NSW Syllabuses

# Mathematics Standard Stage 6 - Year 12 Standard 1 - Networks MS-N1 Networks and Paths

## Outcomes

#### A student:

• MS1-12-8

applies network techniques to solve network problems

• MS1-12-9

chooses and uses appropriate technology effectively and recognises appropriate times for such use

• MS1-12-10

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

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 appreciation of the applicability of networks throughout their lives, for example social networks, and their ability to use associated techniques to optimise practical problems.

## Content

• N1.1: 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
• N1.2: 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
• 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