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WMA11/01 Jun 2019, Question 6: When a Line Meets, Touches or Misses a Curve

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 1 (WMA11) · Calculator · 7 marks

The question, in short

A line y = 4x + c touches the curve y = x(x − 3) at exactly one point. Find c and the coordinates where they meet.

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

Part (a) · 4 marks

Use the single-point intersection condition to form and solve an equation for the constant c.

  1. 14x + c = x² − 3x
  2. 2x² − 7x − c = 0
  3. 3One point of contact: b² = 4ac, so 49 = 4(1)(−c)
  4. 449 + 4c = 0, so c = −12.25

Answerc = −12.25 (−49/4)

Part (b) · 3 marks

Using your value of c, find the x and y coordinates of the single intersection point.

  1. 1x² − 7x + 12.25 = 0, so (x − 3.5)² = 0
  2. 2x = 3.5
  3. 3y = 4(3.5) − 12.25 = 1.75
  4. 4Point (7/2, 7/4)

Answer(7/2, 7/4)

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Also searched as: WMA11 June 2019 · WMA11/01 · wma11 jun19 · IAS Maths Pure Mathematics 1 June 2019 · question 6.
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