The diagram shows a circle with centre O and a chord AB. The radius of the circle is 12 cm and angle AOB is 1.4 radians. [Figure showing a circle with centre O, radius 12cm, chord AB, angle AOB = 1.4 rad, shaded region is the major segment]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2013). The mark or mark type is shown in brackets.

1. [M1] AB² =12²+12²–2×12×12×cos 1.4 AB = 2x12 sin 0.7 (May be implied)
2. [A1] 15.4 to 15.5
3. [B1] θ = 2π – 1.4(= 4.88) May be implied
4. [M1] Use s = rθ(=58.6) 12x4.9 or better oe
5. [A1] 74.1
6. [M1] (Sector) = ½×12²×(2π−1.4)(=352) or May be implied. π×12² - ½×12²×1.4
7. [M1] (Triangle) = ½×12×12×sin1.4(= 70.9 or 71)
8. [M1] Area of major sector + Area of triangle May be implied
9. [A1] 422 or 423