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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 7

The coordinates of points X, Y and Z are (4,0), (6,2) and (-2,1) respectively.
              →         →
Find (a) 2 XY  +  3YZ ;  
                                                       →
(b) the unit vector in the direction of XZ

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Observation

                                                                                                                      →           →
In this question, candidates were expected to compute vectors  XY  and YZ                      
from the given co-ordinates of the points.     
                 →                                               
                XY  =    ( 6 - 4)     =    2    , YZ   =     ( -2-6)      =   ( -8)
                             ( 2 - 0)           2                      ( 1 -2)            (-1 )                                             
                                                           →       →
With these, they can simplify    2XY + 3XZ.  However, a good number  of the candidates
                  →
had it that XY  =  √(6-4)2 + (2-0)2 i.e distance between X and Y which is very wrong.     
              →                                                                                                              
In 7(b), XZ   =   -6  ,  thus /XZ/ = √(36+1) = √]37.   Hence required unit vector is         
                            1                                                                                                                  
   1     (-6)       or     (-6i + j)
√37   (-1)              √37       

Rationalizing the denominator gives √37  (-6) .  Many candidates did not rationalize
                                                                    37   (1)
 the denominator hence, lost the final mark.

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