Edexcel A Level Maths: Pure

Revision Notes

9.1.3 Parametric Equations - Sketching Graphs

A Level Only

How do I sketch a graph from parametric equations? 

  • Plotting a graph is covered in Parametric Equations – Basics


Notes sketch_eg1, AS & A Level Maths revision notes

  • 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

Exam 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.

A Level Only

Worked Example

Example soltn, AS & A Level Maths revision notes


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