2026 PHS P2 Q10

Singapore relies on four water sources for its water supply.

It comprises water from local catchment, imported water, recycled water and desalinated water.

Recycled water (R) and desalinated water (D) are produced at five water plants respectively.

The matrix \(\mathbf M\) shows information about the production capacity for each water plant, measured in million gallons per day (mgd).

\(\mathbf M=\begin{array}{c}\begin{array}{cc}\mathrm R&\mathrm D\end{array} \\ \begin{pmatrix}20&30 \\ 35&70 \\ 50&30 \\ 50&30 \\ 50&30\end{pmatrix}\end{array}\ \begin{array}{l}\phantom{\mathrm R} \\ \text{Plant 1} \\ \text{Plant 2} \\ \text{Plant 3} \\ \text{Plant 4} \\ \text{Plant 5}\end{array}\)

1. Evaluate the matrix \(\mathbf K=\mathbf{TMS}\), where \(\mathbf T=\begin{pmatrix}1&1&1&1&1\end{pmatrix}\) and \(\mathbf S=\begin{pmatrix}1 \\ -1\end{pmatrix}\).[2]
2. State what the element(s) of matrix \(\mathbf K\) represent.[1]
3. The four water sources supply Singapore’s daily water demand of 440 million gallons a day (mgd).
   If a pie chart is drawn to represent these four water sources, calculate the sum of the angle of the sectors representing the water from local catchment and imported water.[2]
4. In 2060, Singapore’s daily water demand will be double that of the value in part (c).
   To meet this demand, the production of recycled water and desalinated water must reach the target percentages shown below.
   Source: PUB; STRAITS TIMES GRAPHICS.
   Hence, Singapore plans to raise the production capacity of its water plants as follows:
   Recycled water
   • Plant 1 will increase its capacity by 150%, while the other plants remain unchanged.
   • A new Plant 6, with the same production capacity as Plant 5, will be built.
   • A new Plant 7, with a production capacity 1.5 times that of Plant 6, will be built.
   Desalinated water
   • All existing plants will remain unchanged.
   • A new Plant 6, with a production capacity 1.2 times that of Plant 2, will be built.
   Using the given information, justify with calculations whether the new production capacities will meet the respective target percentages set for 2060.[5]
5. In order to increase its water supply, Singapore aims to expand its local catchment area.
   The bar chart compares the percentage of Singapore’s land area used as local catchment. However, the chart is misleading.
   Suggest one adjustment to the chart to avoid misinterpretation of the data. Justify your reason.[2]