IGCSE Quadratic Equations and Inequalities: Complete Guide for Cambridge IGCSE Mathematics

IGCSE quadratic equations and inequalities are essential algebra topics in Cambridge IGCSE Mathematics that appear in both Paper 2 and Paper 4. Mastering solving quadratics by factorisation, quadratic formula, and completing the square is essential for achieving top grades in IGCSE exams.

This comprehensive IGCSE quadratic equations and inequalities guide covers everything you need to know, including three methods for solving quadratics, quadratic inequalities, worked examples, common exam questions, and expert tips from Tutopiya’s IGCSE maths tutors. We’ll also show you how to avoid the most common mistakes that cost students valuable marks.

🎯 What you’ll learn: By the end of this guide, you’ll know how to solve quadratic equations using three different methods, solve quadratic inequalities, and apply these skills to solve problems in IGCSE exams.

Already studying with Tutopiya? Practice these skills with our dedicated IGCSE Algebra practice deck featuring exam-style questions and instant feedback.

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Why IGCSE Quadratic Equations and Inequalities Matter

IGCSE quadratic equations and inequalities are essential algebra topics. Here’s why they’re so important:

• High frequency topic: Quadratic questions appear regularly in IGCSE maths papers
• Foundation skill: Essential for advanced mathematics and calculus
• Exam weight: Typically worth 5-10 marks per paper
• Real-world applications: Used in physics, engineering, and optimization problems
• Problem-solving skills: Develops algebraic thinking and multiple solution strategies

Key insight from examiners: Students often struggle with choosing the right method or make errors with the quadratic formula. This guide will help you master all three methods systematically.

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Understanding Quadratic Equations

A quadratic equation has the form ax² + bx + c = 0 where a ≠ 0.

Examples:

• x² - 5x + 6 = 0
• 2x² + 3x - 5 = 0
• x² - 9 = 0

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Method 1: Factorisation

Factorise the quadratic and use the fact that if ab = 0, then a = 0 or b = 0.

Example 1: Solve x² - 5x + 6 = 0

Solution: Factorise: (x - 2)(x - 3) = 0 Either x - 2 = 0 or x - 3 = 0 Therefore: x = 2 or x = 3

Answer: x = 2 or x = 3

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Method 2: Quadratic Formula

Formula: x = (-b ± √(b² - 4ac)) / 2a

Example 2: Solve 2x² + 3x - 5 = 0

Solution: a = 2, b = 3, c = -5 x = (-3 ± √(9 + 40)) / 4 x = (-3 ± √49) / 4 x = (-3 ± 7) / 4 x = 1 or x = -2.5

Answer: x = 1 or x = -2.5

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Method 3: Completing the Square

Example 3: Solve x² - 6x + 5 = 0

Solution: (x - 3)² - 9 + 5 = 0 (x - 3)² = 4 x - 3 = ±2 x = 5 or x = 1

Answer: x = 5 or x = 1

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Quadratic Inequalities

Example 4: Solve x² - 5x + 6 > 0

Solution: Factorise: (x - 2)(x - 3) > 0 Critical points: x = 2 and x = 3 Test regions: x < 2, 2 < x < 3, x > 3 Solution: x < 2 or x > 3

Answer: x < 2 or x > 3

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Common Examiner Traps

• Wrong method choice - Use factorisation when possible, formula when needed
• Quadratic formula errors - Watch signs and calculate discriminant correctly
• Inequality sign errors - Test regions carefully for inequalities
• Forgetting both solutions - Quadratics usually have two solutions

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Practice Questions

Question 1

Solve x² - 7x + 12 = 0

Solution: Factorise: (x - 3)(x - 4) = 0 x = 3 or x = 4

Answer: x = 3 or x = 4

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Tutopiya Advantage: Personalised IGCSE Quadratic Equations and Inequalities Coaching

• Live whiteboard walkthroughs of quadratic solving methods
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📞 Ready to turn shaky quadratic skills into exam-ready confidence? Book a free IGCSE maths trial and accelerate your revision plan.

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Frequently Asked Questions About IGCSE Quadratic Equations and Inequalities

What is a quadratic equation?

A quadratic equation has the form ax² + bx + c = 0 where a ≠ 0.

What are the three methods for solving quadratics?

1. Factorisation - When the quadratic factors easily
2. Quadratic formula - Always works: x = (-b ± √(b² - 4ac)) / 2a
3. Completing the square - Useful for some problems

When should I use each method?

• Factorisation: When the quadratic factors easily
• Quadratic formula: When factorisation is difficult
• Completing the square: When asked specifically or for some inequalities

How do I solve quadratic inequalities?

Find critical points, test regions, and determine which regions satisfy the inequality.

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Related IGCSE Maths Resources

Strengthen your IGCSE Mathematics preparation with these comprehensive guides:

• IGCSE Factorisation: Complete Guide - Master factorisation techniques
• IGCSE Linear Equations: Complete Guide - Master linear equations
• IGCSE Maths Revision Notes, Syllabus and Preparation Tips - Complete syllabus overview, topic breakdown, and revision strategies
• IGCSE Past Papers Guide - Access free IGCSE past papers and exam resources

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Next Steps: Master IGCSE Quadratic Equations and Inequalities with Tutopiya

Ready to excel in IGCSE quadratic equations and inequalities? Our expert IGCSE maths tutors provide:

• Personalized 1-on-1 tutoring tailored to your learning pace
• Exam-focused practice with real Cambridge IGCSE past papers
• Interactive whiteboard sessions for visual learning
• Progress tracking to identify and strengthen weak areas
• Flexible scheduling to fit your revision timetable

Book a free IGCSE maths trial lesson and get personalized support to master quadratic equations and achieve your target grade.

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