of miles equivalent to 1 kilometre.
- 14.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.
- 15.The number of members of a running club increases from 45 to 54. Work out the percentage increase.
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