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Further Mathematics Paper 2, Nov/Dec. 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 12

  1. (a)      The polynomial f(x) = 2x3 + Px + qx + r  is divisible by (2x2 – 7x + 3).  It has a remainder of -36 when it is divided by (x + 1).  Find the
              (i)      values of constants P, q and r;
              (ii)      zeroes of f(x)

  2. Find the truth set of x2 – 3x + 2 < 0.
_____________________________________________________________________________________________________
Observation
  • Two linear transformations are defined by

P:(x,y)  (-2 + 3y, 5x – 4y)
T:(x,y) (-3x – 4y, 6x – 5y)

          Find the

  • inverse of T;
  • image of (1,3) under the transformation P.
  • Find the volume, in terms of p, of the solid formed when the area enclosed by the lines y = 1, 2y = x + 1 and x = 0 is rotated through two right angles about the y – axis. 

Very few candidates reportedly attempted this question and they performed poorly.  The matrix of transformation T =  .
    =   15 + 24  =  39.   T-1  =      .  Therefore, required inverse T-1 (x, y)  =            = 
 
(ii)    P =    .  Therefore the image of (1,3) under P =      =     =  (7, -7).
         
For part (b), since the volume generated was half of the total volume, the formular becomes V = . 2y = x + 1. Hence x = 2y – 1. When x = 0, y = ½ and when y = 1, x = 1. Thus, V =  =        =  cubic units.

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