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Unit 4 Mathematical Methods

The calculus in this unit deals with derivatives of logarithmic functions. In probability and statistics, continuous random variables and their applications are introduced and the normal distribution is used in a variety of contexts. The study of statistical …

Unit 4 | Mathematical Methods | Mathematics | Senior secondary curriculum

Links to Foundation to Year 10 Specialist Mathematics

For all content areas of Specialist Mathematics, the proficiency strands of the F–10 curriculum are still very much applicable and should be inherent in students’ learning of the subject. The strands of Understanding, Fluency, Problem solving and Reasoning …

Links to Foundation to Year 10 | Specialist Mathematics | 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

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

ACMSM094

determine if a function is one-to-one

ACMGM046

sketch piece-wise linear graphs and step graphs, using technology when appropriate

ACMSM095

consider inverses of one-to-one function

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 …

ACMEM012

determine one amount expressed as a percentage of another

ACMEM034

convert from one unit of energy to another.

ACMEM062

review one amount expressed as a percentage of another.

ACMMM022

understand the concept of a function as a mapping between sets, and as a rule or a formula that defines one variable quantity in terms of another

ACMSM035

When two chords of a circle intersect, the product of the lengths of the intervals on one chord equals the product of the lengths of the intervals on the other chord

ACMSM042

find all solutions of \(\mathrm f\left(\mathrm a\left(\mathrm x-\mathrm b\right)\right)=\mathrm c\) where \(f\) is one of \(\sin\), \(\cos\) or \(\tan\)

ACMSM043

graph functions with rules of the form \(\mathrm y=\mathrm f(\mathrm a\left(\mathrm x-\mathrm b\right))\) where \(f\) is one of \(\sin\), \(\cos\) or \(\tan\)

ACMGM079

identify practical situations that can be represented by a network, and construct such networks; for example, trails connecting camp sites in a National Park, a social network, a transport network with one-way streets, a food web, the results of a round-robin …

ACMGM088

describe time series plots by identifying features such as trend (long term direction), seasonality (systematic, calendar-related movements), and irregular fluctuations (unsystematic, short term fluctuations), and recognise when there are outliers; for …

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