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.The density of a liquid is 0.92 g/cm³. Work out the density of the liquid in kg/m³.
(a)9.2 kg/m³
(b)92 kg/m³
(c)920 kg/m³
(d)0.00092 kg/m³
2.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
3.A bag of potatoes has a mass of 3 kg. A bag of carrots has a mass of 5 kg. Write the mass of the potatoes as a fraction of the mass of the carrots.
(a)3/5
(b)5/3
(c)2/5
(d)3/8
4.A car travels 150 km in 3 hours at a constant speed. Work out the average speed of the car, in km/h.
(a)450
(b)153
(c)147
(d)50
5.A road sign 3 m tall casts a shadow 5 m long. At the same time, a nearby lamppost casts a shadow 10 m long. Work out the height of the lamppost.
(a)1.50 m
(b)16.67 m
(c)6.00 m
(d)8.00 m
6.Two numbers a and b are in the ratio a : b = 3 : 4. Given that a = 15, work out the value of b.
(a)60
(b)16
(c)11.25
(d)20
7.Rice costs £3.20 per kg. Work out the cost of the rice in pence per 100 g.
(a)3200p
(b)32p
(c)3.2p
(d)0.32p
8.A box contains 12 red counters and 18 blue counters. Write the number of red counters as a fraction of the number of blue counters. Give your answer in its simplest form.
(a)1/2
(b)3/2
(c)2/3
(d)2/5
9.Two quantities x and y are inversely proportional. When x = 2, the value of y is 15. Work out the value of y when x = 5.
(a)6
(b)12
(c)30
(d)37.5
10.Order these three values from smallest to largest: 3/8, 0.43, 41%.
(a)3/8, 41%, 0.43
(b)0.43, 41%, 3/8
(c)3/8, 0.43, 41%
(d)41%, 0.43, 3/8
11.x × y is used to test whether two quantities are in inverse proportion. For the pairs x = 4, y = 15 and x = 6, y = 10, which statement is correct?
(a)They are not in inverse proportion, because y ÷ x is different for each pair (3.75 and 1.67).
(b)They are in inverse proportion, because x × y = 60 for both pairs.
(c)They are in inverse proportion, because x × y = 40 for both pairs.
(d)They are not in inverse proportion, because x + y is different for each pair (19 and 16).
12.Two mathematically similar jugs have heights 8 cm and 12 cm. The smaller jug holds 200 ml when it is full. Work out how much the larger jug holds when it is full.
(a)675 ml
(b)300 ml
(c)450 ml
(d)900 ml
13.In a fruit bowl, the number of bananas is 3/4 of the number of apples. There are 16 apples in the bowl. Write the number of apples as a fraction of the number of bananas. Give your answer in its simplest form.
(a)3/4
(b)4/3
(c)4/7
(d)4/1
14.A garden centre has 90 rose bushes in stock. It receives a delivery that increases its stock of rose bushes by 20%. In the same week it sells 150 lavender bushes. Work out the new number of rose bushes, then write it as a fraction of the number of lavender bushes sold, giving your answer in its simplest form.
(a)18/25
(b)25/18
(c)3/25
(d)3/5
15.The ratio of the amount Noah has saved to the amount Grace has saved is 4:5. Noah has saved £200. Work out how much they have saved altogether.
(a)£250
(b)£400
(c)£450
(d)£360

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