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WMA11/01 Jun 2023, Question 2: Simultaneous Equations with a Curve

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 1 (WMA11) · Calculator · 6 marks

The question, in short

Form and solve simultaneous equations from a rectangle's perimeter 350 m and area 7350 m², finding length x and width y with x > y.

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

Part (a) · 1 mark

Write an equation relating x and y using the 350 m perimeter.

  1. 1Perimeter = 2 × length + 2 × width
  2. 22x + 2y = 350 (or x + y = 175)

Answer2x + 2y = 350

Part (b) · 1 mark

Write a second equation relating x and y using the 7350 m² area.

  1. 1Area = length × width
  2. 2xy = 7350

Answerxy = 7350

Part (c) · 4 marks

Solve the two equations to find x and y.

  1. 1From (a): y = 175 − x
  2. 2Substitute: x(175 − x) = 7350
  3. 3x² − 175x + 7350 = 0, so (x − 70)(x − 105) = 0
  4. 4x = 70 or x = 105
  5. 5Since x > y: x = 105 and y = 175 − 105 = 70

Answerx = 105, y = 70

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