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WMA11/01 Jun 2024, Question 11: Trig Graphs: Amplitude and Period

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

The question, in short

For y = 12 sin x in radians, find coordinates of the second maximum P, then use a vertical shift k giving maximum 3, and a phase shift B for a minimum at x = π/4.

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

Part (a) · 2 marks

Find the coordinates of the maximum point P on y = 12 sin x, the second maximum to the right of the origin.

  1. 1Maxima of 12 sin x are at x = π/2, 5π/2, ... with y = 12
  2. 2P is the second maximum to the right of O: x = 5π/2
  3. 3P = (5π/2, 12)

AnswerP = (5π/2, 12)

Part (b) · 2 marks

Given the maximum y-value on y = 12 sin x + k is 3, find coordinates of the minimum point with smallest positive x.

  1. 1Maximum of C₂ is 12 + k = 3, so k = −9
  2. 2Minimum value = −12 − 9 = −21
  3. 3First minimum of sin x for x > 0 is at x = 3π/2
  4. 4Minimum point: (3π/2, −21)

Answer(3π/2, −21)

Part (ci) · 1 mark

Given (π/4, A) is the minimum point on y = 12 sin(x + B) with smallest positive x, find A.

  1. 1The minimum value of 12 sin(x + B) is −12
  2. 2A = −12

AnswerA = −12

Part (cii) · 1 mark

Find the smallest possible positive value of the constant B.

  1. 1Minimum when x + B = 3π/2 (+ 2nπ)
  2. 2At x = π/4: B = 3π/2 − π/4 = 5π/4
  3. 3B > 0 and π/4 is the first positive minimum, so B = 5π/4

AnswerB = 5π/4

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Also searched as: WMA11 June 2024 · WMA11/01 · wma11 jun24 · IAS Maths Pure Mathematics 1 June 2024 · question 11.
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