IGCSE Algebra
The single biggest topic area in both IGCSE maths syllabi. Here is exactly what is examined, with a worked example and the mistakes that lose marks.
What the syllabus expects
Cambridge 0580 / 0980
Listed as one of the eight main content areas under Algebra. . Core covers straight-line work, simple equations and sequences; Extended adds quadratics, algebraic fractions, matrices of transformation and fuller graph work.
Edexcel 4MA1
Split across Equations, formulae and identities and Sequences, functions and graphs. Foundation covers linear and quadratic simultaneous equations, while Higher extends into the full range of targeted grades 4 to 9.
- ✓Simplify expressions, expand brackets and factorise
- ✓Solve linear equations, including those with brackets and fractions
- ✓Form equations from a worded or geometric problem
- ✓Simultaneous equations (linear; quadratics on Extended/Higher)
- ✓Inequalities and simple algebraic proof
- ✓Sequences: nth term, arithmetic and geometric patterns
- ✓Straight-line graphs: gradient, intercept, y = mx + c
- ✓Curves: parabolas, reflections and translations (Extended/Higher)
Worked example: solve and verify
A typical 3-4 mark structured question. Method marks matter as much as the final answer.
Solve 3(2x − 5) = 4x + 7
Step 1. Expand the left side: 6x − 15 = 4x + 7
Step 2. Collect x terms on one side: 6x − 4x = 7 + 15 → 2x = 22
Step 3. Divide: x = 11
Check. Substitute back: 3(22 − 5) = 3 × 17 = 51, and 4(11) + 7 = 51 ✓
Factorise fully: x² + 5x + 6
Two numbers that multiply to 6 and add to 5 are 2 and 3, so x² + 5x + 6 = (x + 2)(x + 3).
Extended and Higher papers expect you to then solve (x + 2)(x + 3) = 0, giving x = −2 or x = −3 from the equals-zero rule.
Exam technique
- 1.On the Cambridge non-calculator paper, practise collecting terms and fraction arithmetic mentally before relying on working.
- 2.Keep every step on a new line. Structured questions award method marks even when arithmetic slips later.
- 3.Later parts often reuse your answer from an earlier part. Writing x = 11 clearly makes that possible.
- 4.Sketch the graph before calculating. Identifying intercept and gradient visually catches sign errors early.
More IGCSE guides
IGCSE Geometry →
Shapes, mensuration, transformations and vectors, from Core basics to Extended proofs
IGCSE Trigonometry →
Trig ratios, bearings, 3D problems and the sine and cosine rules on Higher/Extended papers
IGCSE Statistics & Probability →
Averages, charts, cumulative frequency, histograms and probability, including set notation
IGCSE Maths Revision Plan →
A term-by-term revision timetable that adapts to Core, Extended, Foundation or Higher entry
IGCSE Past Papers →
Where to find official past papers and how to turn them into a marking-backed study loop
IGCSE Grade Boundaries →
How raw marks become grades, why boundaries move each series, and how to read official documents
IGCSE vs O-Level →
Recognition, syllabus and entry differences between IGCSE and GCE O-Levels
IGCSE Math Tuition →
What to evaluate in an IGCSE maths tutor, and how adaptive practice compares
← Back to the IGCSE Math hub
Syllabus comparison, tier decisions and grade guides in one place
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