Functions and differentiation

About this lab: Functions and differentiation

Interactive simulation for Cambridge IGCSE Mathematics 0580 Extended topics 2.12 and 2.13: use function notation with function machines and mapping diagrams, find inverse functions and see them reflected in y = x, build composite functions fg(x) and gf(x), estimate the gradient of a curve as a chord closes in on a tangent, differentiate ax^n term by term with the gradient graph underneath, and find and classify stationary points.

IGCSE Mathematics 0580 Extended, topics 2.12 and 2.13. Function notation and mapping diagrams, inverse and composite functions, gradients of curves from tangents, the gradient function and stationary points.

Functions and differentiation is a free, browser-based simulation for Cambridge IGCSE Mathematics 0580 (topic 2 Algebra and graphs, sections 2.12 Differentiation (Extended), 2.13 Functions (Extended)). 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

• 2.12 Differentiation (Extended). Lessons: Differentiation: gradient functions, Stationary points.
• 2.13 Functions (Extended). Lessons: Functions: notation, inverse and composite.

Full syllabus map: IGCSE Mathematics 0580 topic 2.

How to use this simulation

1. 1. Functions.
2. 2. Inverse functions.
3. 3. Composite functions.
4. 4. Gradient of a curve.
5. 5. Gradient function.
6. 6. Stationary points.
7. 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.

All simulation labs · IGCSE Mathematics 0580 · TheLucidSTEM home