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ACMGM061

use the equation of a fitted line to make predictions

This unit has three topics: ‘Bivariate data analysis’, ‘Growth and decay in sequences’ and ‘Graphs and networks’. ‘Bivariate data analysis’ introduces students to some methods for identifying, analysing and describing associations between pairs of variables, …

Unit 3 | General Mathematics | Mathematics | Senior secondary curriculum

ACMGM069

deduce a rule for the nth term of a particular arithmetic sequence from the pattern of the terms in an arithmetic sequence, and use this rule to make predictions

ACMGM073

deduce a rule for the nth term of a particular geometric sequence from the pattern of the terms in the sequence, and use this rule to make predictions

ACMGM058

use a residual plot to assess the appropriateness of fitting a linear model to the data

ACMGM062

distinguish between interpolation and extrapolation when using the fitted line to make predictions, recognising the potential dangers of extrapolation

ACMGM065

identify possible non-causal explanations for an association, including coincidence and confounding due to a common response to another variable, and communicate these explanations in a systematic and concise manner.

ACMGM052

construct a scatterplot to identify patterns in the data suggesting the presence of an association

ACMGM057

model a linear relationship by fitting a least-squares line to the data

ACMGM048

review the statistical investigation process; for example, identifying a problem and posing a statistical question, collecting or obtaining data, analysing the data, interpreting and communicating the results.

ACMGM051

describe an association in terms of differences observed in percentages across categories in a systematic and concise manner, and interpret this in the context of the data.

ACMGM067

use recursion to generate an arithmetic sequence

ACMGM071

use recursion to generate a geometric sequence

ACMGM056

use a scatterplot to identify the nature of the relationship between variables

ACMGM060

use the coefficient of determination to assess the strength of a linear association in terms of the explained variation

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

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, …

ACMGM086

explain the meaning of the terms: Hamiltonian graph and semi-Hamiltonian graph, and use these concepts to investigate and solve practical problems; for example, planning a sight-seeing tourist route around a city, the travelling-salesman problem (by trial-and-error …

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