The answer
(a) \(\mathbf{P} = \begin{pmatrix} 28 & 170 & 95 \\ x & 176 & 89 \end{pmatrix}\)
(b) \(\mathbf{R} = \begin{pmatrix} 1314 \\ 3x + 1236 \end{pmatrix}\)
(c) the weekly total hire charge in $
(d) \(x = 26\)
O-Level E-Math 2017 Paper 1 Question 19 · Verified worked solution by the Genius Plus Academy teaching team
What this question tests
This is Question 19 of the O-Level E-Math 2017 Paper 1. It tests writing a data matrix, in the Matrices area. It is worth 5 marks: 1 + 2 + 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) Rows are the two weeks, columns are C, A, S: \(\mathbf{P} = \begin{pmatrix} 28 & 170 & 95 \\ x & 176 & 89 \end{pmatrix}\).
(b) Multiply the \(2 \times 3\) matrix by the \(3 \times 1\) charge column to get a \(2 \times 1\) matrix: \[\mathbf{R} = \begin{pmatrix} 28(3) + 170(5) + 95(4) \\ x(3) + 176(5) + 89(4) \end{pmatrix} = \begin{pmatrix} 84 + 850 + 380 \\ 3x + 880 + 356 \end{pmatrix} = \begin{pmatrix} 1314 \\ 3x + 1236 \end{pmatrix}.\]
(c) Each element of \(\mathbf{R}\) is the total amount of money (in dollars) collected for court hire that week: the top entry is Week 1's total ($1314) and the bottom entry is Week 2's total.
(d) Equal totals: \(1314 = 3x + 1236 \Rightarrow 3x = 78 \Rightarrow x = 26\).
Answer: (a) \(\mathbf{P} = \begin{pmatrix} 28 & 170 & 95 \\ x & 176 & 89 \end{pmatrix}\)
(b) \(\mathbf{R} = \begin{pmatrix} 1314 \\ 3x + 1236 \end{pmatrix}\)
(c) the weekly total hire charge in $
(d) \(x = 26\)
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 writing a data matrix question from Matrices, worth 5 marks: 1 + 2 + 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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