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.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
2.In one batch of shortbread, a bakery uses 240 g of butter and 160 g of sugar. Another batch, made in the same ratio, uses 90 g of sugar. Work out how much butter is needed for the second batch.
(a)240 g
(b)170 g
(c)135 g
(d)60 g
3.A recipe uses flour, sugar and butter in the ratio 8 : 3 : 5. Write the ratio of flour to the rest of the mixture (sugar and butter combined) in its simplest form.
(a)3 : 5
(b)8 : 3
(c)1 : 2
(d)1 : 1
4.y is directly proportional to x. When x = 7, the value of y is 21. Work out the value of x when y = 12.
(a)4
(b)36
(c)84
(d)9
5.A plumber's charge, C pounds, for a job lasting h hours is shown on a straight-line graph. The line passes through the points (1, 45) and (3, 85). Work out what the gradient of this line represents, in context.
(a)The plumber charges £20 for each extra hour worked
(b)The plumber charges £20 in total, however long the job takes
(c)The plumber charges £45 for each extra hour worked
(d)The plumber charges £40 for each extra hour worked
6.A map has a scale of 1 : 1000. A road is 300 m long in real life. Work out the length of the road on the map, in centimetres.
(a)3 cm
(b)300000 cm
(c)0.3 cm
(d)30 cm
7.£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
8.The speed of a car is given by v = d ÷ t. A car travels 180 km in 3 hours. Work out the average speed of the car in km/h.
(a)90 km/h
(b)540 km/h
(c)18 km/h
(d)60 km/h
9.Two numbers are in the ratio 5 : 8. The larger number is 40. Work out the smaller number.
(a)64
(b)45
(c)25
(d)35
10.A journey to school takes 12 minutes. A journey to the gym takes 20 minutes. Write the time for the journey to school as a fraction of the time for the journey to the gym, giving your answer in its simplest form.
(a)2/5
(b)5/3
(c)3/8
(d)3/5
11.Water flows into a tank at a constant rate. After 8 minutes the tank holds 200 litres. Write the ratio of time in minutes to volume in litres, in its simplest form.
(a)25:1
(b)1:25
(c)25:8
(d)8:25
12.A map has a scale of 1 : 100. A path measures 5 cm on the map. Work out the real length of the path, in metres.
(a)500 m
(b)50 m
(c)5 m
(d)0.05 m
13.In a recipe the mass of chocolate to the mass of milk is in the ratio 1:4. Amelia uses 200 g of milk. Work out the mass of chocolate she needs.
(a)800 g
(b)250 g
(c)40 g
(d)50 g
14.A concert hall has 54 seats in total, of which 24 are reserved and the rest are free. Write the number of free seats as a fraction of the number of reserved seats. Give your answer in its simplest form.
(a)4/5
(b)5/6
(c)5/9
(d)5/4
15.Two hikers' journeys are shown on separate distance-time graphs. Hiker A's graph has gradient 4.5 km/h. Hiker B's graph has gradient 3.2 km/h. Work out how much faster Hiker A walks than Hiker B, in km/h.
(a)1.3
(b)−1.3
(c)7.7
(d)14.4

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