Printable · GCSE Higher · ages 14-16
Ratio, proportion and rates of change worksheet — GCSE Higher
Fifteen questions across the ratio, proportion and rates of change statements at Higher 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 Higher
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- 1.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.
- 2.A worker is paid £13.20 per hour. Work out this rate of pay in pence per minute.
- 3.A road sign 3 m tall casts a shadow 5 m long. At the same time, a nearby lamppost casts a shadow 10 m long. Work out the height of the lamppost.
- 4.A model car is built at a scale of 1 : 20 compared with the real car. Work out the factor by which the surface area to be painted on the real car is bigger than the surface area of the model.
- 5.y is directly proportional to x. When x = 7, the value of y is 21. Work out the value of x when y = 12.
- 6.A shop sells fruit juice concentrate that must be diluted with water in the ratio 2 : 5 (concentrate : water) to make squash. Priya has 8 litres of concentrate. Work out how much water she needs to keep the same ratio.
- 7.Butter costs £2.40 per kg. Work out the cost of the butter in pence per 100 g.
- 8.A stall sells bottles of juice. Two bottles cost £3.00, five bottles cost £7.50 and eight bottles cost £12.00. The cost, C pounds, is in a fixed ratio to the number of bottles, n. Write down a formula for C in terms of n.
- 9.The length of ribbon A is 5/12 of the length of ribbon B. Write the length of ribbon B as a fraction of the length of ribbon A.
- 10.Write 400 g : 1.5 kg as a ratio in its simplest form.
- 11.A vehicle is worth £18000. Its value decreases by 15% each year. Using the recurrence V_{n+1} = 0.85V_n, with V_0 = 18000, find the first whole number of years after which the vehicle's value drops below £10000.
- 12.In a fruit squash mix, the ratio of squash to water is 2 : 9. A shop wants to make up the mix using 3.4 litres of squash. Work out how many litres of water are needed.
- 13.A straight line passes through the points (1, 20) and (5, 8). Work out the gradient of the line.
- 14.Noah runs 2 km in 10 minutes. Work out how long he takes to run 5 km at the same speed.
- 15.A rectangular garden has its length and width in the ratio 5:3. Given that the perimeter of the garden is 64 m, work out the width of the garden.
Build your own mix at the worksheet builder.