The answer
(a) \(n = \dfrac{2}{3}\) (\(\approx 0.67\))
(b) $109.00
O-Level E-Math 2019 Paper 1 Question 23 · Verified worked solution by the Genius Plus Academy teaching team
What this question tests
This is Question 23 of the O-Level E-Math 2019 Paper 1. It tests scale 1 cm : n m and area, in the Scale & map ratio / best value area. It is worth 5 marks: 2 + 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) Measuring the plan gives a rectangle about 6 cm by 7.2 cm, so the actual room is \((6n) \times (7.2n) = 43.2\,n^2\) square metres. Setting \(43.2\,n^2 = 19.2\) gives \(n^2 = \dfrac{19.2}{43.2} = \dfrac{4}{9}\), so \(n = \dfrac{2}{3} \approx 0.67\). (The room is then \(4 \text{ m} \times 4.8 \text{ m} = 19.2 \text{ m}^2\).) (This part depends on measuring the printed plan; see the discrepancy tracker.)
(b) Varnish needed \(= \dfrac{19.2}{16} = 1.2\) litres \(= 1200\) ml. She must buy whole tins totalling at least 1200 ml, as cheaply as possible. Per millilitre, the 500 ml tin is cheapest (\(\$0.085\)/ml) vs the 1 litre (\(\$0.08595\)/ml) and 250 ml (\(\$0.096\)/ml). The cheapest total of at least 1200 ml is \(500 + 500 + 250 = 1250\) ml: \(\$42.50 + \$42.50 + \$24.00 = \$109.00\). (Cheaper than \(1\text{ L} + 250\text{ ml} = \$109.95\).) Least cost \(= \$109.00\).
Answer: (a) \(n = \dfrac{2}{3}\) (\(\approx 0.67\))
(b) $109.00
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 scale 1 cm : n m and area question from Scale & map ratio / best value, worth 5 marks: 2 + 3.
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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