GCSE-InequalityRegions.pptxxxxxxxxxxxxxx

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1. GCSE: Inequalities – Shading Regions Dr J Frost ([email protected] ) www.drfrostmaths.com Last modified: 31 st August 2015 Associated Resources: GCSE-InequalitiesRegionsWorksheet.docx ~ }

2. Means: x is less than or equal to 4. x > 3 Means: x is (strictly) greater than 3. 0 1 2 3 4 5 ? This is known as a ‘strict’ inequality. ? x < -1 Means: x is (strictly) less than -1. -3 -2 -1 0 1 2 ? ? x ≥ 4 Means: x is greater than or equal to 4. 2 3 4 5 6 7 ? ? x ≤ 5 2 3 4 5 6 7 ? ? RECAP : Inequalities on a Number Line

3. STARTER : Solving Inequalities         ? ? ? ? (On your worksheet)

4. -10 -8 -6 -4 -2 2 4 6 8 10 8 6 4 2 -2 -4 -6 Sketch the region representing   Think: How are the values of x constrained, and how are the values of y constrained? can be any number greater than 2, but can be ANY value because it is not constrained.   The dotted line indicates that can’t be 2.  

5. -10 -8 -6 -4 -2 2 4 6 8 10 8 6 4 2 -2 -4 -6 -4 < y ≤ - 2

6. -10 -8 -6 -4 -2 2 4 6 8 10 8 6 4 2 -2 -4 -6 y ≥ x How can we tell which way round the inequality is? Just try a point on one side, e.g. (0, 4). Is y ≥ x? Yes, so we’re on the right side.

7. Quickfire Regions Is the region on the correct side of the line? y > x + 2 2    Win Fail y > 1 - x 1    Win Fail y – x > 1 1    Win Fail x + y > 1 1    Win Fail x > 2y - 3 1.5 y > -x    Win Fail Bro Tip : An easier way to see if the region is on the correct side is to see whether is on the smaller side of the inequality or the greater side. If the greater, we’re above.      Win Fail

8. -10 -8 -6 -4 -2 2 4 6 8 10 8 6 4 2 -2 -4 -6 y ≤ x + 1 and x ≤ 6 and y > 2 Combining Inequalities Bro Tip : In GCSE exam questions, the region you want is almost always the region enclosed by your 3 lines.

9. Question 4 Worksheet Answers     Click to Sketch >

10. Question 5 Worksheet Answers    Click to Sketch >

11. Question 6 Worksheet Answers   ? Click to Sketch > R

12. Question 7 Worksheet Answers       Click to Sketch >

13. Question 8 Worksheet Answers 3 2     Click to Sketch > ? ?

14. Question 9 Worksheet Answers     R 1 1 Click to Sketch > ? ? ?