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WMA11/01 Oct 2019, Question 3: When a Line Meets, Touches or Misses a Curve

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 1 (WMA11) · Calculator · 10 marks

The question, in short

For curve y = x² − 5x + 13 and line l through O meeting C at minimum M and point N, find M, N, and define shaded region R using inequalities.

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

Part (a) · 3 marks

Find the coordinates of the minimum point M of the curve y = x² − 5x + 13, showing working without calculator methods.

  1. 1x² − 5x + 13 = (x − 2.5)² − 6.25 + 13
  2. 2= (x − 2.5)² + 6.75
  3. 3Minimum point M = (2.5, 6.75)

AnswerM = (2.5, 6.75)

Part (b) · 5 marks

Find the coordinates of the second intersection point N where line l through the origin meets curve C.

  1. 1Gradient of l = 6.75 ÷ 2.5 = 2.7, so l is y = 2.7x
  2. 22.7x = x² − 5x + 13, so x² − 7.7x + 13 = 0
  3. 3(x − 2.5)(x − 5.2) = 0, so x = 2.5 (at M) or x = 5.2
  4. 4y = 2.7 × 5.2 = 14.04, so N = (5.2, 14.04)

AnswerN = (5.2, 14.04)

Part (c) · 2 marks

Use inequalities to define the finite region R bounded by curve C, line l and the y-axis.

  1. 1R is below the curve: y < x² − 5x + 13
  2. 2R is above the line l: y > 2.7x
  3. 3R runs from the y-axis to M: 0 ≤ x < 2.5

Answery < x² − 5x + 13, y > 2.7x, 0 ≤ x < 2.5

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Also searched as: WMA11 October 2019 · WMA11/01 · wma11 oct19 · IAS Maths Pure Mathematics 1 October 2019 · question 3.
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