x² + bx + c = 0: Error Analysis & Misconceptions
Mathematics
GCSE Foundation
13 questions
~26 mins
1 views0 downloads
About This Worksheet
A worksheet focusing on identifying and correcting misconceptions when solving quadratics of the form x² + bx + c = 0, with emphasis on error analysis and misconceptions.
Worksheet Preview
Full preview • 13 questions
x² + bx + c = 0: Error Analysis & Misconceptions
Subject: MathematicsGrade: GCSE Foundation
Name:
Date:
TeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizzTeachWhizz
Untitled Worksheet
Grade GCSE Foundation
A
Introduction
Review the key formula: To solve x² + bx + c = 0 by factorising, find two numbers that multiply to c and add to b. Use these to factorise and solve for x.
B
Fluency & Practice
Answer all questions. Show your working in the grid spaces provided.
1.
Factorise the quadratic x² + 5x + 6 = 0 and find the solutions for x.
[3 marks]2.
Solve the quadratic x² - 3x - 4 = 0 by factorising.
[3 marks]3.
Factorise and solve: x² + 2x - 8 = 0.
[3 marks]C
Problem Solving & Reasoning
Answer all questions with detailed working.
1.
A rectangle's area is represented by the quadratic x² + 7x + 10. Find the dimensions of the rectangle.
[4 marks]2.
A student attempts to solve x² + 4x + 4 = 0 by factorising as (x + 2)^2 = 0. Identify and explain the mistake if any.
[4 marks]3.
Explain why the quadratic x² + 2x + 3 cannot be factorised using real numbers.
[4 marks]D
Real-world Applications
Answer all questions in detail.
1.
A ball is thrown upwards. Its height after t seconds is modeled by h(t) = -5t² + 20t + 2. Find when the ball hits the ground.
[4 marks]E
Challenge & Extension
Attempt these more difficult problems.
1.
Given the quadratic x² + bx + 9 = 0, find the value of b if the roots are real and equal.
[3 marks]2.
Construct a quadratic with roots at x = -1 and x = 4. Write its factorised form and solve for x.
[3 marks]F
Mixed Review
Answer a variety of questions on solving quadratics.
1.
Solve the quadratic: 2x² + 8x + 6 = 0 by factorising.
[3 marks]2.
Identify the error in solving x² - 6x + 9 = 0 as (x - 3)^2 = 0 and explain.
[3 marks]G
Error Analysis & Misconceptions
Examine each problem and identify the mistake. Correct it and solve.
1.
A student factorises x² + 7x + 12 as (x + 3)(x + 4) and finds solutions. Is this correct? If not, identify and correct the mistake.
[4 marks]2.
A student attempts to solve x² + 2x + 1 = 0 by cancelling the common factor (x + 1) from numerator and denominator. Explain why this is incorrect.
[4 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