QUESTION 13
- An operation * is defined by x * y = x + y + 2xy, x, y
R. - Calculate (2 * 3) * 5.
- Find the truth set of (x * 7) = (x * 5) *2.
- PQRS is a trapezium in which
is parallel to 
and 2
= 3
. If 
= 
and 
= 
, find in component form, the vector; 
;
.
Observation
The Chief Examiner reported that this question was unpopular among the Candidates’ as most of them avoided it and the few that attempted it performed poorly.
In part (ai), they ought to substitute to get (2 * 3) * 5 = (2 + 3 + 12) * 5 = 17 * 5 and simplifying this will yield
(17 * 5) = 17 + 5 +170 = 192.
In part (aii), they were to substitute and get (x * 7) = x + 7 + 14x = 15x + 7 and also
(x * 5) * 2 = 11x + 7 + 44x + 20 = 55x + 27, thereafter, equating and solving to get –40x = 20. Then, the
truth set = { x = 
}
In part (b i), the Candidates’ had difficulties in understanding the concept of vectors. It was expected that they make use of the given relation 2
= 3
and dividing both sides by 2 yields 
so that 
In part (bii), 
= 
.