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ACMMM078

use the Leibniz notation \(\delta x\) and \(\delta y\) for changes or increments in the variables \(x\) and \(y\)

ACMMM100

establish and use the formula \(\frac d{dx}\left(e^x\right)=e^x\)

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

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 Geography Geography

Units In Senior Secondary Geography, students develop their understanding about themes of immediate relevance to them and which have scope for application at a variety of scales, from the local to the global. There are four units: Unit 1: Natural and …

Structure of Geography | Geography | Humanities and Social Sciences | Senior secondary curriculum

Structure of Biology Biology

Units Biology is the study of the fascinating diversity of life as it has evolved and as it interacts and functions. Investigation of biological systems and their interactions, from cellular processes to ecosystem dynamics, has led to biological knowledge …

Structure of Biology | Biology | Science | Senior secondary curriculum

Structure of Chemistry Chemistry

Units In Chemistry, students develop their understanding of chemical systems, and how models of matter and energy transfers and transformations can be used to describe, explain and predict chemical structures, properties and reactions. There are four …

Structure of Chemistry | Chemistry | Science | Senior secondary curriculum

Structure of Earth and Environmental Science Earth and Environmental Science

Units In Earth and Environmental Science, students develop their understanding of the ways in which interactions between Earth systems influence Earth processes, environments and resources. There are four units: Unit 1: Introduction to Earth systems Unit …

Structure of Earth and Environmental Science | Earth and Environmental Science | Science | Senior secondary curriculum

Structure of Physics Physics

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

ACMEM122

generate tables of values for linear functions, including for negative values of \(x\)

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