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GCSE Maths / Edexcel

Substitution into expressions and formulae

Replace letters with values, follow the correct order of operations, and handle negative numbers accurately.

AlgebraFoundation and HigherGrades 3 to 6Skill

Curriculum path: GCSE Maths > Edexcel > Algebra > Substitution

Pearson Edexcel GCSE Maths algebra A2 and A5: substitute numerical values into expressions and formulae, and understand standard formulae.

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Revision notes

Theory, examples, and quick checks.

Keep the method short, then practise straight away. This note is written for GCSE Maths Edexcel students who need clear working and reliable method marks.

Theory

Substitution means replacing a letter with the number you have been given.

In algebra, 3x means 3 multiplied by x. If x = 5, then 3x becomes 3 * 5.

If the value is negative, put it in brackets before calculating. This is especially important with powers.

If a letter appears more than once, replace every occurrence of that letter.

After substituting, use the normal order of operations: brackets, powers, multiplication/division, then addition/subtraction.

Edexcel often gives formulae in context. Write the substituted line first so method marks are clear even if an arithmetic slip happens later.

Key ruleSubstitute first, then calculate using the order of operations.

Worked examples

One value

Find 3x + 4 when x = 5.

  1. Replace x with 5: 3(5) + 4.
  2. Calculate 15 + 4.

Answer: 19

Two values

Find 2a - 3b when a = 7 and b = 4.

  1. Replace a and b: 2(7) - 3(4).
  2. Calculate 14 - 12.

Answer: 2

Negative value

Find x² + 2x when x = -3.

  1. Replace every x with -3: (-3)² + 2(-3).
  2. Work out the power first: (-3)² = 9.
  3. Then work out 2(-3) = -6.
  4. 9 + -6 = 3.

Answer: 3

Common mistakes

  • Forgetting brackets around negative values.
  • Calculating -3² as positive when the expression actually means -(3²).
  • Substituting for only one occurrence of a repeated letter.
  • Adding before multiplying when the expression needs multiplication first.

Quick exercise

Try these before moving to the exam-style questions.

  1. Find 4x + 1 when x = 3.
  2. Find 5a - 2 when a = 6.
  3. Find 2x + 3y when x = 4 and y = 5.
  4. Find x² + 1 when x = -4.
  5. Find 3p - q when p = -2 and q = 5.
Exam-style questions

Practise the same skill at three levels.

These are original GCSE-style questions with mark schemes, common wrong answers, and AI marking guidance so feedback stays close to exam expectations.

Basic GCSE styleFoundationEither2 marks

y = 4x - 3. Find y when x = 6.

substitutionformulaefoundation algebra
Standard exam styleFoundation and HigherEither3 marks

A = 2l + 2w. Find A when l = 8 and w = 5.

substitutionperimeter formulamulti-step
ChallengeHigherEither4 marks

P = 3a² - 2b. Find P when a = -4 and b = 7.

substitutionnegative numberspowershigher