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4MA1/1H Jun 2018, Question 12: Finding Regions from Multiple Inequalities

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1H (Higher) · Calculator · 4 marks

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The question, in short

Using two lines shown on a coordinate grid, find where the given pair of equations meet and shade the feasible region satisfying five inequalities.

Summarised in our own words. Use the official paper for the exact wording and the diagram.

Part (a) · 1 mark

State the coordinates where the two drawn lines intersect, giving the solution to the pair of equations.

  1. 1The solution is the point where the two lines cross
  2. 2The lines cross at (3, 4)
  3. 3x = 3 and y = 4, written 3, 4

Answer3, 4

Part (b) · 3 marks

On the grid, shade and label R for the area meeting all five listed inequalities.

  1. 1Draw x + y = 4 through (4, 0) and (0, 4)
  2. 2Keep the side of x + y = 4 away from O, and above the x-axis
  3. 3Keep below both 3y = 2x + 6 and 4x + 3y = 24
  4. 4The region has vertices (4, 0), (6, 0), (3, 4) and (1.2, 2.8)
  5. 5Shade this region and label it R

Answerthe region bounded by the x-axis, x + y = 4, 3y = 2x + 6 and 4x + 3y = 24, with vertices (4, 0), (6, 0), (3, 4) and (1.2, 2.8)

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