GCSE: Inequalities – Shading Regions Dr J Frost
Description: GCSE: Inequalities Shading Regions Dr J Frost (jfrosttiffin.kingston.sch.uk) www.drfrostmaths.com Last modified: 31st August 2015 Associated Resources: GCSE-InequalitiesRegionsWorksheet.docx Means: x is less than or equal to 4. x 3
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slide1. GCSE: Inequalities – Shading Regions Dr J Frost (jfrost@tiffin.kingston.sch.uk)
www.drfrostmaths.com Last modified: 31st August 2015 Associated Resources: GCSE-InequalitiesRegionsWorksheet.docx ~ }<br>
slide2. Means: x is less than or equal to 4. x > 3 Means: x is (strictly) greater than 3. ? ? x < -1 Means: x is (strictly) less than -1. ? ? x ≥ 4 Means: x is greater than or equal to 4. ? ? x ≤ 5 ? ?<br>
slide3. ? ? ? ? (On your worksheet)<br>
slide4. Think: How are the values of x constrained, and how are the values of y constrained?<br>
slide5. -4 < y ≤ -2<br>
slide6. 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.<br>
slide7. Is the region on the correct side of the line? y > x + 2 2  ï€ ïƒ» Win Fail y > 1 - x 1  ï€ ïƒ» Win Fail y – x > 1 1  ï€ ïƒ» Win Fail x + y > 1 1  ï€ ïƒ» Win Fail x > 2y - 3 1.5 y > -x  ï€ ïƒ» Win Fail  ï€ ïƒ» Win Fail<br>
slide8. y ≤ x + 1 and x ≤ 6 and y > 2 Bro Tip: In GCSE exam questions, the region you want is almost always the region enclosed by your 3 lines.<br>
slide9. Worksheet Answers     Click to Sketch ><br>
slide10. Worksheet Answers    Click to Sketch ><br>
slide11. Worksheet Answers ? Click to Sketch > R<br>
slide12. Worksheet Answers       Click to Sketch ><br>
slide13. Worksheet Answers 3 2     Click to Sketch > ? ?<br>
slide14. Worksheet Answers R 1 1 Click to Sketch > ? ? ?<br>
www.drfrostmaths.com Last modified: 31st August 2015 Associated Resources: GCSE-InequalitiesRegionsWorksheet.docx ~ }<br>
slide2. Means: x is less than or equal to 4. x > 3 Means: x is (strictly) greater than 3. ? ? x < -1 Means: x is (strictly) less than -1. ? ? x ≥ 4 Means: x is greater than or equal to 4. ? ? x ≤ 5 ? ?<br>
slide3. ? ? ? ? (On your worksheet)<br>
slide4. Think: How are the values of x constrained, and how are the values of y constrained?<br>
slide5. -4 < y ≤ -2<br>
slide6. 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.<br>
slide7. Is the region on the correct side of the line? y > x + 2 2  ï€ ïƒ» Win Fail y > 1 - x 1  ï€ ïƒ» Win Fail y – x > 1 1  ï€ ïƒ» Win Fail x + y > 1 1  ï€ ïƒ» Win Fail x > 2y - 3 1.5 y > -x  ï€ ïƒ» Win Fail  ï€ ïƒ» Win Fail<br>
slide8. y ≤ x + 1 and x ≤ 6 and y > 2 Bro Tip: In GCSE exam questions, the region you want is almost always the region enclosed by your 3 lines.<br>
slide9. Worksheet Answers     Click to Sketch ><br>
slide10. Worksheet Answers    Click to Sketch ><br>
slide11. Worksheet Answers ? Click to Sketch > R<br>
slide12. Worksheet Answers       Click to Sketch ><br>
slide13. Worksheet Answers 3 2     Click to Sketch > ? ?<br>
slide14. Worksheet Answers R 1 1 Click to Sketch > ? ? ?<br>