SPM Mathematics Trial 2021 (Selangor), Paper 2 (Question 9 & 10)

Question 9:
Diagram 5 shows a rhombus KLMN.


Given that KN = 10 units.

Find
(a) gradient of straight line LM.
(b) the equation of straight line MN.
[4 marks]


Solution:
(a)

$\begin{array}{l}\text{Point }k=\left(-6,0\right)\\ m_{LM}=m_{KN}\\ m_{LM}=\frac{y_2-y_1}{x_2-x_1}\\ m_{LM}=\frac{6-0}{2-\left(-6\right)}\\ m_{LM}=\frac{6}{8}=\frac{3}{4}\end{array}$


(b)

$\begin{array}{l}KL=KN=10\text{ units}\\ \therefore OL=\sqrt{K{L}^2-O{K}^2}\\ =\sqrt{{10}^2-6^2}\\ =\sqrt{64}\\ =8\text{ units}\\ \\ m_{MN}=m_{KL}\\ =-\frac{\text{y-intercept}}{\text{x-intercept}}\\ =-\frac{8}{\left(-6\right)}\\ =\frac{4}{3}\\ \\ y_1=m{x}_1+c\\ 6=\frac{4}{3}\left(2\right)+c\\ c=6-\frac{8}{3}\\ c=\frac{10}{3}\\ \\ \therefore \text{ Equation of the straight line }MN\\ y=mx+c\\ y=\frac{4}{3}x+\frac{10}{3}\end{array}$

Soalan 10:
Mr. Eric and Mrs. Lisa have bought a house. They plan to buy fire insurance for their house. The insurable value of their house is RM375 000. The insurance policy chosen by them has a co-insurance provision to insure 80% of the insurable value of his home. The deductible value is RM3 200.

(a) Calculate the amount of insurance that they should buy for their house.

(b) A small fire occured in their house resulting in a loss value of RM27 500 .
Calculate the compensation payment that would be received if they insured their house on amount of insurance they would have to buy.

(c) If their entire house was burnt down in a fire, would they receive compensation of RM375 000 if they insure their house according to the amount in 10(a) ?
Give your justification and state the value of compensation received.
[4 marks]


Penyelesaian:
(a)

$\begin{array}{l}\text{Amount of insurance should be bought}\\ =\text{RM}375000\times \frac{80}{100}\\ =\text{RM}300000\end{array}$

(b)
Compensation payment
= loss value – deductible
= RM27 500 – RM3 200
= RM24 300


(c)
No, they would not receive compensation of RM375 000.

Maximum compensation will receive
= RM300 000 – RM3 200
= RM296 800

Thus, Mr. Eric and Mrs. Lisa would only receive compensation of RM296 800 because the deductible value is RM3 200.