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GCSE: Inequalities – Shading Regions
Associated Resources: GCSE-InequalitiesRegionsWorksheet.docx GCSE: Inequalities – Shading Regions Dr J Frost } ~ Last modified: 31st August 2015
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RECAP: Inequalities on a Number Line
This is known as a ‘strict’ inequality. x > 3 x < -1 Means: x is (strictly) greater than 3. ? Means: x is (strictly) less than -1. ? ? ? x ≥ 4 x ≤ 5 Means: x is greater than or equal to 4. ? Means: x is less than or equal to 4. ? ? ?
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STARTER: Solving Inequalities
(On your worksheet) ? −𝟐,−𝟏,𝟎,𝟏,𝟐,𝟑 𝒙<𝟒 ? ? 𝒙<−𝟒 ? 𝟔<𝒙≤𝟗
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Sketch the region representing 𝑥>2
8 6 4 2 -2 -4 -6 Sketch the region representing 𝑥>2 Think: How are the values of x constrained, and how are the values of y constrained? Get students to sketch axes and tables in their books. 𝒙 can be any number greater than 2, but 𝒚 can be ANY value because it is not constrained. The dotted line indicates that 𝒙 can’t be 2.
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8 6 4 2 -2 -4 -6 -4 < y ≤ -2 Get students to sketch axes and tables in their books.
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y ≥ x How can we tell which way round the inequality is?
8 6 4 2 -2 -4 -6 y ≥ x Get students to sketch axes and tables in their books. 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.
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Quickfire Regions Fail Win Fail Win Fail
Bro Tip: An easier way to see if the region is on the correct side is to see whether 𝑦 is on the smaller side of the inequality or the greater side. If the greater, we’re above. Is the region on the correct side of the line? y > x + 2 y – x > 1 y > 1 - x 2 1 1 Fail Win Fail Win Fail Win x > 2y - 3 y > -x x + y > 1 1.5 1 Fail Win Fail Win Fail Win
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y ≤ x + 1 and x ≤ 6 and y > 2 Combining Inequalities 8 6 4 2 -2 -4
8 6 4 2 -2 -4 -6 Combining Inequalities y ≤ x + 1 and x ≤ 6 and y > 2 Get students to sketch axes and tables in their books. Bro Tip: In GCSE exam questions, the region you want is almost always the region enclosed by your 3 lines.
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Question 4 Worksheet Answers Click to Sketch >
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Question 5 Worksheet Answers Click to Sketch >
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Question 6 ? Worksheet Answers Click to Sketch > R
𝟐,𝟐 , 𝟐,𝟑 , 𝟐,𝟒 , (𝟑,𝟑) ?
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Question 7 Worksheet Answers Click to Sketch >
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Question 8 Worksheet Answers Click to Sketch > ? 3 ? 2
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R Question 9 ? ? ? Worksheet Answers 𝟓 𝟐 − 𝟓 𝟔 𝒙 𝟐𝟎
Click to Sketch > ?
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