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ACMMM069

use the formula $t_n=t_1+\left(n-1\right)d$ for the general term of an arithmetic sequence and recognise its linear nature

ACMMM131

understand the formula $\int_a^b{f\left(x\right)dx=F\left(b\right)-F(a)}$ and use it to calculate definite integrals.

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

ACMSM117

use substitution $u = g(x)$ to integrate expressions of the form $f\left(g\left(x\right)\right)g'\left(x\right)$

use currency exchange rates to determine the cost in Australian dollars of purchasing a given amount of a foreign currency, such as US$1500, or the value of a given amount of foreign currency when converted to Australian dollars, such as the value of …

ACMGM012

use a spreadsheet or an equivalent technology to construct a table of values from a formula, including two-by-two tables for formulas with two variable quantities; for example, a table displaying the body mass index (BMI) of people of different weights …

ACMGM094

use a recurrence relation to model a compound interest loan or investment, and investigate (numerically or graphically) the effect of the interest rate and the number of compounding periods on the future value of the loan or investment

ACMGM103

use minimal spanning trees to solve minimal connector problems; for example, minimising the length of cable needed to provide power from a single power station to substations in several towns.

ACMGM110

use a bipartite graph and/or its tabular or matrix form to represent an assignment/ allocation problem; for example, assigning four swimmers to the four places in a medley relay team to maximise the team’s chances of winning

ACMMM079

use the notation $\frac{\delta y}{\delta x}$ for the difference quotient $\frac{f\left(x+h\right)-f(x)}h$ where $y=f(x)$

ACMMM083

use the Leibniz notation for the derivative: $\frac{dy}{dx}=\lim_{\mathit{δx}\rightarrow0}\frac{\delta y}{\delta x}$ and the correspondence $\frac{dy}{dx}=f'\left(x\right)$ where $y=f(x)$

ACMMM107

use the increments formula: $\delta y\cong\frac{dy}{dx}\times\delta x$ to estimate the change in the dependent variable $y$ resulting from changes in the independent variable $x$

ACMMM124

examine the area problem, and use sums of the form $\sum\nolimits_if\left(x_i\right)\;\delta x_i$ as area under the curve $y=f(x)$

ACMMM130

understand and use the theorem $F'\left(x\right)=\frac d{dx}\left(\int_a^xf\left(t\right)dt\right)=f\left(x\right)$, and illustrate its proof geometrically

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 …

ACMSM080

use the modulus $\left|z\right|$ of a complex number z and the argument $Arg\;(z)$ of a non-zero complex number $z$ and prove basic identities involving modulus and argument

ACMGM009

use a spreadsheet to display examples of the above computations when multiple or repeated computations are required; for example, preparing a wage-sheet displaying the weekly earnings of workers in a fast food store where hours of employment and hourly …

ACMGM016

use matrices, including matrix products and powers of matrices, to model and solve problems; for example, costing or pricing problems, squaring a matrix to determine the number of ways pairs of people in a communication network can communicate with each …

ACMGM077

use first-order linear recurrence relations to model and analyse (numerically or graphically only) practical problems; for example, investigating the growth of a trout population in a lake recorded at the end of each year and where limited recreational …

ACMGM085

explain the meaning of the terms: Eulerian graph, Eulerian trail, semi-Eulerian graph, semi-Eulerian trail and the conditions for their existence, and use these concepts to investigate and solve practical problems; for example, the Königsberg Bridge problem, …

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