2026 NORTHBROOKS P2 Q4

2026 NORTHBROOKS P2 Q4

Secondary 4
15 marks
  1. Sophia pays a monthly rent of \$3174.20.
    This is 18% more than her monthly rent last year.
    Calculate her monthly rent last year.[2]
  2. A new building is drawn on two maps of different scales.
    The area of the building drawn on the first map with a scale of \(1:50\,000\) is \(16\text{ cm}^2\).
    Given that the area of the same building drawn on the second map is \(25\text{ cm}^2\), find the scale of the second map in the form of \(1:n\).[4]
  3. In a Secondary 3 cohort, students join one of three activities: Dance, Music or Art.
    The ratio of the number of students in Dance to the number of students in Music is 4 : 7.
    The ratio of the number of students in Music to the number of students in Art is 3 : 5.
    \(\dfrac15\) of students from Art transfer to Dance.
    There are now 95 students in Dance.
    Find the total number of students in the cohort.[3]
  4. A bakery sells 3 types of whole pies, Apple Pie, Nutella Pie and Strawberry Pie.
    The table shows the number of each type of pie sold on a particular Saturday and Sunday, along with the price of each type of pie.
    Apple PieNutella PieStrawberry Pie
    Saturday131518
    Sunday102022
    Price of each pie\$50\$40\$75
    It is given that \(Q=\begin{pmatrix}13&15&18\\ 10&20&22\end{pmatrix}\) and \(P=\begin{pmatrix}50\\ 40\\ 75\end{pmatrix}\).
    1. The bakery had a promotion over the weekend, offering a 10% discount on Apple Pies and a 20% discount on Strawberry Pies.
      Represent this information in a \(3\times3\) matrix \(D\).[1]
    2. Evaluate the matrix \(T=DP\).[1]
    3. State what each element of matrix \(T\) represents.[1]
    4. Using matrix multiplication, find the total amount of money collected by the bakery over the weekend from selling the pies at discounted prices.[3]

Solution:

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Answer:(a) \$2690. (b) \(1:40\,000\). (c) 340 students. (d)(i) \(D=\operatorname{diag}(0.9,1,0.8)\) (ii) \(T=(45,40,60)^T\) (iii) Discounted pie prices in the stated order. (iv) \$4835.

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