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WMA11/01 Jan 2021, Question 2: Simultaneous Equations with a Curve

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

The question, in short

Given tree heights 2 m at 3 years and 2.4 m at 5 years, use the model H³ = pt² + q to find p and q, then find T when the height is 5 m.

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Part (a) · 4 marks

Use the two height-time pairs to form simultaneous equations in p and q, then solve for both constants, giving values to 3 significant figures where needed.

  1. 1t = 3, H = 2: 9p + q = 8
  2. 2t = 5, H = 2.4: 25p + q = 2.4³ = 13.824
  3. 3Subtract: 16p = 5.824, so p = 0.364
  4. 4q = 8 − 9(0.364) = 4.724, so q = 4.72

Answerp = 0.364, q = 4.72

Part (b) · 2 marks

Substitute H = 5 and the found p and q into the model, then solve for T to one decimal place.

  1. 15³ = 0.364T² + 4.724
  2. 2T² = (125 − 4.724)/0.364 = 330.4…
  3. 3T = 18.2

AnswerT = 18.2

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