SmarterEd

Aussie Maths & Science Teachers: Save your time with SmarterEd

Networks, STD2 N2 2023 HSC 17

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)

Show Answers Only

a.

 

b.   

Show Worked Solution

a. 

       

 

b.   

 
   
   

Networks, STD2 N2 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)
     

Show Answers Only
  1.  
     
     
  2.   
     
Show Worked Solution

a. 

 

b.   

Networks, STD2 N2 SM-Bank 28

In central Queensland, there are four petrol stations , , and . 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 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)

Show Answers Only
  1.  
Show Worked Solution
a.   

 

b.   

 

Networks, STD2 N2 2009 FUR2 1

The city of Robville is divided into five suburbs labelled as to on the map below. 

A lake which is situated in the city is shaded on the map.

 

NETWORKS, FUR2 2009 VCAA 11

A table is constructed to represent the number of land borders between suburbs.

If there is no land border between two suburbs, the table records a '0'. If there is a single land border between two suburbs, the table records a '1', and if there are two separate land borders between the same two suburbs, the table records a '2'.
 

 

  1. Explain why all values in the final row and final column of the table are zero.  (1 mark)

In the network diagram below, vertices represent suburbs and edges represent land borders between suburbs. 

The diagram has been started but is not finished.

 

Networks, FUR2 2009 VCAA 1_1

  1. The network diagram is missing one edge and one vertex. 

     

    On the diagram

    1. draw the missing edge  (1 mark)
    2. draw and label the missing vertex.  (1 mark)

Show Answers Only
  2. i. & ii.
    Networks, FUR2 2009 VCAA 1 Answer
Show Worked Solution

a.  

 

b.i. & ii.    Networks, FUR2 2009 VCAA 1 Answer