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Further Mathematics Paper 2, May/June. 2009  
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 18
(a) The position vectors of points A, B and C are i + j, 3i + 9j and      – i + j respectively.

          (i)      Show that points A, B and C are collinear
         (ii)      Determine the ratio /AB/ : /BC/.

(b) A uniform beam XY of mass 10kg and length 24 m is hung horizontally from a cross bar by two vertical inextensible strings, one attached to X and the other at a point M, 4m away from Y.  A mass of 50kg is suspended at a point N which is 8m from X.  If the system remains in equilibrium, calculate the tension in the strings.
          [Take g = ms-2]

_____________________________________________________________________________________________________
Observation

The report stated that more candidates attempted this question than question 17 even though it may not be described as being popular among the candidates. Their performance was also described as fair.  Many candidates were able to prove the co- linearity of points and determine the required ratio.
In part (b), as stated in the report, many candidates could not draw the correct diagram.  The report attributed this to their inability to interpret the question correctly.  Candidates’ expected responses were:


  1. In the diagram,

   

                  
Taking the moment about X gave T2 x 20 = (500 x 8) + (100 x 12) thus
T2 = = 260N.  Since the body was in equilibrium, the total upward
force balanced the total downward force i.e. T1 + T2 = 100 + 500 which

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