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ACMMM158

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

ACMMM160

recognise and use the inverse relationship of the functions \(y=e^x\) and \(y=\ln x\)

ACMMM161

establish and use the formula \(\frac d{dx}\left(\ln x\right)=\frac1x\)

ACMMM170

calculate probabilities and quantiles associated with a given normal distribution using technology, and use these to solve practical problems.

ACMMM180

use simulation to illustrate variations in confidence intervals between samples and to show that most but not all confidence intervals contain \(p\)

ACMSM005

determine and use the formulas for finding the number of elements in the union of two and the union of three sets.

ACMSM052

define and use addition and subtraction of matrices, scalar multiplication, matrix multiplication, multiplicative identity and inverse

ACMSM082

define and use multiplication, division, and powers of complex numbers in polar form and the geometric interpretation of these

ACMSM098

use and apply the notation \(\left|x\right|\) for the absolute value for the real number \(x\) and the graph of \(y=\left|x\right|\)

ACMSM104

use vector equations of curves in two or three dimensions involving a parameter, and determine a ‘corresponding’ Cartesian equation in the two-dimensional case

ACMSM109

recognise the general form of a system of linear equations in several variables, and use elementary techniques of elimination to solve a system of linear equations

ACMSM118

establish and use the formula \(\int\frac1xdx=\ln{\;\vert x\;\vert}+c\) for x ≠ 0

ACMSM128

use implicit differentiation to determine the gradient of curves whose equations are given in implicit form

ACMSM142

use simulation to illustrate variations in confidence intervals between samples and to show that most but not all confidence intervals contain \(\mu\)

ACMEM054

use informal ways of describing spread, such as spread out/dispersed, tightly packed, clusters, gaps, more/less dense regions, outliers

ACMEM084

optimise distances through trial-and-error and systematic methods; for example, shortest path, routes to visit all towns, and routes to use all roads.

solve practical problems involving the trigonometry of right-angled and non-right-angled triangles, including problems involving angles of elevation and depression and the use of bearings in navigation.

ACMGM097

use a recurrence relation to model a reducing balance loan and investigate (numerically or graphically) the effect of the interest rate and repayment amount on the time taken to repay the loan

ACMGM099

use a recurrence relation to model an annuity, and investigate (numerically or graphically) the effect of the amount invested, the interest rate, and the payment amount on the duration of the annuity

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

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