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ACMMM048

use Pascal’s triangle and its properties.

ACMMM049

review the concepts and language of outcomes, sample spaces and events as sets of outcomes

use set language and notation for events, including \(\overline A\) (or \(A'\)) for the complement of an event \(A,\) \(A?B\) for the intersection of events \(A\) and \(B\), and \(A?B\) for the union, and recognise mutually exclusive events

ACMMM051

use everyday occurrences to illustrate set descriptions and representations of events, and set operations.

ACMMM052

review probability as a measure of ‘the likelihood of occurrence’ of an event

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

ACMMM054

review the rules: \(P\left(\overline A\right)=1-P\left(A\right)\) and \(P\left(A\cup B\right)=P\left(A\right)+P\left(B\right)-P\left(A\cap B\right)\)

ACMMM055

use relative frequencies obtained from data as point estimates of probabilities.

ACMMM056

understand the notion of a conditional probability and recognise and use language that indicates conditionality

ACMMM057

use the notation \(P(A\vert B)\) and the formula \(P(A\vert B)=P(A\cap B) / P(B)\)

ACMMM058

understand the notion of independence of an event \(A\) from an event \(B\), as defined by \(P(A\vert B)=P(A)\)

ACMMM059

establish and use the formula \(P(A\cap B)=P(A)P(B)\) for independent events \(A\) and \(B\), and recognise the symmetry of independence

ACMMM060

use relative frequencies obtained from data as point estimates of conditional probabilities and as indications of possible independence of events.

ACMMM061

review indices (including fractional indices) and the index laws

ACMMM062

use radicals and convert to and from fractional indices

ACMMM063

understand and use scientific notation and significant figures.

ACMMM064

establish and use the algebraic properties of exponential functions

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 \(y=a^{x+c}\)

ACMMM066

identify contexts suitable for modelling by exponential functions and use them to solve practical problems

ACMMM067

solve equations involving exponential functions using technology, and algebraically in simple cases.

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