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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

to recognise standard curves/asymptotes\text{to recognise standard curves/asymptotes}

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

Attempt a matching question on the sheet, then check the Answers PDF.\text{Attempt a matching question on the sheet, then check the Answers PDF.}

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

Attempt a matching question on the sheet, then check the Answers PDF.\text{Attempt a matching question on the sheet, then check the Answers PDF.}

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

Attempt a matching question on the sheet, then check the Answers PDF.\text{Attempt a matching question on the sheet, then check the Answers PDF.}

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

Attempt a matching question on the sheet, then check the Answers PDF.\text{Attempt a matching question on the sheet, then check the Answers PDF.}

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.

Coordinate Systems summary — worksheet & answers PDF