2026 CSS P2 Q4

A community club is organising a sports carnival for children. Children can choose to participate in one of three events – badminton, table tennis or floorball.

Matrix \(E\) shows the number of boys and girls in each category for the age group 7 to 10 years old.

\(\begin{array}{rcl}&\begin{array}{cc}\text{Boys}&\text{Girls}\end{array}& \\ E=&\begin{pmatrix}6&8 \\ 9&5 \\ 4&10\end{pmatrix}&\begin{array}{l}\text{Badminton} \\ \text{Table tennis} \\ \text{Floorball}\end{array}\end{array}\)

Matrix \(F\) shows the number of boys and girls in each category for the age group 11 to 14 years old.

\(\begin{array}{rcl}&\begin{array}{cc}\text{Boys}&\text{Girls}\end{array}& \\ F=&\begin{pmatrix}12&9 \\ 7&13 \\ 11&6\end{pmatrix}&\begin{array}{l}\text{Badminton} \\ \text{Table tennis} \\ \text{Floorball}\end{array}\end{array}\)

1. Evaluate the matrix \(T=E+F\).[1]
2. Each participant is charged an entry fee. The entry fee is $28 for badminton, $24 for table tennis and $20 for floorball.
   Represent the fees in a \(1\times3\) matrix \(C\).[1]
3. Evaluate the matrix \(M=CT\)[2]
   and state what the elements in matrix \(M\) represent.[1]
4. Calculate the total amount of entry fees collected for the sports carnival.[1]
5. The community club has decided to organise a similar sports carnival for teenagers aged 15 to 18 years old. As compared to the fees for children aged 7 to 14 years old, the entry fees for teenagers are increased by 15% for badminton, 10% for table tennis and 20% for floorball.
   Using matrix multiplication, calculate the entry fees for teenagers for each category. Give your answer in matrix form.[2]