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 · 15 questions

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1.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.
(a)144
(b)18
(c)23
(d)48
2.A jug holds 2 litres. Given that 1 litre = 1000 cm³, work out the capacity of the jug in cm³.
(a)20 cm³
(b)2000 cm³
(c)200 cm³
(d)20000 cm³
3.The ratio of the amount of money Harry has to the amount of money Isla has is 5:3. Harry has £35. Work out how much money Isla has.
(a)£7
(b)£28
(c)£21
(d)£33
4.A runner's speed is 8 m/s. Given that there are 3600 seconds in an hour and 1000 metres in a kilometre, work out the runner's speed in km/h.
(a)28.8 km/h
(b)2.88 km/h
(c)28800 km/h
(d)2.22 km/h
5.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.
(a)1:55
(b)5:12
(c)12:1
(d)1:12
6.A mortar mix is made from sand and cement in the ratio 5 : 3. Write the ratio of sand to the total mix in its simplest form.
(a)8:5
(b)5:8
(c)3:8
(d)5:3
7.A straight-line graph shows the cost, C pounds, of hiring a bike for h hours. The line passes through the points (1, 12) and (4, 27). Which of these statements about the line is true?
(a)The hourly rate is £5 and the fixed fee is £7
(b)The hourly rate is £5 and the fixed fee is £12
(c)The hourly rate is £7 and the fixed fee is £5
(d)The hourly rate is £15 and the fixed fee is £7
8.y is directly proportional to x, and y = 3x. Work out the value of y when x = 4.
y = 3x
(a)1
(b)12
(c)7
(d)34
9.A garden plan is enlarged by a scale factor of 3. A flower bed on the original plan is 5 cm long. Work out the length of the flower bed on the enlarged plan, in centimetres.
(a)45 cm
(b)8 cm
(c)1.7 cm
(d)15 cm
10.A cordial drink is made by mixing cordial concentrate and water in the ratio 1 : 6. Freya says that a 700 ml jug of this drink contains 100 ml of concentrate. Is she correct? Give a reason for your answer.
(a)No — half of 700 ml (350 ml) should be concentrate
(b)No — 600 ml is concentrate, 100 ml is water
(c)Yes — 700 ÷ 7 = 100 ml for the 1 part of concentrate
(d)No — divide 700 by 6, not 7: about 117 ml
11.In a test, Amelia answered 18 of the 24 questions correctly. Work out the percentage of the questions she answered correctly.
(a)75%
(b)133%
(c)25%
(d)18%
12.An amount of money is shared in the ratio 1:2:3. The largest share is £90 more than the smallest share. Work out the total amount that was shared.
(a)£180
(b)£540
(c)£135
(d)£270
13.A coach journey of 240 km takes 3 hours. For this fixed distance the average speed needed is inversely proportional to the time taken. Work out the average speed needed to complete the same journey in 2 hours.
(a)160 km/h
(b)480 km/h
(c)120 km/h
(d)80 km/h
14.To make a shade of green paint, the amount of yellow paint used is always 0.75 times the amount of blue paint used. Write the amount of blue paint as a fraction of the amount of yellow paint, in its simplest form.
(a)40/3
(b)1/4
(c)3/4
(d)4/3
15.Work out the value of x when 4/x = 2/5.
(a)10
(b)2.5
(c)20
(d)8

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