Robinson Tuition
Grade 5 · Foundation and Higher · free GCSE maths worksheet

Solving quadratic equations by factorising

Factorising then setting each bracket to zero.

13 original questions, 43 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 + 3)(x - 9) = 0

2 marks
Show answer
x = -3 or x = 9
2

Solve  x2 + 8x + 12 = 0

3 marks
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x = -2 or x = -6
3

Solve x2 − 36 = 0

2 marks
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x = 6 or x = -6
4

Solve  x2 - 5x - 24 = 0

3 marks
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x = 8 or x = -3
5

Solve  x2 - 11x + 28 = 0

3 marks
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x = 4 or x = 7
6

Solve x2 − 10x + 25 = 0

3 marks
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x = 5
7

Solve  x2 = 7x

3 marks
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x = 0 or x = 7
8

Solve  x2 - 2x = 35

3 marks
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x = 7 or x = -5
9

Solve x2 + 5x − 4 = 3x + 11

4 marks
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x = 3 or x = -5
10

A triangle has a base of (x + 2) cm and a perpendicular height of x cm. The area of the triangle is 12 cm2.

Work out the value of x.

4 marks
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x = 4
11

The width of a rectangle is w cm.

The length of the rectangle is 3 cm more than its width.

The area of the rectangle is 40 cm2.

Find the value of w.

4 marks
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w = 5
12

Two positive whole numbers differ by 5.

The product of the two numbers is 84.

By forming and solving a quadratic equation, find the two numbers.

4 marks
Show answer
7 and 12
13

A rectangular garden is x metres wide. It is 5 metres longer than it is wide. The area of the garden is 84 m2.

  1. Show that x2 + 5x − 84 = 0
  2. Solve the equation and so work out the perimeter of the garden.
5 marks
Show answer
a) x(x + 5) = 84 gives x2 + 5x - 84 = 0 b) x = 7 (reject -12), perimeter 38 m

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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