The answer
\(\approx 1.38\) cm
O-Level E-Math 2023 Paper 1 Question 26 · Verified worked solution by the Genius Plus Academy teaching team
What this question tests
This is Question 26 of the O-Level E-Math 2023 Paper 1. It tests face diagonal, in the Pythagoras & trigonometry area. It is worth 4 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.
Against face \(AEHD\) (an \(8 \times 6\) face), the greatest length of rod that can lie inside is the face diagonal \(\sqrt{8^2 + 6^2} = 10\) cm. With 7 cm outside, the rod is \(10 + 7 = 17\) cm long. To make the outside part as short as possible, fit the greatest possible length inside, the space diagonal of the cuboid: \(\sqrt{12^2 + 8^2 + 6^2} = \sqrt{244} = 15.62\) cm. Shortest length outside \(= 17 - 15.62 = 1.38\) cm (3 s.f.).
Answer: \(\approx 1.38\) cm
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 face diagonal question from Pythagoras & trigonometry, worth 4 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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