Question 5
- Find the range of values of x which satisfy the following inequalities simultaneously: 5 – x> 1 and 9 + x ≥ 8.
In the diagram, O is the centre of the circle, |PQ| = |QR| and ∠PSR = 56°. Find ∠QRS.
Observation
The Chief Examiner pointed out that Candidates performance in this question was fair.
In part (a), majority of them were able to solve the inequalities independently to arrive
at x<4 or -1 ≤ x. They were also able to state that the range of values of x is -1 ≤ x < 4.
But in part (b), only few of the Candidates solved correctly.
First, ∠PQR + 56°= 180° so that ∠PQR = 180°- 56°= 124°
From triangle PQR, ∠PQR+ ∠QRP+ ∠QPR= 180°. But |RQ| = |QP| so that ∠QRP = ∠QPR.
124° + 2 ∠QRP = 180° and ∠QRP =28°.
But ∠PRS = 90° (angle on a semi-circle), therefore, ∠QRS = 28°+ 90° = 118°.