Parametric Equations - Sketching Graphs (CIE A Level Maths: Pure 3)

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Parametric Equations - Sketching Graphs

How do I sketch a graph from parametric equations? 

  • Plotting a graph is covered in Parametric Equations - Basics

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  • Still find the key features of a graph …
    • … the y-axis intercept
    • … the x-axis intercept(s)
    • … asymptotes
    • … location of (and if required coordinates of) stationary points (see Parametric Differentiation)
  • Sketch these points and join up accordingly

 

Notes sketch_eg2_1, AS & A Level Maths revision notes

Notes sketch_eg2_2, AS & A Level Maths revision notes

Examiner Tip

  • Not all curves defined parametrically lead to familiar shaped graphs and it may be worth plotting a few extra points by calculating them.
  • Your calculator may be able to produce a table of values quickly, however, remember you are sketching and not plotting.
  • It may be easier to find the Cartesian equation first and draw the graph from that – this will depend on the question.
  • It is only a definite strategy if you cannot make progress otherwise.
  • If you are given the sketch of a graph it is usually only for reference and can be used to check answers for axes intercepts, etc.

Worked example

Example soltn, AS & A Level Maths revision notes

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Paul

Author: Paul

Expertise: Maths

Paul has taught mathematics for 20 years and has been an examiner for Edexcel for over a decade. GCSE, A level, pure, mechanics, statistics, discrete – if it’s in a Maths exam, Paul will know about it. Paul is a passionate fan of clear and colourful notes with fascinating diagrams – one of the many reasons he is excited to be a member of the SME team.