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WMA11/01 Jan 2025, Question 3: Simultaneous Equations with a Curve

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 1 (WMA11) · Calculator · 5 marks

The question, in short

Population P thousand after t years satisfies P² = a + bt³. Use the data at t = 5 (P = 58) and t = 10 (P = 65) to find a and b, then find T when P = 85.

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Part (a) · 3 marks

Substitute t = 5, P = 58 and t = 10, P = 65 into P² = a + bt³ and solve the resulting equations for the constants a and b.

  1. 158² = a + 5³b gives 3364 = a + 125b
  2. 265² = a + 10³b gives 4225 = a + 1000b
  3. 3Subtract: 875b = 861, so b = 0.984
  4. 4a = 3364 − 125 × 0.984 = 3364 − 123 = 3241

Answera = 3241, b = 0.984 (= 123/125)

Part (b) · 2 marks

Using your values of a and b, solve P² = a + bT³ with P = 85 for T, giving the answer to one decimal place and showing clear non-calculator working.

  1. 185² = 3241 + 0.984T³
  2. 27225 − 3241 = 0.984T³, so T³ = 3984/0.984 = 4048.78…
  3. 3T = ∛4048.78… = 15.94…
  4. 4T = 15.9 (1 d.p.)

AnswerT = 15.9

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