The answer
(a) \(6.36\%\)
(b) $972.06
(c)(i) London is dearer
(ii) $1767
O-Level E-Math 2018 Paper 2 Question 2 · Verified worked solution by the Genius Plus Academy teaching team
What this question tests
This is Question 2 of the O-Level E-Math 2018 Paper 2. It tests percentage increase, in the Percentage & money (compound interest, exchange rates) area. It is worth 10 marks: (a) 2, (b) 3, (c) 1 + 4. 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) 2017 earnings \(= 3900 \times 12 = \$46\,800\). Percentage increase \(= \dfrac{46\,800 - 44\,000}{44\,000} \times 100 = \dfrac{2800}{44\,000} \times 100 = 6.36\%\) (3 s.f.).
(b) Amount after 6 years \(= 6500(1.0235)^6 = \$7472.06\). Interest \(= 7472.06 - 6500 = \$972.06\) (nearest cent).
(c)(i) Convert each price to Singapore dollars. London: \(\pounds 145 = 145 \times 1.97 = \$285.65\). Paris: \(\text{\texteuro}145 = 145 \div 0.66 = \$219.70\). Since $285.65 > $219.70, the London hotel costs more per night.
(ii) London 3 nights \(= 3 \times 145 \times 1.97 = \$856.95\). Paris 4 nights \(= 4 \times 145 \div 0.66 = \$878.79\). Subtotal \(= 856.95 + 878.79 = \$1735.74\). With the 1.8% fee: \(1735.74 \times 1.018 = \$1766.98\), so Ken pays \(\$1767\) (nearest dollar).
Answer: (a) \(6.36\%\)
(b) $972.06
(c)(i) London is dearer
(ii) $1767
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 percentage increase question from Percentage & money (compound interest, exchange rates), worth 10 marks: (a) 2, (b) 3, (c) 1 + 4.
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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