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Further Mathematics Paper 2, Nov/Dec. 2008  
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 9

(a) A curve has gradient 3x2 – 2x + 1 at point (x,y).  If it passes through the point (1,3), find its equation.

(b) the first term of an Arithmetic Progression is 3 and the nth term is 48.  If the sum of the first n terms is 255, find the:

  • value of n
  • smallest value of r for which the rth term exceeds 149. 
_____________________________________________________________________________________________________
Observation

A good number of the candidates who attempted the question performed well in the part (a) of the question. They were able to integrate 3x2 – 2x+1 and applied the given conditions to get the required curve y = x3 – x2 + x + 2.  However, some candidates argued wrongly that since 3x2 – 2x+1 is the gradient function of the required curve, then                              
          
y - y1  =  3 x2 – 2x + 1. This only holds when the gradient is a constant.
x - x1    
The part (b) of the question was satisfactorily handled by the candidates.  Majority of them were able to apply the formula Sn = n/2 (a + l), where a = 3, l = 48.

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