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Further Mathematics Paper 2, Nov/Dec. 2013  
Questions: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Main
General Comments
Weakness/Remedies
Strength
Question 16

 

Question 16

Given that  = 5 + ,  = 4 – 2j and  = i + 5j, find:
(a)        ;
(b)        the unit vector in the direction of  ;
(c)        angle PQR, correct to the nearest degree;
(d)       the area of triangle PQR, correct to one decimal place.

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Observation

The Chief Examiner reported that this question was quite popular among the candidates and majority of those who attempted it performed poorly. Teachers were encouraged to put in more effort at teaching this topic. Candidates expected response was as follows:                                                                                                                                                         
     =    +    +   = (4i – 2j) + (-5i – j) + (-i – 5j) = -2i  - 8j
||   =     = . Therefore unit vector in the direction of  =  (-2 – 8)
=   ( +4).

 

 

 

In part (c) candidates were expected to apply the dot product as follows:
If   was the required angle then cos  =    = (-5i - j).(-4i + 2j) = 20 - 2 =  18.

| =  =   | =  = .  Therefore, Cos =   =  0.07894. Hence  = 38o, correct to the nearest degree. Using the formula Area =½ absin C, the area of the triangle was obtained as ½ × × × sin 37.8705 = 7.0 square units, correct to one decimal place
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