The answer
(a) \(47.5\) cm
(b) \(827\) cm² (3 s.f.)
O-Level E-Math 2020 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 2020 Paper 1. It tests length scale, in the Scale & map ratios area. It is worth 4 marks: (a) 2, (b) 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) \(950\) km \(= 950 \times 100\,000 = 9.5 \times 10^{7}\) cm in reality. Dividing by the scale factor \(2\,000\,000\): map distance \(= \dfrac{9.5 \times 10^{7}}{2 \times 10^{6}} = 47.5\) cm.
(b) Area scales by the square of the length factor, \(\left(\dfrac{1}{2\,000\,000}\right)^2\). Now \(330\,803\) km² \(= 330\,803 \times (10^{5})^2 = 330\,803 \times 10^{10}\) cm². On the map: \(\dfrac{330\,803 \times 10^{10}}{(2 \times 10^{6})^2} = \dfrac{330\,803 \times 10^{10}}{4 \times 10^{12}} = \dfrac{330\,803}{400} = 827.0\ldots \approx 827\) cm².
Answer: (a) \(47.5\) cm
(b) \(827\) cm² (3 s.f.)
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 length scale question from Scale & map ratios, worth 4 marks: (a) 2, (b) 2.
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