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WMA11/01 Jan 2021, Question 4: Equation of a Line Through Two Points

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 1 (WMA11) · Calculator · 8 marks

The question, in short

Given P(−2, 13) and Q(4, −5), find the line through them, the quadratic with minimum at Q through P, and inequalities for shaded region R in the second quadrant.

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

Part (a) · 3 marks

Find the equation of line l through P and Q in the form y = mx + c with integer m and c.

  1. 1Gradient = (−5 − 13)/(4 − (−2)) = −18/6 = −3
  2. 2y − 13 = −3(x + 2)
  3. 3y = −3x + 7

Answery = −3x + 7

Part (b) · 3 marks

Find the equation of quadratic curve C with minimum point Q that passes through P.

  1. 1Minimum at (4, −5): y = a(x − 4)² − 5
  2. 2Through (−2, 13): 13 = a(36) − 5
  3. 336a = 18, a = 1/2
  4. 4y = ½(x − 4)² − 5 = ½x² − 4x + 3

Answery = ½(x − 4)² − 5, i.e. y = ½x² − 4x + 3

Part (c) · 2 marks

Use inequalities to define the region R bounded by C and l in the second quadrant.

  1. 1R is to the left of P, so x < −2
  2. 2R is above the line l: y > −3x + 7
  3. 3R is below the curve C: y < ½(x − 4)² − 5

Answery > −3x + 7, y < ½(x − 4)² − 5, x < −2

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Also searched as: WMA11 January 2021 · WMA11/01 · wma11 jan21 · IAS Maths Pure Mathematics 1 January 2021 · question 4.
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