The diagram shows the right-angled triangle OAB. The point C lies on the line OB. Angle OAB = π/2 radians and angle AOB = θ radians. AC is an arc of the circle, centre O, radius 12cm and AC has length 9.6 cm. [Figure 5.1]

Mark scheme

Marking points from the official mark scheme (May/June 2019). The mark or mark type is shown in brackets.

1. [M1] 9.6 = 12θ For use of arc length
2. [A1] θ = 0.8
3. [M1] Either tan θ = AB/12, (AB = 12.36) Or OB = 12/cos θ, (OB = 17.22) For attempt to find AB or OB using their θ May be implied by a correct triangle area Allow if using degrees consistently
4. [M1] Either Area ΔOAB = 1/2 × 12 × their 12.36 Or Area ΔOAB = 1/2 × 12 × their 17.22 × sin θ (= 74.1 or 74.2) For attempt to find area of triangle using their θ Allow if using degrees consistently
5. [B1] Area of sector OAC = 1/2 × 12² × 0.8 = 57.6 Allow unsimplified
6. [A1] Area of shaded region = 16.5 or 16.6