The answer
(a) \(137^{\circ}\)
(b) \(262^{\circ}\)
O-Level E-Math 2019 Paper 1 Question 14 · Verified worked solution by the Genius Plus Academy teaching team
What this question tests
This is Question 14 of the O-Level E-Math 2019 Paper 1. It tests back-bearing, in the Bearings area. It is worth 3 marks: 1 + 2. 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) The bearing of Singapore from Delhi is the back-bearing of \(317^{\circ}\): \(317^{\circ} - 180^{\circ} = 137^{\circ}\).
(b) At \(S\), the directions to \(D\) (bearing \(317^{\circ}\)) and to \(T\) (bearing \(044^{\circ}\)) differ by \(317^{\circ} - 44^{\circ} = 273^{\circ}\), so the interior angle \(\angle DST = 360^{\circ} - 273^{\circ} = 87^{\circ}\). In triangle \(SDT\), \(\angle DTS = 180^{\circ} - 55^{\circ} - 87^{\circ} = 38^{\circ}\). The bearing of \(S\) from \(T\) is the back-bearing of \(044^{\circ}\), namely \(044^{\circ} + 180^{\circ} = 224^{\circ}\). From \(T\), \(D\) lies \(\angle DTS = 38^{\circ}\) further round (clockwise, towards the west), so the bearing of Delhi from Tokyo is \(224^{\circ} + 38^{\circ} = 262^{\circ}\).
Answer: (a) \(137^{\circ}\)
(b) \(262^{\circ}\)
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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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 back-bearing question from Bearings, worth 3 marks: 1 + 2.
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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