A LITTLE PRACTICE, EVERY DAY·GCSE MATHS
AQA·Edexcel·OCR|Foundation + Higher
📐
Algebra · Foundation & Higher

Substitution

Substitution means replacing letters in an expression or formula with given numerical values, then calculating the result. Always follow BIDMAS.

Put your revision into practice

Choose a topic and try a short quiz with instant explanations. Free, with no signup.

Choose a free quizFind a worked example

Revising substitution the night before an exam? These are condensed revision notes — the facts, formulas and mistakes examiners actually mark, with no long explanations. Prefer a full walkthrough with step-by-step reasoning instead? Search “Substitution GCSE” on the site for the complete guide.

🔑

Key facts to remember

  • 1Replace each letter with its numerical value, in brackets if negative.
  • 2Apply BIDMAS — indices before multiplication, multiplication before addition.
  • 3Show every substitution step for method marks.
  • 42x means 2 × x, so 2x when x = 5 is 10.
  • 5x² when x = −3 means (−3)² = 9, not −9.
✍️

Worked examples

Example 1

If a = 4, b = −3, find 2a² − 5b.

Working

  1. Substitute: 2 × (4)² − 5 × (−3)
  2. Indices: 4² = 16 → 2 × 16 − 5 × (−3)
  3. Multiplications: 32 − (−15)
  4. Subtract a negative: 32 + 15 = 47
Answer47
⚠️

Common mistakes

✗Forgetting to square the negative sign.
✗Doing operations in the wrong order.
✗Writing 2x as 2 + x instead of 2 × x.
🎯

Exam tips

✓Always use brackets around negative numbers before you substitute.
✓Write the expression, then the substitution, then the answer — show every step.
✓Use your calculator carefully; place brackets around negatives.

Ready to test yourself on Substitution?

Get AI-marked practice questions on exactly this subtopic.

Practice this topic →
← All topicsDashboard

▶️ Watch on YouTube

Free video lessons

Click a topic to search

▶substitution GCSE maths▶substituting into formulae GCSE▶evaluating expressions GCSE▶plugging in values algebra GCSE

Opens YouTube — pick any free GCSE video.