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ACMGM072

display the terms of a geometric sequence in both tabular and graphical form and demonstrate that geometric sequences can be used to model exponential growth and decay in discrete situations

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

ACMGM043

construct and analyse a straight-line graph to model a given linear relationship; for example, modelling the cost of filling a fuel tank of a car against the number of litres of petrol required.

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

Structure of Mathematical Methods Mathematical Methods

Mathematical Methods is organised into four units. The topics broaden students’ mathematical experience and provide different scenarios for incorporating mathematical arguments and problem solving. The units provide a blending of algebraic and geometric …

Structure of Mathematical Methods | Mathematical Methods | Mathematics | Senior secondary curriculum

Structure of Specialist Mathematics Specialist Mathematics

Specialist Mathematics is structured over four units. The topics in Unit 1 broaden students’ mathematical experience and provide different scenarios for incorporating mathematical arguments and problem solving. The unit provides a blending of algebraic …

Structure of Specialist Mathematics | Specialist Mathematics | Mathematics | Senior secondary curriculum

Structure of Essential Mathematics Essential Mathematics

Essential Mathematics has four units each of which contains a number of topics. It is intended that the topics be taught in a context relevant to students’ needs and interests. In Essential Mathematics, students use their knowledge and skills to investigate …

Structure of Essential Mathematics | Essential Mathematics | Mathematics | Senior secondary curriculum

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 …

ACMGM047

interpret piece-wise linear and step graphs used to model practical situations; for example, the tax paid as income increases, the change in the level of water in a tank over time when water is drawn off at different intervals and for different periods …

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 …

ACMSM127

use numerical integration using technology \(f\left(t\right)=\lambda e^{-\lambda t}\) for \(t\geq0\) of the exponential random variable with parameter \(\lambda>0,\), and use the exponential random variables and associated probabilities and quantiles …

Rationale General Mathematics

Mathematics is the study of order, relation and pattern. From its origins in counting and measuring it has evolved in highly sophisticated and elegant ways to become the language now used to describe many aspects of the world in the twenty-first century. …

Rationale | General Mathematics | Mathematics | Senior secondary curriculum

Rationale Mathematical Methods

Mathematics is the study of order, relation and pattern. From its origins in counting and measuring it has evolved in highly sophisticated and elegant ways to become the language now used to describe much of the modern world. Statistics is concerned with …

Rationale | Mathematical Methods | Mathematics | Senior secondary curriculum

Rationale Specialist Mathematics

Rationale Mathematics is the study of order, relation and pattern. From its origins in counting and measuring it has evolved in highly sophisticated and elegant ways to become the language now used to describe much of the modern world. Statistics is concerned …

Rationale | Specialist Mathematics | Mathematics | Senior secondary curriculum

ACMGM070

use arithmetic sequences to model and analyse practical situations involving linear growth or decay; for example, analysing a simple interest loan or investment, calculating a taxi fare based on the flag fall and the charge per kilometre, or calculating …

ACMGM074

use geometric sequences to model and analyse (numerically, or graphically only) practical problems involving geometric growth and decay; for example, analysing a compound interest loan or investment, the growth of a bacterial population that doubles in …

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