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ACMMM017

recognise features of the graphs of \(y=x^3\), \(y=a{(x-b)}^3+c\) and \(y=k(x-a)(x-b)(x-c)\), including shape, intercepts and behaviour as \(x\rightarrow\infty\) and \(x\rightarrow-\infty\)

In this unit the study of calculus continues with the derivatives of exponential and trigonometric functions and their applications, together with some differentiation techniques and applications to optimisation problems and graph sketching. It concludes …

Unit 3 | Mathematical Methods | Mathematics | Senior secondary curriculum

Unit 2 Mathematical Methods

The algebra section of this unit focuses on exponentials and logarithms. Their graphs are examined and their applications in a wide range of settings are explored. Arithmetic and geometric sequences are introduced and their applications are studied. Rates …

Unit 2 | Mathematical Methods | Mathematics | Senior secondary curriculum

Units 3 and 4 Mathematical Methods Achievement Standard

demonstrates knowledge of concepts of functions, integration and distributions in routine and non-routine problems in a variety of contexts selects and applies techniques in functions, integration and distributions to solve routine and non-routine problems …

Units 3 and 4 | Achievement standards | Mathematical Methods | Mathematics | Senior secondary curriculum

Units 1 and 2 Mathematical Methods Achievement Standard

demonstrates knowledge of concepts of functions, calculus and statistics in routine and non-routine problems in a variety of contexts selects and applies techniques in functions, calculus and statistics to solve routine and non-routine problems in a …

Units 1 and 2 | Achievement standards | Mathematical Methods | Mathematics | Senior secondary curriculum

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

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

ACMMM021

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

Rationale Mathematical Methods

Mathematics is the study of order, relation and pattern. From its origins in counting and measuring it has evolved in highly sophisticated and elegant ways to become the language now used to describe much of the modern world. Statistics is concerned with …

Rationale | Mathematical Methods | Mathematics | Senior secondary curriculum

Structure of Mathematical Methods Mathematical Methods

Mathematical Methods is organised into four units. The topics broaden students’ mathematical experience and provide different scenarios for incorporating mathematical arguments and problem solving. The units provide a blending of algebraic and geometric …

Structure of Mathematical Methods | Mathematical Methods | Mathematics | Senior secondary curriculum

ACMMM106

apply the product, quotient and chain rule to differentiate functions such as \(xe^x\), \(\tan x,\), \(\frac1{x^n}\), \(x\sin x,\text{ }e^{-x}\sin x\) and \(f(ax+b)\)

ACMMM037

examine amplitude changes and the graphs of \(y=a\sin x\) and \(y=a\cos x\)

ACMMM036

recognise the graphs of \(y=\sin x,\;y=\cos x,\) and \(y=\tan x\) on extended domains

ACMMM039

examine phase changes and the graphs of \(y=\sin{(x+c)}\), \(y=\cos{(x+c)}\) and \(y=\tan{(x+c)}\) and the relationships \(\sin\left(x+\frac\pi2\right)=\cos x\) and \(\cos\left(x-\frac\pi2\right)=\sin x\)

ACMMM065

recognise the qualitative features of the graph of \(y=a^x(a>0)\) including asymptotes, and of its translations \(y=a^x+b\) and \(y=a^{x+c}\)

ACMMM082

define the derivative \(f'\left(x\right)\) as \(\lim_{h\rightarrow0}\frac{f\left(x+h\right)-f(x)}h\)

ACMMM079

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

ACMMM080

interpret the ratios \(\frac{f\left(x+h\right)-f(x)}h\) and \(\frac{\delta y}{\delta x}\) as the slope or gradient of a chord or secant of the graph of \(y=f(x)\)

ACMMM088

establish the formula \(\frac d{dx}\left(x^n\right)=nx^{n-1}\) for positive integers \(n\) by expanding \({(x+h)}^n\) or by factorising \({(x+h)}^n-x^n\)

ACMMM159

define the natural logarithm \(\ln x=\log_ex\)

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