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O-LevelAdditional MathematicsDifferentiation and integration4037/12 · May/June 2014 · Q46 Marks

The region enclosed by the curve y = 2 sin 3x, the x-axis and the line x = a, where 0 < a < 1 radian, lies entirely above the x-axis. Given that the area of this region is 1/3 square unit, find the value of a.

  1. The region enclosed by the curve y = 2 sin 3x, the x-axis and the line x = a, where 0 < a < 1 radian, lies entirely above the x-axis. Given that the area of this region is 1/3 square unit, find the value of a.[6]

Mark scheme

Marking points from the official mark scheme (May/June 2014). The mark or mark type is shown in brackets.

  1. [B1,B1] B1 for ∫ k cos 3x only, B1 for - 2/3 cos 3x only
  2. [M1] M1 for correct substitution of the correct limits into their result
  3. [A1] A1 for correct equation
  4. [M1] M1 for correct method of solution of equation of the form cos ma = k
  5. [A1] A1 allow 0.349, must be a radian answer

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About this question

Topic
Differentiation and integration, O-Level Additional Mathematics (syllabus 4037). Structured question, 6 marks.
Source
O-Level Additional Mathematics, May/June 2014 Paper 1 Variant 2, question 4.

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