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4PM1/01 Jun 2020, Question 4: Solving Equations by Graphical Methods

Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 1 · Calculator · 7 marks

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The question, in short

Using the given graph of y = x + 5/x² on a grid for 1 ≤ x ≤ 4, draw suitable straight lines to estimate roots of two cubic equations to one decimal place.

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

Part (a) · 3 marks

Draw a suitable straight line on the grid to estimate, to one decimal place, the roots of x³ − 4x² + 5 = 0 for 1 ≤ x ≤ 4.

  1. 1Divide by x²: x − 4 + 5/x² = 0
  2. 2x + 5/x² = 4
  3. 3Draw the line y = 4
  4. 4Read the intersections: x = 1.4 and x = 3.6

Answerx = 1.4, 3.6

Part (b) · 4 marks

Draw a suitable straight line on the grid to estimate, to one decimal place, the root of x³ − x² − 5 = 0 for 1 ≤ x ≤ 4.

  1. 1Divide by x²: x − 1 − 5/x² = 0
  2. 2So 2x − 1 = x + 5/x²
  3. 3Draw the line y = 2x − 1 (through (0.5, 0) and (2.5, 4))
  4. 4Read the intersection: x = 2.1

Answerx = 2.1 or 2.2

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

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