SPM Mathematics 2016, Paper 2 (Questions 5 & 6)

Question 5 (4 marks):
Diagram 5 shows a cylindrical tank in a residential area which have 125 houses. Each house received equal volume of water.

Diagram 5

The diameter of the cylindrical tank is 4 m. It is given that each house has a cuboid tank with a base area of 0.8 m².
Using $\pi =\frac{22}{7}$ , calculate the height of the water level, in m, of each tank in the house.


Solution:
$\begin{array}{l}\text{Volume of water in cylindrical tank}\\ =\pi r^{2}h\\ =\frac{22}{7}\times 2^2\times 3.5\\ =44{\text{ m}}^3\\ \\ \text{Volume of water in each cuboid}\\ \text{tank}=\frac{44}{125}\\ 0.8\times h=\frac{44}{125}\\ h=0.44\text{ m}\\ \\ \therefore \text{Height of water level in each }\\ \text{cuboid tank}=0.44\text{ m}.\end{array}$

Question 6 (5 marks):
Diagram 6 shows two parallel straight lines, POQ and RMS drawn on a Cartesian plane.

Diagram 6

Find
(a) the equation of the straight line RMS,
(b) the x-intercept of the straight line MN.


Solution:
(a)
$\begin{array}{l}{m}_{RMS}=m_{POQ}\\ =\frac{1-0}{-2-0}\\ =-\frac{1}{2}\\ \\ \text{At point }\left(4,6\right)\\ y_1=m{x}_1+c\\ 6=-\frac{1}{2}\left(4\right)+c\\ 6=-2+c\\ c=8\\ \\ \text{The equation of straight line }RMS\text{ is}\\ y=-\frac{1}{2}x+8\end{array}$


(b)
$\begin{array}{l}\text{When }y=0,\\ -\frac{1}{2}x+8=0\\ \frac{1}{2}x=8\\ x=16\\ \\ x\text{-intercept of straight line }MN\text{ is }16.\end{array}$