GCSE MATHS • ALGEBRA
GCSE Substitution Made Simple
Learn how to substitute values into algebraic expressions and formulae, work confidently with powers and negative numbers, and avoid common GCSE exam mistakes.
Clear method
Exam practice
Worked proofs
Substitution in Four Steps
1
Write
Write down the expression or formula clearly.
2
Replace
Replace each variable with the numerical value you have been given.
3
Apply BIDMAS
Follow the correct order of operations after substituting the values.
4
Calculate
Complete the calculation carefully and write the final answer.
What You’ll Learn
Understand Substitution
Learn what substitution means and how letters in algebra can be replaced by numerical values.
Substitute into Expressions
Replace one or more variables correctly before evaluating an expression.
Work with Powers
Understand how squares and other powers affect substituted values.
Use Negative Numbers
Learn why brackets are particularly important when substituting negative numbers.
Apply BIDMAS
Use the correct order of operations after substitution.
Substitute into Formula
Use given values in mathematical and real-life formulae.
Key Rules for Substitution
Replace Every Variable
Use Brackets
Powers Come Before Multiplication
Follow BIDMAS
Worked Proof: Substituting into an Expression
1. Write
3x + 2y
2. Substitute
3(4) + 2(5)
3. Calculate
12 + 10 = 22
More Worked Examples
1
One Variable
Evaluate 5x
Substitute: 5 × 3
Calculate: = 15
2
Variable and Constant
Evaluate 2a + 4
Substitute: 2(6) + 4
Calculate: = 12 + 4 = 16
3
Two Variables
Evaluate 3x + 2y
Substitute: 3(4) + 2(5)
Calculate: = 12 + 10 = 22
4
Substitution with Powers
Evaluate x² + 3
Substitute: 5² + 3
Calculate: = 25 + 3 = 28
5
Powers and Two Variables
Evaluate 2a² − b
Substitute: 2(3²) − 4
Calculate: = 2(9) − 4 = 18 − 4 = 14
6
Variable and Squared Variable
Evaluate 4x − y²
Substitute: 4(7) − 2²
Calculate: 28 − 4 = 24
- Common GCSE Mistakes
- Forgetting to Replace Every Variable
- Ignoring Powers
- Incorrect Use of Negative Numbers
- Not Following BIDMAS
- Calculator Input Errors
- Exam Tips
- Write substituted values clearly.
- Use brackets when substituting values.
- Be particularly careful with negative numbers.
- Check powers before completing multiplication or addition.
- Use BIDMAS after substitution.
- Show your working rather than trying to calculate everything mentally.
- Check that every variable has been replaced.
- Practise expressions containing more than one variable.
Skills Used in Substitution
Ready to Practise?
Printable Worksheet
Use a printable worksheet to practise the substitution method independently.
Interactive Quiz
Work through substitution questions involving one variable, several variables, powers and negative numbers.
Exam-Style Questions
Apply substitution in questions similar to those found in GCSE examinations.
Watch the Substitution Tutorial
Follow a step-by-step explanation of substitution, including expressions, powers, negative numbers and formula questions.
Frequently Asked Questions
Substitution means replacing a letter or variable with a given numerical value and then calculating the resulting expression.
Write the expression, replace the variables with their values, apply BIDMAS where necessary, and calculate the final answer.
Brackets make it clear that the entire negative number is being substituted. This is especially important when powers are involved. For example: (−3)² = 9.
Yes. Once values have been substituted, the expression should be calculated using the normal BIDMAS order.
Yes. Each variable should be replaced with its corresponding numerical value before the expression is calculated.
Yes. Many GCSE questions require values to be substituted into formulae before the answer can be calculated.
