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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 \(\mu\)

ACSBL087

Biotechnology can involve the use of bacterial enzymes, plasmids as vectors, and techniques including gel electrophoresis, bacterial transformations and PCR

ACSCH109

Fuel cells can use metal nanoparticles as catalysts to improve the efficiency of energy production

ACSES079

The cost-effective use of renewable energy resources is constrained by the efficiency of available technologies to collect, store and transfer the energy

ACHAH024

The reconstructions of the ancient site/s, for example paintings, historical fiction, film, documentaries, museum displays, and virtual worlds; and use for propaganda.

ACHAH033

The ethical issues relevant to the treatment, display and ownership of the remains, for example the use of invasive methods of scientific analysis

The development of Athens’ domestic politics for example the use of ostracisms in the 480s, the ascendency of Themistocles, the construction of the fleet, and the enhancement of the position of strategoi

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