Mastering x² + bx + c: Challenge & Extension
Mathematics
Year 9
10 questions
~20 mins
1 views0 downloads
About This Worksheet
A challenging worksheet designed to deepen understanding of factorising quadratics of the form x² + bx + c, including procedural practice, reasoning, real-world applications, and extension problems.
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Mastering x² + bx + c: Challenge & Extension
Subject: MathematicsGrade: Year 9
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Untitled Worksheet
Grade Year 9
A
Fluency & Practice
Solve the following quadratic expressions by factorising. Show all your working in the grid spaces provided.
1.
Factorise x² + 7x + 12.
[2 marks]2.
Factorise x² - 9x + 20.
[2 marks]3.
Factorise x² + 5x + 6.
[2 marks]B
Problem Solving & Reasoning
Answer the following multi-step problems, explaining your reasoning clearly.
1.
A rectangular garden has dimensions that can be expressed as (x + 3) meters and (x + 5) meters. Write an expression for the area and factorise it if possible.
[4 marks]2.
The quadratic x² + bx + c has roots at x = 2 and x = -5. Find the values of b and c by factorising.
[4 marks]C
Real-world Applications
Solve these contextual problems involving quadratics.
1.
A ball is launched such that its height in meters after t seconds is given by h(t) = -2t² + 8t + 1. When does the ball reach its maximum height? Use factorising to determine this.
[3 marks]D
Challenge & Extension
Attempt these more challenging problems to extend your understanding of factorising quadratics.
1.
Factorise the quadratic 2x² + 4x - 6, then explain why it cannot be factorised into linear factors with integer coefficients.
[4 marks]2.
Given the quadratic x² + bx + c, find b and c if the quadratic factors as (x + 4)(x - n) and has a root at x = -1.
[4 marks]E
Mixed Review & Error Analysis
Review the following common mistakes and identify what went wrong or correct the errors.
1.
A student factors x² + 6x + 9 as (x + 2)(x + 3). Identify and explain the mistake.
[3 marks]2.
Correct the factorisation of x² - 4x + 4 if it was initially written as (x - 2)(x + 2).
[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