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4PM1/02R Jun 2022, Question 5: Solving Equations by Graphical Methods

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

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The question, in short

Complete a table for y = e^(3x − 2), plot the curve for 0 ≤ x ≤ 1, then use a straight line to estimate a root of 3x = 2 + ln(3 − x).

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

Part (a) · 2 marks

Fill in the missing y-values for x = 0.25, 0.5 and 0.75, giving each to 2 decimal places.

  1. 1x = 0.25: e^(−1.25) = 0.2865… ≈ 0.29
  2. 2x = 0.5: e^(−0.5) = 0.6065… ≈ 0.61
  3. 3x = 0.75: e^(0.25) = 1.2840… ≈ 1.28

Answerx = 0.25: y = 0.29; x = 0.5: y = 0.61; x = 0.75: y = 1.28

Part (b) · 2 marks

Draw the graph of y = e^(3x − 2) on the grid for x from 0 to 1.

  1. 1Plot each point from the table
  2. 2Join with a smooth curve, increasing and getting steeper

AnswerThe points (0, 0.14), (0.25, 0.29), (0.5, 0.61), (0.75, 1.28), (1, 2.72) plotted and joined by a smooth increasing curve

Part (c) · 3 marks

Draw a suitable straight line and use it to estimate, to one decimal place, the root of 3x = 2 + ln(3 − x).

  1. 13x − 2 = ln(3 − x)
  2. 2e^(3x − 2) = 3 − x
  3. 3Draw the line y = 3 − x (through (0, 3) and (1, 2))
  4. 4Read off the x-coordinate where the line meets the curve: x ≈ 0.9

Answerx = 0.9

Stuck on a step? Read the free lesson: Solving Equations by Graphical Methods

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