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.Amelia uses 2 kg of flour to bake 5 cakes. Using the same recipe, work out how many cakes she can bake with 6 kg of flour.
(a)10
(b)12
(c)15
(d)20
2.Two quantities x and y are in the ratio x : y = 2 : 5, and y = kx for a constant k. Work out the value of k.
(a)5
(b)3
(c)2.5
(d)0.4
3.A parcel has a mass of 2400 g. Given that 1 kg = 1000 g, work out the mass of the parcel in kilograms.
(a)2.4 kg
(b)24 kg
(c)240 kg
(d)0.24 kg
4.Write £3.60 : £2.40 as a ratio in its simplest form.
(a)360 : 240
(b)36 : 24
(c)2 : 3
(d)3 : 2
5.A straight-line graph shows the number of pages printed, p, plotted against the time in minutes, t, since a printer started a print job. The line passes through the points (2, 30) and (5, 90). Work out the gradient of the line.
(a)18
(b)20
(c)0.05
(d)−20
6.A coach travels 210 miles at an average speed of 70 mph. Work out how long the journey takes.
(a)14700 hours
(b)140 hours
(c)3 hours
(d)280 hours
7.Write the ratio 27 : 45 in its simplest form.
(a)27 : 45
(b)3 : 5
(c)5 : 3
(d)9 : 15
8.A sculptor makes two mathematically similar statues. The smaller statue is 20 cm tall and 80 ml of varnish covers its surface. The larger statue is 50 cm tall. Work out how much varnish is needed to cover the surface of the larger statue.
(a)200 ml
(b)1250 ml
(c)32 ml
(d)500 ml
9.A footpath is drawn 3 cm long on a map with a scale of 1 : 50 000. Work out the real length of the footpath, in metres.
(a)15000 m
(b)1500 m
(c)50000 m
(d)150 m
10.The rent on a flat increases by 10% one year and by a further 10% the following year. Work out the overall percentage increase over the two years.
(a)121%
(b)11%
(c)21%
(d)20%
11.5 tins of soup cost £8 in total. Work out the multiplier that changes the number of tins into the total cost in pounds.
(a)0.625
(b)40
(c)1.6
(d)3
12.A savings account pays 3.5% compound interest each year. Bilal invests £1200. Work out how much interest, in total, he earns after 2 years, to the nearest penny.
(a)£85.47
(b)£1285.47
(c)£84.00
(d)£42.00
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.A shop sells rope by the metre. 3 m costs £7.50 and 5 m costs £11.00. Does this data show that the cost is directly proportional to the length of rope bought? Choose the correct verdict and reason.
(a)No — the cost per metre differs: £2.50/m vs £2.20/m
(b)Yes — because both amounts increase as length increases
(c)No — because 5 m costs more than 3 m in total
(d)Yes — the cost per metre is £2.50 in both cases
15.A car uses fuel at a constant rate. It uses 24 litres of fuel to travel 300 km. Assuming the same rate, work out how many litres of fuel are needed for a journey of 175 km.
(a)21 litres
(b)1.4 litres
(c)14 litres
(d)24 litres

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