NSW Syllabuses

# Mathematics Standard Stage 6 - Year 12 Standard 2 - Networks MS-N2 Network Concepts

## Outcomes

#### A student:

• MS2-12-8

solves problems using networks to model decision-making in practical problems

• MS2-12-9

chooses and uses appropriate technology effectively in a range of contexts, and applies critical thinking to recognise appropriate times and methods for such use

• MS2-12-10

uses mathematical argument and reasoning to evaluate conclusions, communicating a position clearly to others and justifying a response

Related Life Skills outcomes: MALS6-11, MALS6-12, MALS6-13, MALS6-14

• ## Subtopic Focus

• The principal focus of this subtopic is to identify and use network terminology and to solve problems involving networks.
• Students develop their awareness of the applicability of networks throughout their lives, for example social media networks, and their ability to use associated techniques to optimise practical problems.
• ## Content

• N2.1: Networks
• Students:
• recognise circumstances in which networks could be used, eg the cost of connecting various locations on a university campus with computer cables
• given a map, draw a network to represent the map, eg travel times for the stages of a planned journey
• draw a network diagram to represent information given in a table
• investigate and solve practical problems, eg the Königsberg Bridge problem or planning a garbage bin collection route
• N2.2: Shortest paths
• Students:
• determine the minimum spanning tree by using Kruskal's or Prim's algorithms or by inspection
• determine the definition of a tree and a minimum spanning tree for a given network
• use minimum spanning trees to solve minimal connector problems, eg minimising the length of cable needed to provide power from a single power station to substations in several towns (ACMGM103)
• find the shortest path from one place to another in a network with no more than 10 vertices
• identify the shortest path on a network diagram
• recognise a circumstance in which a shortest path is not necessarily the best path or contained in any minimum spanning tree