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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

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

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 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

ACMMM068

recognise and use the recursive definition of an arithmetic sequence: \(t_{n+1}=t_n+d\)

ACMMM072

recognise and use the recursive definition of a geometric sequence:\(t_{n+1}=rt_n\)

ACMSM101

review the concepts of vectors from Unit 1 and extend to three dimensions including introducing the unit vectors i, j and k.

ACSCH028

Nanomaterials are substances that contain particles in the size range 1–100 nm and have specific properties relating to the size of these particles

ACMMM178

use the approximate confidence interval \(\left(\widehat p-z\sqrt[{}]{(\widehat p(1-\widehat p)/n},\;\;\widehat p+z\sqrt[{}]{(\widehat p(1-\widehat p)/n}\right),\) as an interval estimate for \(p\), where \(z\) is the appropriate quantile for the standard …

ACMMM053

review the probability scale: \(0\leq P(A)\leq1\) for each event \(A,\) with \(P\left(A\right)=0\) if \(A\) is an impossibility and \(P\left(A\right)=1\) if \(A\) is a certaint

ACMSM116

integrate using the trigonometric identities \(\mathrm s\mathrm i\mathrm n^2x=\frac12(1-\mathrm c\mathrm o\mathrm s\;2x)\), \(\mathrm c\mathrm o\mathrm s^2x=\frac12(1+\mathrm c\mathrm o\mathrm s\;2x)\) and \(1+\;\mathrm t\mathrm a\mathrm n^2x=\mathrm …

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 \(x\rightarrow-\infty\)

ACMMM156

recognise the qualitative features of the graph of \(y=\log_ax\) \((a>1)\) including asymptotes, and of its translations \(y=\log_ax+b\) and \(y=\log_a{(x+c)}\)

ACMMM179

define the approximate margin of error \(E=z\sqrt[{}]{(\widehat p(1-\widehat p)/n}\) and understand the trade-off between margin of error and level of confidence

ACMMM176

simulate repeated random sampling, for a variety of values of \(p\) and a range of sample sizes, to illustrate the distribution of \(\widehat p\) and the approximate standard normality of \(\frac{\widehat p\;-p}{\sqrt[{}]{(\widehat p(1-\widehat p)/n}}\) …

ACMSM055

define and use basic linear transformations: dilations of the form \((\mathrm x,\mathrm y)\longrightarrow({\mathrm\lambda}_1\mathrm x,{\mathrm\lambda}_2\mathrm y)\) , rotations about the origin and reflection in a line which passes through the origin, …

ACMMM149

determine and use the probabilities \(\mathrm P\left(\mathrm X=\mathrm r\right)=\begin{pmatrix}\mathrm n\\\mathrm r\end{pmatrix}\mathrm p^\mathrm r{(1-\mathrm p)}^{\mathrm n-\mathrm r}\) associated with the binomial distribution with parameters \(n\) …

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