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WMA11/01 Jan 2021, Question 3: Trig Graphs: Amplitude and Period

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

The question, in short

Using the sketch of y = 4 cos x°, state coordinates of points P and Q, then for y = 4 cos x° + k with minimum −1, give coordinates of R.

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

Part (ai) · 2 marks

State the coordinates of P, the lowest point of the trough just left of the y-axis.

  1. 1The minimum of 4 cos x° is −4
  2. 2The nearest minimum to the left of the y-axis is at x = −180
  3. 3P(−180, −4)

AnswerP(−180, −4)

Part (aii) · 1 mark

State the coordinates of Q, the third positive x-axis crossing shown.

  1. 14 cos x° = 0 at x = 90, 270, 450, …
  2. 2Q is the third positive root
  3. 3Q(450, 0)

AnswerQ(450, 0)

Part (b) · 2 marks

Given C₂ has minimum y value −1, state coordinates of R, its maximum point with smallest positive x.

  1. 1Minimum of C₂ is −4 + k = −1, so k = 3
  2. 2Maximum value = 4 + 3 = 7
  3. 3Maxima at x = 0, 360, …; smallest positive is x = 360
  4. 4R(360, 7)

AnswerR(360, 7)

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