The diagram shows the sector OPQ of a circle, centre O, radius r cm, where angle POQ = θ radians. The perimeter of the sector is 10cm. [Figure X.X]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2018). The mark or mark type is shown in brackets.

1. [M1] For use of arc length and attempt to get perimeter, must have 2 terms involving r
2. [M1] Dep For attempt to get r in terms of θ
3. [A1]
4. [M1] For attempt to obtain the area of the sector in terms of θ only, using their r
5. [A1] For manipulation to get the required answer nfww AG
6. [M1] For attempt to differentiate a quotient or an equivalent product
7. [A1] All correct, allow unsimplified
8. [M1] For equating their dA/dθ to 0 and attempt to solve – need to see at least one line of working
9. [A1] Condone inclusion of -2
10. [A1]
11. [M1] A complete method to obtain dA/dr
12. [A1]
13. [M1] For equating to zero and attempt to solve
14. [A1]
15. [A1]