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4PM1/01R Jun 2020, Question 1: Solving Trig Equations

Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 1R · Calculator · 7 marks

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The question, in short

Given P = 3 + 2sin(3πt/8) for 0 ≤ t ≤ 12, work out P at a stated t, the extreme values of P, and the first t giving P = 4.

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

Part (a) · 2 marks

Substitute t = 10/3 into the formula and give P exactly.

  1. 1t = 10/3: 3πt/8 = 5π/4
  2. 2P = 3 + 2sin(5π/4) = 3 + 2(−√2/2)
  3. 3= 3 − √2

Answer3 − √2

Part (b) · 2 marks

State the maximum and minimum values that P can take.

  1. 1−1 ≤ sin(3πt/8) ≤ 1, and both extremes occur for 0 ≤ t ≤ 12
  2. 2Largest P = 3 + 2 = 5
  3. 3Smallest P = 3 − 2 = 1

Answer(i) 5 (ii) 1

Part (c) · 3 marks

Determine the smallest t in the range for which P equals 4.

  1. 14 = 3 + 2sin(3πt/8)
  2. 2sin(3πt/8) = 1/2
  3. 33πt/8 = π/6
  4. 4t = 4/9

Answert = 4/9

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