The answer
(a) $50.69 cheaper
(b) $835
(c)(i) \(9.2\times10^5\)
(ii) \(\approx 52.9\%\)
(iii) \(\approx 5.64\)
O-Level E-Math 2019 Paper 2 Question 3 · Verified worked solution by the Genius Plus Academy teaching team
What this question tests
This is Question 3 of the O-Level E-Math 2019 Paper 2. It tests currency conversion & comparison, in the Percentage & numbers in context area. It is worth 10 marks: 2 + 2 + 1 + 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) Convert the UK price to Singapore dollars: \(\pounds 389 \div 0.58 = \$670.69\). The phone in Singapore costs $620, so it is \(670.69 - 620 = \$50.69\) cheaper (to the nearest cent).
(b) The sale price is \(100\% - 6\% = 94\%\) of the original. So original \(\times 0.94 = 785 \Rightarrow\) original \(= 785 \div 0.94 = \$835.11 \approx \$835\).
(c)(i) \(8.21\times10^6 - 7.29\times10^6 = 0.92\times10^6 = 9.2\times10^5\).
(ii) Increase \(= 1.20\times10^7 - 7.85\times10^6 = 12\,000\,000 - 7\,850\,000 = 4\,150\,000\). Percentage increase \(= \dfrac{4\,150\,000}{7\,850\,000}\times100 = 52.87 \approx 52.9\%\).
(iii) SMS in 2015 \(= 1.14\times10^{10}\). Per person: \(\dfrac{1.14\times10^{10}}{5.54\times10^6} = 2057.8\) per year. Per day: \(\dfrac{2057.8}{365} = 5.638 \approx 5.64\) messages per person per day.
Answer: (a) $50.69 cheaper
(b) $835
(c)(i) \(9.2\times10^5\)
(ii) \(\approx 52.9\%\)
(iii) \(\approx 5.64\)
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 currency conversion & comparison question from Percentage & numbers in context, worth 10 marks: 2 + 2 + 1 + 2 + 3.
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