Question 3
- If
= - 1, y = -3, z = - 4 and w = -7, evaluate: 
.
In the diagram, 
and 
are tangents to the circle centre O. If ∠MNQ = x, ∠NMQ = y and ∠NQP = 46o, find the value of
(i) x;
(ii) y.
Observation
The Chief Examiner reported this question was poorly attempted by majority of the candidates. According to the report, candidates did not manipulate the directed numbers correctly. Others showed poor knowledge of circle geometry.
In part (a), Candidates were expected to substitute the given numbers into the expression to obtain 
= 
= 
= 1.
In part (b), candidates were expected to know that since MN and MQ were tangents to the circle from the same external point, then triangle MNQ was isosceles and angle MNQ = angle MQN = (90 – 46)o = 44o. Angle y = (180 – 44 – 44)o (sum of angles of a triangle) = 92o.