The answer
(a) 26
(b) \(3n + 2\)
(c) 155 is not a multiple of 3
O-Level E-Math 2022 Paper 1 Question 4 · Verified worked solution by the Genius Plus Academy teaching team
What this question tests
This is Question 4 of the O-Level E-Math 2022 Paper 1. It tests nth term of a linear sequence, in the Algebraic manipulation / Sequences area. It is worth 4 marks: 1 + 2 + 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.
The counts increase by 3 each time (arithmetic, first term 5).
(a) Diagram 8 \(= 5 + 3(8 - 1) = 26\) dots.
(b) Diagram \(n = 5 + 3(n - 1) = 3n + 2\).
(c) If \(3n + 2 = 157\) then \(3n = 155\). Since 155 is not divisible by 3, \(n\) is not a whole number, so no diagram has exactly 157 dots.
Answer: (a) 26
(b) \(3n + 2\)
(c) 155 is not a multiple of 3
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 nth term of a linear sequence question from Algebraic manipulation / Sequences, worth 4 marks: 1 + 2 + 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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