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0580/21 May/Jun 2025, Question 11: Equation of the Tangent Line

Cambridge IGCSE Mathematics 0580 · Paper 21 (Extended) · Non-calculator · 5 marks

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The question, in short

Using the given graph of y = f(x) and point P(−2, 11), draw the tangent from P and use it to find the integer contact point and the tangent's equation.

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

Part (a) · 2 marks

Draw the tangent from P to the curve and read off the integer coordinates a and b of its point of contact.

  1. 1Place a ruler through P(−2, 11) and turn it until it just touches the curve without crossing it
  2. 2The ruled tangent touches the curve at (1, 2)
  3. 3a = 1, b = 2

AnswerCorrect ruled tangent and a = 1, b = 2

Part (b) · 3 marks

Find the tangent's equation in the form y = mx + c.

  1. 1Gradient = (2 − 11)/(1 − (−2)) = −9/3 = −3
  2. 2y = −3x + c; at (1, 2): 2 = −3 + c, so c = 5
  3. 3y = 5 − 3x

Answery = −3x + 5

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Also searched as: 0580/21/M/J/25 · 0580_s25_qp_21 · 0580 s25 21 · question 11.
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