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4PM1/01 Jan 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

On a grid from −6 to 6, draw two straight lines, 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 5x + 2y = 10 and y = x on the grid.

  1. 15x + 2y = 10 meets the axes at (2, 0) and (0, 5): join them with a ruler
  2. 2y = x passes through (0, 0), (1, 1), (2, 2), (3, 3): draw it across the grid

AnswerStraight line through (2, 0) and (0, 5); straight line y = x through (0, 0), (1, 1), (2, 2)

Part (b) · 2 marks

Shade and label region R satisfying y ≤ x, 5x + 2y ≤ 10, y ≥ −2 and x ≥ 1.

  1. 1Draw the horizontal line y = −2 and the vertical line x = 1
  2. 2y ≤ x: below the line y = x
  3. 35x + 2y ≤ 10: on the same side as the origin
  4. 4y ≥ −2: above y = −2; x ≥ 1: right of x = 1
  5. 5The region is the quadrilateral with corners (1, 1), (10/7, 10/7), (2.8, −2), (1, −2); label it R

AnswerLines y = −2 and x = 1 drawn; R is the region to the right of x = 1, above y = −2, below y = x and below 5x + 2y = 10 (the quadrilateral with vertices (1, 1), (10/7, 10/7), (14/5, −2) and (1, −2))

Stuck on a step? Read the free lesson: Drawing Straight-Line Graphs

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