The answer
(a) 1232.5 km (≈ 1230 km)
(b) \(\approx 66.1 \text{ cm}^2\)
O-Level E-Math 2016 Paper 1 Question 20 · Verified worked solution by the Genius Plus Academy teaching team
What this question tests
This is Question 20 of the O-Level E-Math 2016 Paper 1. It tests linear scale conversion to km, in the Scale & map ratio 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.
(a) Each map centimetre represents \(2\,500\,000\) cm on the ground. Actual length \(= 49.3 \times 2\,500\,000 = 123\,250\,000\) cm \(= 1\,232\,500\) m \(= 1232.5\) km.
(b) For areas the scale factor is squared: \(1 \text{ cm}^2\) on the map represents \((2\,500\,000)^2 \text{ cm}^2\) of ground. Convert the real area to \(\text{cm}^2\): \(1 \text{ km}^2 = (10^5 \text{ cm})^2 = 10^{10} \text{ cm}^2\), so \(41\,285 \text{ km}^2 = 41\,285 \times 10^{10} = 4.1285 \times 10^{14} \text{ cm}^2\). Map area \(= \dfrac{4.1285 \times 10^{14}}{(2.5 \times 10^6)^2} = \dfrac{4.1285 \times 10^{14}}{6.25 \times 10^{12}} = 66.056 \approx 66.1 \text{ cm}^2\) (3 s.f.).
Answer: (a) 1232.5 km (≈ 1230 km)
(b) \(\approx 66.1 \text{ cm}^2\)
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 linear scale conversion to km question from Scale & map ratio, 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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