Robinson Tuition
Grade 6 · Higher · free GCSE maths worksheet

Setting up proportion equations

y proportional to x, x^2 or 1/x with a constant.

13 original questions, 42 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 directly proportional to x. y = 24 when x = 8.

  1. Find y when x = 5.
  2. Find x when y = 45.
3 marks
Show answer
a) 15 b) 15
2

The cost, C pounds, of a square tile is directly proportional to the square of the length of its side, s cm.

A tile with side 10 cm costs £12.

  1. Show that C = 0.12s2.
  2. Work out the cost of a tile with side 15 cm.
4 marks
Show answer
a) C = 0.12s2 b) £27
3

The time, T hours, taken to paint a fence is inversely proportional to the number of painters, n.

4 painters take 9 hours.

  1. Write down a formula for T in terms of n.
  2. How long would 6 painters take?
  3. How many painters are needed to paint the fence in 2.4 hours?
4 marks
Show answer
a) T = 36/n b) 6 hours c) 15 painters
4

y is directly proportional to the square of x.

When x = 4, y = 48.

Find the value of y when x = 5.

3 marks
Show answer
y = 75
5

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
6

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
7

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
8

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
9

y is inversely proportional to the cube of x. y = 4 when x = 2.

  1. Show that y = 12 when x = 4.
  2. Find the value of x when y = 32125.
4 marks
Show answer
a) Shown: y = 32/64 = 1/2 b) x = 5
10

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
11

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
12

The distance d metres a dropped object falls is directly proportional to the square of the time t seconds.

When t = 3, d = 45.

Work out the value of d when t = 6.

2 marks
Show answer
180
13

y is directly proportional to the square of x.

x is increased by 20%.

Show that y increases by 44%.

Assume x and y are positive.

3 marks
Show answer
New y = k(1.2x)2 = 1.44kx2, which is a 44% increase

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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