Mastering Factorising
Mathematics
GCSE Higher
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A worksheet covering Factorising for GCSE Higher students.
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Mastering Factorising
Subject: MathematicsGrade: GCSE Higher
Name:
Date:
Untitled Worksheet
Grade GCSE Higher
A
Introduction
Review the key concept: factorising quadratic expressions and common algebraic techniques.
B
Practice Questions
Answer all questions. Show your working in the grid spaces provided.
1.
Factorise the expression: x^2 + 5x + 6
[2 marks]2.
Factorise the expression: 3x^2 - 12
[2 marks]3.
Factorise the quadratic: 2x^2 + 7x + 3
[2 marks]4.
Factorise the expression: x^2 - 9
[2 marks]5.
Factorise the expression: 4x^2 + 4x
[2 marks]6.
Factorise the quadratic: 6x^2 + 11x + 3
[2 marks]7.
Reasoning: Explain why x^2 + 7x + 12 can be factorised as (x + 3)(x + 4).
[3 marks]8.
Solve for x: 2x^2 - 8x = 0 by factorising.
[3 marks]9.
Factorise: 9x^2 + 24x + 16
[2 marks]10.
Challenge: A rectangle has length 3x + 2 and width x + 4. Express its area as a factorised algebraic expression.
[4 marks]11.
Real-world application: A garden is designed with quadratic features. The height h (in meters) of a fountain is modeled by h = -2x^2 + 12x + 4. Factorise the quadratic to find the x-values where the fountain reaches its maximum height.
[4 marks]Quick Actions
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Details
- Created
- 12/30/2025
- Updated
- 12/30/2025
- Type
- worksheet