ACMMM151

define logarithms as indices: \(a^x=b\) is equivalent to \(x=\log_ab\) i.e. \(a^{\log_ab}=b\)

ACMMM151 | Content Descriptions | Unit 4 | Mathematical Methods | Mathematics | Senior secondary curriculum

ACMMM153

recognise the inverse relationship between logarithms and exponentials: \(y=a^x\) is equivalent to \(x=\log_ay\)

ACMMM153 | Content Descriptions | Unit 4 | Mathematical Methods | Mathematics | Senior secondary curriculum

ACMMM160

recognise and use the inverse relationship of the functions \(y=e^x\) and \(y=\ln x\)

ACMMM160 | Content Descriptions | Unit 4 | Mathematical Methods | Mathematics | Senior secondary curriculum

ACMSM118

establish and use the formula \(\int\frac1xdx=\ln{\;\vert x\;\vert}+c\) for x ≠ 0

ACMSM118 | Content Descriptions | Unit 4 | Specialist Mathematics | Mathematics | Senior secondary curriculum

ACMNA001

Establish understanding of the language and processes of counting by naming numbers in sequences, initially to and from 20, moving from  any starting point

Elaborations ScOT Terms

ACMNA001 | Content Descriptions | Foundation Year | Mathematics | F-10 curriculum

Mathematics - Foundation Year

Number and place value Establish understanding of the language and processes of counting by naming numbers in sequences, initially to and from 20, moving from any starting point (ACMNA001) Connect number names, numerals and quantities, including zero, …

Mathematics - Foundation Year | Knowledge and understanding | Dimensions | Curriculum connections | Resources

ACMMM014

recognise features of the graphs of \(y=x^n\) for \(n\in\boldsymbol N,\) \(n=-1\) and \(n=½\), including shape, and behaviour as \(x\rightarrow\infty\) and \(x\rightarrow-\infty\)

ACMMM014 | Content Descriptions | Unit 1 | Mathematical Methods | Mathematics | Senior secondary curriculum

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 \(y=f(x)\)

ACMMM083 | Content Descriptions | Unit 2 | Mathematical Methods | Mathematics | Senior secondary curriculum

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 \(y=f(x)\)

ACMMM124 | Content Descriptions | Unit 3 | Mathematical Methods | Mathematics | Senior secondary curriculum

ACMMM125

interpret the definite integral \(\int_a^bf\left(x\right)dx\;\) as area under the curve \(y=f\left(x\right)\) if \(f\left(x\right)>0\;\)

ACMMM125 | Content Descriptions | Unit 3 | Mathematical Methods | Mathematics | Senior secondary curriculum

ACMMM126

recognise the definite integral \(\int_a^bf\left(x\right)dx\;\;\) as a limit of sums of the form \(\sum\nolimits_if\left(x_i\right)\;\delta x_i\)

ACMMM126 | Content Descriptions | Unit 3 | Mathematical Methods | Mathematics | Senior secondary curriculum

ACMMG199

Solve problems involving duration, including using 12- and 24-hour time within a single time zone

Elaborations ScOT Terms

ACMMG199 | Content Descriptions | Year 8 | Mathematics | F-10 curriculum

ACMEM122

generate tables of values for linear functions, including for negative values of \(x\)

ACMEM122 | Content Descriptions | Unit 3 | Essential Mathematics | Mathematics | Senior secondary curriculum

ACMEM123

graph linear functions for all values of \(x\) with pencil and paper and with graphing software.

ACMEM123 | Content Descriptions | Unit 3 | Essential Mathematics | Mathematics | Senior secondary curriculum

ACMMM046

expand \(\left(x+y\right)^n\) for small positive integers \(n\)

ACMMM046 | Content Descriptions | Unit 1 | Mathematical Methods | Mathematics | Senior secondary curriculum

ACMMM085

interpret the derivative as the slope or gradient of a tangent line of the graph of \(y=f(x)\)

ACMMM085 | Content Descriptions | Unit 2 | Mathematical Methods | Mathematics | Senior secondary curriculum

ACMMM102

establish the formulas \(\frac d{dx}\left(\sin x\right)=\cos x,\;\text{ and }\frac d{dx}\left(\cos x\right)=-\sin x\) by numerical estimations of the limits and informal proofs based on geometric constructions

ACMMM102 | Content Descriptions | Unit 3 | Mathematical Methods | Mathematics | Senior secondary curriculum

ACMMM117

establish and use the formula  \(\int e^xdx=e^x+c\)

ACMMM117 | Content Descriptions | Unit 3 | Mathematical Methods | Mathematics | Senior secondary curriculum

ACMMM127

interpret \(\int_a^bf\left(x\right)dx\;\) as a sum of signed areas

ACMMM127 | Content Descriptions | Unit 3 | Mathematical Methods | Mathematics | Senior secondary curriculum

ACMMM162

establish and use the formula \(\int\frac1xdx=\ln\;x\;+c\) for \(x>0\)

ACMMM162 | Content Descriptions | Unit 4 | Mathematical Methods | Mathematics | Senior secondary curriculum