2026 NASS P2 Q7

2026 NASS P2 Q7

Secondary 4
11 marks

A café offers the following menu.

Main DishPrice
Chicken Burger\$5.80
Vegan Burger\$4.80
DrinkPrice
Apple Juice\$2.00
Orange Juice\$2.00
SoupPrice
Chicken Soup\$2.20
Mushroom Soup\$2.80
Onion Soup\$3.00
Set MealPrice
Chicken Set Meal (Chicken Burger + Chicken Soup + a drink)\$8.80
Vegan Set Meal (Vegan Burger + Mushroom Soup + a drink)\$8.50
  1. A customer orders the vegan set meal.
    1. Find the percentage saving when the customer orders the set meal instead of ordering the items separately.[2]
    2. The customer receives an \(x\%\) discount as a member of the café’s loyalty programme.
      The total bill, inclusive of a 10% service charge and 9% Goods and Services Tax (GST), is \$9.70.
      Find \(x\).
      Give your answer to the nearest whole number.[3]
  2. Every month, the café owner reviews the cost and selling prices of the set meals.
    The owner uses a \(1\times2\) matrix \(D\) to represent the new cost prices of the two set meals.
    \(D=PC\), where
    \(P=\begin{pmatrix}1.2&1.4&1.3\end{pmatrix}\quad\text{and}\quad C=\begin{pmatrix}2.20&1.80\\ 0.85&1.10\\ 0.40&0.40\end{pmatrix}\)
    The columns of \(C\) are Chicken and Vegan; the rows are Main Dish, Soup and Drinks, respectively.
    \(C\) represents the original cost prices of the main dish, soup and drink for each set meal.
    1. State what the elements of \(P\) represent.[1]
    2. Evaluate the matrix \(D\).[2]
    3. The owner revises the selling price if the percentage profit from selling a set meal is less than 90%.
      Determine whether the owner should revise the selling price of the Chicken Set Meal.
      Justify your answer with working.[3]

Solution:

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Answer:(a)(i) 11.5% (ii) \(x=5\). (b)(i) Cost increases of 20%, 40%, 30% (ii) \(D=\begin{pmatrix}4.35&4.22\end{pmatrix}\) (iii) Do not revise; profit is about 102%.

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