4MA1/1H Jan 2020, Question 10: Finding Regions from Multiple Inequalities
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1H (Higher) · Calculator · 3 marks
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The question, in short
From a grid diagram with one boundary given as y = 1/3 x − 2, write down the three inequalities whose region is shaded.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 3 marks
- 1The left-hand boundary is the vertical line x = −1 and the shaded region lies to the right of it, so x ≥ −1
- 2The sloping boundary at the top right passes through (0, 4) and (4, 0), so its gradient is −1 and its equation is y = 4 − x
- 3The shaded region lies below that line, so y ≤ 4 − x, which can be written x + y ≤ 4
- 4The remaining boundary is the given line y = (1/3)x − 2 and the shaded region lies above it, so y ≥ (1/3)x − 2
- 5The three inequalities are x ≥ −1, x + y ≤ 4 and y ≥ (1/3)x − 2
Answerx ≥ −1, x + y ≤ 4, y ≥ (1/3)x − 2
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