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Grade 5 · Foundation and Higher · free GCSE maths worksheet

Inverse proportion

Quantities that decrease as the other increases.

16 original questions, 46 marks. Print the worksheet, mark it with the answers sheet, and use the solutions to see every step written out by hand.

Worksheet PDFWorked solutions PDFAnswers PDF

The questions

1

4 identical pumps can drain a flooded basement in 18 hours.

Work out how long it would take 6 of these pumps to drain the basement.

2 marks
Show answer
12 hours
2

3 identical machines take 10 hours to print an order of leaflets.

Work out how long 5 of these machines would take to print the same order.

2 marks
Show answer
6 hours
3

8 friends hire a minibus and share the cost equally. Each friend pays £15.

4 more friends join the group and the cost is shared equally between everyone.

Work out how much each person now pays.

2 marks
Show answer
£10
4

Here are four graphs, A, B, C and D, each drawn for positive values of x and y.

  1. Which graph shows y directly proportional to x?
  2. Which graph shows y inversely proportional to x?
  3. Explain why graph B does not show direct proportion.
xyAxyBxyCxyD
3 marks
Show answer
a) D b) C c) It does not pass through the origin
5

5 identical pipes can fill a storage tank in 4.8 hours.

Only 3 of the pipes are working.

Work out how long the 3 pipes will take to fill the tank.

3 marks
Show answer
8 hours
6

Here are some values of x and y.

x2356
y30201210
  1. Show that y is inversely proportional to x.
  2. Work out the value of y when x = 12.
3 marks
Show answer
a) xy = 60 each time b) 5
7

It takes 8 bricklayers 15 days to build a wall.

  1. Work out how many days it would take 12 bricklayers to build the same wall.
  2. State one assumption you have made.
3 marks
Show answer
a) 10 days b) All the bricklayers work at the same rate
8

y is inversely proportional to x.

When x = 5, y = 8.

  1. Find a formula for y in terms of x.
  2. Work out the value of y when x = 16.
  3. Work out the value of x when y = 10.
4 marks
Show answer
a) y = 40/x b) 2.5 c) 4
9

y is inversely proportional to x. The point (2, 6) lies on the graph of y against x, as shown.

  1. Find a formula for y in terms of x.
  2. On the grid, sketch the graph of y against x for 1 ≤ x ≤ 6. Mark the points where x = 4 and x = 6.
012345602468101214xy(2, 6)
4 marks
Show answer
a) y = 12/x; b) A smooth curve through (1, 12), (2, 6), (4, 3) and (6, 2)
10

x is a positive quantity. For each relationship, write down what happens to y when x is doubled.

  1. y is directly proportional to x
  2. y is inversely proportional to x
  3. y is directly proportional to x2
2 marks
Show answer
a) y is doubled b) y is halved c) y is multiplied by 4
11

The pressure, P, of a gas in a sealed container is inversely proportional to its volume, V.

When V = 0.5 m3, P = 240 units.

Work out the pressure when the volume is 0.8 m3.

3 marks
Show answer
150
12

y is inversely proportional to x.

When x = 4, y = 9.

  1. Find the value of y when x = 6.
  2. Find the value of y when x = 12.
3 marks
Show answer
a) 6 b) 3
13

t is inversely proportional to s.

When s = 60, t = 2.5.

Work out the value of s when t = 4.

3 marks
Show answer
37.5
14

y is inversely proportional to x.

When x = 3, y = 20.

Work out the value of y when x = 5.

2 marks
Show answer
12
15

6 identical machines can complete an order in 14 days.

The 6 machines work for 4 days. Then 2 more identical machines are added.

Work out how many more days are needed to complete the order.

3 marks
Show answer
7.5 days
16

6 decorators can paint a hotel in 10 days. They all work at the same rate.

After 4 days, 2 of the decorators leave. The other decorators carry on at the same rate.

Work out how many more days it takes to finish painting the hotel.

4 marks
Show answer
9 days

Every question here is original and written by Robinson Tuition. The grade follows the Edexcel grade descriptors and suits AQA and OCR too; this is not an exam-board paper.

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