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.

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Ratio, proportion and rates of change worksheet — GCSE Higher

Maths · GCSE Higher · Ratio, proportion and rates of change · 15 questions

MathsUKwww.geekhero.co.uk

1.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.
(a)40 litres
(b)3.2 litres
(c)11 litres
(d)20 litres
2.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.
(a)20 cm
(b)80 cm
(c)4 cm
(d)12 cm
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.
(a)1000m
(b)m − 1000
(c)m/1000
(d)1000 + m
4.A shop sells ribbon by the metre. 2 m costs £3.00, 4 m costs £6.00, and 7 m costs £10.50. Does this data show that the cost is directly proportional to the length of ribbon bought? Choose the correct verdict and reason.
(a)Yes — the cost per metre is £1.50 each time
(b)Yes — the cost increases as the length increases
(c)No — 10.50 ÷ 7 gives 1.05, unlike the other rates
(d)No — the cost must double whenever length doubles
5.Write the ratio 0.75 : 2 as a ratio of whole numbers in its simplest form.
(a)0.75 : 2
(b)75 : 200
(c)3 : 2
(d)3 : 8
6.Write the ratio 2 : 1/4 as a ratio of whole numbers in its simplest form.
(a)8:1
(b)8:4
(c)1:8
(d)2:4
7.A train travels at a constant speed of 90 km/h. Work out the speed in m/s.
(a)1.5 m/s
(b)25 m/s
(c)324 m/s
(d)90000 m/s
8.A candle burns down at a constant rate. Its height, h cm, is plotted against time, t minutes, on a straight-line graph. The gradient of the line is −0.3. Which statement correctly describes what the gradient means?
(a)The candle's height decreases by 3 cm every minute.
(b)The candle burns for 0.3 minutes in total.
(c)The candle's height increases by 0.3 cm every minute.
(d)The candle's height decreases by 0.3 cm every minute.
9.The time taken for a train journey is inversely proportional to the average speed of the train. At an average speed of 60 km/h the journey takes 2 hours. Work out the time taken at an average speed of 40 km/h.
(a)2 hours
(b)1.5 hours
(c)3 hours
(d)1 hour 20 minutes
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.
(a)7/10
(b)4/3
(c)3/7
(d)7/3
11.A jumper normally costs £45. In a sale it is reduced by 20%. Work out the sale price, then write the sale price as a fraction of the normal price. Give your answer in its simplest form.
(a)1/5
(b)5/9
(c)4/5
(d)6/5
12.A dog walker's charge, C pounds, for walking a dog for m minutes is shown on a straight-line graph. The line passes through the points (20, 14) and (50, 26). Work out the charge for a 65-minute walk.
(a)£33.80
(b)£40
(c)£32
(d)£26
13.Write 350 ml : 1.4 l as a ratio in its simplest form.
(a)2:8
(b)25:1
(c)4:1
(d)1:4
14.A process is modelled by the recurrence P_{n+1} = 0.6P_n + 40. As n increases, P_n approaches a long-run value L, which satisfies L = 0.6L + 40. Solve this equation to find L.
(a)66.7
(b)40
(c)−100
(d)100
15.A jug of squash is made by mixing water and syrup in the ratio 6:1. Nia wants to make 8.4 litres of squash. Work out how much syrup she needs, in litres.
(a)0.84
(b)1.4
(c)1.2
(d)7.2

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