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ACSPH097

Gravitational field strength is defined as the net force per unit mass at a particular point in the field

ACMSM121

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

ACSPH104

A positively charged body placed in an electric field will experience a force in the direction of the field; the strength of the electric field is defined as the force per unit charge

ACMSM063

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

ACMGM008

calculate the dividend paid on a portfolio of shares, given the percentage dividend or dividend paid per share, for each share; and compare share values by calculating a price-to-earnings ratio.

The relative atomic mass of an element is the ratio of the weighted average mass per atom of the naturally occurring form of the element to \(\frac1{12}\) the mass of an atom of carbon-12; relative atomic masses reflect the isotopic composition of the …

ACSPH040

The energy available to charges moving in an electrical circuit is measured using electric potential difference, which is defined as the change in potential energy per unit charge between two defined points in the circuit

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 \(x^2=-1\)

ACMEM002

apply arithmetic operations according to their correct order

ACMMM007

recognise features of the graphs of \(y=x^2\), \(y=a{(x-b)}^2+c\), and \(y=a\left(x-b\right)\left(x-c\right)\) including their parabolic nature, turning points, axes of symmetry and intercepts

ACMSM131

examine slope (direction or gradient) fields of a first order differential equation

ACMGM082

apply Euler’s formula, \(v+f-e=2\), to solve problems relating to planar graphs.

ACMMM021

recognise features of the graph of \(y^2=x\) including its parabolic shape and its axis of symmetry.

ACMSM066

prove divisibility results, such as \(3^{2n+4}-2^{2n}\) is divisible by 5 for any positive integer n.

ACMGM070

use arithmetic sequences to model and analyse practical situations involving linear growth or decay; for example, analysing a simple interest loan or investment, calculating a taxi fare based on the flag fall and the charge per kilometre, or calculating …

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