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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

ACMMM117

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

ACMMM127

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

ACMMM162

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

ACMSM067

define the imaginary number i as a root of the equation \(x^2=-1\)

ACMMM077

interpret the difference quotient \(\frac{f\left(x+h\right)-f(x)}h\) as the average rate of change of a function \(f\)

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

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 \(x\rightarrow-\infty\)

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 …

Achievement Standard Indonesian Years 7 and 8

By the end of Year 8, students use Indonesian to interact and exchange ideas, experiences and interests with teachers, peers and others. They pronounce familiar polysyllabic words such as mendengarkan, pekerjaan and mengerjakan, stressing the penultimate …

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

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 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 …

Structure Design and Technologies

The Australian Curriculum: Design and Technologies (F–10) comprises two related strands: Design and Technologies knowledge and understanding – the use, development and impact of technologies and design ideas across a range of technologies contexts Design …

Structure | Design and Technologies | Technologies | F-10 curriculum

Structure Digital Technologies

The Australian Curriculum: Digital Technologies (F–10) comprises two related strands: Digital Technologies knowledge and understanding – the information system components of data, and digital systems (hardware, software and networks) Digital Technologies …

Structure | Digital Technologies | Technologies | F-10 curriculum

Context statement Japanese

The place of Japanese culture and language in Australia and in the world Japanese is the official language of Japan, Australia’s northern neighbour in the Asia region. It is also widely used by communities of speakers in Hawaii, Peru and …

Context statement | Japanese | Languages | F-10 curriculum

Achievement Standard Mathematics Year 4

By the end of Year 4, students choose appropriate strategies for calculations involving multiplication and division. They recognise common equivalent fractions in familiar contexts and make connections between fraction and decimal notations up to two …

Achievement Standard | Achievement Standards | Year 4 | Mathematics | F-10 curriculum

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