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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 11

(a)(i)    Differentiate with respect to x,  x2  +  4xy - y2 = 7.
(ii)   If x = -2 and y = 4, evaluate dy/dx in (a) (i)

(b) Express   x  +  3       in  partial fractions.
                x2 - 9x + 18 

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Observation

Candidates performed creditably well in this question.  In part (a) they were able to  find  dy/dx of x2 + 4xy – y2 = 7  as  x + 2y , substitute -2 for x and 4 for y
             y - 2x
            to get dy/dx  = ¾ or 0.75;
In part (b) candidates factorised the denominator x2 – 9x + 18 correctly to get (x – 6)(x-3), and got     
            x + 3          =   A          +        B    , multiply through by x2-9x +18 to get
            x2-9+18       (x – 6)            (x – 3)
  From  x + 3 = A(x-3)  +  B(x-6) they were able to determine the values of A and B as A = 3, B = -2.

 
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