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Networks, STD1 N1 2023 HSC 15

The table shows some of the flight distances (rounded to the nearest 10 km between various Australian cities.

  1. Use the information in the table to complete the network diagram where the edges are labelled with distances.  (2 marks)
     


 

  1. Mahsa wants to travel from Hobart to Darwin. She wants to change planes only once.
  2. Using the network diagram, calculate how many kilometres she will travel by plane.  (1 mark)

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a.  

b.    \(4190\text{ km}\)

Show Worked Solution

a.

b.    \(\text{Changing planes only once}\Rightarrow H\rightarrow S\rightarrow D\)

\(\text{Kilometres travelled}=1040+3150=4190\text{ km}\)

Networks, STD1 N1 2022 HSC 20

The table below shows the distances, in kilometres, between a number of towns.
 

  1. Using the vertices given, draw a weighted network diagram to represent the information shown in the table.  (2 marks)
     

     
  2. A tourist wishes to visit each town.
  3. Draw the minimum spanning tree which will allow for this AND determine its length.  (3 marks)
     

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  1.  
     
     
  2.   
     
  3. `1015\ text{km}`
Show Worked Solution

a. 

b.   `text{Using Prim’s algorithm (starting at}\ Y):`

`text{1st edge:}\ YC`

`text{2nd edge:}\ CB`

`text{3rd edge:}\ SB`

`text{4th edge:}\ YM`

`text{Length of minimum spanning tree}`

`=275 + 150+60+530`

`=1015\ text{km}`

Networks, STD1 N1 2019 HSC 17

A regional airline operates flights in Queensland. Flight times between connected towns are shown in the table.
 


 

Draw a network diagram to show how the towns are connected, with weights on the edges showing the flight times.  (2 marks)

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Show Worked Solution

`text(Edge weights are in minutes duration.)`

Networks, STD2 N2 SM-Bank 28

In central Queensland, there are four petrol stations `A`, `B`, `C` and `D`. The table shows the length, in kilometres, of roads connecting these petrol stations.
 


 

  1. Construct a network diagram to represent the information in the table.  (2 marks)

  2. A petrol tanker needs to refill each station. It starts at Station `A` and visits each station.

     

    Calculate the shortest distance that can be travelled by the petrol tanker. In your answer, include the order the petrol stations are refilled.  (2 marks)

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  1.  
  2. `380\ text(km)`
Show Worked Solution
a.   

 

b.   `text(Shortest Path from)\ A\ (text(visiting all stations))`

`A – B – D – C`

`text(Distance)` `= 170 + 90 + 120`
  `= 380\ text(km)`