The answer
(a) all of \(A\) plus everything outside \(B\)
(b) the region outside both ellipses
O-Level E-Math 2016 Paper 1 Question 3 · Verified worked solution by the Genius Plus Academy teaching team
What this question tests
This is Question 3 of the O-Level E-Math 2016 Paper 1. It tests shading union with a complement, in the Set language & notation area. It is worth 2 marks: 1 + 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.
(a) \(A \cup B'\) is everything that is in \(A\) or not in \(B\) (or both). So shade the whole of ellipse \(A\) together with the entire region outside ellipse \(B\). Equivalently, the only region left unshaded is the part of \(B\) that lies outside \(A\).
(b) \(A' \cap B'\) is everything that is not in \(A\) and not in \(B\). By De Morgan this is \((A \cup B)'\), the region inside the rectangle but outside both ellipses. Shade that outer region.
Answer: (a) all of \(A\) plus everything outside \(B\)
(b) the region outside both ellipses
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 shading union with a complement question from Set language & notation, worth 2 marks: 1 + 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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