Revision NotesPast Papers
IGCSEMathsCambridge (CIE)International MathsExtendedRevision NotesCoordinate Geometry & GraphsSketching 2D InequalitiesFinding Inequalities from Regions

Finding Inequalities from Regions (Cambridge (CIE) IGCSE International Maths)

Revision Note

Jamie Wood

Written by: Jamie Wood

Reviewed by: Dan Finlay

Cambridge (CIE) International Maths: ExtendedEdexcel Maths A (Modular): Higher Unit 2Edexcel Maths A: HigherCambridge (CIE) Maths: Extended

Did this video help you?

Interpreting Graphical Inequalities

How do I know which inequalities are shown on a graph of shaded regions?

  • To identify the inequalities represented by the shaded regions on a graph:

    • Find the equation of each line on the graph

      • You may have to calculate the gradient and find the y-intercept to use y equals m x plus c

      • Vertical lines have the form x equals k

      • Horizontal lines have the form y equals k

    • Remember that lines are drawn using:

      • a solid line for ≤ or ≥, indicating a line included in the region

      • a dotted line for < or >, indicating a line not included in the region

    • Replace the = sign with the relevant inequality

      • ≤ or < if region is below line

      • ≥ or > if region is above line

      • (Use a point to test if not sure)

Examiner Tips and Tricks

Always read the question carefully to see if the diagram shades the wanted region or the unwanted region.

Worked Example

Write down the three inequalities which define the shaded region shown on the axes below.

A graph showing a shaded region and three inequalities.

Find the equations of the three lines shown (ignoring inequality signs for now)

You may be able to see the lines x equals 1 and y equals x
The other line has the form y equals m x plus c with y-intercept 7 and gradient -1

A graph showing a shaded region with three inequalities and a highlighted point within the shaded region.

Now decide which inequality signs to use

For y equals x, the shaded region is above the line, and the line is dotted, so the inequality is

y greater than x

If unsure, check by substituting in coordinates from the shaded region
For example, using (2, 4) as marked on the graph above

"4 greater than 2" is true, so the inequality y greater than x is correct

For y equals negative x plus 7, the shaded region is below the line, and the line is solid, so the inequality is 

y less or equal than negative x plus 7

Again, check by substituting (2, 4) into the inequality

"4 less or equal than negative 2 plus 7" is true, so the inequality y less or equal than negative x plus 7 is correct

For x equals 1, the shaded region is to the right of the solid line so the inequality is

x greater or equal than 1

Write all three inequalities together as your final answer

y greater than x, y less or equal than negative x plus 7 and x greater or equal than 1

Last updated:

You've read 0 of your 5 free revision notes this week

Sign up now. It’s free!

Join the 100,000+ Students that ❤️ Save My Exams

the (exam) results speak for themselves:

    Did this page help you?

    Previous:Representing Inequalities as RegionsNext:Translations of Graphs
    Author
    Reviewer
    Jamie Wood

    Author: Jamie Wood

    Expertise: Maths

    Jamie graduated in 2014 from the University of Bristol with a degree in Electronic and Communications Engineering. He has worked as a teacher for 8 years, in secondary schools and in further education; teaching GCSE and A Level. He is passionate about helping students fulfil their potential through easy-to-use resources and high-quality questions and solutions.

    Dan Finlay

    Author: Dan Finlay

    Expertise: Maths Lead

    Dan graduated from the University of Oxford with a First class degree in mathematics. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. Dan has a keen interest in statistics and probability and their real-life applications.