Mastering x² + bx + c = 0: Mixed Review
Mathematics
GCSE Foundation
11 questions
~22 mins
1 views0 downloads
About This Worksheet
This worksheet provides a mixed review of solving quadratic equations of the form x² + bx + c = 0 by factorising, designed for GCSE Foundation students. It includes procedural questions, problem-solving tasks, real-world contexts, and extension challenges.
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Mastering x² + bx + c = 0: Mixed Review
Subject: MathematicsGrade: GCSE Foundation
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Untitled Worksheet
Grade GCSE Foundation
A
Fluency & Practice
Solve each quadratic equation by factorising. Show all working in the grid spaces provided.
1.
Solve for x: x² + 5x + 6 = 0
[2 marks]2.
Factorise and solve: x² - 9 = 0
[2 marks]3.
Solve: x² + 4x + 4 = 0
[2 marks]B
Problem Solving & Reasoning
Answer the following multi-step problems. Show your reasoning and working clearly.
1.
A rectangle’s length is modeled by the quadratic x² + 7x + 10. Find the possible lengths of the rectangle when the length is a positive integer.
[4 marks]2.
A student factors the quadratic x² + 3x + 8. Explain why they cannot find real solutions and suggest the correct approach.
[3 marks]C
Real-world Applications
Apply your knowledge to solve these contextual problems.
1.
A ball is thrown upwards, and its height in meters after t seconds is given by h = -5t² + 20t + 2. When does the ball hit the ground?
[4 marks]D
Challenge & Extension
Tackle these advanced problems to extend your understanding.
1.
Solve the quadratic equation 2x² + 4x - 6 = 0 by factorising, if possible. If not, explain why.
[3 marks]2.
Construct a quadratic equation with roots x = -1 and x = 4. Write the equation in the form x² + bx + c = 0.
[3 marks]E
Mixed Review
Answer these varied questions to consolidate your understanding.
1.
Factorise: x² + 2x - 15
[2 marks]2.
Solve for x: -x² + 6x + 7 = 0
[2 marks]F
Error Analysis
Review the common mistake in solving quadratic equations and correct the error.
1.
A student solves x² + 4x + 4 = 0 by writing (x + 2)² = 0 and concluding x = 2. Identify and correct the mistake.
[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