GCSE Maths • Foundation & Higher
GCSE Formulas Revision Guide
Substitute values accurately, rearrange formulae and solve problems using inverse operations.
Foundation
Exam practice
Worked examples
What You'll Learn
Understand Formulae
Recognise that letters represent quantities and identify the subject of a formula.
Substitute Values
Replace variables with given numerical values and calculate the result accurately.
Use Negative Numbers
Use brackets when substituting negative values to avoid sign errors.
Follow the Correct Order
Apply the correct order of operations after values have been substituted.
Change the Subject
Rearrange a formula so that a required variable is isolated on one side.
Use Inverse Operations
Undo addition, subtraction, multiplication, division, powers and roots while keeping the formula balanced.
Key Rules and Formulas
Ratio Lessons
Substitution into Formulae
Replace variables with numbers, use brackets for negative values and calculate using the correct order of operations.
Changing the Subject of a Formula
Rearrange formulae using inverse operations so that the required variable is isolated.
CORE SUBTOPICS
Simple Substitution
Substitute positive values into formulae and calculate the result.
Negative Number Substitution
Put negative values in brackets before applying powers or other operations.
Substitution with Powers
Substitute first, then apply squares or other powers correctly.
Substitution with Several Variables
Replace every variable with its stated value before calculating.
Simple Rearrangement
Use inverse operations to remove additions, subtractions, multiplications and divisions.
Fractions and Powers in Formulae
Remove denominators carefully and use roots when the required variable is raised to a power.
Worked Example
Substituting into a Formula
QUESTION 1.
Find the value of y when y = x² + 2x and x = 6.
- Given information: The formula is y = x² + 2x and x = 6.
- Method: Replace x with 6, then follow the correct order of operations.
- Substitute x = 6: y = 6² + 2(6).
- Work out the square: 6² = 36.
- Multiply: 2 × 6 = 12.
- Add: 36 + 12 = 48.
- Answer: y = 48.
- Key idea: Substitute the value first and complete powers before addition.
- Common mistake: Do not calculate 6 + 2 first. Follow the correct order of operations.
Changing the Subject of a Formula
QUESTION 2.
Make x the subject of y = 2x + 5.
- Given information: x must be isolated on one side of the formula.
- Method: Undo the operations in reverse order using inverse operations.
- Subtract 5 from both sides: y − 5 = 2x.
- Divide both sides by 2: x = (y − 5) / 2.
- Answer: x = (y − 5) / 2.
- Key idea: Keep the formula balanced by applying the same operation to both sides.
- Common mistake: Do not move a term across the equals sign without applying the correct inverse operation.
- Common GCSE Mistakes
- Forgetting brackets around negative numbers.
- Substituting the wrong value for a variable.
- Ignoring the correct order of operations.
- Changing only one side when rearranging.
- Using the wrong inverse operation.
- Exam Tips
- Write the formula before substituting values.
- Use brackets around negative numbers.
- Show each rearrangement step clearly.
- Keep both sides of the formula balanced.
- Check that the required variable is fully isolated.
Ready to Practice?
Printable Worksheet
Practise simplifying, unit conversions, sharing totals, recipe scaling, combined ratios and best-buy comparisons.
Interactive Quiz
Check ratio order, equivalent ratios, total parts, unit prices and common misconceptions.
Exam-Style Questions
Apply ratio methods to money, measures, recipes, maps and multi-stage GCSE contexts.
Watch the Formulas Tutorial
Clear, step-by-step explanation of expanding brackets, simplifying complex expressions, and solving for x. Perfect for visual learners who need a breakdown of the rules in action.
- 12 minute comprehensive guide
- High-definition whiteboard walk-through
Continue Your GCSE Maths Revision
Continue Your GCSE Maths Revision
Frequently Asked Questions
Substitution means replacing a variable with a given numerical value and then calculating the result.
Brackets keep the negative value together and help prevent sign errors, especially when powers are involved.
Use inverse operations to undo the operations around the required variable, applying the same operation to both sides.
It is often helpful to multiply both sides by the denominator first, then continue rearranging.
