Date | May 2021 | Marks available | 3 | Reference code | 21M.1.SL.TZ2.1 |
Level | Standard Level | Paper | Paper 1 (without calculator) | Time zone | Time zone 2 |
Command term | Hence and Find | Question number | 1 | Adapted from | N/A |
Question
The following diagram shows a circle with centre O and radius r.
Points A and B lie on the circumference of the circle, and AˆOB=1 radian.
The perimeter of the shaded region is 12.
Find the value of r.
Hence, find the exact area of the non-shaded region.
Markscheme
minor arc AB has length r (A1)
recognition that perimeter of shaded sector is 3r (A1)
3r=12
r=4 A1
[3 marks]
EITHER
θ=2π-AˆOB (M1)
Area of non-shaded region (A1)
OR
area of circle area of shaded sector (M1)
(A1)
THEN
area A1
[3 marks]