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4MA1/1HR Jan 2020, Question 22: Trigonometric Graphs and Equations

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1HR (Higher) · Calculator · 4 marks

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The question, in short

From a drawn cosine curve of the form y = a cos(x + b)° on 0 ≤ x ≤ 360, determine a and b, then relocate the minimum point (4, 5) of y = f(x) under two transformations.

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

Part (a) · 2 marks

Use the graph to work out the values of the constants a and b in y = a cos(x + b)°.

  1. 1The curve goes up to 2.5 and down to −2.5, so a = 2.5.
  2. 2The first maximum is at x = 60, not 0: the curve moved 60° right.
  3. 3Moving right by 60 means cos(x − 60), so b = −60.
  4. 4a and b: 2.5, −60

Answer2.5, −60

Part (bi) · 1 mark

State the coordinates of the minimum point of y = f(2x), given the original minimum is at (4, 5).

  1. 1The transformation y = f(2x) compresses the graph horizontally by scale factor 1/2
  2. 2The x-coordinate of the minimum point is halved: 4 ÷ 2 = 2
  3. 3The y-coordinate remains unchanged
  4. 4(2, 5)

Answer(2, 5)

Part (bii) · 1 mark

State the coordinates of the minimum point of y = f(x) − 7, given the original minimum is at (4, 5).

  1. 1The transformation y = f(x) − 7 shifts the graph down by 7 units
  2. 2The y-coordinate of the minimum point decreases by 7: 5 − 7 = −2
  3. 3The x-coordinate remains unchanged
  4. 4(4, −2)

Answer(4, −2)

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