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0580/22 May/Jun 2024, Question 18: Speed from a Curved Travel Graph

Cambridge IGCSE Mathematics 0580 · Paper 22 (Extended) · Calculator · 3 marks

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The question, in short

Given a graph of y = f(x) on a grid for 0 ≤ x ≤ 4.5, draw a tangent at x = 3 and use it to estimate the curve's gradient there.

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

Part (a) · 1 mark

Draw the tangent line to the curve at the point where x = 3.

  1. 1At x = 3 the curve is at about (3, 5.4)
  2. 2Rule a straight line that touches the curve at this point only, with the same steepness as the curve there

Answertangent ruled at x = 3

Part (b) · 2 marks

Use the tangent drawn in part a to estimate the gradient of the curve at x = 3.

  1. 1Take two points on your tangent far apart, e.g. about (2, 0) and (4, 10.8)
  2. 2Gradient = rise ÷ run = (10.8 − 0)/(4 − 2)
  3. 3≈ 5.4

Answer4.8 to 5.8

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