Forming & Solving Equations

Revise Forming & Solving Equations for Mathematics 0580 (O Level) — revision notes and instant AI marking.

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1. Translating Words into Expressions

What's an Expression?

Expression:

A mathematical phrase made up of variables, numbers, and operations — but NO equals sign. Think of it as an incomplete sentence that describes something mathematically. For example, 2x + 5 is an expression. You can't solve an expression; you can only simplify it.

To form expressions from words, you need to recognize common phrases that signal mathematical operations.

Common Word-to-Math Translations

Phrase	Expression	Operation
2 less than something	x − 2	Subtraction
Double something	2x	Multiplication
5 lots of something	5x	Multiplication
3 more than something	x + 3	Addition
Half of something	x/2 or ½x	Division
Triple something	3x	Multiplication

Key Operation Words:

Addition: sum, total, more than, increase, and

Subtraction: difference, less than, decrease, take away

Multiplication: product, lots of, times as many, double, triple

Division: shared, split, grouped, halved, quartered

Why Brackets Matter: Order of Operations

The order in which you do operations completely changes the expression. Brackets force operations to happen in the right order.

Scenario 1: "Add 1 to something, then multiply by 3"
Expression: (x + 1) × 3 or 3(x + 1)

If x = 5: (5 + 1) × 3 = 6 × 3 = 18 ✓

Scenario 2: "Multiply something by 3, then add 1"
Expression: 3x + 1

If x = 5: (5 × 3) + 1 = 15 + 1 = 16 ✗ (different answer!)

💡 Top Tip: Always read the phrase in order and use brackets whenever "something" needs multiple operations applied before moving on.

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Also in the full note

2. Forming Equations
3. Forming Equations from Shapes & Geometry
4. Problem Solving with Equations
5. Common Mistakes & How to Avoid Them
Summary: The Big Picture
Concepts Checklist
What to Memorize
Exam Tips & Tricks

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Forming & Solving Equations