Writing formulae (Edexcel GCSE Maths): Revision Notes
Writing formulae
What are formulae?
A formula is a mathematical rule that shows the relationship between different quantities. You can write formulae in two ways:
- Word formula - using everyday language to describe the relationship
- Algebraic formula - using letters and mathematical symbols
Converting word rules into algebraic formulae is a key skill that makes calculations much easier to work with.
The ability to transform word rules into algebraic expressions is fundamental to mathematics - it allows you to work with complex relationships in a much more efficient and systematic way.
Converting word rules to algebraic formulae
When you have a rule written in words, you can turn it into an algebraic formula by following these essential steps:
- Identifying the quantities involved in the rule
- Choosing letters to represent each quantity
- Writing the mathematical relationship using these letters
- Defining what each letter means
Essential points to remember:
- Always explain what each letter represents when writing an algebraic formula
- Check your units are consistent - make sure all quantities use the same units
- Keep formulae as simple as possible - don't include unnecessary units in the algebraic version
Worked examples
Understanding how to apply these principles is best shown through practical examples that demonstrate the step-by-step conversion process.
Worked Example 1: Cooking time calculation
Word formula: Cooking time in minutes = 25 × Weight in kg + 30
Algebraic formula:
Where:
- is the cooking time in minutes
- is the weight in kg
This algebraic formula is much quicker to use than writing out the full word formula each time.
Worked Example 2: Cost calculations with mixed units
Problem: The cost of hiring a car is £80 plus 50p per mile.
Solution:
Where:
- is the cost in pounds
- is the number of miles driven
Important: Notice that 50p has been converted to £0.50 to keep all units consistent (pounds).
Worked Example 3: Perimeter of regular shapes
Problem: Find the perimeter of a regular hexagon with side length s.
Solution:
Where:
- is the perimeter
- is the length of one side
Explanation: A regular hexagon has 6 equal sides, so the perimeter equals 6 times the length of one side.
Exam tips
Success in formula questions depends on following a systematic approach and avoiding common pitfalls.
Key strategies for exam success:
- Read the question carefully to identify what quantities are involved
- Choose sensible letters for your variables (T for time, C for cost, etc.)
- Always state what each letter represents - this often gets you marks even if the formula is wrong
- Check your units - convert everything to the same units if needed
- Simplify your final formula as much as possible
Common question types
In examinations, you will encounter several standard types of formula questions that test different aspects of your understanding:
You might be asked to:
- Write a formula for the total cost when buying different items
- Create a formula for the area or perimeter of shapes
- Convert a word rule into an algebraic expression
- Complete a partially written formula
Key Points to Remember:
- Formulae show relationships between different quantities using mathematical symbols
- Word formulae can be converted to algebraic formulae by using letters to represent quantities
- Always define your variables - explain what each letter means
- Keep units consistent throughout your formula
- Algebraic formulae are more efficient than word formulae for calculations