Inequalities on Graphs (CIE A Level Maths: Pure 1)

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Inequalities on Graphs

Inequalities on graphs

  • Inequalities can be represented on graphs by shaded regions and dotted or solid lines

2.4.3 Inequalities on Graphs Notes Diagram 1, Edexcel A Level Maths: Pure revision notes

  • These inequalities have two variables, x and y
  • Several inequalities are used at once
  • The solution is an area on a graph (often called a region)
  • The inequalities can be linear or quadratic

How do I draw inequalities on a graph?

  • Sketch each graph
    • If the inequality is strict (< or >) then use a dotted line
    • If the inequality is weak (≤ or ≥) then use a solid line
  • Decide which side of the line satisfies the inequality
    • Choose a coordinate on each side and test it in the inequality
      • The origin is an easy point to use
    • If it satisfies the inequality then that whole side of the line satisfies the inequality
      • For example: (0,0) satisfies the inequality y < x2 + 1 so you want the side of the curve that contains the origin

2.4.3 Inequalities on Graphs Notes Diagram 2, Edexcel A Level Maths: Pure revision notes

Examiner Tip

  • Recognise this type of inequality by the use of two variables
  • You may have to deduce the inequalities from a given graph
  • Pay careful attention to which region you are asked to shade
  • Sometimes the exam could ask you to shade the region that satisfies the inequalities this means you should shade the region that is wanted.
    • If you're unsure, you could …
    • … draw the (dotted and/or solid) lines in on the answer diagram and use a rough sketch to find the region required …

   … and/or …

    • … write clearly you have “shaded the unwanted area”
  • As long as your final answer is clear you should get the marks!

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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.