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4024/12 May/Jun 2024, Question 22: Solving Equations by Graphical Methods

Cambridge O Level Mathematics 4024 · Paper 12 (Non-calculator) · Non-calculator · 5 marks

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The question, in short

Using the given graph of y = 1/x + x/2, estimate a gradient from a tangent and solve a related equation graphically.

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

Part (a) · 2 marks

Draw a tangent at x = 2 on the curve and use it to estimate the gradient there.

  1. 1Draw the tangent to the curve at (2, 1.5) [y = 1/2 + 1 = 1.5]
  2. 2Gradient = rise ÷ run from two points on the tangent
  3. 3Gradient ≈ 0.25

Answer0.2 to 0.4

Part (b) · 3 marks

Draw a suitable straight line on the grid to find the solutions of 1/x − (5x)/2 + 1 = 0.

  1. 11/x − 5x/2 + 1 = 0 → 1/x + x/2 = 3x − 1
  2. 2Draw the line y = 3x − 1, e.g. through (0, −1) and (2, 5)
  3. 3Read the x-values where it crosses the curve
  4. 4x ≈ −0.46 and x ≈ 0.86

Answer−0.6 to −0.4 and 0.7 to 0.9

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

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