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.Work out the difference between 45% of 70 and 35% of 80.
(a)11.5
(b)3.5
(c)59.5
(d)10
2.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
3.Two numbers A and B are in the ratio 3:5. When 6 is added to B, the ratio of A to the new value of B is 1:2. Work out the value of A.
(a)18
(b)30
(c)9
(d)6
4.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
5.A room plan is drawn to a scale of 1 : 50. A wall in the room is 4 m long in real life. Work out the length of the wall on the plan, in centimetres.
(a)80 cm
(b)20000 cm
(c)0.08 cm
(d)8 cm
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.Write the ratio 27 : 45 in its simplest form.
(a)27 : 45
(b)3 : 5
(c)5 : 3
(d)9 : 15
8.A water tank has a capacity of 500 litres. It currently holds 350 litres of water. Write the amount of empty space in the tank as a fraction of the tank's capacity. Give your answer in its simplest form.
(a)3/7
(b)3/10
(c)1/2
(d)7/10
9.A plan of a garden is drawn to a scale of 1 : 200. A path measures 3 cm on the plan. Work out the real length of the path, in centimetres.
(a)600 cm
(b)60 cm
(c)203 cm
(d)6000 cm
10.The number of calories burned, E, by a runner is plotted against the time, m minutes, on a straight-line graph. The line passes through the origin and the point (10, 80). Work out the gradient of the line.
(a)90
(b)8
(c)70
(d)0.125
11.Write the ratio 0.75 : 2 as a ratio of whole numbers in its simplest form.
(a)0.75 : 2
(b)75 : 200
(c)3 : 2
(d)3 : 8
12.A shade of paint is made by mixing blue paint and white paint. To make 5 litres of the shade, 2 litres of blue paint is used and the rest is white paint. Write the ratio of blue paint to white paint in its simplest form.
(a)5:3
(b)2:5
(c)2:3
(d)3:2
13.The ratio of the amount of money Harry has to the amount of money Isla has is 5:3. Harry has £35. Work out how much money Isla has.
(a)£7
(b)£28
(c)£21
(d)£33
14.A map has a scale of 1 : 50 000. Two villages are 4 cm apart on the map. Work out the real distance between the villages, in kilometres.
(a)2 km
(b)20 km
(c)200 km
(d)0.2 km
15.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

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