IGCSE Changing the Subject of the Formula: Complete Guide for Cambridge IGCSE Mathematics

IGCSE changing the subject of the formula is a fundamental algebra skill in Cambridge IGCSE Mathematics that appears in both Paper 2 and Paper 4. Mastering formula rearrangement and inverse operations is essential for solving problems where you need to isolate a specific variable.

This comprehensive IGCSE changing the subject of the formula guide covers everything you need to know, including step-by-step rearrangement methods, inverse operations, 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 rearrange formulas to make any variable the subject, use inverse operations correctly, and apply these skills to solve problems in IGCSE exams.

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Why IGCSE Changing the Subject of the Formula Matters

IGCSE changing the subject of the formula is an essential algebra skill. Here’s why it’s so important:

• High frequency topic: Formula rearrangement questions appear regularly in IGCSE maths papers
• Foundation skill: Essential for solving equations and word problems
• Exam weight: Typically worth 3-6 marks per paper
• Real-world applications: Used in physics, chemistry, and engineering problems
• Problem-solving skills: Develops algebraic manipulation and logical thinking

Key insight from examiners: Students often make errors with inverse operations or forget to apply operations to both sides. This guide will help you master these systematically.

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Understanding Changing the Subject

Changing the subject of a formula means rearranging a formula so that a different variable becomes the subject (the variable on its own on one side).

Original formula: v = u + at (v is the subject) Make t the subject: t = (v - u) / a

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Step-by-Step Method

1. Identify the target variable - Which variable do you want to make the subject?
2. Use inverse operations - Work backwards from the formula
3. Apply to both sides - Whatever you do to one side, do to the other
4. Simplify - Combine like terms and simplify
5. Check your answer - Substitute values to verify

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Basic Inverse Operations

Operation	Inverse
Addition (+)	Subtraction (-)
Subtraction (-)	Addition (+)
Multiplication (×)	Division (÷)
Division (÷)	Multiplication (×)
Square (²)	Square root (√)
Square root (√)	Square (²)

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Worked Examples

Example 1: Simple Addition/Subtraction

Make x the subject of: y = x + 5

Solution: Subtract 5 from both sides: y - 5 = x + 5 - 5 y - 5 = x

Answer: x = y - 5

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Example 2: Multiplication/Division

Make x the subject of: y = 3x

Solution: Divide both sides by 3: y / 3 = 3x / 3 y / 3 = x

Answer: x = y / 3

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Example 3: Two-Step Operations

Make x the subject of: y = 2x + 7

Solution: Step 1: Subtract 7 from both sides: y - 7 = 2x + 7 - 7 y - 7 = 2x

Step 2: Divide both sides by 2: (y - 7) / 2 = 2x / 2 (y - 7) / 2 = x

Answer: x = (y - 7) / 2

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Example 4: With Fractions

Make x the subject of: y = (x + 3) / 4

Solution: Step 1: Multiply both sides by 4: 4y = x + 3

Step 2: Subtract 3 from both sides: 4y - 3 = x

Answer: x = 4y - 3

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Example 5: With Squares

Make x the subject of: y = x² + 5

Solution: Step 1: Subtract 5 from both sides: y - 5 = x²

Step 2: Take square root of both sides: √(y - 5) = x

Answer: x = √(y - 5) or x = ±√(y - 5)

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Common Examiner Traps

• Not applying to both sides - Always do the same operation to both sides
• Order of operations - Work in reverse BODMAS order
• Forgetting brackets - Use brackets when necessary
• Sign errors - Watch positive/negative signs carefully
• Square roots - Remember ± when taking square root

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Practice Questions

Question 1

Make x the subject of: y = 5x - 3

Solution: Add 3 to both sides: y + 3 = 5x Divide by 5: (y + 3) / 5 = x

Answer: x = (y + 3) / 5

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Frequently Asked Questions About IGCSE Changing the Subject of the Formula

What is changing the subject of a formula?

Changing the subject means rearranging a formula so a different variable becomes the subject (on its own on one side).

How do I change the subject?

Use inverse operations and apply them to both sides of the equation.

What are inverse operations?

Inverse operations reverse each other: addition/subtraction, multiplication/division, square/square root.

What order should I work in?

Work in reverse BODMAS order - undo operations from outside in.

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Related IGCSE Maths Resources

Strengthen your IGCSE Mathematics preparation with these comprehensive guides:

• IGCSE Substitution: Complete Guide - Master substitution in formulas
• IGCSE Simplifying Algebraic Expressions: Complete Guide - Master algebraic manipulation
• 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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