PT3 Mathematics 2016, Question 9

Question 9 (a):
Diagram 9 shows two ships.
(i) Compare the length of both ships by filling in the box with the correct values.
$\boxed{}>\boxed{}$

(ii) Table 9 shows the number of crews of both ships represented by x and y.


What is the maximum number of crews for each of the ships?

Solution:
(i)
$\boxed{397}>\boxed{342}$

(ii)
Maximum number of crews for ship R, x = 44
Maximum number of crews for ship W, y = 40

Question 9 (b):
Diagram 9.1 shows the price of two types of ladies handbags.


In conjunction with Women’s Day, a supermarket offers discounts for a few brands of ladies handbags. Puan Chan bought a Brand v handbag for the price of RM425.00 while Puan Aida bought a brand w handbag for the price of RM478.40.
Who receives a higher discount?

Solution:
$\begin{array}{l}\text{Brand }v:\\ \text{Discount}=\text{RM500}-\text{RM425}=\text{RM75}\\ \text{Percentage of discount}\\ =\frac{75}{500}\times 100\%\\ =15\%\\ \\ \text{Brand }w:\\ \text{Discount}=\text{RM598}-\text{RM478}\text{.40}=\text{RM119}\text{.60}\\ \text{Percentage of discount}\\ =\frac{119.60}{598}\times 100\%\\ =20\%\\ \\ \text{Puan Aida receives a higher discount}\text{.}\end{array}$

Question 9 (c):
A seminar hall in the shape of a regular polygon will be built next to the foyer as shown in Diagram 9.2.

Calculate
(i) the value of y,
(ii) the number of sides of the seminar hall.

Solution:
(i)
$\begin{array}{l}\text{Interior angle of regular pentagon}\\ =\frac{\left(n-2\right)\times {180}^o}{5}\\ =\frac{\left(5-2\right)\times {180}^o}{5}\\ ={108}^o\\ \\ y+{108}^o={180}^o\\ y={72}^o\end{array}$

(ii)
$\begin{array}{l}\text{Lets the interior angle of hall}=w\\ w+{112}^o+{108}^o={360}^o\\ w={360}^o-{220}^o\\ w={140}^o\\ \\ \text{Exterior angle}\\ ={180}^o-{140}^o\\ ={40}^o\\ \\ \text{Number of sides}=\frac{360}{40}=9\end{array}$