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O-LevelAdditional MathematicsCircular measure4037/21 · May/June 2015 · Q47 Marks

The diagram shows a circle, centre O, radius 8 cm. The points P and Q lie on the circle. The lines PT and QT are tangents to the circle and angle POQ = (3π/4) radians. [Figure 4.1]

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

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Mark scheme

Marking points from the official mark scheme (May/June 2015). The mark or mark type is shown in brackets.

  1. [M1] PT = 8 tan(3π/8) oe
  2. [A1] awrt 19.3
  3. [M1] (1/2) x 8² x (3π/4) oe (75.4) (Area of sector)
  4. [M1] 8 x their PT - their sector oe (=154.5-'75.4') (Area of quadrilateral OPTQ minus sector)
  5. [A1] awrt 79.1
  6. [M1] 8(3π/4) oe (18.8) (Arc length PQ)
  7. [A1] Accept 57.4 to 57.5

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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 2015 Paper 2 Variant 1, question 4.

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