Date | May 2014 | Marks available | 6 | Reference code | 14M.2.hl.TZ2.4 |
Level | HL only | Paper | 2 | Time zone | TZ2 |
Command term | Find | Question number | 4 | Adapted from | N/A |
Question
The following diagram shows two intersecting circles of radii 4 cm and 3 cm. The centre C of the smaller circle lies on the circumference of the bigger circle. O is the centre of the bigger circle and the two circles intersect at points A and B.
Find:
(a) BˆOC;
(b) the area of the shaded region.
Markscheme
(a) METHOD 1
2arcsin(1.54) M1
α=0.769c (44.0∘) A1
METHOD 2
using the cosine rule:
32=42+42−2(4)(4)cosα M1
α=0.769c (44.0∘) A1
[2 marks]
(b) one segment
A1=12×42×0.76879−12×42sin(0.76879) M1A1
=0.58819K (A1)
2A1=1.18 (cm2) A1
Note: Award M1 only if both sector and triangle are considered.
[4 marks]
Total [6 marks]