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 metal block has a mass of 270 g and a volume of 30 cm³. Work out the density of the block, in g/cm³.
(a)8100 g/cm³
(b)240 g/cm³
(c)9 g/cm³
(d)270 g/cm³
2.Freya buys three items whose prices are in the ratio 2:3:5. Altogether she pays £400. Work out the price of the most expensive item.
(a)£120
(b)£80
(c)£40
(d)£200
3.A 5 kg bag of potatoes costs £4.50. Work out the cost per kilogram.
(a)£22.50
(b)£0.50
(c)£0.90
(d)£1.11
4.Jamal is paid £54 for working 6 hours. Work out his rate of pay, in £ per hour.
(a)£9.00
(b)£324.00
(c)£0.11
(d)£48.00
5.A river 120 km long is drawn as a line 6 cm long on a map. Work out the scale of the map.
(a)1 : 2 000 000
(b)1 : 200 000
(c)1 : 12 000 000
(d)1 : 20 000
6.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
7.y is directly proportional to x, so y = kx. When x = 2, the value of y is 10. Work out the value of k.
(a)20
(b)12
(c)8
(d)5
8.A laptop priced at £520 is first increased by 15%, and then the new price is decreased by 20%. Work out the final price of the laptop.
(a)£598
(b)£494
(c)£478.40
(d)£416
9.Leah puts £4000 into a savings account paying 3% compound interest each year. At the end of 2 years she takes out all of the money and spends £1500 of it on a laptop. Work out how much of the money she has left.
(a)£2620.00
(b)£2740.00
(c)£2743.60
(d)£4243.60
10.y is always the same multiple of x. When x = 6, y = 15. Work out the value of y when x = 10.
(a)4
(b)15
(c)25
(d)19
11.£1 is worth 1.25 US dollars. Write the ratio of pounds to dollars in its simplest form, using whole numbers.
(a)1:1
(b)5:4
(c)1:5
(d)4:5
12.y is directly proportional to x. When x = 2, y = 9. Which of these pairs of values is also consistent with this proportion?
(a)x = 6, y = 27
(b)x = 6, y = 13
(c)x = 6, y = 3
(d)x = 6, y = 24
13.Two quantities y and z are each in direct proportion to x, and are given by y = 3x and z = 7x. Work out the difference between the value of y and the value of z when x = 4.
y = 3x
(a)40
(b)16
(c)28
(d)4
14.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
15.A graph shows two quantities, x and y, in direct proportion. Write down which statement about the graph must be true.
(a)The line is straight but does not pass through the origin.
(b)The line curves upward through the origin.
(c)The line is straight, passes through the origin, and slopes downward.
(d)The line is straight and passes through the origin.

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