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 garden plan is enlarged by a scale factor of 3. A flower bed on the original plan is 5 cm long. Work out the length of the flower bed on the enlarged plan, in centimetres.
(a)45 cm
(b)8 cm
(c)1.7 cm
(d)15 cm
2.The amount of fuel left in a car's tank, F litres, is plotted against the distance travelled, d miles, and the points lie on a straight line. The line passes through (0, 45) and (150, 15). Work out the gradient of the line and say what it tells you.
(a)−5, the car uses 5 litres of fuel for each mile
(b)−30, the car uses 30 litres of fuel for each mile
(c)−0.2, the car uses 0.2 litres of fuel for each mile
(d)0.2, the car gains 0.2 litres of fuel for each mile
3.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
4.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
5.A journey takes 4 hours at an average speed of 60 km/h. The time taken is inversely proportional to the average speed. Work out how long the same journey takes at an average speed of 80 km/h.
(a)4 hours
(b)2 hours 40 minutes
(c)3 hours
(d)5 hours 20 minutes
6.It takes 2 identical pumps 10 hours to empty a flooded basement. Working at the same rate, work out how many hours 5 of these pumps would take to empty the same basement.
(a)4 hours
(b)7 hours
(c)20 hours
(d)25 hours
7.Ravi has 5 pears. He has 4 times as many apples as pears. Write the number of pears as a fraction of the number of apples.
(a)4/1
(b)5/9
(c)4/5
(d)1/4
8.Write 2 m : 150 cm : 50 cm as a ratio of whole numbers in its simplest form.
(a)4:3:1
(b)4:3:2
(c)2:150:50
(d)3:4:1
9.A train journey takes 2 hours 15 minutes. A bus journey to the same place takes 3 hours 45 minutes. Write the time for the train journey as a fraction of the time for the bus journey, giving your answer in its simplest form.
(a)2/5
(b)5/3
(c)3/8
(d)3/5
10.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
11.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
12.Work out the value of x when 4/x = 2/5.
(a)10
(b)2.5
(c)20
(d)8
13.A stall sells bottles of juice. Two bottles cost £3.00, five bottles cost £7.50 and eight bottles cost £12.00. The cost, C pounds, is in a fixed ratio to the number of bottles, n. Write down a formula for C in terms of n.
(a)C = n + 1
(b)C = n/1.5
(c)C = 1.5n
(d)C = 3n
14.A bag contains red counters and blue counters in the ratio 5:3. There are 56 counters in the bag altogether. Work out how many counters are blue.
(a)35
(b)7
(c)28
(d)21
15.Simplify the ratio 45 : 30 : 75 to its simplest form.
(a)2 : 3 : 5
(b)15 : 10 : 25
(c)9 : 6 : 15
(d)3 : 2 : 5

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