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Unit 4 Mathematical Methods

The calculus in this unit deals with derivatives of logarithmic functions. In probability and statistics, continuous random variables and their applications are introduced and the normal distribution is used in a variety of contexts. The study of statistical …

Unit 4 | Mathematical Methods | Mathematics | Senior secondary curriculum

ACMMM164

use relative frequencies and histograms obtained from data to estimate probabilities associated with a continuous random variable

ACMMM173

use graphical displays of simulated data to investigate the variability of random samples from various types of distributions, including uniform, normal and Bernoulli.

ACMMM152

establish and use the algebraic properties of logarithms

ACMMM163

use logarithmic functions and their derivatives to solve practical problems.

ACMMM162

establish and use the formula \(\int\frac1xdx=\ln\;x\;+c\) for \(x>0\)

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 \(p\)

ACMMM169

recognise features of the graph of the probability density function of the normal distribution with mean \(\mu\) and standard deviation \(\sigma\) and the use of the standard normal distribution

ACMMM165

understand the concepts of a probability density function, cumulative distribution function, and probabilities associated with a continuous random variable given by integrals; examine simple types of continuous random variables and use them in appropriate …

ACMMM178

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 …

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