- Networks has accounted for a very healthy 9% and 7.5% of the HSC Std1 paper in the first two years of this exam.
- We have split N1 Networks and Paths into three categories for the purposes of this analysis: 1-Basic Concepts, 2-Shortest Paths and 3-Minimum Spanning Trees.
- This analysis will look at 1-Basic Concepts.
- Network diagram, table, matrix: Completing a table (or matrix) from a network graph and vice versa is a core competency that should be reviewed closely.
- This was last examined in the 2019 Std1 paper and numerous examples are included in our database to revise this important topic area.
- Basic Concepts: Questions review basic concepts such as; the degree of vertices (2020 Std1 1 MC, 2019 Std1 1 MC), tree and path definitions (2020 Std1 5 MC), connected network, weighted edge, etc..
- Networks were allocated 3 separate multiple choice questions in the 2020 Std1 exam. Our database includes many multiple choice examples which can be useful for targeting specific basic concepts and evaluate student understanding.
- Practical problems: a number of practical problems requiring simple network design and representation are included. We recommend reviewing 2020 Std1 9 MC where a lack of understanding of networks representing "competitions" was flagged.
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.
- Construct a network diagram to represent the information in the table. (2 marks)
- 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)
A directed network diagram is pictured below.
The information in the network diagram is used to complete the network table below, with a "0" used to signify that no connection exists. Complete the table. (2 marks)
The city of Robville is divided into five suburbs labelled as `A` to `E` on the map below.
A lake which is situated in the city is shaded on the map.
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'.
- 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.
- The network diagram is missing one edge and one vertex.
On the diagram
- draw the missing edge (1 mark)
- draw and label the missing vertex. (1 mark)
The map of Australia shows the six states, the Northern Territory and the Australian Capital Territory (ACT).
In the network diagram below, each of the vertices `A` to `H` represents one of the states or territories shown on the map of Australia. The edges represent a border shared between two states or between a state and a territory.
- In the network diagram, what is the order of the vertex that represents the Australian Capital Territory (ACT)? (1 mark)
- In the network diagram, Queensland is represented by which letter? Explain why. (2 marks)
The graph below represents a friendship network. The vertices represent the four people in the friendship network: Kwan (K), Louise (L), Milly (M) and Narelle (N).
An edge represents the presence of a friendship between a pair of these people. For example, the edge connecting K and L shows that Kwan and Louise are friends.
Which one of the following graphs does not contain the same information?
Two graphs, labelled Graph 1 and Graph 2, are shown below.
The sum of the degrees of the vertices of Graph 1 is
- two less than the sum of the degrees of the vertices of Graph 2.
- one less than the sum of the degrees of the vertices of Graph 2.
- equal to the sum of the degrees of the vertices of Graph 2.
- two more than the sum of the degrees of the vertices of Graph 2.
A store manager is directly in charge of five department managers.
Each department manager is directly in charge of six sales people in their department.
This staffing structure could be represented graphically by
A. a tree.
B. a path.
C. a cycle.
D. a weighted graph.