The answer
Diagram 3
O-Level E-Math 2020 Paper 1 Question 2 · Verified worked solution by the Genius Plus Academy teaching team
What this question tests
This is Question 2 of the O-Level E-Math 2020 Paper 1. It tests inverse proportion, in the Proportion / variation area. It is worth 1 mark. 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.
Inverse proportion to \(x^2\) means \(y = \dfrac{k}{x^2}\). Writing \(X = x^2\), this is \(y = \dfrac{k}{X}\), a reciprocal relationship. The graph of \(y\) against \(x^2\) is therefore a decreasing curve that falls steeply then levels off towards the axis (Diagram 3). (A straight line would mean direct, not inverse, proportion.)
Answer: Diagram 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 inverse proportion question from Proportion / variation, worth 1 mark.
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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