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Unit 4 General Mathematics

This unit has three topics: ‘Time series analysis’; ‘ Loans, investments and annuities’ and ‘Networks and decision mathematics’. ‘Time series analysis’ continues students’ study of statistics by introducing them to the concepts and techniques of time …

Unit 4 | General Mathematics | Mathematics | Senior secondary curriculum

ACMGM089

smooth time series data by using a simple moving average, including the use of spreadsheets to implement this process

ACMGM095

calculate the effective annual rate of interest and use the results to compare investment returns and cost of loans when interest is paid or charged daily, monthly, quarterly or six-monthly

ACMGM092

fit a least-squares line to model long-term trends in time series data.

ACMGM093

implement the statistical investigation process to answer questions that involve the analysis of time series data.

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

ACMGM091

deseasonalise a time series by using a seasonal index, including the use of spreadsheets to implement this process

ACMGM105

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

ACMGM111

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

ACMGM097

use a recurrence relation to model a reducing balance loan and investigate (numerically or graphically) the effect of the interest rate and repayment amount on the time taken to repay the loan

ACMGM099

use a recurrence relation to model an annuity, and investigate (numerically or graphically) the effect of the amount invested, the interest rate, and the payment amount on the duration of the annuity

ACMGM094

use a recurrence relation to model a compound interest loan or investment, and investigate (numerically or graphically) the effect of the interest rate and the number of compounding periods on the future value of the loan or investment

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.

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

ACMGM109

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 …

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