Writing formulae (AQA 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:
- As a word formula using everyday language
- As an algebraic formula using letters and mathematical symbols
Understanding how to convert between these two forms is essential for solving real-world problems in mathematics.
Converting word rules to algebraic formulae
When you have a rule written in words, you can transform it into an algebraic formula by following a systematic approach:
Process for Converting Word Rules to Algebra:
Step 1: Identify the quantities involved Look for the different measurements or values mentioned in the problem.
Step 2: Choose letters to represent each quantity Pick appropriate letters that make sense (often the first letter of the quantity name).
Step 3: Write the mathematical relationship Use mathematical operations (+, -, ×, ÷) to show how the quantities relate to each other.
Step 4: Define your variables Always state clearly what each letter represents, including units.
Key principles for writing formulae
Always include units
When describing quantities in a formula, you must specify the units being used. This prevents confusion and ensures accurate calculations.
For example: "T is the cooking time in minutes" rather than just "T is the cooking time"
Define each letter clearly Every letter in your formula must be explained. State exactly what it represents and include the appropriate units.
Simplify where possible
Make your formula as simple as possible by combining like terms and removing unnecessary complexity.
For example: write 25a instead of 25 × a, and avoid including units like "pence" directly in the algebraic expression.
Worked examples
Worked Example 1: Cooking time formula
Problem: The cooking time for chicken is 25 minutes per kilogramme plus an extra 30 minutes.
Word formula: Cooking time in minutes = 25 × weight in kg + 30
Algebraic formula:
Where: T is the cooking time in minutes and w is the weight in kg
Worked Example 2: Cost calculation
Problem: Chloe buys pens costing 25 pence each and pencils costing 15 pence each.
Algebraic formula:
Where: T is the total cost in pence, a is the number of pens, and b is the number of pencils
Important note: The coefficient 25a means 25 × a, which should be simplified rather than written as 25 × a in the final formula.
Worked Example 3: Car hire costs
Problem: Car hire costs £80 plus 50p per mile driven.
Algebraic formula:
Where: C is the cost in pounds and m is the number of miles driven
Key point: Notice that 50p has been converted to £0.50 to keep all values in the same units (pounds).
Worked Example 4: Perimeter of regular shapes
Problem: Find the perimeter of a regular hexagon.
Since a regular hexagon has 6 equal sides, the perimeter equals 6 times the length of one side.
Algebraic formula:
Where: P is the perimeter and s is the length of one side
Common mistakes to avoid:
- Mixing units: Ensure all quantities use the same units throughout your formula
- Forgetting to define letters: Always explain what each letter represents
- Not simplifying: Combine like terms and write expressions in their simplest form
- Including units in the algebra: Keep units in your definitions, not in the algebraic expression itself
Exam tips
Key Exam Strategies:
- Read the question carefully to identify all quantities involved
- Choose sensible letters that relate to the quantities (T for time, C for cost, etc.)
- Always write what each letter means, including units
- Check your formula makes mathematical sense
- Verify your answer by substituting simple values
Key Points to Remember:
- Formulae show relationships between different quantities using mathematical expressions
- Always define your variables clearly, stating what each letter represents and its units
- Keep units consistent throughout your calculations - convert if necessary
- Simplify expressions where possible to make them easier to work with
- Practice converting between word formulae and algebraic formulae to build confidence