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O-LevelAdditional MathematicsCircular measure4037/12 · May/June 2012 · Q87 Marks

[Figure X.X] The figure shows a circle, centre O, with radius 10cm. The lines XA and XB are tangents to the circle at A and B respectively, and angle AOB is 2π/3 radians.

  1. (i)Find the perimeter of the shaded region.[3]
  2. (ii)Find the area of the shaded region.[4]

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Mark scheme

Marking points from the official mark scheme (May/June 2012). The mark or mark type is shown in brackets.

  1. [B1] B1 for arc length correct
  2. [B1] B1 for AX/XB
  3. [B1] B1 for final answer
  4. [B1] B1 for sector area correct
  5. [M1] M1 for valid attempt at area OAXB, using their BX from part (i) (10 × their BX)
  6. [M1] M1 for area OAXB - sector area used (independent)
  7. [A1] Must be considering a quadrilateral, not a triangle.

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About this question

Topic
Circular measure, O-Level Additional Mathematics (syllabus 4037). Structured question, 7 marks.
Source
O-Level Additional Mathematics, May/June 2012 Paper 1 Variant 2, question 8.

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