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Date November 2018 Marks available 6 Reference code 18N.2.AHL.TZ0.H_7
Level Additional Higher Level Paper Paper 2 Time zone Time zone 0
Command term Find Question number H_7 Adapted from N/A

Question

Boat A is situated 10km away from boat B, and each boat has a marine radio transmitter on board. The range of the transmitter on boat A is 7km, and the range of the transmitter on boat B is 5km. The region in which both transmitters can be detected is represented by the shaded region in the following diagram. Find the area of this region.

Markscheme

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

use of cosine rule       (M1)

CÂB = arccos (49+100252×7×10)=0.48276(=27.660)      (A1)

CBA = arccos (25+100492×5×10)=0.70748(=40.535)      (A1)

attempt to subtract triangle area from sector area       (M1)

area =12×49(2CABsin2CAB)+12×25(2CBAsin2CBA)

= 3.5079… + 5.3385…      (A1)

Note: Award this A1 for either of these two values.

= 8.85 (km2)      A1

Note: Accept all answers that round to 8.8 or 8.9.

 

[6 marks]

Examiners report

[N/A]

Syllabus sections

Topic 3—Geometry and trigonometry » SL 3.2—2d and 3d trig
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