The diagram shows two circles, centres A and B, each of radius 10cm. The point B lies on the circumference of the circle with centre A. The two circles intersect at the points C and D. The point E lies on the circumference of the circle centre B such that ABE is a diameter. [Figure 10.1]

Mark scheme

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

1. [B1] for a convincing argument
2. [B1] Angle CBE = 2π/3 (must be in terms of π, allow 0.667π, or better)
3. [M1] for correct attempt to find DE using their angle CBE
4. [A1] for correct DE, allow 17.3 or better
5. [M1] for attempt to find arc length with their angle CBE (20.94)
6. [M1] for 10 + 10 + DE + an arc length
7. [A1] allow unsimplified
8. [M1] for sector area using their angle CBE allow unsimplified, may be implied
9. [M1] for triangle area using their angle DBE which must be the same as their angle CBE, allow unsimplified, may be implied
10. [A1] allow in either form