The answer
(a) \(A \cup B'\)
(b) \((A \cup B) \cap (A \cap B)'\)
O-Level E-Math 2018 Paper 1 Question 7 · Verified worked solution by the Genius Plus Academy teaching team
What this question tests
This is Question 7 of the O-Level E-Math 2018 Paper 1. It tests describe a shaded region, 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) The only unshaded region is "in \(B\) but not in \(A\)", which is \(A' \cap B\). The shaded region is its complement: \((A' \cap B)' = A \cup B'\). (Equivalently: everything that is in \(A\), together with everything outside \(B\).)
(b) The shaded crescents are the points in \(A\) or in \(B\) but not in their overlap, i.e. the symmetric difference \((A \cup B) \cap (A \cap B)'\). (The intersection \(A \cap B\) and the region outside both circles are unshaded.)
Answer: (a) \(A \cup B'\)
(b) \((A \cup B) \cap (A \cap B)'\)
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 describe a shaded region 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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