The answer
(a) \(Q = \begin{pmatrix} 24 & 14 \\ 29 & x \\ 20 & 15 \end{pmatrix}\)
(b) \(T = \begin{pmatrix} 800 & 822 \\ 290+40x & 232+45x \\ 800 & 835 \end{pmatrix}\)
(c) \(x = 11\)
O-Level E-Math 2019 Paper 1 Question 21 · Verified worked solution by the Genius Plus Academy teaching team
What this question tests
This is Question 21 of the O-Level E-Math 2019 Paper 1. It tests writing a data matrix, in the Matrices area. It is worth 4 marks: 1 + 2 + 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 = Koh, Min, Suman; columns = B/W, C: \(Q = \begin{pmatrix} 24 & 14 \\ 29 & x \\ 20 & 15 \end{pmatrix}\).
(b) \(T = QP\) is \(3 \times 2\) (cost on printer \(A\), cost on printer \(B\) for each person): \[T = \begin{pmatrix} 24(10)+14(40) & 24(8)+14(45) \\ 29(10)+x(40) & 29(8)+x(45) \\ 20(10)+15(40) & 20(8)+15(45) \end{pmatrix} = \begin{pmatrix} 800 & 822 \\ 290+40x & 232+45x \\ 800 & 835 \end{pmatrix}.\]
(c) On printer \(A\): Koh pays 800 cents, Min pays \(290 + 40x\) cents. Min pays 70 cents less: \(290 + 40x = 800 - 70 = 730 \Rightarrow 40x = 440 \Rightarrow x = 11\).
Answer: (a) \(Q = \begin{pmatrix} 24 & 14 \\ 29 & x \\ 20 & 15 \end{pmatrix}\)
(b) \(T = \begin{pmatrix} 800 & 822 \\ 290+40x & 232+45x \\ 800 & 835 \end{pmatrix}\)
(c) \(x = 11\)
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 4 marks: 1 + 2 + 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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