Date | November 2008 | Marks available | 4 | Reference code | 08N.2.sl.TZ0.6 |
Level | SL only | Paper | 2 | Time zone | TZ0 |
Command term | Find | Question number | 6 | Adapted from | N/A |
Question
A ship leaves port A on a bearing of 030∘ . It sails a distance of 25 km to point B. At B, the ship changes direction to a bearing of 100∘ . It sails a distance of 40 km to reach point C. This information is shown in the diagram below.
A second ship leaves port A and sails directly to C.
Find the distance the second ship will travel.
Find the bearing of the course taken by the second ship.
Markscheme
finding AˆBC=110∘ (=1.92 radians) (A1)
evidence of choosing cosine rule (M1)
e.g. AC2=AB2+BC2−2(AB)(BC)cosAˆBC
correct substitution A1
e.g. AC2=252+402−2(25)(40)cos110∘
AC=53.9 (km) A1
METHOD 1
correct substitution into the sine rule A1
e.g. sinBˆAC40=sin110∘53.9 A1
BˆAC=44.2∘
bearing =074∘ A1 N1
METHOD 2
correct substitution into the cosine rule A1
e.g. cosBˆAC=402−252−53.92−2(25)(53.9) A1
BˆAC=44.3∘
bearing =074∘ A1 N1
[3 marks]
Examiners report
A good number of candidates found this question very accessible, although some attempted to use Pythagoras' theorem to find AC.
Often candidates correctly found BˆAC in part (b), but few added the 30∘ to obtain the required bearing. Some candidates calculated BˆCA , misinterpreting that the question required the course of the second ship.