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ACMGM102

identify a minimum spanning tree in a weighted connected graph either by inspection or by using Prim’s algorithm

ACMGM103

use minimal spanning trees to solve minimal connector problems; for example, minimising the length of cable needed to provide power from a single power station to substations in several towns.

ACMGM104

construct a network to represent the durations and interdependencies of activities that must be completed during the project; for example, preparing a meal

ACMGM105

use forward and backward scanning to determine the earliest starting time (EST) and latest starting times (LST) for each activity in the project

ACMGM106

use ESTs and LSTs to locate the critical path(s) for the project

ACMGM107

use the critical path to determine the minimum time for a project to be completed

ACMGM108

calculate float times for non-critical activities.

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 …

ACMGM110

use a bipartite graph and/or its tabular or matrix form to represent an assignment/ allocation problem; for example, assigning four swimmers to the four places in a medley relay team to maximise the team’s chances of winning

ACMGM111

determine the optimum assignment(s), by inspection for small-scale problems, or by use of the Hungarian algorithm for larger problems.

ACMMM001

determine the coordinates of the midpoint of two points

ACMMM002

examine examples of direct proportion and linearly related variables

ACMMM003

recognise features of the graph of \(y=mx+c\), including its linear nature, its intercepts and its slope or gradient

ACMMM004

find the equation of a straight line given sufficient information; parallel and perpendicular lines

ACMMM005

solve linear equations.

ACMMM006

examine examples of quadratically related variables

ACMMM007

recognise features of the graphs of \(y=x^2\), \(y=a{(x-b)}^2+c\), and \(y=a\left(x-b\right)\left(x-c\right)\) including their parabolic nature, turning points, axes of symmetry and intercepts

ACMMM008

solve quadratic equations using the quadratic formula and by completing the square

ACMMM009

find the equation of a quadratic given sufficient information

ACMMM010

find turning points and zeros of quadratics and understand the role of the discriminant

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