GCSE MATHS • HIGHER TIER
Substitution into Formulae Made Simple
Learn how to replace variables with values, handle negative numbers correctly, follow the order of operations, and evaluate GCSE formulae accurately.
Clear method
Exam practice
Worked proofs
Substitution into Formulae in Four Moves
1
Write
Write down the formula clearly.
2
Substitute
Replace every variable with its given value.
3
Calculate
Use brackets where needed and follow the correct order of operations.
4
Check
Make sure every letter was replaced correctly and record the final answer.
What You’ll Learn
Understand Substitution
Know what it means to replace variables with numerical values.
Substitute Accurately
Replace each letter with the correct given number.
Handle Negative Numbers
Use brackets around negative values to avoid sign errors.
Use the Correct Order
Apply BIDMAS when evaluating the substituted expression.
Apply Formulae
Use substitution in area, volume, science and other real-world calculations.
Key Rules
What Is Substitution?
Substitution means replacing variables (letters) with numbers. Once the numbers have been substituted into the formula, the calculation can be completed using the correct order of operations. GCSE questions often require students to substitute positive numbers, negative numbers, fractions and decimals.
Why Is Substitution Important?
Many mathematical and scientific formulas use letters to represent values. Substitution allows us to use these formulas to solve specific problems. Examples include formulas for area, speed, density and interest calculations.
Worked Proof: Substitution into Formulae
Step-by-Step Method
- 1. Write down the formula.
- 2. Identify the values of each variable.
- 3. Replace each letter with its value.
- 4. Use brackets around negative numbers.
- 5. Follow the correct order of operations.
- 6. Write the final answer clearly.
More Worked Examples
1
Question: Find the value of y when y = 3x + 4 and x = 5.
Substitute x = 5.
y = 3(5) + 4
y = 15 + 4
Add
y = 19
y = 15 + 4
Add
y = 19
2
Question: Find the value of y when y = 2a - 7 and a = 8.
Substitute a = 8.
y = 2(8) - 7
= 16 - 7
= 9
= 16 - 7
= 9
3
Question: Find the value of y when y = x² + 3 and x = 4.
Substitute x = 4.
y = 4² + 3
= 16 + 3
= 19
Answer: 19.
= 16 + 3
= 19
Answer: 19.
4
Question: Find the value of y when y = x² + 2x and x = 6.
Substitute x = 6.
y = 6² + 2(6)
= 36 + 12
= 48
= 36 + 12
= 48
- Common GCSE Mistakes
- Negative numbers: Always put substituted negative values in brackets.
- Wrong values: Check that each number replaces the correct variable.
- Powers: Apply powers before addition or subtraction.
- Order of operations: Follow BIDMAS carefully.
- Calculator errors: Enter fractions and decimals accurately.
- Exam Tips
- Write the formula first: This keeps your substitution organised.
- Use brackets for negatives: It prevents sign mistakes.
- Replace every letter: Check no variable has been missed.
- Follow BIDMAS: Calculate in the correct order.
- Show your substitution: Clear working can earn method marks.
Skills Used in Substitution into Formulae
Algebra
Formulae
Rearranging Formulae
Equations
Negative Numbers
Area
Volume
Graphs
Ready to Practise?
Printable Worksheet
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Interactive Quiz
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Exam-Style Questions
Timed questions to build confidence for the real exam.
Watch the Substitution into Formulae Tutorial
Step-by-step walkthroughs of Substitution into Formulea with clear methods and exam tips.
Frequently Asked Questions
Substitution means replacing variables in a formula with given numerical values.
Brackets make the negative value part of the substitution and help prevent sign errors.
Use the correct order of operations, usually remembered as BIDMAS.
Yes. GCSE questions can involve positive numbers, negative numbers, fractions and decimals.
Replace the variable first, use brackets if needed, then apply the square before other operations.
It is used in geometry, science, engineering, finance, business and many other formula-based calculations.
