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Year 8 · Key Stage 3 · free KS3 maths worksheet

Algebraic expressions

12 original questions, 32 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
  1. Simplify  5 × 2m
  2. Simplify  n × n × n × n
  3. Simplify  3c × 4d
3 marks
Show answer
a) 10m b) n4 c) 12cd
2

Here are four pieces of algebra.

A:  3x + 2 = 11     B:  A = lw     C:  4y − 7     D:  2(x + 3) ≡ 2x + 6

Write down which one is

  1. an expression
  2. an equation
  3. a formula
  4. an identity
2 marks
Show answer
a) C b) A c) B d) D
3

Simplify  6x + 3y − 2x + 5y

2 marks
Show answer
4x + 8y
4

Simplify

  1. 5a2 + 3a − 2a2 + 4a − 9
  2. 4xy − 7 + 2yx + 10
2 marks
Show answer
a) 3a2 + 7a - 9 b) 6xy + 3
5
  1. Expand 4(2x − 5)
  2. Factorise 6y + 15
2 marks
Show answer
a) 8x - 20 b) 3(2y + 5)
6
  1. Expand and simplify  3(2x + 5) − 2(x − 4)
  2. Expand  x(x + 7)
3 marks
Show answer
a) 4x + 23 b) x2 + 7x
7
  1. Factorise 5x + 20
  2. Factorise x2 − 9x
2 marks
Show answer
a) 5(x + 4) b) x(x - 9)
8

The diagram shows a rectangle with sides (x + 4) and (x + 3).

It is split into four smaller rectangles.

  1. Write down an expression for the area of each of the four smaller rectangles.
  2. Hence expand and simplify (x + 4)(x + 3)
x4x3Diagram NOT accurately drawn
3 marks
Show answer
a) x2, 4x, 3x and 12 b) x2 + 7x + 12
9

Expand and simplify  (x - 3)(x + 8)

2 marks
Show answer
x2 + 5x - 24
10

Each bar in the diagram has length x.

The top bar is split into halves, the middle bar into thirds and the bottom bar into sixths.

  1. Use the diagram to write x2 and x3 in sixths.
  2. Hence simplify  x2 + x3
  3. Simplify  x2 − x3
x/2x/2x/3x/3x/3x/6x/6x/6x/6x/6x/6
3 marks
Show answer
a) x2 = 3x6 and x3 = 2x6 b) 5x6 c) x6
11

Simplify fully

  1. 6x9
  2. x3 + x4
  3. 5y6 − y3
  4. 2a3 × 94a
4 marks
Show answer
a) 2x3 b) 7x12 c) y2 d) 32
12
  1. Expand and simplify (y − 3)(y − 8)
  2. Factorise fully 4a2b + 6ab2
4 marks
Show answer
a) y2 - 11y + 24 b) 2ab(2a + 3b)

Your score

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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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