The answer
\(40.1^{\circ}\)
O-Level E-Math 2022 Paper 1 Question 22 · Verified worked solution by the Genius Plus Academy teaching team
What this question tests
This is Question 22 of the O-Level E-Math 2022 Paper 1. It tests right-angled trig (sine to find a side, in the Pythagoras & trigonometry area. It is worth 3 marks. 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.
In right-angled \(\triangle ABD\) (right angle at \(B\)), \(AD = 12.8\) is the hypotenuse and \(BD\) is opposite the \(38^{\circ}\) angle: \(BD = 12.8 \sin 38^{\circ} = 7.88\) cm. In right-angled \(\triangle BDC\) (right angle at \(D\)), \(BC = 10.3\) is the hypotenuse and \(BD\) is adjacent to angle \(CBD\): \(\cos\angle CBD = \dfrac{BD}{BC} = \dfrac{7.88}{10.3} = 0.7651\), so angle \(CBD = 40.1^{\circ}\) (1 d.p.).
Answer: \(40.1^{\circ}\)
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 right-angled trig (sine to find a side question from Pythagoras & trigonometry, worth 3 marks.
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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