The answer
(a)(i)(a) \(\approx 41.6\) h
(b) IQR \(\approx 4.4\) h
(ii) \(15\%\)
(iii) curve shifts 3 left
(b) Men 2/5, Women 3/6
O-Level E-Math 2021 Paper 2 Question 9 · Verified worked solution by the Genius Plus Academy teaching team
What this question tests
This is Question 9 of the O-Level E-Math 2021 Paper 2. It tests cumulative-frequency curve (median, in the Dispersion / Probability area. It is worth 10 marks: (a)(i)(a) 1 + (b) 2, (ii) 2, (iii) 1, (b) 4. 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)(a) Median is the value at cumulative frequency \(250\): \(\approx 41.6\) hours.
(b) Lower quartile (CF \(125\)) \(\approx 39.6\); upper quartile (CF \(375\)) \(\approx 44.0\). IQR \(\approx 44.0 - 39.6 = 4.4\) hours.
(ii) At 45.1 hours the cumulative frequency is about \(425\), so \(500 - 425 = 75\) employees worked more than this. Percentage \(= \dfrac{75}{500} \times 100 = 15\%\).
(iii) Each employee's hours fall by 3, so the whole curve is translated 3 units (hours) to the left; its shape stays the same.
(b) \(P(\text{man part-time}) = \tfrac18 \Rightarrow\) men part-time \(= \tfrac18 \times 16 = 2\). Let women full-time \(= w\): \(\dfrac{w}{16}\cdot\dfrac{w - 1}{15} = \dfrac18 \Rightarrow w(w - 1) = 30 \Rightarrow w = 6\). Then women part-time \(= 16 - 2 - 5 - 6 = 3\).
| Part-time | Full-time | |
|---|---|---|
| Men | 2 | 5 |
| Women | 3 | 6 |
Answer: (a)(i)(a) \(\approx 41.6\) h
(b) IQR \(\approx 4.4\) h
(ii) \(15\%\)
(iii) curve shifts 3 left
(b) Men 2/5, Women 3/6
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-frequency curve (median question from Dispersion / Probability, worth 10 marks: (a)(i)(a) 1 + (b) 2, (ii) 2, (iii) 1, (b) 4.
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