The answer
construction (described below)
O-Level E-Math 2017 Paper 1 Question 10 · Verified worked solution by the Genius Plus Academy teaching team
What this question tests
This is Question 10 of the O-Level E-Math 2017 Paper 1. It tests perpendicular bisector, in the Constructions & loci area. It is worth 3 marks: 1 + 1 + 1. It is a worded / diagram-based question, so open your Ten-Year Series (TYS) or the official paper at this question, then follow our full worked solution below.
(a) With compasses set to more than half \(BC\), draw arcs from \(B\) and from \(C\) on both sides of \(BC\); the straight line through the two intersection points is the perpendicular bisector of \(BC\) (the locus of points equidistant from \(B\) and \(C\)).
(b) With compasses centred at \(D\), draw an arc cutting \(DA\) and \(DC\); from those two points draw equal arcs that cross; join \(D\) to the crossing point. This line bisects angle \(ADC\) (the locus of points equidistant from lines \(DA\) and \(DC\)).
(c) "Nearer to \(C\) than to \(B\)" is the side of the perpendicular bisector of \(BC\) that contains \(C\). "Nearer to \(AD\) than to \(CD\)" is the side of the angle bisector of \(ADC\) towards \(AD\). Shade the region inside \(ABCD\) that satisfies both conditions (the overlap of those two half-regions).
Answer: construction (described below)
Same structure, different numbers
Swap the constants, dress a quadratic as a length, hide a derivative inside an integral, and a student sees a brand new problem. The structure underneath is the same, and so is the method. Once a student can name the structure, a whole row of questions that look different start to open the same way.
That is where marks really leak: in choosing the method, not in the algebra that follows. We call it Lock and Key, name the lock, then the key follows.
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Same skill, different papers. Each has a verified worked solution.
Genius Plus Academy · O-Level & IP Mathematics
Our O-Level E-Math tuition trains the same recognise-the-structure method these worked solutions show, taught by a team that has marked these papers for years. It runs within our weekly Secondary Math programme, Sec 1 to 4 and IP.
It is a perpendicular bisector question from Constructions & loci, worth 3 marks: 1 + 1 + 1.
Yes. IP (Integrated Programme) schools teach the same O-Level Mathematics content; they just sequence it differently and set their own internal exams, so these worked solutions apply to IP students too.
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