Printable · GCSE Foundation · ages 14-16

Direct and inverse proportion worksheet — GCSE Foundation

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 Foundation

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

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1.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
2.y is directly proportional to x. When x = 2, y = 9. Which of these pairs of values is also consistent with this proportion?
(a)x = 6, y = 27
(b)x = 6, y = 13
(c)x = 6, y = 3
(d)x = 6, y = 24
3.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
4.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
5.The exchange rate is £1 = 1.28 US dollars. Convert £350 into US dollars.
(a)273.44 US dollars
(b)4,480.00 US dollars
(c)448.00 US dollars
(d)351.28 US dollars
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.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
8.The exchange rate is £1 = €1.15. Convert £200 to euros.
(a)€30.00
(b)€230.00
(c)€2300.00
(d)€201.15
9.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
10.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
11.3 pencils cost £1.20. Work out the cost of 7 pencils.
(a)£2.80
(b)£8.40
(c)£0.40
(d)£1.20
12.3 kg of apples cost £6. Work out the cost of 5 kg of the same apples.
(a)£3.60
(b)£10
(c)£11
(d)£30
13.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
14.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
15.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

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