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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

ACMMM066

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

ACMMM068

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

ACMMM070

use arithmetic sequences in contexts involving discrete linear growth or decay, such as simple interest

ACMMM072

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

ACMMM073

use the formula \(t_n=r^{n-1}t_1\) for the general term of a geometric sequence and recognise its exponential nature

ACMMM075

establish and use the formula \(S_n=t_1\frac{r^n-1}{r-1}\) for the sum of the first \(n\) terms of a geometric sequence

ACMMM078

use the Leibniz notation \(\delta x\) and \(\delta y\) for changes or increments in the variables \(x\) and \(y\)

ACMMM100

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

ACMMM105

understand the notion of composition of functions and use the chain rule for determining the derivatives of composite functions

ACMMM115

use the notation \(\int f\left(x\right)dx\) for anti-derivatives or indefinite integrals

ACMMM116

establish and use the formula \(\int x^ndx=\frac1{n+1}x^{n+1}+c\) for \(n\neq-1\)

ACMMM118

establish and use the formulas, \(\int\sin xdx=-\cos x+c\) and \(\int\cos xdx=\sin x+c\)

ACMMM138

recognise uniform discrete random variables and use them to model random phenomena with equally likely outcomes

ACMMM154

interpret and use logarithmic scales such as decibels in acoustics, the Richter Scale for earthquake magnitude, octaves in music, pH in chemistry

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 \(p\)

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