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4024/22 May/Jun 2022, Question 6: Drawing Straight-Line Graphs

Cambridge O Level Mathematics 4024 · Paper 22 (Calculator) · Calculator · 8 marks

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The question, in short

On a grid with y = x + 2 drawn, draw x + 2y = 7, use the graph to solve the simultaneous equations, then work with region R from three inequalities.

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

Part (a) · 2 marks

Draw the line x + 2y = 7 on the grid.

  1. 1x = 0: 2y = 7, y = 3.5; y = 0: x = 7
  2. 2Rule the line through (0, 3.5) and (7, 0)

AnswerRuled line through (0, 3.5) and (7, 0)

Part (b) · 1 mark

From the graph, find the x and y values solving y = x + 2 and x + 2y = 7.

  1. 1The lines cross at (1, 3)
  2. 2x = 1, y = 3

Answer(1, 3)

Part (ci) · 2 marks

Shade and label region R satisfying y ≤ x + 2, x + 2y ≥ 7 and x ≤ 5.

  1. 1Draw the line x = 5
  2. 2R is the triangle with vertices (1, 3), (5, 7) and (5, 1): below y = x + 2, above x + 2y = 7, left of x = 5
  3. 3Shade and label this triangle R

AnswerCorrect region clearly indicated

Part (ciia) · 1 mark

Find how many integer-coordinate points lie inside region R, not on its boundary.

  1. 1x = 2: 2.5 < y < 4 gives y = 3 (1 point)
  2. 2x = 3: 2 < y < 5 gives y = 3, 4 (2 points)
  3. 3x = 4: 1.5 < y < 6 gives y = 2, 3, 4, 5 (4 points)
  4. 41 + 2 + 4 = 7

Answer7

Part (ciib) · 2 marks

For integer points in R with y one more than x, write down all possible coordinates.

  1. 1Need y = x + 1 from the points found above
  2. 2(2, 3), (3, 4), (4, 5)

Answer(2, 3), (3, 4), (4, 5)

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Also searched as: 4024/22/M/J/22 · 4024_s22_qp_22 · 4024 s22 22 · question 6.
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