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.

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Ratio, proportion and rates of change worksheet — GCSE Foundation

Maths · GCSE Foundation · Ratio, proportion and rates of change · Non-calculator · 15 questions

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1.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.
(a)8000
(b)40
(c)20
(d)400
2.A worker is paid £13.20 per hour. Work out this rate of pay in pence per minute.
(a)22p
(b)79200p
(c)2.2p
(d)1320p
3.Ravi has 5 pears. He has 4 times as many apples as pears. Write the number of pears as a fraction of the number of apples.
(a)4/1
(b)5/9
(c)4/5
(d)1/4
4.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.
(a)72 m
(b)7.2 m
(c)0.72 m
(d)0.31 m
5.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.
6.A map has a scale of 1 : 25 000. A footpath measures 6 cm on the map. Work out the real length of the footpath, in kilometres.
(a)1.5 km
(b)0.15 km
(c)150 km
(d)150000 km
7.It takes 8 painters 6 days to paint a fence. Working at the same rate, work out how many days 4 painters would take to paint the same fence.
(a)3 days
(b)12 days
(c)10 days
(d)48 days
8.A rectangle has its height and its width in the ratio 3:2. The height of the rectangle is 18 cm. Work out the width of the rectangle.
(a)17 cm
(b)12 cm
(c)27 cm
(d)6 cm
9.Last week Priya worked 5 shifts of 7 hours. This week she worked 4 shifts of 8 hours. Write the number of hours she worked last week as a fraction of the number of hours she worked this week.
(a)35/32
(b)35/67
(c)32/35
(d)3/32
10.A cyclist rides 30 km in 1 hour 30 minutes. Work out the average speed of the cyclist in km/h.
(a)15 km/h
(b)30 km/h
(c)45 km/h
(d)20 km/h
11.A cleaning solution is made by mixing disinfectant and water in the ratio 1 : 9. Priti wants to make 6 litres of the solution in total. Work out how much disinfectant she needs.
(a)0.6 litres
(b)5.4 litres
(c)0.667 litres
(d)6 litres
12.Which of these ratios is equivalent to 2:3?
(a)12:8
(b)8:12
(c)4:5
(d)8:3
13.Write the ratio 2/3 : 1/2 as a ratio of whole numbers, in its simplest form.
(a)4:3
(b)2:3
(c)3:4
(d)1:2
14.In a fruit drink, 3/8 of the total volume is orange juice and the rest is apple juice. Write down the ratio of orange juice to apple juice, in its simplest form.
(a)8 : 5
(b)5 : 3
(c)3 : 5
(d)3 : 8
15.Work out the difference between 45% of 70 and 35% of 80.
(a)11.5
(b)3.5
(c)59.5
(d)10

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