GCSE Mathematics Revision — Quadratic Equations
Revise Quadratic Equations for GCSE Mathematics. Step-by-step explanation, worked examples, common mistakes and exam-style practice aligned to AQA, Edexcel, OCR, WJEC, Eduqas, CCEA, Cambridge International (CIE), Pearson Edexcel International, OxfordAQA International, SQA, IB, AP.
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What is Quadratic Equations?
A quadratic equation has the form ax² + bx + c = 0. You can solve quadratics by factorising, using the quadratic formula x = (-b ± √(b²-4ac)) / 2a, or completing the square. Factorising is fastest when it works, but the formula always works. The discriminant b²-4ac tells you how many solutions exist: positive means two, zero means one (repeated), negative means none (no real roots).
Board notes: All boards require factorising and the quadratic formula at Higher. Completing the square is also Higher content. AQA sometimes asks students to derive the formula.
Step-by-step explanationWorked examples
Worked example 1: Core method
Solve x² - 5x + 6 = 0. Factorise: (x - 2)(x - 3) = 0. So x = 2 or x = 3.
Worked example 2: Exam variation
Now change one detail in the question and keep the same structure: name the Quadratic Equations idea being tested, show the method or evidence, then explain why it answers the command word. This helps GCSE Mathematics students avoid memorising one surface pattern.
Worked example 3: Mark-scheme check
Finish by checking the answer against marks: one point for the correct Quadratic Equations idea, one for accurate working or evidence, and one for a precise final statement. If any step is vague, rewrite it before moving to timed practice.
Mini lesson for Quadratic Equations
1. Understand the core idea
A quadratic equation has the form ax² + bx + c = 0. You can solve quadratics by factorising, using the quadratic formula x = (-b ± √(b²-4ac)) / 2a, or completing the square.
Can you explain Quadratic Equations without copying the notes?
2. Turn it into marks
Solve x² - 5x + 6 = 0. Factorise: (x - 2)(x - 3) = 0.
Underline the method, evidence, or command-word move that would earn credit in GCSE Algebra.
3. Fix the likely mark leak
Watch for this mistake: Forgetting to rearrange the equation to = 0 before factorising.
Write one correction rule before doing another practice question.
Practise this topic
Start with low-focus cards for Quadratic Equations, then move into full exam-style practice when you want the heavier session.
Mini quiz: Quadratic Equations
Three quick checks for revision practice. They are original StudyVector prompts, not official exam-board questions.
Question 1
In one GCSE sentence, explain what Quadratic Equations is testing.
Answer: A quadratic equation has the form ax² + bx + c = 0. You can solve quadratics by factorising, using the quadratic formula x = (-b ± √(b²-4ac)) / 2a, or completing the square.
Mark focus: Precise definition and topic focus.
Question 2
A student sees a Quadratic Equations question but is not sure how to start. What should the first method line establish?
Answer: It should identify the rule, equation, diagram feature, or transformation before any calculation. That protects method marks and makes later checking easier.
Mark focus: Method selection and command-word control.
Question 3
A student makes this mistake: "Forgetting to rearrange the equation to = 0 before factorising." What should their next repair task be?
Answer: Do one Quadratic Equations question and review the mistake type.
Mark focus: Error correction and next-step practice.
Quadratic Equations flashcards
Core idea
What is the main idea in Quadratic Equations?
A quadratic equation has the form ax² + bx + c = 0. You can solve quadratics by factorising, using the quadratic formula x = (-b ± √(b²-4ac)) / 2a, or completing the square.
Common mistake
What mistake should you avoid in Quadratic Equations?
Forgetting to rearrange the equation to = 0 before factorising.
Practice
What is one useful practice task for Quadratic Equations?
Answer one Quadratic Equations question and review the mistake type.
Exam board
How should you use board notes for Quadratic Equations?
All boards require factorising and the quadratic formula at Higher. Completing the square is also Higher content.
Common mistakes
- 1Forgetting to rearrange the equation to = 0 before factorising.
- 2Sign errors in the quadratic formula, especially with the -b term when b is already negative.
- 3Giving only one solution when there are two (forgetting the ± in the formula).
- 4Not checking whether the question asks for exact answers (surds) or decimal approximations.
Quadratic Equations exam questions
Exam-style questions for Quadratic Equations with mark-scheme style solutions and timing practice. Aligned to AQA, Edexcel, OCR, WJEC, Eduqas, CCEA, Cambridge International (CIE), Pearson Edexcel International, OxfordAQA International, SQA, IB, AP specifications.
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Step-by-step method
Step-by-step explanation
4 steps · Worked method for Quadratic Equations
Core concept
A quadratic equation has the form ax² + bx + c = 0. You can solve quadratics by factorising, using the quadratic formula x = (-b ± √(b²-4ac)) / 2a, or completing the square. Factorising is fastest whe…
Frequently asked questions
When should I use the quadratic formula instead of factorising?
Use the formula when the quadratic does not factorise neatly, or when the question specifically asks for answers to a given number of decimal places or significant figures.
What does the discriminant tell you?
The discriminant is b² - 4ac. If it is positive, there are two distinct real roots. If zero, there is one repeated root. If negative, there are no real roots.