Robinson Tuition
Year 9 · Key Stage 3 · free KS3 maths worksheet

Simplifying, expanding and factorising

14 original questions, 51 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. Write each of these in the correct algebraic way.
    (i)  a × 4 × b     (ii)  m ÷ 3     (iii)  y × y × 5
  2. Simplify  5p + 3q − 2p + q
3 marks
Show answer
a) 4ab, m/3, 5y2 b) 3p + 4q
2

Here are four lines of algebra.

A   3x + 2      B   v = u + at      C   4x − 1 = 11      D   2(x + 3) ≡ 2x + 6

  1. Which one is an expression?
  2. Which one is a formula?
  3. Which one is an identity?
  4. Write ≡ in the box if the two sides are identical, or ≢ if they are not.
    (i)  5(n − 2) 5n − 10     (ii)  n2 + n2 n4     (iii)  3y + 2y 5y
4 marks
Show answer
a) A b) B c) D d) ≡, ≢, ≡
3
  1. Simplify  t3 × t4
  2. Simplify  12h5 ÷ 3h2
  3. Simplify  5u + 3v − 2u + 7v
4 marks
Show answer
a) t7 b) 4h3 c) 3u + 10v (accept 10v + 3u)
4
  1. Work out the value of  2a − 3b  when a = −1 and b = 4.
  2. Work out the value of  4a2 + b  when a = −3 and b = −7.
4 marks
Show answer
a) -14 b) 29
5
  1. The perimeter of a rectangle is given by the formula  P = 2(l + w)
    Work out P when l = 7.5 and w = 4
  2. Work out the value of  3(x − 2)2  when x = 5
  3. Work out the value of  a2 + 2ab  when a = −3 and b = 4
4 marks
Show answer
a) 23 b) 27 c) -15
6
  1. In science, the distance s metres travelled by a cart is given by
    s = ut + 12at2
    Work out s when u = 3, t = 4 and a = 2.5
  2. To change a temperature from °C to °F you can use  F = 9C5 + 32
    Ruby's thermometer reads 25 °C. Change this temperature to °F.
3 marks
Show answer
a) 32 b) 77 °F
7
  1. Expand and simplify 3(x + 2) + 2(x − 5)
  2. Solve 5(x − 3) = 20
4 marks
Show answer
a) 5x - 4 b) x = 7
8
  1. Write down the highest common factor of  6x2y  and  9xy
  2. Factorise  8a − 12
  3. Factorise fully  10x2y + 15xy2
4 marks
Show answer
a) 3xy b) 4(2a - 3) c) 5xy(2x + 3y)
9
  1. Expand and simplify  (x + 9)(x - 2)
  2. Factorise  x2 - 3x - 28
4 marks
Show answer
a) x2 + 7x - 18 b) (x - 7)(x + 4)
10

A rectangular garden is (x + 4) metres long and (x + 1) metres wide.

  1. Write an expression for the perimeter of the garden. Give your answer in its simplest form.
  2. Show that the area of the garden is (x2 + 5x + 4) m2.
  3. Work out the area of the garden when x = 6
4 marks
Show answer
a) 4x + 10 b) (x + 4)(x + 1) = x2 + 5x + 4 c) 70 m2
11
  1. Simplify  t8 ÷ t3
  2. Simplify  (k4)5
  3. Simplify  12x6y34x2y
3 marks
Show answer
a) t5 b) k20 c) 3x4y2

Extension questions: beyond the core Year 9 objectives, for pupils who want a stretch.

12
  1. Simplify  4a2b × 3ab3
  2. Simplify  20p5q2 ÷ 4p2q
  3. Expand and simplify  (3x + 2)(2x − 5)
4 marks
Show answer
a) 12a3b4 b) 5p3q c) 6x2 - 11x - 10
13

Expand and simplify (x + 2)(x + 3)(x + 4)

3 marks
Show answer
x3 + 9x2 + 26x + 24
14

Solve 2x2 + 5x - 12 = 0

3 marks
Show answer
x = 32, x = -4

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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