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WMA11/01 Jan 2019, Question 8: Sketching Cubics and Reciprocal Curves

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 1 (WMA11) · Calculator · 6 marks

The question, in short

A question on sketching cubics and reciprocal curves.

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

Part (a) · 1 mark

  1. 1y = f(−x) is a reflection in the y-axis
  2. 2A horizontal asymptote is unchanged, so it is still y = 4

Answery = 4

Part (b) · 1 mark

  1. 1y = f(¼x) is a stretch parallel to the x-axis, scale factor 4
  2. 2x-coordinates are multiplied by 4: (4, 9) becomes (16, 9)

Answer(16, 9)

Part (c) · 2 marks

  1. 1The line y = 9 touches C only at the maximum (4, 9)
  2. 2For k ≤ 4 the line meets only the left branch once (the curve never reaches 4 on the right)
  3. 3For 4 < k < 9 there are two intersections, and none for k > 9

Answerk ≤ 4 or k = 9

Part (di) · 1 mark

  1. 1The curve crosses the y-axis at (0, 6)
  2. 2Translating down by 6 moves it to the origin, so a = 6

Answera = 6

Part (dii) · 1 mark

  1. 1The curve crosses the x-axis at (−3, 0)
  2. 2Translate 3 units right: y = f(x − 3) passes through the origin

Answery = f(x − 3)

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Also searched as: WMA11 January 2019 · WMA11/01 · wma11 jan19 · IAS Maths Pure Mathematics 1 January 2019 · question 8.
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