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ACMMM116

establish and use the formula \(\int x^ndx=\frac1{n+1}x^{n+1}+c\) for \(n\neq-1\)

ACMMM118

establish and use the formulas, \(\int\sin xdx=-\cos x+c\) and \(\int\cos xdx=\sin x+c\)

ACMMM122

determine \(f\left(x\right),\) given \(f^{'\;}(x)\;\) and an initial condition \(f\left(a\right)=b\)

ACMMM151

define logarithms as indices: \(a^x=b\) is equivalent to \(x=\log_ab\) i.e. \(a^{\log_ab}=b\)

ACMMM153

recognise the inverse relationship between logarithms and exponentials: \(y=a^x\) is equivalent to \(x=\log_ay\)

ACMMM160

recognise and use the inverse relationship of the functions \(y=e^x\) and \(y=\ln x\)

ACMSM118

establish and use the formula \(\int\frac1xdx=\ln{\;\vert x\;\vert}+c\) for x ≠ 0

Units In Physics, students develop their understanding of the core concepts, models and theories that describe, explain and predict physical phenomena. There are four units: Unit 1: Thermal, nuclear and electrical physics Unit 2: Linear motion and waves Unit …

Structure of Physics | Physics | Science | Senior secondary curriculum

ACEEN066

the selection of mode, medium, genre and type of text

ACMMM014

recognise features of the graphs of \(y=x^n\) for \(n\in\boldsymbol N,\) \(n=-1\) and \(n=½\), including shape, and behaviour as \(x\rightarrow\infty\) and \(x\rightarrow-\infty\)

ACMMM083

use the Leibniz notation for the derivative: \(\frac{dy}{dx}=\lim_{\mathit{δx}\rightarrow0}\frac{\delta y}{\delta x}\) and the correspondence \(\frac{dy}{dx}=f'\left(x\right)\) where \(y=f(x)\)

ACMMM124

examine the area problem, and use sums of the form \(\sum\nolimits_if\left(x_i\right)\;\delta x_i\) as area under the curve \(y=f(x)\)

ACMMM125

interpret the definite integral \(\int_a^bf\left(x\right)dx\;\) as area under the curve \(y=f\left(x\right)\) if \(f\left(x\right)>0\;\)

ACMMM126

recognise the definite integral \(\int_a^bf\left(x\right)dx\;\;\) as a limit of sums of the form \(\sum\nolimits_if\left(x_i\right)\;\delta x_i\)

Structure of English as an Additional Language or Dialect English as an Additional Language or Dialect

Units 1–4 Unit 1 focuses on investigating how language and culture are interrelated and expressed in a range of contexts. A variety of oral, written and multimodal texts are used to develop understanding of text structures and language features. The relationship …

Structure of English as an Additional Language or Dialect | English as an Additional Language or Dialect | English | Senior secondary curriculum

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 Essential 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 used to describe much of the physical world. Statistics is the …

Rationale | Essential Mathematics | Mathematics | Senior secondary curriculum

Rationale/Aims Earth and Environmental Science

Rationale Earth and Environmental Science is a multifaceted field of inquiry that focuses on interactions between the solid Earth, its water, its air and its living organisms, and on dynamic, interdependent relationships that have developed between these …

Rationale/Aims | Earth and Environmental Science | Science | Senior secondary curriculum

Rationale/Aims Ancient History

Rationale The Ancient History curriculum enables students to study life in early civilisations based on the analysis and interpretation of physical and written remains. The ancient period, as defined in this curriculum, extends from the development of …

Rationale/Aims | Ancient History | Humanities and Social Sciences | Senior secondary curriculum

Rationale/Aims Modern History

Rationale The Modern History curriculum enables students to study the forces that have shaped today’s world and provides them with a broader and deeper comprehension of the world in which they live. While the focus is on the 20th century, the curriculum …

Rationale/Aims | Modern History | Humanities and Social Sciences | Senior secondary curriculum

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