The answer
(a) $813.54
(b) \(6144\) m²
(c) \(222\) students
(d)(i) \(T = \begin{pmatrix} 0.3 & 0.35 & 0.35 \end{pmatrix}\)
(ii) \(P = \begin{pmatrix} 73.4 & 55.1 \end{pmatrix}\)
(iii) the final course grades of Koh and Min
O-Level E-Math 2025 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 2025 Paper 2. It tests percentage increase, in the Percentage / Map scale / Ratio / Matrices area. It is worth 10 marks: 1 + 3 + 3 + (1 + 1 + 1). 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) This year \(= 780 \times (1 + 0.043) = 780 \times 1.043 = \$813.54\).
(b) Length scale: \(35\) cm represents \(5.6\) km \(= 560\,000\) cm, so \(1\) cm represents \(\dfrac{560\,000}{35} = 16\,000\) cm \(= 160\) m. Area scale: \(1\) cm² represents \(160^2 = 25\,600\) m². Real area \(= 0.24 \times 25\,600 = 6144\) m².
(c) \(A:B = 2:3\) and \(B:C = 5:4\). Make \(B\) common: \(A:B = 10:15\), \(B:C = 15:12\), so \(A:B:C = 10:15:12\). Let the counts be \(10x\), \(15x\), \(12x\). When \(\tfrac38\) of Team C move to A, the new Team A \(= 10x + \tfrac38(12x) = 10x + 4.5x = 14.5x = 87 \Rightarrow x = 6\). Total students \(= (10+15+12)x = 37 \times 6 = 222\).
(d)(i) Test 1 is \(30\% = 0.3\); the remaining \(70\%\) is split equally between Tests 2 and 3, so each is \(35\% = 0.35\). Thus \(T = \begin{pmatrix} 0.3 & 0.35 & 0.35 \end{pmatrix}\).
(ii) \(P = TR = \begin{pmatrix} 0.3 & 0.35 & 0.35 \end{pmatrix}\begin{pmatrix} 86 & 74 \\ 56 & 70 \\ 80 & 24 \end{pmatrix}\). Koh: \(0.3(86) + 0.35(56) + 0.35(80) = 25.8 + 19.6 + 28 = 73.4\). Min: \(0.3(74) + 0.35(70) + 0.35(24) = 22.2 + 24.5 + 8.4 = 55.1\). So \(P = \begin{pmatrix} 73.4 & 55.1 \end{pmatrix}\).
(iii) The elements of \(P\) are the overall (weighted) final grades for the course for Koh (\(73.4\)) and Min (\(55.1\)).
Answer: (a) $813.54
(b) \(6144\) m²
(c) \(222\) students
(d)(i) \(T = \begin{pmatrix} 0.3 & 0.35 & 0.35 \end{pmatrix}\)
(ii) \(P = \begin{pmatrix} 73.4 & 55.1 \end{pmatrix}\)
(iii) the final course grades of Koh and Min
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 / Map scale / Ratio / Matrices, worth 10 marks: 1 + 3 + 3 + (1 + 1 + 1).
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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