[Figure Circle with rectangle ABCD] The diagram shows a circle, centre O, radius 12 cm. The points A and B lie on the circumference of the circle and form a rectangle with the points C and D. The length of AD is 8 cm and the area of the minor sector AOB is 150 cm².

Mark scheme

Marking points from the official mark scheme (May/June 2017). The mark or mark type is shown in brackets.

1. [M1] 1/2 × 12² × θ = 150 use of sector area
2. [A1] θ=2.083, so θ = 2.08 to 2dp
3. [M1] Area of triangle AOB = 1/2 × 12² sin 2.08 correct method for area of triangle
4. [A1] Area of segment = 150 - 1/2 × 12² × sin 2.08 allow unsimplified, using θ = 2.08, 2.083 or 150/72
5. [M1] sin 1.04 = AB/2 / 12 correct trigonometric statement using θ = 2.08, 2.083 or 150/72 with attempt to obtain AB
6. [A1] AB = awrt 20.7
7. [M1] Shaded area = their AB×8 – their segment area execution of a correct 'plan' (rectangle – segment)
8. [A1] awrt 78.4 or 78.5
9. [B1] Arc AB = 25 or 24.96
10. [M1] Perimeter = 25 + their AB + 16 correct 'plan' ( arc + their AB + 2×8)
11. [A1] awrt 61.7