SPM Mathematics 2019, Paper 2 (Question 4 & 5)

Question 4:
Diagram 2 in the answer space shows a rectangle door with the height of 2.5 m and the width of 1 m. The distance between P and Q is 1.2 m.
(a) On Diagram 2 in the answer space, mark the angle between the door and the wall. [1 mark]
(b) Hence, calculate the angle of opening of the door. [3 marks]

Answer:


Solution:
(b)

$\begin{array}{l}\sin x=\frac{0.6}{1}\\ x={36}^{o}52‘\\ \text{angle of opening}=x+x\\ ={36}^{o}52‘+{36}^{o}52‘\\ ={73}^{o}44‘\end{array}$

Question 5:
A furniture factory distributes plastic chairs and wooden chairs to supplier A and supplier B. Supplier A received 4 containers of plastic chairs and 3 containers of wooden chairs, with a total of 290 chairs. Supplier B received 5 containers of plastic chairs and 7 containers of wooden chairs, with a total of 460 chairs.
Using matrix method, find the number of plastic chairs and the number of wooden chairs in each containers.            [5 marks]


Solution:
x = Number of plastic chairs in a container
y = Number of wooden chairs in a container

$\begin{array}{l}4x+3y=290\mathrm{\dots \dots \dots \dots ..}\text{ (1)}\\ 5x+7y=460\mathrm{\dots \dots \dots \dots \dots }\text{ (2)}\\ \left(\begin{array}{l}4\text{ 3}\\ 5\text{ 7}\end{array}\right)\left(\begin{array}{l}x\\ y\end{array}\right)=\left(\begin{array}{l}290\\ 460\end{array}\right)\\ \left(\begin{array}{l}x\\ y\end{array}\right)=\frac{1}{28-15}\left(\begin{array}{l}\text{7 }-3\\ -5\text{ 4}\end{array}\right)\left(\begin{array}{l}290\\ 460\end{array}\right)\\ \left(\begin{array}{l}x\\ y\end{array}\right)=\frac{1}{13}\left(\begin{array}{l}\left(7\right)\left(290\right)\text{+}\left(-3\right)\left(460\right)\\ \left(-5\right)\left(290\right)\text{+}\left(4\right)\left(460\right)\end{array}\right)\\ \left(\begin{array}{l}x\\ y\end{array}\right)=\frac{1}{13}\left(\begin{array}{l}2030-1380\\ -1450+1840\end{array}\right)\\ \left(\begin{array}{l}x\\ y\end{array}\right)=\left(\begin{array}{l}50\\ 30\end{array}\right)\\ x=50\text{ and }y=30\end{array}$

∴ Number of plastic chairs in a container = 50
Number of wooden chairs in a container = 30