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NSW Syllabuses

Mathematics Standard Stage 6 - Year 12 Standard 2 - Networks MS-N3 Critical Path Analysis


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 use critical path analysis in the optimisation of real-life problems.

Students develop awareness that critical path analysis is a useful tool in project planning, management and logistics.


  • Students:
  • construct a network to represent the duration and interdependencies of activities that must be completed during a particular project, for example a student schedule, or preparing a meal (ACMGM104) AAM CCTICTLPSC
  • given activity charts, prepare network diagrams and use critical path analysis to determine the minimum time for a project to be completed (ACMGM107) AAM
  • use forward and backward scanning to determine the earliest starting time (EST) and latest starting time (LST) for each activity in a project (ACMGM105)
  • understand why the EST for an activity could be zero, and in what circumstances it would be greater than zero L
  • calculate float times of non-critical activities (ACMGM108) L
  • understand what is meant by critical path
  • use ESTs and LSTs to locate the critical path(s) for the project (ACMGM106)
  • solve small-scale network flow problems, including the use of the ‘maximum-flow minimum-cut’ theorem, for example determining the maximum volume of oil that can flow through a network of pipes from an oil storage tank (the source) to a terminal (the sink) (ACMGM109) AAM
  • convert information presented in a table into a network diagram
  • determine the flow capacity of a network and whether the flow is sufficient to meet the demand in various contexts