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
ACMSM067
define the imaginary number i as a root of the equation \(x^2=-1\)
ACMSM067 | Content Descriptions | Unit 2 | Specialist Mathematics | Mathematics | Senior secondary curriculum
ACMMM077
interpret the difference quotient \(\frac{f\left(x+h\right)-f(x)}h\) as the average rate of change of a function \(f\)
ACMMM077 | Content Descriptions | Unit 2 | Mathematical Methods | Mathematics | Senior secondary curriculum
ACMMM081
examine the behaviour of the difference quotient \(\frac{f\left(x+h\right)-f(x)}h\) as \(h\rightarrow0\) as an informal introduction to the concept of a limit
ACMMM081 | Content Descriptions | Unit 2 | Mathematical Methods | Mathematics | Senior secondary curriculum
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 \(x\rightarrow-\infty\)
ACMMM095 | Content Descriptions | Unit 2 | Mathematical Methods | Mathematics | Senior secondary curriculum
ACMSM048
convert sums \(\mathrm a\cos\mathrm x+\mathrm b\;\sin\mathrm x\) to \(\mathrm R\;\cos{(\mathrm x\pm\mathrm\alpha)}\) or \(\mathrm R\sin{(\mathrm x\pm\mathrm\alpha)}\) and apply these to sketch graphs, solve equations of the form \(\mathrm a\cos\mathrm …
ACMSM048 | Content Descriptions | Unit 2 | Specialist Mathematics | Mathematics | Senior secondary curriculum
Year 7 History
The ancient world The Year 7 curriculum provides a study of history from the time of the earliest human communities to the end of the ancient period, approximately 60 000 BC (BCE) – c.650 AD (CE). It was a period defined by the development of cultural …
Year 7 | History | Humanities and Social Sciences | F-10 curriculum
Elaboration ACMSP249
understanding that box plots are an efficient and common way of representing and summarising data and can facilitate comparisons between data sets
Elaboration | ACMSP249 | Content Descriptions | Year 10 | Mathematics | F-10 curriculum
Elaboration ACLASFU160
exploring similarities and differences in Auslan dialects through building webcam relationships with other schools or through identifying and collecting signs that differ in the northern (Qld and NSW) and southern (Vic., SA, WA and Tas.) dialects, such …
Elaboration | ACLASFU160 | Content Descriptions | Years 3 and 4 | Years F–10 Sequence | Second Language Learner Pathway | Auslan | Languages | F-10 curriculum
Mathematics - Year 10
Money and financial mathematics Connect the compound interest formula to repeated applications of simple interest using appropriate digital technologies (ACMNA229) Patterns and algebra Substitute values into formulas to determine an unknown (ACMNA234) Linear …
Mathematics - Year 10 | Competencies and skills | Dimensions | Curriculum connections | Resources
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
ACMMM020 | Content Descriptions | Unit 1 | Mathematical Methods | Mathematics | Senior secondary curriculum
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 \(x\)
ACMMM107 | Content Descriptions | Unit 3 | Mathematical Methods | Mathematics | Senior secondary curriculum
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
ACMMM130 | Content Descriptions | Unit 3 | Mathematical Methods | Mathematics | Senior secondary curriculum
ACMSM049
prove and apply other trigonometric identities such as \(\cos3\mathrm x=4\;\mathrm c\mathrm o\mathrm s^{3\;}\mathrm x-3\cos\mathrm x\)
ACMSM049 | Content Descriptions | Unit 2 | Specialist Mathematics | Mathematics | Senior secondary curriculum
ACMSM137
examine the concept of the sample mean X as a random variable whose value varies between samples where X is a random variable with mean μ and the standard deviation σ
ACMSM137 | Content Descriptions | Unit 4 | Specialist Mathematics | Mathematics | Senior secondary curriculum
Context statement Vietnamese
The place of the Vietnamese language and culture in Australia and in the world Vietnamese is the official language of Vietnam. It is spoken by approximately 90 million people in Vietnam and approximately four million Vietnamese people living …
Context statement | Vietnamese | Languages | F-10 curriculum