Algebraic manipulation · IGCSE Mathematics 0580 Simulation

About this lab: Algebraic manipulation

Interactive simulation for Cambridge IGCSE Mathematics 0580 topics 2.1 to 2.4: substitute values into formulas, watch like terms slide together, expand brackets with the grid method and an area model, factorise common factors, quadratics, differences of two squares and by grouping step by step, complete the square with algebra tiles, see the laws of indices including zero, negative and fractional powers, and simplify algebraic fractions.

IGCSE Mathematics 0580, topics 2.1 to 2.4. Substitution, collecting like terms, expanding and factorising, completing the square, the laws of indices and algebraic fractions.

Algebraic manipulation is a free, browser-based simulation for Cambridge IGCSE Mathematics 0580 (topic 2 Algebra and graphs, sections 2.1 Introduction to algebra, 2.2 Algebraic manipulation, 2.3 Algebraic fractions (Extended) and more). The course is assessed in Paper 1 (Core non-calculator), Paper 2 (Extended non-calculator), Paper 3 (Core calculator), Paper 4 (Extended calculator). Syllabus for examination in 2025-2027. There are 6 tabs, each a self-contained experiment with its own controls and live readings, and nothing to install: it runs on a laptop, tablet or classroom projector.

Syllabus coverage

2.1 Introduction to algebra. Lessons: Algebraic notation and substitution.
2.2 Algebraic manipulation. Lessons: Expanding brackets and simplifying, Factorising expressions, Completing the square.
2.3 Algebraic fractions (Extended). Lessons: Algebraic fractions.
2.4 Indices II. Lessons: Indices II: algebraic and fractional indices.

Full syllabus map: IGCSE Mathematics 0580 topic 2.

How to use this simulation

1. Substitute and simplify.
2. Expanding.
3. Factorising.
4. Completing the square.
5. Indices.
6. Algebraic fractions.
The buttons at the end of the tab strip give the scene the whole window (Full screen, Hide controls) and, on a dark stage, a projector-friendly palette (Light scene). Many scenes also have drag handles: drag them to change the set-up directly.

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