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 blue ribbon is 45 cm long. A red ribbon is 30 cm long. Write the length of the blue ribbon as a fraction of the length of the red ribbon. Give your answer in its simplest form.
(a)3/5
(b)2/3
(c)1/2
(d)3/2
2.Two taxi firms show their charges on straight-line graphs, with the cost in pounds on the vertical axis and the distance in miles on the horizontal axis. Firm A's line passes through (0, 4) and (5, 14). Firm B's line passes through (0, 6) and (5, 21). Work out which firm charges more per mile.
(a)Firm A — £3 per mile against Firm B's £2 per mile
(b)Firm A — £0.50 per mile against Firm B's £0.33 per mile
(c)Firm B — £3 per mile against Firm A's £2 per mile
(d)Neither — both lines start with a positive fixed charge
3.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
4.2.4 kg of cheese costs £36. Work out the cost of 1.5 kg of the same cheese.
(a)£15
(b)£57.60
(c)£22.50
(d)£54
5.For the pairs x = 6, y = 15 and x = 10, y = 25, which statement is correct?
(a)They are not in direct proportion, because y − x is different for each pair (9 and 15).
(b)They are not in direct proportion, because x + y is different for each pair (21 and 35).
(c)They are in direct proportion, because y ÷ x = 2.5 for both pairs.
(d)They are in direct proportion, because x × y = 90 and 250.
6.A force of 250 N acts on an area of 0.5 m². Using pressure = force ÷ area, work out the pressure, in pascals.
(a)50
(b)125
(c)500
(d)249.5
7.y is inversely proportional to x, so y = k ÷ x. When x = 5, the value of y is 8. Work out the value of k.
(a)3
(b)1.6
(c)13
(d)40
8.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
9.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
10.A room is drawn on a plan with a scale of 1 : 200. On the plan the room has an area of 12 cm². Work out the real area of the room, in square metres.
(a)4800 m²
(b)48 m²
(c)24 m²
(d)2400 m²
11.Two investors put money into a business in the ratio 3:5. The first investor puts in £1,200. Work out the total amount invested by both investors.
(a)£2,400
(b)£2,000
(c)£3,200
(d)£6,000
12.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
13.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.
(a)12/5
(b)5/12
(c)12/7
(d)7/12
14.£96 is shared between Ben, Cara and Dev in the ratio 2:3:7. Work out how much Cara receives.
(a)£16
(b)£56
(c)£28.80
(d)£24
15.The population of a village is 1200. It is predicted to grow by 5% next year. Work out the predicted population after 1 year, to the nearest whole number.
(a)1260
(b)1800
(c)1205
(d)60

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