The answer
(a)(i) 41
(ii) 24%
(iii) 61
(b) \(\approx 1\,088\,100\)
(c) comparison below
O-Level E-Math 2022 Paper 2 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 2022 Paper 2. It tests cumulative-percentage curve, in the Dispersion / Central tendency area. It is worth 8 marks: (a) 1 + 1 + 1, (b) 2, (c) 3. 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)(i) The Singapore curve reaches 50% cumulative at age \(\approx 41\), so the median age is about 41.
(ii) The UK curve is at \(\approx 76\%\) at age 60, so the percentage aged over 60 is \(100\% - 76\% = 24\%\).
(iii) The Singapore curve reaches 80% cumulative at age \(\approx 61\), so the 80th percentile is about 61.
(b) At age 25 the Singapore curve is at \(\approx 27\%\), so the number under 25 \(\approx 27\% \times 4.03 \times 10^6 = 1\,088\,100\).
(c) Median: Singapore's median (41) is higher than the UK's (\(\approx 40\)), so on average Singapore's population is slightly older. Spread (interquartile range): Singapore's IQR \(= 58 - 24 = 34\) years is smaller than the UK's \(59 - 21 = 38\) years, so Singapore's ages are more consistent (less spread out).
Answer: (a)(i) 41
(ii) 24%
(iii) 61
(b) \(\approx 1\,088\,100\)
(c) comparison below
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 cumulative-percentage curve question from Dispersion / Central tendency, worth 8 marks: (a) 1 + 1 + 1, (b) 2, (c) 3.
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