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Grade 3 · Foundation · free GCSE maths worksheet

Solving one-step and two-step equations

Using inverse operations.

22 original questions, 60 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

Solve  x + 7 = 12

1 mark
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x = 5
2

Solve w4 + 2 = 9

2 marks
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w = 28
3

Solve

  1. x + 7 = 12
  2. 4y = 28
  3. m3 = 5
3 marks
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a) x = 5 b) y = 7 c) m = 15
4

Solve  y − 9 = 14

1 mark
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y = 23
5

Solve 5x − 7 = 23

2 marks
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x = 6
6
  1. Solve  4m = 28
  2. Solve  t ÷ 5 = 6
2 marks
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a) m = 7 b) t = 30
7

Solve 3(x + 4) = 27

2 marks
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x = 5
8
  1. Solve  w + 13 = 40
  2. Solve  8k = 60
2 marks
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a) w = 27 b) k = 7.5
9
  1. Solve  c − 8 = 11
  2. Solve  6d = 54
  3. Solve  e ÷ 4 = 7
3 marks
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a) c = 19 b) d = 9 c) e = 28
10

Solve 2x + 53 = 7

3 marks
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x = 8
11
  1. Solve 2x + 5 = 21
  2. Solve 3x − 4 = 11
3 marks
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a) x = 8 b) x = 5
12

I think of a number. I multiply it by 4 and then subtract 7. The answer is 29.

Work out my number.

3 marks
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9
13

Solve x4 + 3 = 8

3 marks
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x = 20
14
  1. Solve  3f = 19.5
  2. Solve  g + 4.7 = 9.2
  3. Solve  h ÷ 6 = 2.5
3 marks
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a) f = 6.5 b) g = 4.5 c) h = 15
15

Priya thinks of a number.

She multiplies the number by 4 and then subtracts 9.

Her answer is 35.

Work out the number Priya thought of.

3 marks
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11
16
  1. Solve  p + 9 = 4
  2. Solve  5q = −30
  3. Solve  r − 3 = −10
3 marks
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a) p = -5 b) q = -6 c) r = -7
17

Tom is y years old.

His sister Freya is 7 years older than Tom.

  1. Write down an expression, in terms of y, for Freya's age.
  2. The sum of Tom's age and Freya's age is 23 years.
    Work out Tom's age.
3 marks
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a) y + 7 (accept 7 + y) b) 8
18

A rectangle has length (2x + 3) cm and width 5 cm.

The perimeter of the rectangle is 36 cm.

Work out the value of x.

4 marks
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x = 5
19
  1. Solve  7s = 42
  2. Solve  2t + 5 = 17
3 marks
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a) s = 6 b) t = 6
20
  1. Solve  15 = v + 8
  2. Solve  4w − 3 = 25
3 marks
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a) v = 7 b) w = 7
21
  1. Solve  x − 17 = 26
  2. Solve  5y + 8 = 43
  3. Solve  20 − z = 12
4 marks
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a) x = 43 b) y = 7 c) z = 8
22

The angles of a triangle are x°, (2x + 10)° and (3x + 20)°.

Work out the size of the largest angle.

4 marks
Show answer
95°

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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