The answer
\(1, 2, 15, 21, 21\)
O-Level E-Math 2021 Paper 1 Question 6 · Verified worked solution by the Genius Plus Academy teaching team
The question
Five positive integers: mean 12, median 15, mode 21. Find the five numbers. [2]
Mean 12 \(\Rightarrow\) sum \(= 60\). Median 15 \(\Rightarrow\) the 3rd (middle) value is 15. The mode is 21, which is \(> 15\), so the two 21s must be the two largest (4th and 5th) values. Then the first two sum to \(60 - 15 - 21 - 21 = 3\), so they are \(1\) and \(2\) (positive integers, each \(\leqslant 15\)). The numbers are \(1, 2, 15, 21, 21\).
Answer: \(1, 2, 15, 21, 21\)
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 reconstructing data from mean/median/mode question from Central tendency, worth 2 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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