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+100−252×7×10)=0.48276…(=27.660…∘) (A1)
C∧BA = arccos (25+100−492×5×10)=0.70748…(=40.535…∘) (A1)
attempt to subtract triangle area from sector area (M1)
area =12×49(2C∧AB−sin2C∧AB)+12×25(2C∧BA−sin2C∧BA)
= 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]