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WMA11/01 Oct 2020, Question 5: Transformations of Graphs

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 1 (WMA11) · Calculator · 9 marks

The question, in short

Sketch transformations of a cubic curve and find the constant and x-axis crossing values for a cosine curve from its graph.

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

Part (ia) · 3 marks

Sketch y = f(x + 2) from the given cubic graph, showing axis intercept coordinates.

  1. 1f(x + 2) is f(x) translated 2 units to the left
  2. 2(−5, 0) moves to (−7, 0)
  3. 3The touching point (2, 0) moves to (0, 0), so the maximum is at the origin
  4. 4The minimum stays below the x-axis, now between x = −7 and x = 0

AnswerSame negative cubic moved 2 units left: crosses the x-axis at (−7, 0), minimum in the third quadrant, maximum touching the x-axis at the origin (0, 0), then falling to the bottom right

Part (ib) · 3 marks

Sketch y = f(−x) from the given cubic graph, showing axis intercept coordinates.

  1. 1f(−x) is f(x) reflected in the y-axis
  2. 2(−5, 0) becomes (5, 0); the touching point (2, 0) becomes (−2, 0)
  3. 3The y-intercept (0, −3) stays the same
  4. 4The minimum moves into the fourth quadrant

AnswerReflection of the curve in the y-axis: a positive cubic that rises from the bottom left, touches the x-axis at (−2, 0) (maximum), passes through (0, −3), has a minimum in the fourth quadrant, and crosses the x-axis at (5, 0)

Part (iia) · 1 mark

Use the y-axis intercept (0, √3) to find the constant k in y = k cos(x + π/6).

  1. 1At x = 0: y = k cos(π/6) = √3
  2. 2k × (√3/2) = √3
  3. 3k = 2

Answerk = 2

Part (iib) · 2 marks

Find the exact x-values p and q where the cosine curve crosses the x-axis.

  1. 1y = 0 when cos(x + π/6) = 0
  2. 2x + π/6 = π/2 or 3π/2
  3. 3p = π/2 − π/6 = π/3
  4. 4q = 3π/2 − π/6 = 4π/3

Answerp = π/3, q = 4π/3

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Also searched as: WMA11 October 2020 · WMA11/01 · wma11 oct20 · IAS Maths Pure Mathematics 1 October 2020 · question 5.
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