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4PM1/02R Jun 2019, Question 5: Drawing Straight-Line Graphs

Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 2R · Calculator · 7 marks

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The question, in short

Linear programming: plot three boundary lines, mark the region they enclose with the x-axis, then find the biggest value of a linear expression in x and y over that region.

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

Part (a) · 3 marks

Plot the three boundary lines on the grid.

  1. 12x + 3y = 24: (0, 8) and (12, 0)
  2. 2y = 2x: (0, 0) and (6, 12)
  3. 33y = 2x − 12: (6, 0) and (12, 4)
  4. 4Plot two points for each line and join them

AnswerThree correct straight lines: 2x + 3y = 24 through (0, 8) and (12, 0); y = 2x through (0, 0) and (6, 12); 3y = 2x − 12 through (6, 0) and (12, 4)

Part (b) · 1 mark

Shade the region the four conditions describe.

  1. 1R lies below 2x + 3y = 24, below y = 2x, above 3y = 2x − 12 and above the x-axis
  2. 2Its corners are (0, 0), (3, 6), (9, 2) and (6, 0)

AnswerR is the quadrilateral with vertices (0, 0), (3, 6), (9, 2) and (6, 0), shaded in or out

Part (c) · 3 marks

Find the maximum of F over the region, checking its corners.

  1. 1Greatest F is at A, where y = 2x meets 2x + 3y = 24
  2. 22x + 6x = 24 ⇒ x = 3, y = 6
  3. 3F = 2 × 3 + 5 × 6 = 36

Answer36

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