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๐Ÿ“˜ Algebra โ€ข Lesson 6 of 22

Formulae

Formulae are mathematical shortcuts that help us solve the same type of problem again and again without starting from scratch.

โœ๏ธ Algebra ๐Ÿ“˜ Worked examples included ๐Ÿง  Step-by-step learning

Learning Objectives

Introduction

This lesson develops Formulae from meaning and patterns before moving to calculations. Look for what the quantities, shapes or symbols represent, then connect that idea to the method.

Key Notes

Read the definitions and key facts below carefully. Each rule is most useful when you can explain why it fits the situation, not simply recall it.

๐ŸŽฌ A formula as an input-output machine

r = 3
โ†’
A = ฯ€rยฒ
โ†’
A = 9ฯ€

A formula connects known quantities to an unknown one.

๐Ÿค” Think About This...

Suppose one cinema ticket costs $8. If two friends go, they pay:

2 ร— 8 = 16

If five friends go, they pay:

5 ร— 8 = 40

Instead of writing a new calculation every time, we can write one rule that always works.

C = 8n

where C is the total cost and n is the number of people.

That rule is called a formula.

๐Ÿ“– What is a Formula?

A formula is a mathematical rule that shows the relationship between different quantities.

Instead of solving the same problem repeatedly, we write one formula that can be used over and over again.

Think of a formula as a recipe. If you follow the recipe correctly, you will always get the correct answer.

๐ŸŒ Formulae Around Us

๐Ÿš• Taxi Fare

Cost = Fare ร— Trips

๐Ÿž Bread

Cost = Price ร— Loaves

โšฝ Football

Total = Ticket Price ร— Number of Tickets

๐Ÿ“ฑ Mobile Data

Cost = Price ร— Bundles

๐Ÿ“ Worked Examples

Example 1

The formula for the perimeter of a square is

P = 4s

Find the perimeter when s = 6 cm.

Thinking...

P = 4 ร— 6
P = 24 cm

Example 2

The total cost of apples is

C = 3a

Find C when a = 5

C = 3 ร— 5
C = 15

Example 3

Area of a rectangle:

A = l ร— w

Find A when l = 8 and w = 5

A = 8 ร— 5
A = 40

โญ The StudyNest Shortcut

Read โ†’ Replace โ†’ Calculate
  1. Read the formula carefully.
  2. Replace every letter with its value.
  3. Calculate the answer.

โš  Common Mistakes

Students often replace the wrong letter. Always check which value belongs to which variable before calculating.

Practice Questions

  1. P = 4s Find P when s = 9
  2. C = 5n Find C when n = 7
  3. A = l ร— w Find A when l = 6 and w = 4
  4. M = 3x + 2 Find M when x = 8
โœ… Show Answers
  1. 36
  2. 35
  3. 24
  4. 26

๐Ÿง  Did You Know?

Scientists, engineers, accountants and architects all use formulae every day. Even weather forecasts and mobile apps use thousands of mathematical formulae behind the scenes.

โญ What You Can Do Now

๐ŸŽ‰ Well Done!

Formulae may look complicated at first, but they are simply rules that make solving problems quicker and easier.

Remember: A formula is just a mathematical recipe.

๐Ÿง  Let’s Think Together

Before calculating, identify the information given, the result required and the mathematical relationship that connects them. Predict whether the answer should be larger, smaller or unchanged, then use that prediction to check the result.

๐Ÿ“ˆ Your Progress

Lesson 6 of 22

Course Progress 37%

Exam Focus

Show the mathematical relationship you are using, keep notation consistent and give a clear final answer. Use a quick estimate, diagram or inverse operation to check that the result is reasonable.

Summary