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4PM1/01R Jan 2022, Question 9: Solving Equations by Graphical Methods

Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 1R · Calculator · 9 marks

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The question, in short

Complete a table for y = (x³ + 4)/(5 − x) to 2 decimal places, plot the curve for −2 ≤ x ≤ 2, and use a straight line to estimate a root of x³ − x² + 8x − 11 = 0.

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 in the table for y = (x³ + 4)/(5 − x), giving answers to 2 decimal places.

  1. 1x = −0.5: (−0.125 + 4)/5.5 = 0.70
  2. 2x = 0.5: 4.125/4.5 = 0.92
  3. 3x = 1.5: 7.375/3.5 = 2.11

Answerx = −0.5: y = 0.70; x = 0.5: y = 0.92; x = 1.5: y = 2.11

Part (b) · 2 marks

Draw the graph of y = (x³ + 4)/(5 − x) on the grid for −2 ≤ x ≤ 2.

  1. 1Plot the nine points from the table
  2. 2Join them with a smooth curve

AnswerPoints from the completed table plotted and joined with a smooth increasing curve from (−2, −0.57) to (2, 4)

Part (c) · 5 marks

Draw a suitable straight line on the grid and estimate, to one decimal place, the root of x³ − x² + 8x − 11 = 0 in −2 ≤ x ≤ 2.

  1. 1x³ − x² + 8x − 11 = 0 gives x³ + 4 = x² − 8x + 15
  2. 2x² − 8x + 15 = (5 − x)(3 − x)
  3. 3So (x³ + 4)/(5 − x) = 3 − x
  4. 4Draw the line y = 3 − x
  5. 5It meets the curve at x ≈ 1.3

AnswerDraw y = 3 − x; x = 1.3 or 1.4

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

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