Factorising First: Challenge & Extension
Mathematics
Grade 8
11 questions
~22 mins
1 views0 downloads
About This Worksheet
A worksheet focused on factorising expressions first to simplify algebraic fractions, designed to challenge and extend Grade 8 students' understanding.
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Factorising First: Challenge & Extension
Subject: MathematicsGrade: Grade 8
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Untitled Worksheet
Grade Grade 8
A
Fluency & Practice
Simplify the following algebraic fractions by factorising the numerator and denominator first. Show all working in the grid spaces.
1.
Factorise and simplify: (6x^2 + 9x) / (3x).
[2 marks]2.
Factorise numerator and denominator: (x^2 - 16) / (x - 4).
[2 marks]3.
Simplify: (4x^2 - 25) / (2x + 5).
[2 marks]B
Problem Solving & Reasoning
Solve these multi-step problems involving factorising first. Explain your reasoning clearly.
1.
Simplify the algebraic fraction: ((x^2 + 5x + 6) / (x + 2)). Describe each step of your factorising process.
[4 marks]2.
Given the expression (2x^2 + 3x - 5) / (x + 1), factorise numerator fully and simplify the fraction.
[4 marks]C
Real-world Applications
Apply factorising first to solve these word problems.
1.
A rectangular garden's length is modeled by (x + 3) meters, and its width by (x - 1) meters. Express and simplify the ratio of the perimeter to the area in terms of x, factorising where necessary.
[3 marks]D
Challenge & Extension
Tackle these advanced problems that require deeper understanding of factorising first. Show detailed working.
1.
Factorise completely: 3x^3 + 6x^2 - 9x, then simplify if possible.
[3 marks]2.
Express as a single simplified fraction: (x^3 - 8) / (x^2 - 4). Use factorising first.
[3 marks]E
Mixed Review
Solve a variety of questions involving factorising first to consolidate understanding.
1.
Factorise: 5x^2 + 20x.
[2 marks]2.
Simplify: (x^2 - 9) / (x - 3).
[2 marks]F
Error Analysis
Identify and correct the common mistake made in the following problem.
1.
A student factors (x^2 + 5x + 6) as (x + 2)(x + 3) instead of the correct (x + 2)(x + 3). Correct the mistake and explain the importance of correct factorising.
[3 marks]Quick Actions
What is Remix?
Create a new worksheet based on this one. Change the grade level, topic, number of questions, or difficulty - then generate a fresh version.
- • Change grade level (Grade 6 → Grade 7)
- • Swap topics (Harry Potter → Macbeth)
- • Add more questions (10 → 15)
- • Adjust difficulty
Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet