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ACMMM057

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

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

Representation of General capabilities Essential English

General capabilities covered in Essential English include: Literacy, Numeracy, Information and communication technology (ICT) capability, Critical and creative thinking, Personal and social capability, Ethical understanding and Intercultural understanding. Literacy Literacy …

Representation of General capabilities | Essential English | English | Senior secondary curriculum

ACMMM050

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

ACMMM058

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

ACMMM151

define logarithms as indices: \(a^x=b\) is equivalent to \(x=\log_ab\) i.e. \(a^{\log_ab}=b\)

ACMMM054

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

ACMSM068

use complex numbers in the form a+bi where a and b are the real and imaginary parts

ACMMM131

understand the formula \(\int_a^b{f\left(x\right)dx=F\left(b\right)-F(a)}\) and use it to calculate definite integrals.

ACMSM053

calculate the determinant and inverse of 2x2 matrices and solve matrix equations of the form AX=B , where A is a 2x2 matrix and X and B are column vectors.

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

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 \(x\rightarrow-\infty\)

ACMMM013

recognise features of the graphs of \(y=\frac1x\) and \(y=\frac a{x-b}\), including their hyperbolic shapes, and their asymptotes.

ACMMM025

examine translations and the graphs of \(y=f\left(x\right)+a\) and \(y=f(x+b)\)

ACMMM120

determine indefinite integrals of the form \(\int f\left(ax+b\right)dx\)

ACMMM122

determine \(f\left(x\right),\) given \(f^{'\;}(x)\;\) and an initial condition \(f\left(a\right)=b\)

ACMEM102

recognise relations between volume and capacity, recognising that \(1\mathrm c\mathrm m^3=1\mathrm m\mathrm L\) and \(1\mathrm m^3=1\mathrm k\mathrm L\)

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

ACMSM117

use substitution \(u = g(x)\) to integrate expressions of the form \(f\left(g\left(x\right)\right)g'\left(x\right)\)

ACMEM072

convert between units for rates; for example, km/h to m/s, mL/min to L/h

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