The diagram shows a right-angled triangle ABC with AB = 8cm and angle ABC = π/2 radians. The points D and E lie on AC and BC respectively. BAD and ECD are sectors of the circles with centres A and C respectively. Angle BAD = 2π/9 radians. [Figure 8.1]

Mark scheme

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

1. [B1] [angle ECD =] 5π/18 oe or 0.873 soi
2. [M1] Attempts to find AC and subtract 8 (e.g. AC = 8/cos(2π/9))
3. [A1] [DC =] 2.44
4. [M2] 1/2 * 8 * 8tan(π/2 - 2π/9) - 1/2 * 8² * (2π/9) - 1/2 * their 2.44² * their 5π/18 (M1 for 1/2 * 8² * (2π/9) or for 1/2 * their 2.44² * their 5π/18 seen)
5. [A1] awrt 1.91
6. [M2] their(6.712-2.443) + their 2.443 * (5π/18) + 8 * (2π/9) (M1 for either arc seen)
7. [A1] awrt 12.0