Question 13
- The operation (
) is defined on the set of real numbers, R, by 
(i) Evaluate 
(ii) If 
- In
. If P is the mid-point of 
, express 
as a column vector.
Observation
The Chief Examiner reported that majority of the Candidates’ who attempted this question did very well in part (a) but relatively poor in part (b). The report suggested that Mathematics Teachers should teach the Principles of Vector Algebra to their students so that the can be fully equipped to answer accurately such questions in subsequent examinations.
In part (a) (i), Candidates’ responded as expected by substituting 3 for y and 
for x in the definition to get 
= 
and simplifying to get 1.7.
Also, for part (b) (ii), after substituting 8 for x and simplifying to get 
, and solving to get y = 
.
In part (b), the Candidates’ were expected to proceed as follows:
Given that P is the mid-point of 
then 
.
But 
. Therefore, 
Then 
.