GCSE: Inequalities – Shading Regions Associated Resources: GCSE-InequalitiesRegionsWorksheet.docx GCSE: Inequalities – Shading Regions Dr J Frost (jfrost@tiffin.kingston.sch.uk) www.drfrostmaths.com } ~ Last modified: 31st August 2015

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. ? 0 1 2 3 4 5 -3 -2 -1 0 1 2 ? ? x ≥ 4 x ≤ 5 Means: x is greater than or equal to 4. ? Means: x is less than or equal to 4. ? 2 3 4 5 6 7 2 3 4 5 6 7 ? ?

STARTER: Solving Inequalities (On your worksheet) ? −𝟐,−𝟏,𝟎,𝟏,𝟐,𝟑 𝒙<𝟒 ? ? 𝒙<−𝟒 ? 𝟔<𝒙≤𝟗

Sketch the region representing 𝑥>2 -10 -8 -6 -4 -2 2 4 6 8 10 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.

-10 -8 -6 -4 -2 2 4 6 8 10 8 6 4 2 -2 -4 -6 -4 < y ≤ -2 Get students to sketch axes and tables in their books.

y ≥ x How can we tell which way round the inequality is? -10 -8 -6 -4 -2 2 4 6 8 10 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.

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

y ≤ x + 1 and x ≤ 6 and y > 2 Combining Inequalities 8 6 4 2 -2 -4 -10 -8 -6 -4 -2 2 4 6 8 10 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.

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

Question 5 Worksheet Answers    Click to Sketch >

Question 6 ? Worksheet Answers Click to Sketch > R 𝟐,𝟐 , 𝟐,𝟑 , 𝟐,𝟒 , (𝟑,𝟑) ?

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

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

R Question 9 ? ? ? Worksheet Answers 𝟓 𝟐 − 𝟓 𝟔 𝒙 𝟐𝟎 Click to Sketch > ? 1 1