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4PM1/01 Jun 2020, Question 2: Drawing Straight-Line Graphs

Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 1 · Calculator · 4 marks

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The question, in short

Sketch three straight lines on the given axes, marking where each crosses the coordinate axes, then shade the region satisfying four inequalities.

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

Part (a) · 3 marks

Sketch y = 6, y + x = 10 and y = 2x − 5, giving the coordinates where each line meets the axes.

  1. 1y = 6: horizontal, meets the y-axis at (0, 6) only
  2. 2y + x = 10: x = 0 ⇒ y = 10; y = 0 ⇒ x = 10
  3. 3y = 2x − 5: x = 0 ⇒ y = −5; y = 0 ⇒ x = 2.5
  4. 4Sketch each line through its intercepts

Answery = 6: horizontal line crossing the y-axis at (0, 6); y + x = 10: crosses the axes at (0, 10) and (10, 0); y = 2x − 5: crosses the axes at (0, −5) and (2.5, 0)

Part (b) · 1 mark

Shade region R satisfying y ≤ 6, y + x ≤ 10, y ≥ 2x − 5 and x ≥ 0 on the sketch.

  1. 1R is to the right of the y-axis, under y = 6 and under y + x = 10
  2. 2and on the upper-left side of y = 2x − 5

AnswerR is the region with x ≥ 0 below y = 6, below y + x = 10 and above y = 2x − 5 (shaded in or out)

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