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0580/22 May/Jun 2025, Question 15: Solving Equations by Graphical Methods

Cambridge IGCSE Mathematics 0580 · Paper 22 (Extended) · Non-calculator · 6 marks

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The question, in short

Using the graph of y = 2/x − 1, find where it meets the x-axis, state its asymptotes, and solve 2/x − x − 1 = 0 by adding a straight line to the grid.

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

Part (a) · 1 mark

Give the coordinates of the point where the curve y = 2/x − 1 crosses the x-axis.

  1. 1On the x-axis y = 0: 2/x − 1 = 0, so x = 2
  2. 2(2, 0)

Answer(2, 0)

Part (b) · 2 marks

State the equation of each asymptote of the graph y = 2/x − 1.

  1. 12/x is undefined at x = 0: asymptote x = 0
  2. 2As x gets large 2/x → 0, so y → −1: asymptote y = −1

Answerx = 0, y = −1

Part (c) · 3 marks

Draw a suitable straight line on the grid and use it to solve 2/x − x − 1 = 0.

  1. 12/x − x − 1 = 0 gives 2/x − 1 = x
  2. 2Draw the line y = x on the grid
  3. 3It meets the curve where x = −2 and x = 1
  4. 4Check: x = −2 gives −1 − 1 = −2; x = 1 gives 2 − 1 = 1
  5. 5x = −2 and x = 1

Answerx = −2 and x = 1

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

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