Topic summary · Further maths (FP1)
Coordinate Systems summary
Further coordinate work describes curves with parametric or alternative coordinate descriptions beyond basic Cartesian graphs.
Files: FP1-Coordinate Systems.pdf · FP1-Coordinate Systems answers.pdf · free public downloads · diagrams in the PDFs
Key learning points
- Convert between forms when a sketch or Cartesian equation helps.
- Use symmetry to sketch efficiently.
- Watch the domain of any parameter.
- Differentiate parametrically when gradients are required.
Worked example 1 — Why convert?
Why seek a Cartesian equation from parametric form?
Working
If conversion is messy, sketch from the parameter instead.
Worked example 2 — Convert between forms when a sketch or Cartesian equati
Use this method from the Coordinate Systems sheet: Convert between forms when a sketch or Cartesian equation helps.
Working
Each key learning point matches a question type on the printable worksheet.
Worked example 3 — Use symmetry to sketch efficiently
Use this method from the Coordinate Systems sheet: Use symmetry to sketch efficiently.
Working
Each key learning point matches a question type on the printable worksheet.
Worked example 4 — Watch the domain of any parameter
Use this method from the Coordinate Systems sheet: Watch the domain of any parameter.
Working
Each key learning point matches a question type on the printable worksheet.
Worked example 5 — Differentiate parametrically when gradients are require
Use this method from the Coordinate Systems sheet: Differentiate parametrically when gradients are required.
Working
Each key learning point matches a question type on the printable worksheet.
Scaffolded Learning Sheet and answers (PDFs)
This page is a short, searchable overview for revision and search engines. Use the Scaffolded Learning Sheet first, then the Answers PDF for a full written solution. The printable PDFs remain the main classroom resource.