Question 5:
Diagram 4 shows a cuboid with a volume of 120 000 cm3.
The length of the cuboid is 10 cm more than its width, w cm.
(a) Show that w2 + 10 w – 2000 = 0.
[2 marks]
(b) Hence, find the width of the cuboid.
[2 marks]
Answer:
(a)
$$ \begin{aligned} \text { Volume } & =(w+10)(w)(60) \\ 120000 & =(w+10)(60 w) \\ 60 w^2+600 w-120000 & =0 \\ w^2+10 w-2000 & =0 \end{aligned} $$
(b)
$$ \begin{aligned} &\begin{aligned} & (w-40)(w+50)=0 \\ & w=40, w=-50 \end{aligned}\\ &\text { ∴ } \text { The width} \text { of the cuboid }=40 \mathrm{~cm} \end{aligned} $$
Diagram 4 shows a cuboid with a volume of 120 000 cm3.
The length of the cuboid is 10 cm more than its width, w cm.
(a) Show that w2 + 10 w – 2000 = 0.
[2 marks]
(b) Hence, find the width of the cuboid.
[2 marks]
Answer:
(a)
$$ \begin{aligned} \text { Volume } & =(w+10)(w)(60) \\ 120000 & =(w+10)(60 w) \\ 60 w^2+600 w-120000 & =0 \\ w^2+10 w-2000 & =0 \end{aligned} $$
(b)
$$ \begin{aligned} &\begin{aligned} & (w-40)(w+50)=0 \\ & w=40, w=-50 \end{aligned}\\ &\text { ∴ } \text { The width} \text { of the cuboid }=40 \mathrm{~cm} \end{aligned} $$
Question 6:
Diagram 5 is an undirected and weighted graph that shows the bus fares between four places.
(a) Based on Diagram 5,
(i) list the set of vertices,
(ii) determine the sum of degrees.
[2 marks]
(b) Lily wants to travel from Melaka to Ipoh. The bus ticket from Melaka directly to Ipoh has been sold out. Determine the cheapest alternative route that Lily can choose and calculate the total fare for this route.
[2 marks]
Answer:
(a)(i) Set of vertices = {Melaka, Kuala Lumpur, Shah Alam, Ipoh}
(a)(ii) 2 × 6 = 12
(b)
$$ \text { The cheapest alternative route }=\text { Melaka → Kuala Lumpur } \text { → Ipoh } $$$$ \begin{aligned} & =\text { RM14.40 + RM25.50 } \\ & =\text { RM39.90 } \end{aligned} $$
Diagram 5 is an undirected and weighted graph that shows the bus fares between four places.
(a) Based on Diagram 5,
(i) list the set of vertices,
(ii) determine the sum of degrees.
[2 marks]
(b) Lily wants to travel from Melaka to Ipoh. The bus ticket from Melaka directly to Ipoh has been sold out. Determine the cheapest alternative route that Lily can choose and calculate the total fare for this route.
[2 marks]
Answer:
(a)(i) Set of vertices = {Melaka, Kuala Lumpur, Shah Alam, Ipoh}
(a)(ii) 2 × 6 = 12
(b)
$$ \text { The cheapest alternative route }=\text { Melaka → Kuala Lumpur } \text { → Ipoh } $$$$ \begin{aligned} & =\text { RM14.40 + RM25.50 } \\ & =\text { RM39.90 } \end{aligned} $$