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Date November 2017 Marks available 4 Reference code 17N.2.hl.TZ0.3
Level HL only Paper 2 Time zone TZ0
Command term Find Question number 3 Adapted from N/A

Question

This diagram shows a metallic pendant made out of four equal sectors of a larger circle of radius OB=9 cmOB=9 cm and four equal sectors of a smaller circle of radius OA=3 cm.
The angle BOC= 20°.

N17/5/MATHL/HP2/ENG/TZ0/03

Find the area of the pendant.

Markscheme

METHOD 1

area = (four sector areas radius 9) + (four sector areas radius 3)     (M1)

=4(1292π9)+4(12327π18)     (A1)(A1)

=18π+7π

=25π (=78.5 cm2)     A1

METHOD 2

area =

(area of circle radius 3) + (four sector areas radius 9) – (four sector areas radius 3)     (M1)

π32+4(1292π9)4(1232π9)     (A1)(A1)

 

Note:     Award A1 for the second term and A1 for the third term.

 

=9π+18π2π

=25π (= 78.5 cm2)     A1

 

Note:     Accept working in degrees.

 

[4 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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