Printable · GCSE Higher · ages 14-16

Direct and inverse proportion worksheet — GCSE Higher

Fifteen questions on "direct and inverse proportion" — DfE statement R10. Print it, or print three versions so neighbours cannot copy by letter; the key gives the letter for each version.

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Direct and inverse proportion worksheet — GCSE Higher

Maths · GCSE Higher · R10 · Direct and inverse proportion · 15 questions

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1.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
2.y is directly proportional to x. When x = 4, y = 10. Work out the value of y when x = 6.
(a)10
(b)15
(c)60
(d)12
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 factory machine produces bottles at a constant rate. In 45 minutes it produces 810 bottles. The factory needs 2,160 bottles for an order. Working at the same rate, work out how many minutes it will take to produce the order.
(a)48 minutes
(b)120 minutes
(c)108 minutes
(d)1,350 minutes
5.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
6.A spring's extension is directly proportional to the force applied to it. A force of 5 N produces an extension of 12 mm. Work out the extension produced by a force of 20 N.
(a)32 mm
(b)3 mm
(c)48 mm
(d)36 mm
7.A shop sells rope by the metre. 3 m costs £7.50 and 5 m costs £11.00. Does this data show that the cost is directly proportional to the length of rope bought? Choose the correct verdict and reason.
(a)No — the cost per metre differs: £2.50/m vs £2.20/m
(b)Yes — because both amounts increase as length increases
(c)No — because 5 m costs more than 3 m in total
(d)Yes — the cost per metre is £2.50 in both cases
8.A shop sells ribbon by the metre. 2 m costs £3.00, 4 m costs £6.00, and 7 m costs £10.50. Does this data show that the cost is directly proportional to the length of ribbon bought? Choose the correct verdict and reason.
(a)Yes — the cost per metre is £1.50 each time
(b)Yes — the cost increases as the length increases
(c)No — 10.50 ÷ 7 gives 1.05, unlike the other rates
(d)No — the cost must double whenever length doubles
9.y is inversely proportional to x. When x = 5, y = 8. Work out the value of y when x = 10.
(a)4
(b)0.8
(c)16
(d)3
10.A 750 g box of cereal costs £2.70. A 500 g box of the same cereal costs £1.95. Work out which box is better value, and its cost per 100 g.
(a)The 750 g box, at 54p per 100 g
(b)The 500 g box, because £1.95 is the lower total price
(c)The 500 g box, at 39p per 100 g
(d)The 750 g box, at 36p per 100 g
11.A machine fills bottles at a constant rate. It fills 18 bottles in 3 minutes. Working at the same rate, work out how many bottles the machine fills in 8 minutes.
(a)144
(b)18
(c)23
(d)48
12.It takes 8 painters 6 days to paint a fence. Working at the same rate, work out how many days 4 painters would take to paint the same fence.
(a)3 days
(b)12 days
(c)10 days
(d)48 days
13.The exchange rate is £1 = €1.15. Convert £200 to euros.
(a)€30.00
(b)€230.00
(c)€2300.00
(d)€201.15
14.6 identical printers can print a batch of exam papers in 40 minutes, all working at the same rate. Working at the same rate, work out how many minutes 4 of these printers would take to print the same batch.
(a)60 minutes
(b)40 minutes
(c)26.7 minutes
(d)24 minutes
15.y is directly proportional to x. When x = 5, y = 18. Work out the value of y when x = 15.
(a)60
(b)28
(c)54
(d)6

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