Algebraic: Problem Solving & Reasoning on Factorising (Common Factor)
Mathematics
Year 9
15 questions
~30 mins
1 views0 downloads
About This Worksheet
A comprehensive worksheet focusing on factorising algebraic expressions by extracting common factors, designed to develop procedural skills, reasoning, and real-world application for Year 9 students.
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Algebraic: Problem Solving & Reasoning on Factorising (Common Factor)
Subject: MathematicsGrade: Year 9
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Untitled Worksheet
Grade Year 9
A
Fluency & Practice
Solve the following to build your procedural mastery of factorising algebraic expressions.
1.
Factorise completely: 3x + 6
[2 marks]2.
Factorise: 8a + 12b
[2 marks]3.
Simplify: 5y - 15
[2 marks]4.
Factorise: 10m - 5n
[2 marks]B
Targeted Practice
Work through these questions to deepen your understanding of algebraic factorisation with common factors.
1.
Factorise: 9x^2 + 15x
[3 marks]2.
Factorise: 14a^2 - 21a
[3 marks]3.
Factorise: 16b^3 + 24b^2
[3 marks]4.
Factorise: 18p^2q - 12pq^2
[3 marks]5.
Factorise: 20xy + 30xz
[3 marks]C
Real-world Applications
Apply your understanding to solve these contextual word problems involving algebraic expressions.
1.
A gardener is planting rows of trees. The total number of trees in a row is represented by 4x + 8. If each tree takes up the same space, factorise the expression to find how many trees are in each row when x = 3.
[4 marks]2.
A factory produces 6x + 12 units of a product per day. If x represents the number of days, find the minimum units produced when x=5, after factorising.
[4 marks]D
Challenge & Extension
Attempt these more difficult problems to extend your algebraic factorising skills.
1.
Factorise: 12a^2b + 18ab^2 + 6ab
[4 marks]2.
Express as a factorised form: 24m^3 + 36m^2 + 12m
[4 marks]E
Mixed Review & Error Analysis
Solve these questions and identify common mistakes in factorising expressions.
1.
Identify the mistake: Factorise 15x + 25 as 5(3x + 5). Is this correct? Explain.
[3 marks]2.
Factorise: 7x + 14. Show the common mistake and correct it.
[3 marks]Quick Actions
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Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet