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WMA11/01 Oct 2021, Question 4: 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 = cos 2x° for 0 ≤ x ≤ k, find the minimum point Q, the endpoint value k at R, and the range of p giving exactly two solutions.

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

Part (ai) · 2 marks

Give the coordinates of the minimum point Q on the curve.

  1. 1cos 2x° first reaches its minimum −1 when 2x = 180
  2. 2x = 90, so Q is (90, −1)

AnswerQ(90, −1)

Part (aii) · 1 mark

Find the value of k where the curve ends at R(k, 0).

  1. 1After the maximum at x = 180, the curve next meets the x-axis when 2x = 450
  2. 2x = 225, so k = 225

Answerk = 225

Part (b) · 2 marks

Find the range of p for which cos 2x° = p has exactly two solutions for 0 ≤ x ≤ k.

  1. 1The curve goes 1 → −1 (x = 90) → 1 (x = 180) → 0 (x = 225)
  2. 2For 0 ≤ p < 1 the line y = p meets the curve 3 times; at p = 1 it meets at x = 0 and x = 180 (2 times)
  3. 3For −1 < p < 0 it meets twice (once falling, once rising)
  4. 4So −1 < p < 0 or p = 1

Answer−1 < p < 0 or p = 1

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