EST. 2024 · LONDON·MMXXVI SPECIFICATION
AQA·Edexcel·OCR|Foundation + Higher
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Algebra · Foundation & Higher

Substitution

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

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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.
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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
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Common mistakes

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

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