Associated Resources GCSEInequalities Regions Worksheet docx GCSE Inequalities

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

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

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

8 Think: How are the values of x constrained, and how are the values of y constrained? 6 4 2 -10 -8 -6 -4 -2 2 -2 -4 -6 4 6 8 10

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

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

Quickfire Regions Is the region on the correct side of the line? y>x+2 y>1 -x 2 Win Fail y–x>1 1 Fail 1 Win x > 2 y - 3 x+y>1 Win y > -x 1. 5 1 Fail Win

Combining Inequalities 8 y ≤ x + 1 and x ≤ 66 and y > 2 4 2 -10 -8 -6 -4 -2 2 4 6 8 -2 -4 -6 Bro Tip: In GCSE exam questions, the region you want is almost always the region enclosed by your 3 lines. 10

Question 4 Worksheet Answers Click to Sketch >

Question 5 Worksheet Answers Click to Sketch >

Question 6 Worksheet Answers Click to Sketch > R ?

Question 7 Worksheet Answers Click to Sketch >

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

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