The answer
(a) \(\approx 0.5\)
(b) \(\approx 38\)
O-Level E-Math 2016 Paper 1 Question 21 · Verified worked solution by the Genius Plus Academy teaching team
What this question tests
This is Question 21 of the O-Level E-Math 2016 Paper 1. It tests read a count off a cf curve, in the Cumulative frequency area. It is worth 4 marks: 2 + 2. 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 curve tops out at a cumulative frequency of \(200\), so there are \(200\) students in total.
(a) "Overestimated" means an estimate greater than the actual \(300\) g. From the curve, the cumulative frequency at \(300\) g is about \(100\) (the number who estimated \(300\) g or less). So the number who overestimated is about \(200 - 100 = 100\), and the probability is \(\dfrac{100}{200} = 0.5\). (Read from graph.)
(b) "Within 10% of 300 g" means an estimate between \(300 - 30 = 270\) g and \(300 + 30 = 330\) g. From the curve, the cumulative frequency at \(330\) g is about \(120\) and at \(270\) g is about \(82\), so the number in this range is about \(120 - 82 = 38\). (Read from graph; accept roughly 35 to 40.)
Answer: (a) \(\approx 0.5\)
(b) \(\approx 38\)
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 read a count off a cf curve question from Cumulative frequency, worth 4 marks: 2 + 2.
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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