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O-LevelAdditional MathematicsDifferentiation and integration4037/12 · May/June 2016 · Q78 Marks

The diagram shows part of the graph of y = 1 - 2cos 3x, which crosses the x-axis at the point A and has a maximum at the point B.

  1. (i)Find the coordinates of A.[2]
  2. (ii)Find the coordinates of B.[2]
  3. (iii)Showing all your working, find the area of the shaded region bounded by the curve, the x-axis and the perpendicular from B to the x-axis.[4]

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Mark scheme

Marking points from the official mark scheme (May/June 2016). The mark or mark type is shown in brackets.

  1. [1] M1 for x±asin3x attempt to integrate at least one term
  2. [1] A1
  3. [1] B1 for each, must be in correct position or in terms of x = and y =
  4. [1] M1 for x - (2/3)sin3x attempt to integrate at least one term
  5. [1] A1 for correct integration
  6. [1] DM1 for correct use of limits from (i) and (ii), must be in radians
  7. [1] A1

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About this question

Topic
Differentiation and integration, O-Level Additional Mathematics (syllabus 4037). Structured question, 8 marks.
Source
O-Level Additional Mathematics, May/June 2016 Paper 1 Variant 2, question 7.

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