The answer
(a) \(7\) girls
(b) \(\mathbf{F} = \begin{pmatrix} 30 \\ 26 \\ 24 \end{pmatrix}\)
(c) \(\mathbf{M} = \begin{pmatrix} 996 \\ 1316 \end{pmatrix}\)
(d) the daily fees taken, morning \(\$996\), afternoon \(\$1316\)
(e) \(\$11\,560\)
(f) \(\approx 22.0\%\) increase
O-Level E-Math 2020 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 2020 Paper 2. It tests matrix multiplication, in the Matrices & percentage area. It is worth 9 marks: (a) 1, (b) 1, (c) 2, (d) 1, (e) 1, (f) 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) Afternoon group Q children \(= H_{2,2} = 16\); boys \(= B_{2,2} = 9\); girls \(= 16 - 9 = 7\).
(b) \(\mathbf{F} = \begin{pmatrix} 30 \\ 26 \\ 24 \end{pmatrix}\) (rows P, Q, R).
(c) \(\mathbf{M} = \mathbf{HF} = \begin{pmatrix} 10(30) + 12(26) + 16(24) \\ 14(30) + 16(26) + 20(24) \end{pmatrix} = \begin{pmatrix} 996 \\ 1316 \end{pmatrix}\).
(d) Each element is the total fees collected in one day from all three groups: \(\$996\) for the morning session and \(\$1316\) for the afternoon session.
(e) One day's total is \(996 + 1316 = \$2312\). The club runs \(5\) days a week and each child attends every day, so the weekly total is \(2312 \times 5 = \$11\,560\). *(The publisher key gives \(\$2312\), taking the column sum directly without the \(\times 5\) for the five days; we include the 5-day factor that the stem specifies.)*
(f) Daily fees by group in week 1: P \(= 24 \times 30 = 720\), Q \(= 28 \times 26 = 728\), R \(= 36 \times 24 = 864\) (total \(2312\), matching \(\mathbf{M}\)). Week 2: P \(= 720 \times 1.5 = 1080\), Q \(= 728 \times 1.5 = 1092\), R \(= 864 \times 0.75 = 648\) (total \(2820\)). Percentage change \(= \dfrac{2820 - 2312}{2312} \times 100 = 21.97\% \approx 22.0\%\) increase. *(The publisher key gets \(40.7\%\) by mistakenly applying \(\times 1.25\), a \(25\%\) increase, to group R instead of the stated \(25\%\) decrease.)*
Answer: (a) \(7\) girls
(b) \(\mathbf{F} = \begin{pmatrix} 30 \\ 26 \\ 24 \end{pmatrix}\)
(c) \(\mathbf{M} = \begin{pmatrix} 996 \\ 1316 \end{pmatrix}\)
(d) the daily fees taken, morning \(\$996\), afternoon \(\$1316\)
(e) \(\$11\,560\)
(f) \(\approx 22.0\%\) increase
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 matrix multiplication question from Matrices & percentage, worth 9 marks: (a) 1, (b) 1, (c) 2, (d) 1, (e) 1, (f) 3.
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