Robinson Tuition
Grade 7 · Higher · free GCSE maths worksheet

Inverse proportion equations

y = k/x problems.

10 original questions, 39 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

y is inversely proportional to x. Here are some values of x and y.

x25?12
y30124?
  1. Find a formula for y in terms of x.
  2. Find the two missing values in the table.
3 marks
Show answer
a) y = 60/x b) x = 15 and y = 5
2

The graph of y = 12x is drawn for positive values of x. Here is a table of values for the graph.

x1234612
y12?4?2?
  1. Complete the table.
  2. As x gets larger, what happens to the value of y and to the graph? Does the graph ever touch the x-axis? Give a reason.
3 marks
Show answer
a) 6, 3, 1 b) y decreases towards 0 and the graph gets closer to the x-axis; it never touches it because 12/x can never equal 0
3

The time, t days, taken to build a wall is inversely proportional to the number of workers, w.

6 workers take 15 days to build the wall.

  1. Find a formula for t in terms of w.
  2. How many workers are needed to build the wall in 4.5 days?
4 marks
Show answer
a) t = 90/w b) 20 workers
4

p is inversely proportional to q.

When q = 5, p = 12.

  1. Find a formula for p in terms of q.
  2. Find the value of p when q = 8.
3 marks
Show answer
a) p = 60/q b) 7.5
5

y is inversely proportional to the square of x.

When x = 3, y = 4.

Find the negative value of x when y = 9.

3 marks
Show answer
x = -2
6

The force F newtons between two magnets is inversely proportional to the square of the distance d cm between them.

When d = 2, F = 60.

  1. Find a formula for F in terms of d.
  2. Find the positive value of d when F = 15.
4 marks
Show answer
a) F = 240/d2 b) 4
7

y is inversely proportional to the cube of x.

When x = 2, y = 5.

  1. Find a formula for y in terms of x.
  2. Show that when x = 5, y = 825.
  3. Find the value of x when y = 135.
5 marks
Show answer
a) y = 40/x3 b) shown: 40/125 = 8/25 c) x = 2/3
8

x and y are positive quantities.

y is inversely proportional to the square of x.

x is increased by 25%.

Work out the percentage change in y.

4 marks
Show answer
36% decrease
9

y is directly proportional to the square of x.

When x = 5, y = 50.

x is inversely proportional to z.

When z = 2, x = 6.

Find the value of y when z = 4.

5 marks
Show answer
y = 18
10

t is directly proportional to the square root of m.

When m = 9, t = 6.

m is inversely proportional to w.

When w = 4, m = 9.

Find the value of w when t = 3.

5 marks
Show answer
w = 16

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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