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4MA1/1HR Jun 2019, Question 21: 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

A curve y = f(x) has a single maximum at (4, 3). Use transformations to locate new maxima, then use a given sine graph to determine the constants a and b.

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

Part (ai) · 1 mark

State where the maximum moves for y = f(x − 5), starting from (4, 3).

  1. 1The maximum point (4, 3) is shifted 5 units to the right by replacing x with x − 5.
  2. 2So x = 4 becomes x = 4 + 5 = 9.
  3. 3The y-coordinate remains unchanged at 3.
  4. 4(9, 3)

Answer(9, 3)

Part (aii) · 1 mark

State where the maximum moves for y = 3f(x), starting from (4, 3).

  1. 1The transformation y = 3f(x) scales the y-values by a factor of 3.
  2. 2The original y-coordinate of the maximum is 3.
  3. 33 × 3 = 9.
  4. 4The x-coordinate remains 4.
  5. 5(4, 9)

Answer(4, 9)

Part (b) · 2 marks

From the sine curve between 0 and 360 with peaks at 2 and troughs at −2, work out a and b.

  1. 1Height goes from −2 to 2, so the size of a is 2
  2. 2The curve goes down to a minimum first, so a = −2
  3. 33 full cycles in 360°, so b = 3
  4. 4a = −2, b = 3

Answera = −2, b = 3

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