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Year 8 · Key Stage 3 · free KS3 maths worksheet

Solving equations and changing the subject

12 original questions, 37 marks. Type your answers below for an instant mark and a score (algebra in any equivalent form, e.g. 2sqrt(3) or 2√3), or print the worksheet, mark it with the answers sheet, and use the solutions to see every step written out by hand.

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The questions

1

Solve w4 + 2 = 9

2 marks
Show answer
w = 28
2

Solve

  1. x − 8 = −3
  2. 4x + 15 = 7
  3. 10 − 2x = 16
3 marks
Show answer
a) x = 5 b) x = -2 c) x = -3
3

Solve 5(x − 2) = 3x + 8

3 marks
Show answer
x = 9
4

Solve 3(2x − 5) − 2(x − 4) = −15

3 marks
Show answer
x = -2
5

Solve 4x + 13 = x + 3

3 marks
Show answer
x = 8
6

Dan and Ella share 45 sweets.

Ella gets 7 more sweets than Dan.

Dan says, "I got 20 sweets."

Is Dan right? You must show how you get your answer.

3 marks
Show answer
No, Dan got 19 sweets
7

Solve

  1. x2 + x3 = 10
  2. 3x − 24 = x + 62
4 marks
Show answer
a) x = 12 b) x = 14
8

At a cinema, an adult ticket costs £4 more than a child ticket.

Mrs Adeyemi buys 2 adult tickets and 3 child tickets. She pays £38 altogether.

Work out the cost of one child ticket.

3 marks
Show answer
£6
9
  1. Make r the subject of the formula A = πr2
  2. Make u the subject of the formula v2 = u2 + 2as
4 marks
Show answer
a) r = √(A/π) b) u = √(v² - 2as)
10

Make x the subject of the formula

5(x + 2y) = w + 3x

3 marks
Show answer
x = w - 10y2
11

Factorise

  1. x2 + 7x + 12
  2. x2 − 2x − 15
  3. x2 − 81
3 marks
Show answer
a) (x + 3)(x + 4) b) (x - 5)(x + 3) c) (x + 9)(x - 9)
12

Solve  x2 - 5x - 24 = 0

3 marks
Show answer
x = 8 or x = -3

Your score

Answer the questions above and your score appears here.

Every question here is original and written by Robinson Tuition. It follows the Key Stage 3 programme of study; Year 9 sheets end with extension questions for top sets.

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