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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 AHCCCTCC
  • given a map, draw a network to represent the map, eg travel times for the stages of a planned journey CCT
  • 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) ICT
  • find the shortest path from one place to another in a network with no more than 10 vertices AAM CCT
  • 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 CCT