(a).   The 3rd and 8th terms of an arithmetic progression (A.P.) are
          - 9 and 26 respectively.  Find the:

          (i)      common difference;
          (ii)     first term.

(b). In the diagram, PQ||YZ,  |XP| =  2 cm,|PY|  =  3 cm,
         |PQ| =  6 cm and the area of Triangle XPQ  =  24 cm².  Calculate the
          area of the trapezium PQZY.

observation

This question on Arithmetic Progression was well attempted and candidates performed creditably well.

          a + 2d  =  -9  …  (i)
          a + 7d  =  26  …  (ii)
     (ii)  -  (i)  gives  5d  =  35  >>  d  =  7.
                   From (i),  a  +  2(7)  =  -9 >>  a  =  -9  -  14  =  -23.

Candidate’s performance in the (b) part was poor.  They were required to find the scale factor and use it to find the missing sides and the area of the trapezium.  Many candidates were able to find the scale factor but could not apply it appropriately in finding the area of the trapezium.  By the characteristics of similar triangles,

Area of triangle  XPQ   =    |XP|²    i.e          24         =     22    =   4
Area of triangle  XYZ        |XY|²         Area of XYZ        52       25
  Area of DXYZ   =   24  x  25     =   150 cm²
                                          4
Area  of PQZY  =  Area of DXYZ  -  Area of DXPQ  =  150  -  24
 =  126cm²