2026 PCSS P2 Q4

The table below shows the distribution of three types of apartments in three blocks of an Executive Condominium.

This information can be represented by the matrix \(\mathbf A=\begin{pmatrix}25&20&60\\35&45&30\\30&50&10\end{pmatrix}\).

The areas of the 3-room, 4-room and 5-room apartments are \(75\text{ m}^2\), \(95\text{ m}^2\) and \(120\text{ m}^2\) respectively.

1. Represent the areas of the apartments in a \(3\times1\) column matrix \(\mathbf C\).[1]
2. Evaluate the matrix \(\mathbf M=\mathbf{AC}\).[2]
3. State what the elements of \(\mathbf M\) represent.[1]
4. Estate management fees are charged based on the floor area of the apartments in the three blocks per quarter. The estate management fee rate is \(\$15/\text{m}^2\) per quarter. Find the total amount of estate management fee collected in a year for the Executive Condominium.[3]
5. The total estate management fee collected in one year for the Executive Condominium is used in the following areas.

   Areas	Amount
   Day-to-day operating expenses	\(25\%\) of the total amount collected
   Cleaning	\(\dfrac15\) of the total amount collected
   Security guards	\(\$2350\) per month for each security guard. The estate has 2 security guards.
   Landscaping	\(\$50\,000\) per year
   Electricity for common areas	\(\$120\,000\) per year

   The remaining amount is transferred to the sinking fund, which is used for future major repairs and replacement of shared facilities.
   Calculate the amount transferred to the sinking fund.[4]