Robinson Tuition
Grade 4 · Foundation and Higher · free GCSE maths worksheet

Rearranging simple formulae

Changing the subject in one or two steps.

18 original questions, 53 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
  1. Make x the subject of y = x + 5
  2. Make x the subject of y = 3x
2 marks
Show answer
a) x = y - 5 b) x = y/3
2

Make x the subject of the formula

y = 2x + 9

2 marks
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x = y - 92
3

Chloe is making x the subject of the formula y = 3x + 5.

Here is her working.

Step 1:  y - 5 = 3x

Step 2:  x = y3 - 5

Explain the mistake Chloe has made.

1 mark
Show answer
In Step 2 she has only divided y by 3. She should divide the whole of y - 5 by 3, giving x = y - 53.
4

A plumber works out the cost of a job using this rule.

Cost in pounds = 15 + 8 × number of hours

  1. Work out the cost of a job that takes 4 hours.
  2. A job costs £79. Work out how many hours it took.
3 marks
Show answer
a) 47 b) 8
5

The formula v = u + at gives the speed of an object after time t.

  1. Make t the subject of the formula.
  2. Find t when v = 25, u = 7 and a = 3.
3 marks
Show answer
a) t = (v - u)/a b) 6
6

Make a the subject of the formula

P = 3a + 2b

2 marks
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a = P - 2b3
7

F = 5v + 20

  1. Work out the value of F when v = 6.
  2. Work out the value of v when F = 95.
4 marks
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a) 50 b) 15
8

Here is a rule: y = 3x − 4

Complete the table.

x−15
y14−10
4 marks
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x = -1) -7 x = 5) 11 y = 14) 6 y = -10) -2
9

Make k the subject of the formula

m = k5 - 2

2 marks
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k = 5(m + 2)
10

Make c the subject of the formula

a = 4(c + 2d)

2 marks
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c = a4 - 2d
11

y = 5 + √x

  1. Make x the subject of the formula.
  2. Find x when y = 9.
3 marks
Show answer
a) x = (y - 5)2 b) 16
12

Make x the subject of the formula

y = 3x - 52

2 marks
Show answer
x = 2y + 53
13

Make g the subject of the formula

h = 5 + 3g

3 marks
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g = 3h - 5
14

v = u + at

  1. Work out the value of v when u = 7, a = 9.8 and t = 5.
  2. Work out the value of t when v = 87, u = 12 and a = 5.
4 marks
Show answer
a) 56 b) 15
15

m = 3n − 2p

  1. Work out the value of m when n = −5 and p = 4.
  2. Work out the value of n when m = 19 and p = −2.
4 marks
Show answer
a) -23 b) 5
16

Q = 5p − 3r

Work out the value of r when Q = 5 and p = −2.

3 marks
Show answer
-5
17

The formula F = 9C5 + 32 converts a temperature in degrees Celsius (C) to degrees Fahrenheit (F).

Make C the subject of the formula.

3 marks
Show answer
C = 5(F - 32)/9
18
  1. Expand 3x(2x − 5)
  2. Factorise fully 20a2b − 8ab
  3. Make x the subject of y = 4x − 7
6 marks
Show answer
a) 6x2 - 15x b) 4ab(5a - 2) c) x = (y + 7)/4

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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