IGCSE Maths Algebra Notes
IGCSE algebra covers expressions, equations, factorising, functions and graphs. It carries a large share of marks across both papers.
Key concepts
- Expression vs equation
- An expression (3x + 2) is simplified; an equation (3x + 2 = 11) is solved.
- Factorising
- Writing an expression as a product of factors — reverse of expanding and central to IGCSE algebra.
- Function notation
- f(x) means the output of function f for input x. IGCSE also tests inverse and composite functions.
- Edexcel IGCSE Maths is sat as two calculator papers; Cambridge splits into core and extended tiers.
- The extended/higher tier includes functions, algebraic fractions and differentiation.
- Index laws underpin much of the algebra: add powers to multiply, subtract to divide.
Key formulas
Difference of two squares
a² − b² = (a + b)(a − b)
Quadratic formula
x = (−b ± √(b² − 4ac)) / 2a
Worked example
Factorise fully 2x² − 8.
- 1Take out the common factor 2: 2(x² − 4).
- 2Recognise the difference of two squares: x² − 4 = (x + 2)(x − 2).
- 3Write the full factorisation.
Answer: 2(x + 2)(x − 2)
Common mistakes
✗ Not factorising fully, e.g. stopping at 2(x² − 4).
✓ Always check whether a bracket factorises again.
✗ Confusing f(x) with f × x.
✓ f(x) is a function output, not multiplication.
✗ Sign errors when expanding double brackets.
✓ Use FOIL carefully and combine like terms.
Quick check
Try these, then reveal the answers.
Expand (x + 3)(x − 5).Reveal answer
x² − 2x − 15
Factorise x² + 7x + 12.Reveal answer
(x + 3)(x + 4)
If f(x) = 2x + 1, find f(4).Reveal answer
9
Exam tips
- 'Factorise fully' means keep going until no bracket factorises further.
- Show every line of working — method marks are awarded across both IGCSE papers.
- Check factorising by expanding back to the original expression.
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Frequently asked questions
Which boards use IGCSE Maths?+
Edexcel and Cambridge (CIE) are the main IGCSE Maths boards, taken worldwide by international and independent schools.
Is IGCSE Maths harder than GCSE?+
The content overlaps heavily, but IGCSE (extended) includes topics like functions and basic differentiation that stretch beyond some GCSE specifications.
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