This resource provides the foundation for a complete investigation incorporating, pseudo-coding, parametric and cartesian equations (relations), differential calculus including implicit and chain rule, proof and much more.
The purpose of this resource is to provide a platform from which a full investigation applicable to Year 12 Specialist Mathematics can be built. The resource combines multiple areas of the Specialist course and has loads of room for independent student exploration and investigation.
- Parametric Equation(s)
- Cartesian Equation (relation)
- Implicit Differentiation
- Chain Rule
About the Lesson
This resource provides the foundations for a complete investigation for Year 12 Specialist Mathematics. Students write some simple code that incorporates basic transformations and the unit circle, the result is a spectacular series of lines that form an envelope. The shape of the envelope can be defined nicely by parametric equations, which can then be converted into a cartesian equation (relation). Calculus is then used to explore key features of the graph with a delightful comparision between implicit differentiation for the cartesian equation and the chain rule for the parametric equations. Different members of the epicycloids can be generated from the original program and analysed accordingly. Alternatively the investigation can take a different twist to explore hypocycloids.