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4PM1/01R Jan 2022, Question 1: Drawing Straight-Line Graphs

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

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The question, in short

On a grid, draw two straight lines from their equations, then shade and label the region R satisfying four inequalities.

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

Part (a) · 2 marks

Draw the lines 4x + 5y = 20 and 3y − 4x = −12 on the grid.

  1. 14x + 5y = 20 crosses the axes at (5, 0) and (0, 4)
  2. 23y − 4x = −12 crosses the axes at (3, 0) and (0, −4)
  3. 3Draw each as a straight line

Answer(i) straight line through (5, 0) and (0, 4); (ii) straight line through (3, 0) and (0, −4)

Part (b) · 2 marks

Shade and label region R satisfying 4x + 5y ≤ 20, 3y − 4x ≥ −12, y ≤ 3 and x ≥ 1.

  1. 1Draw y = 3 and x = 1
  2. 2R is to the right of x = 1, below y = 3
  3. 3below 4x + 5y = 20 and above 3y − 4x = −12
  4. 4Shade that region and label it R

AnswerLines y = 3 and x = 1 drawn; R is the quadrilateral with vertices (1, 3), (5/4, 3), (15/4, 1) and (1, −8/3), labelled R

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