Formulae (Edexcel GCSE Maths): Revision Notes
Formulae
What is a formula?
A formula is a mathematical rule that shows the relationship between different quantities. The plural of formula is formulae. Formulae use letters (called variables) to represent unknown values or measurements.
Formulae help you calculate one quantity when you know the values of the others. They are used in many areas of maths and science, from working out areas of shapes to solving physics problems.
Formulae are like recipes in cooking - they give you a step-by-step method to find what you're looking for, as long as you have the right ingredients (known values)!
Basic structure of formulae
Most formulae follow a pattern where one variable equals an expression involving other variables. For example:
- (area of a triangle)
- Letters represent different measurements or values
- The equals sign shows what you're calculating
Substituting values into formulae
Substitution means replacing the letters in a formula with actual numbers. This is how you use a formula to find an answer.
Key steps for substitution:
- Write out the formula first
- Substitute the known values for the letters
- Calculate using the correct order of operations
Important: Use BIDMAS for calculations
When working with formulae, always follow BIDMAS for the correct order of operations:
- Brackets first
- Indices (powers) next
- Division and Multiplication (left to right)
- Addition and Subtraction (left to right)
Remember: Multiply before you Add!
Worked example: Triangle area
The formula for the area of a triangle is: Area = ½ × base × height or
This formula lets you find the area when you know the base and height measurements.
Worked Example: Finding Triangle Area
Using the formula :
- If base = 8 cm and height = 6 cm
- Substitute:
- Calculate: cm²
Worked example: Cooking time calculation
A formula for cooking turkey is: Cooking time = Weight in kg × 30 + 45
Worked Example: Turkey Cooking Time
Problem: Find the cooking time for a 7kg turkey.
Solution:
- Substitute: Cooking time = 7 × 30 + 45
- Follow BIDMAS (multiply first): = 210 + 45
- Add: = 255 minutes
Converting units: 255 minutes can be written as 4 hours and 15 minutes (since 4 × 60 = 240, so 255 - 240 = 15 minutes remaining)
Worked example: Physics formula
Worked Example: Physics Motion Formula
Formula: Given: , Find: The value of D
Solution:
- Substitute:
- Calculate indices first:
- Multiply: and
- Subtract:
Exam tips
Essential Exam Strategies:
- Always substitute values before doing any calculations
- Show each step clearly in your working
- Don't try to do multiple operations on one line - this reduces errors
- Check if your answer needs converting to different units
- When answers are larger than 60 minutes, consider giving them in hours and minutes
Key Points to Remember:
- A formula is a mathematical rule using letters to represent quantities
- Always substitute values first, then calculate step by step
- Use BIDMAS to ensure the correct order of operations - multiply before you add
- Show your working clearly to avoid mistakes and gain method marks
- Convert units appropriately when giving your final answer