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ACMGM024

obtain a scale factor and use it to solve scaling problems involving the calculation of the areas of similar figures

ACMGM025

obtain a scale factor and use it to solve scaling problems involving the calculation of surface areas and volumes of similar solids.

ACMGM034

review the use of the trigonometric ratios to find the length of an unknown side or the size of an unknown angle in a right-angled triangle

ACMGM050

use an appropriately percentaged two-way frequency table to identify patterns that suggest the presence of an association

ACMGM075

use a general first-order linear recurrence relation to generate the terms of a sequence and to display it in both tabular and graphical form

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.

solve practical problems involving the trigonometry of right-angled and non-right-angled triangles, including problems involving angles of elevation and depression and the use of bearings in navigation.

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

ACMGM007

use currency exchange rates to determine the cost in Australian dollars of purchasing a given amount of a foreign currency, such as US$1500, or the value of a given amount of foreign currency when converted to Australian dollars, such as the value of …

ACMGM012

use a spreadsheet or an equivalent technology to construct a table of values from a formula, including two-by-two tables for formulas with two variable quantities; for example, a table displaying the body mass index (BMI) of people of different weights …

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

ACMGM009

use a spreadsheet to display examples of the above computations when multiple or repeated computations are required; for example, preparing a wage-sheet displaying the weekly earnings of workers in a fast food store where hours of employment and hourly …

ACMGM016

use matrices, including matrix products and powers of matrices, to model and solve problems; for example, costing or pricing problems, squaring a matrix to determine the number of ways pairs of people in a communication network can communicate with each …

ACMGM077

use first-order linear recurrence relations to model and analyse (numerically or graphically only) practical problems; for example, investigating the growth of a trout population in a lake recorded at the end of each year and where limited recreational …

ACMGM085

explain the meaning of the terms: Eulerian graph, Eulerian trail, semi-Eulerian graph, semi-Eulerian trail and the conditions for their existence, and use these concepts to investigate and solve practical problems; for example, the Königsberg Bridge problem, …

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