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Inequalities on Graphs (Edexcel AS Maths: Pure)
Revision Note
Inequalities on Graphs
Inequalities on graphs
- Inequalities can be represented on graphs by shaded regions and dotted or solid lines
- 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
- Choose a coordinate on each side and test it in the inequality
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 …
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- … write clearly you have “shaded the unwanted area”
- As long as your final answer is clear you should get the marks!
Worked example
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