The answer
(a) 12
(b) 16
O-Level E-Math 2024 Paper 1 Question 17 · Verified worked solution by the Genius Plus Academy teaching team
What this question tests
This is Question 17 of the O-Level E-Math 2024 Paper 1. It tests venn-diagram regions, in the Set language & notation area. It is worth 2 marks: (a) 1, (b) 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 four regions have \(7\) (in \(A\) only), \(3\) (in \(A \cap B\)), \(6\) (in \(B\) only) and \(9\) (outside both).
(a) \((A' \cup B) \cap (A \cup B')\) simplifies to \((A \cap B) \cup (A' \cap B')\), the elements that are in both sets or in neither set. That is the intersection (\(3\)) plus the outside region (\(9\)): \(n = 3 + 9 = 12\).
(b) \(A \cap B'\) is "in \(A\) only" (\(7\)); \((A \cup B)'\) is "outside both" (\(9\)). Their union is \(7 + 9 = 16\).
Answer: (a) 12
(b) 16
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 venn-diagram regions question from Set language & notation, worth 2 marks: (a) 1, (b) 1.
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