◈ Oracle PrepSign Up Free
O-LevelAdditional MathematicsCircular measure4037/12 · May/June 2014 · Q78 Marks

The diagram shows a circle, centre O, radius 8 cm. Points P and Q lie on the circle such that the chord PQ = 12 cm and angle POQ = θ radians.

  1. (i)Show that θ = 1.696, correct to 3 decimal places.[2]
  2. (ii)Find the perimeter of the shaded region.[3]
  3. (iii)Find the area of the shaded region.[3]

This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.

Mark scheme

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

  1. [M1] (i) M1 for a complete method to find either (θ)/2 or θ
  2. [A1] (i) Answer given.
  3. [M1] (i) M1 for using the area of the triangle in 2 different forms
  4. [A1] (i) A1 for choosing the correct angle.
  5. [M1] (ii) M1 for correct attempt at a minor or major arc length
  6. [A1] (ii) A1 for correct major arc length, allow unsimplified
  7. [A1] (ii) A1 for 48.7 or better
  8. [M1,M1] (iii) M1 for correct attempt to find area of major sector
  9. [M1] (iii) M1 for correct attempt to find area of triangle, using any method
  10. [A1] (iii) A1 for 178.5, 178.6, awrt179
  11. [M1] (iii) M1 for attempt at area of circle – area of minor sector
  12. [M1] (iii) M1 for area of triangle

Write your answer and get it marked

On Oracle Prep you can write or photograph your own answer and have it marked by AI against this mark scheme, with feedback on what you missed.

Sign up free →

About this question

Topic
Circular measure, O-Level Additional Mathematics (syllabus 4037). Structured question, 8 marks.
Source
O-Level Additional Mathematics, May/June 2014 Paper 1 Variant 2, question 7.

Questions and mark schemes are from past examination papers and remain the copyright of the exam board. How Oracle Prep builds its content

Related Additional Mathematics questions

Circular measureMay/June 20146m

A sector of a circle of radius r cm has an angle of θ radians, where θ < π. The perimeter of the sector is 30 cm.

Logarithmic and exponential functionsOct/Nov 20188m

Solve

Simultaneous equationsOct/Nov 20185m

Solve the simultaneous equations 8^(p+1)/4^q = 2^11, 3^(2p+5)/27^q = 9^(3q)

Permutations and combinationsOct/Nov 20186m

A 5-character code is to be formed from the 13 characters shown below. Each character may be used once only in any co…

← Browse all past-paper questions

© 2026 Oracle Prep