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WMA11/01 Jan 2022, Question 4: Simultaneous Equations with a Curve

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

The question, in short

Solve algebraically, without calculator, for where line x + y = 6 meets curve y = 6x − 2x² + 1 at P and Q, then describe shaded region R bounded by C, l and x-axis.

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

Part (a) · 4 marks

Use algebra to find the coordinates of both intersection points P and Q of the line and curve.

  1. 1Substitute y = 6 − x: 6 − x = 6x − 2x² + 1
  2. 22x² − 7x + 5 = 0
  3. 3(2x − 5)(x − 1) = 0, so x = 1 or x = 5/2
  4. 4x = 1 gives y = 5; x = 5/2 gives y = 7/2
  5. 5P(1, 5) and Q(2.5, 3.5)

AnswerP(1, 5) and Q(2.5, 3.5)

Part (b) · 3 marks

Give inequalities that define the shaded region R bounded by the curve, the line and the x-axis.

  1. 1R is on or above the curve C: y ≥ 6x − 2x² + 1
  2. 2R is on or below the line l: x + y ≤ 6
  3. 3R is on or above the x-axis: y ≥ 0
  4. 4To cut off the part of the plane to the left of P, add x ≥ 1

Answery ≥ 6x − 2x² + 1, x + y ≤ 6, y ≥ 0 and x ≥ 1 (strict inequalities also accepted)

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