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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 5

 Calculate the value of the acute angle between the vectors (2i – j) and (i – j).

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Observation

This question was reported to have been attempted by majority of the candidates and their performance was described as fair.  Majority of the candidates were reported to have shown that if  was the required angle, then cos =    where aand b are vectors.  If a = (2i - j) and b = (i - j), then cos x =  .
|2i - j| =  = .  |ij| =   =   and (2ij)·(i - j) = 2 + 1 = 3.  Therefore,    cos  =  = 0.94868.  This implied that  = cos-1(0.94868) =18.43o.

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