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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+422(4)(4)cosα     M1

α=0.769c (44.0)     A1

[2 marks]

 

(b)     one segment

A1=12×42×0.7687912×42sin(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]

Examiners report

[N/A]

Syllabus sections

Topic 3 - Core: Circular functions and trigonometry » 3.1 » The circle: radian measure of angles.

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