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ACMSM050

model periodic motion using sine and cosine functions and understand the relevance of the period and amplitude of these functions in the model.

ACMMM020

recognise features of the graphs of \(x^2+y^2=r^2\) and \(\left(x-a\right)^2+\left(y-b\right)^2=r^2\), including their circular shapes, their centres and their radii

ACMSM121

integrate expressions of the form \(\frac{\pm1}{\sqrt[{}]{a^2-x^2}}\) and \(\frac a{a^2+x^2}\)

ACMEM174

use technology and a recurrence relation to model a reducing balance loan

ACMGM057

model a linear relationship by fitting a least-squares line to the data

ACMGM058

use a residual plot to assess the appropriateness of fitting a linear model to the data

ACMMM143

use a Bernoulli random variable as a model for two-outcome situations

ACMSM063

prove irrationality by contradiction for numbers such as \(\sqrt[{}]2\) and \(\log_25\)

A wave model explains a wide range of light-related phenomena including reflection, refraction, total internal reflection, dispersion, diffraction and interference; a transverse wave model is required to explain polarisation

ACMGM042

interpret, in context, the slope and intercept of a straight-line graph used to model and analyse a practical situation

ACMGM092

fit a least-squares line to model long-term trends in time series data.

ACMMM138

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

ACMMM146

use Bernoulli random variables and associated probabilities to model data and solve practical problems.

ACSPH017

The kinetic particle model describes matter as consisting of particles in constant motion, except at absolute zero

ACSPH071

The mechanical wave model can be used to explain phenomena related to reflection and refraction (for example, echoes, seismic phenomena)

ACSPH075

A ray model of light may be used to describe reflection, refraction and image formation from lenses and mirrors

ACSPH146

High-energy particle accelerators are used to test theories of particle physics including the Standard Model

ACSPH147

The Standard Model is used to describe the evolution of forces and the creation of matter in the Big Bang theory

ACMMM011

recognise features of the graph of the general quadratic \(y=ax^2+bx+c\)

ACMSM067

define the imaginary number i as a root of the equation \(x^2=-1\)

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