2025 CHS PRELIMS P2 Q9

2025 CHS PRELIMS P2 Q9

Secondary 4
7 marks

A company produces four types of healthy snacks — granola bars, fruit juices, protein shakes and yoghurt cups. The quantities delivered daily to three health stores are shown in the table below.

Snack TypeGranola BarsFruit JuicesProtein ShakesYoghurt Cups
Store A\(45\)\(30\)\(25\)\(20\)
Store B\(50\)\(25\)\(30\)\(35\)
Store C\(60\)\(40\)\(20\)\(25\)
  1. Write down a \(3\times4\) matrix \(P\) to show the number of each type of snack delivered to each store.[1]
  2. The cost of each granola bar, fruit juice, protein shake and yoghurt cup is $1.50, $2.00, $3.20 and $1.80 respectively. Represent these prices in a \(4\times1\) column matrix \(Q\).[1]
  3. Evaluate the matrix \(T=PQ\).[2]
  4. State what each of the elements in matrix \(T\) represents.[1]
    1. Find the matrix \(\begin{pmatrix}1&1&1\end{pmatrix}P\).[1]
    2. Explain what each element in \(\begin{pmatrix}1&1&1\end{pmatrix}P\) represents.[1]

Solution:

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Answer:(a) \(\begin{pmatrix}45&30&25&20\\50&25&30&35\\60&40&20&25\end{pmatrix}\) (b) \(\begin{pmatrix}1.50\\2.00\\3.20\\1.80\end{pmatrix}\) (c) \(\begin{pmatrix}243.50\\284\\279\end{pmatrix}\) (d) Total delivery value for each store (e)(i) \(\begin{pmatrix}155&95&75&80\end{pmatrix}\) (e)(ii) Total number of each snack type

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