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ACMSM009

derive and use simple identities associated with Pascal’s triangle.

ACMSM045

define the reciprocal trigonometric functions, sketch their graphs, and graph simple transformations of them.

ACMSM102

prove geometric results in the plane and construct simple proofs in three-dimensions.

ACMSM122

use partial fractions where necessary for integration in simple cases

ACMEM172

use technology to compare, numerically and graphically, the growth of simple interest and compound interest loans and investments

ACMGM010

substitute numerical values into linear algebraic and simple non-linear algebraic expressions, and evaluate

ACMGM017

review Pythagoras’ Theorem and use it to solve practical problems in two dimensions and for simple applications in three dimensions.

ACMGM089

smooth time series data by using a simple moving average, including the use of spreadsheets to implement this process

ACMMM070

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

ACMMM096

solve optimisation problems arising in a variety of contexts involving simple polynomials on finite interval domains.

ACMMM097

calculate anti-derivatives of polynomial functions and apply to solving simple problems involving motion in a straight line.

ACMMM140

recognise the mean or expected value of a discrete random variable as a measurement of centre, and evaluate it in simple cases

ACMMM141

recognise the variance and standard deviation of a discrete random variable as a measures of spread, and evaluate them in simple cases

ACMMM166

recognise the expected value, variance and standard deviation of a continuous random variable and evaluate them in simple cases

ACMSM100

sketch the graphs of simple rational functions where the numerator and denominator are polynomials of low degree.

ACMEM130

investigate the different kinds of samples; for example, systematic samples, self-selected samples, simple random samples

ACMEM131

investigate the advantages and disadvantages of these kinds of samples; for example, comparing simple random samples with self-selected samples.

ACMEM133

investigate questionnaire design principles; for example, simple language, unambiguous questions, consideration of number of choices, issues of privacy and ethics, and freedom from bias.

ACMMM095

sketch curves associated with simple polynomials; find stationary points, and local and global maxima and minima; and examine behaviour as \(x\rightarrow\infty\) and \(x\rightarrow-\infty\)

ACMGM078

explain the meanings of the terms: graph, edge, vertex, loop, degree of a vertex, subgraph, simple graph, complete graph, bipartite graph, directed graph (digraph), arc, weighted graph, and network

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