IGCSE Variation: Complete Guide for Cambridge IGCSE Mathematics

IGCSE variation is an essential algebra topic in Cambridge IGCSE Mathematics that appears in both Paper 2 and Paper 4. Mastering direct variation, inverse variation, and joint variation is essential for solving proportional relationship problems.

This comprehensive IGCSE variation guide covers everything you need to know, including types of variation, variation formulas, 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 identify and solve direct, inverse, and joint variation problems, 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 Variation Matters

IGCSE variation is an essential algebra topic. Here’s why it’s so important:

• High frequency topic: Variation questions appear regularly in IGCSE maths papers
• Foundation skill: Essential for understanding proportional relationships
• Exam weight: Typically worth 4-7 marks per paper
• Real-world applications: Used in physics, economics, and engineering
• Problem-solving skills: Develops understanding of relationships between variables

Key insight from examiners: Students often confuse direct and inverse variation or make errors with the constant of proportionality. This guide will help you master these systematically.

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Understanding Variation

Variation describes how one quantity changes in relation to another.

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Direct Variation

Direct variation: y ∝ x means y = kx where k is the constant of proportionality.

Example 1: If y varies directly as x, and y = 12 when x = 3, find y when x = 7.

Solution: y = kx 12 = k(3), so k = 4 When x = 7: y = 4(7) = 28

Answer: y = 28

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Inverse Variation

Inverse variation: y ∝ 1/x means y = k/x where k is the constant.

Example 2: If y varies inversely as x, and y = 8 when x = 4, find y when x = 2.

Solution: y = k/x 8 = k/4, so k = 32 When x = 2: y = 32/2 = 16

Answer: y = 16

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Joint Variation

Joint variation: y ∝ xz means y = kxz

Example 3: If y varies jointly as x and z, and y = 24 when x = 3 and z = 2, find y when x = 5 and z = 4.

Solution: y = kxz 24 = k(3)(2), so k = 4 When x = 5 and z = 4: y = 4(5)(4) = 80

Answer: y = 80

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Common Examiner Traps

• Confusing direct and inverse - Direct: y = kx, Inverse: y = k/x
• Constant errors - Always find the constant first
• Substitution errors - Substitute values carefully

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Practice Questions

Question 1

If y varies directly as x, and y = 15 when x = 5, find y when x = 8.

Solution: y = kx, 15 = 5k, so k = 3 y = 3(8) = 24

Answer: y = 24

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Frequently Asked Questions About IGCSE Variation

What is direct variation?

Direct variation means y = kx where y increases as x increases proportionally.

What is inverse variation?

Inverse variation means y = k/x where y decreases as x increases.

What is joint variation?

Joint variation means y = kxz where y varies with the product of x and z.

How do I find the constant of proportionality?

Use given values to solve for k in the variation equation.

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Related IGCSE Maths Resources

Strengthen your IGCSE Mathematics preparation with these comprehensive guides:

• IGCSE Ratios and Proportions: Complete Guide - Master proportional relationships
• 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 Variation with Tutopiya

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• Personalized 1-on-1 tutoring tailored to your learning pace
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Book a free IGCSE maths trial lesson and get personalized support to master variation and achieve your target grade.

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