Further Mathematics Paper 2, Nov/Dec. 2010
 Questions: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Main
Weakness/Remedies
Strength
Question 7

Vectors p, q and r are given by p =[2,-3] , q =[4,2] and r= [3,-2]
Find:
(a) 4p - 2q + 5r;
(b) The position vector which divides p and q in the ratio 2:3.

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Observation

This question was also reported to be well attempted by majority of the candidates and their performance was commendable.
In part (a), candidates' performance was commended as majority of them obtained full marks. Candidates were able to show that since
=[2,-3] , q =[4,2] and r= [3,-2] , 4p-2q+5r = 4[2,-3] - 2[4,2] + 5[3,-2] = [8,-12] - [8,4] + [15,-10] = [15,-26]
In part (b), candidates' performance was reported not to be as good as it was in part (a).
Nevertheless, majority of the candidates demonstrated a good knowledge of the topic. The
vector which divides p and q in the ratio 2: 3 = 3[2,-3] + 2[4,2] = [[6,-9]+ [8,4] = 1/5[14,-5]
2+3         5
Some candidates were reported to have obtained the num~tor ~t did not divide by the sum of the ratios. Some others either subtracted the ratios or had 2p +3q instead of 3p + 2q
2+3                            2+3