Simplify: 5a + 3b − 2a + 4b.
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Practise IGCSE 0580 questions in the style of recent Extended past papers, organised by syllabus subtopic. Each set comes with an examiner-style mark scheme and a downloadable worksheet.
Everything students ask about Cambridge IGCSE 0580 Algebraic manipulation Topical Past Papers.
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These Algebraic manipulation Topical Past Paper Questions are written in the style of recent Cambridge IGCSE Mathematics 0580 Extended papers and grouped by the Algebra and graphs (E2.2) section of the 2025–2027 syllabus. Use them to revise the exact skills examiners test in this part of the course.
Each question is graded Easy → Medium → Hard, plus an A★ Challenge for top-grade preparation. Tap a question to mark your own answer, then unlock the examiner-style mark scheme with model solutions and examiner tips. A printable Topical Past Papers worksheet is included so you can practise offline.
Simplify expressions by collecting like terms, expand products of brackets, and factorise expressions (including common-factor and quadratic factorisations at Extended).
Simplify: 5a + 3b − 2a + 4b.
Expand: 3(2x − 5).
[1 mark]Expand and simplify: (x + 4)(x − 3).
[2 marks]Factorise fully: 6x² − 9x.
[2 marks]Factorise: x² − 49.
Factorise: x² + 7x + 12.
[2 marks]Hence solve x² + 7x + 12 = 0.
[1 mark]Expand and simplify: (2x − 5)².
[2 marks]Write x² + 6x + 7 in the form (x + a)² + b, where a and b are integers.
[2 marks]