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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

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 …

ACHAH068

The reliability and contestability of interpretations and representations of Alexander in ancient and modern written sources, images and film, including the significance of source selection, omission, emphasis and gaps in evidence

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 …

ACHAH057

The historical context of the interpretations and representations of the ‘fall’ of the Roman Empire and why these have changed over time, for example the importance of the Pagan versus Christian interpretations of events at the time and various modern …

ACHAH061

The different interpretations and representations of the games (from the ancient past to the present), including the cruelty of the gladiatorial games (Seneca and Christians), the political nature of the games as ‘bread and circuses’, the role of blood …

ACHAH071

The different interpretations and representations of Cleopatra (from the ancient past to the present), including how Cleopatra represented herself in monuments and inscriptions; her portrayals as the enemy of Rome, a femme fatale, the saviour of Egypt, …

ACHAH082

The historical context of the interpretations and representations of the Celts and why these have changed over time, for example Ancient Roman interpretations, modern imperialist and nationalistic propaganda, Celtic cultural legacy (art, music, language …

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

ACHAH065

The nature of the sources most relevant to the interpretations and representations of Alexander, for example: the writings of Plutarch, Arrian, and Curtius Rufus (including their own sources); Macedonian and Hellenistic representations (for example coins …

ACHAH056

The different interpretations and representations of the ‘fall’ of the Roman Empire in the West (from the ancient past, to the more recent past, to today), including Gibbon’s Decline and Fall of the Roman Empire, and his view that the Roman Empire fell …

ACHMH028

Modern History Senior secondary Curriculum - The Australian Curriculum v8.3 The main causes of the French Revolution including the influence of the Enlightenment; the increasingly prosperous elite of wealthy commoners who …

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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