ACMMM017
recognise features of the graphs of \(y=x^3\), \(y=a{(x-b)}^3+c\) and \(y=k(x-a)(x-b)(x-c)\), including shape, intercepts and behaviour as \(x\rightarrow\infty\) and \(x\rightarrow-\infty\)
ACMMM017 | Content Descriptions | Unit 1 | Mathematical Methods | Mathematics | Senior secondary curriculum
ACMMM106
apply the product, quotient and chain rule to differentiate functions such as \(xe^x\), \(\tan x,\), \(\frac1{x^n}\), \(x\sin x,\text{ }e^{-x}\sin x\) and \(f(ax+b)\)
ACMMM106 | Content Descriptions | Unit 3 | Mathematical Methods | Mathematics | Senior secondary curriculum
ACMMM037
examine amplitude changes and the graphs of \(y=a\sin x\) and \(y=a\cos x\)
ACMMM037 | Content Descriptions | Unit 1 | Mathematical Methods | Mathematics | Senior secondary curriculum
ACMMM036
recognise the graphs of \(y=\sin x,\;y=\cos x,\) and \(y=\tan x\) on extended domains
ACMMM036 | Content Descriptions | Unit 1 | Mathematical Methods | Mathematics | Senior secondary curriculum
ACMSM098
use and apply the notation \(\left|x\right|\) for the absolute value for the real number \(x\) and the graph of \(y=\left|x\right|\)
ACMSM098 | Content Descriptions | Unit 3 | Specialist Mathematics | Mathematics | Senior secondary curriculum
ACMMM039
examine phase changes and the graphs of \(y=\sin{(x+c)}\), \(y=\cos{(x+c)}\) and \(y=\tan{(x+c)}\) and the relationships \(\sin\left(x+\frac\pi2\right)=\cos x\) and \(\cos\left(x-\frac\pi2\right)=\sin x\)
ACMMM039 | Content Descriptions | Unit 1 | Mathematical Methods | Mathematics | Senior secondary curriculum
Structure of Ancient History Ancient History
Units In Ancient History, students study the key institutions, structures and features of ancient societies and develop a broader and deeper comprehension of the origins, impact and legacy of ideas, beliefs and values of the ancient world. The Ancient …
Structure of Ancient History | Ancient History | Humanities and Social Sciences | Senior secondary curriculum
Structure of Modern History Modern History
Units In Modern History, students study the forces that have shaped the modern world and develop a broader and deeper comprehension of the world in which they live. The Modern History curriculum consists of four units. For each unit there are five to …
Structure of Modern History | Modern History | Humanities and Social Sciences | Senior secondary curriculum
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
ACMMM065
recognise the qualitative features of the graph of \(y=a^x(a>0)\) including asymptotes, and of its translations \(y=a^x+b\) and \(y=a^{x+c}\)
ACMMM065 | Content Descriptions | Unit 2 | Mathematical Methods | Mathematics | Senior secondary curriculum
ACMMM082
define the derivative \(f'\left(x\right)\) as \(\lim_{h\rightarrow0}\frac{f\left(x+h\right)-f(x)}h\)
ACMMM082 | Content Descriptions | Unit 2 | Mathematical Methods | Mathematics | Senior secondary curriculum
ACMSM117
use substitution \(u = g(x)\) to integrate expressions of the form \(f\left(g\left(x\right)\right)g'\left(x\right)\)
ACMSM117 | Content Descriptions | Unit 4 | Specialist Mathematics | Mathematics | Senior secondary curriculum
ACMMM007
recognise features of the graphs of \(y=x^2\), \(y=a{(x-b)}^2+c\), and \(y=a\left(x-b\right)\left(x-c\right)\) including their parabolic nature, turning points, axes of symmetry and intercepts
ACMMM007 | Content Descriptions | Unit 1 | Mathematical Methods | Mathematics | Senior secondary curriculum
ACMMM079
use the notation \(\frac{\delta y}{\delta x}\) for the difference quotient \(\frac{f\left(x+h\right)-f(x)}h\) where \(y=f(x)\)
ACMMM079 | Content Descriptions | Unit 2 | Mathematical Methods | Mathematics | Senior secondary curriculum
ACMMM080
interpret the ratios \(\frac{f\left(x+h\right)-f(x)}h\) and \(\frac{\delta y}{\delta x}\) as the slope or gradient of a chord or secant of the graph of \(y=f(x)\)
ACMMM080 | Content Descriptions | Unit 2 | Mathematical Methods | Mathematics | Senior secondary curriculum
ACMMM088
establish the formula \(\frac d{dx}\left(x^n\right)=nx^{n-1}\) for positive integers \(n\) by expanding \({(x+h)}^n\) or by factorising \({(x+h)}^n-x^n\)
ACMMM088 | Content Descriptions | Unit 2 | Mathematical Methods | Mathematics | Senior secondary curriculum