(a)      Simplify    x²   -  y²   .
                          3x  +  3y

(b)     In the diagram, PQRS is a rectangle.  |PK|  =  15 cm,  |SK|  = |KR| and PKS  =  37°.  Calculate, correct to three significant figures:

(i)      |PS|;
(ii)    |SK| and
(iii)    the area of the shaded portion.

OBSERVATION

In the (a) part, candidates were expected to factorize the numerator and the denominator respectively and cancel out the
common factors.  Thus:  x²   -  y²   =  (x + y)(x – y).  3x + 3y  = 3(x + y).
Therefore,   x²   -  y²   =   x  -  y  .
                         3x+3y             3

This was well handled by the candidates.

Candidates did not fare so well as their performance was poor.  They were supposed to use trigonometrical ratios to get|PS| and|SK| thus,

          (i)    |PS|  =  15 sin 37°  =   15  x  0.6018  =  9.027  =  9.03 cm to 3 sf.
          (ii)     |SK| =  15 cos 37°  =  15  x  0.7986  =  11.979  =  12.0 cm to 3 sf.
          (iii)    Area of shaded portion  =  Area of PQRS  -  Area of PKS
                     =  (9.027  X  11.979  X  2)  -  (1/2  X  11.979  X  9.027)  =
                             216.26887  -  54.067216
                     =   162.20165  =  162 cm2  to  3 significant figures.