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ACMMM133

calculate total change by integrating instantaneous or marginal rate of change

ACMEM171

use technology to calculate the future value of a compound interest loan or investment and the total interest paid or earned

ACMSM065

prove results for sums, such as \(1+4+9\dots+n^2=\frac{n(n+1)(2n+1)}6\) for any positive integer n

ACEEN066

the selection of mode, medium, genre and type of text

ACMEM102

recognise relations between volume and capacity, recognising that \(1\mathrm c\mathrm m^3=1\mathrm m\mathrm L\) and \(1\mathrm m^3=1\mathrm k\mathrm L\)

ACMMM116

establish and use the formula \(\int x^ndx=\frac1{n+1}x^{n+1}+c\) for \(n\neq-1\)

Keystone species play a critical role in maintaining the structure of the community; the impact of a reduction in numbers or the disappearance of keystone species on an ecosystem is greater than would be expected based on their relative abundance or total …

ACSPH076

A wave model explains a wide range of light-related phenomena including reflection, refraction, total internal reflection, dispersion, diffraction and interference; a transverse wave model is required to explain polarisation

ACMMM099

recognise that \(e\) is the unique number \(a\) for which the above limit is 1

ACMSM067

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

ACMEM040

determine which type of graph is best used to display a dataset

ACMMM068

recognise and use the recursive definition of an arithmetic sequence: \(t_{n+1}=t_n+d\)

ACMMM072

recognise and use the recursive definition of a geometric sequence:\(t_{n+1}=rt_n\)

ACMSM101

review the concepts of vectors from Unit 1 and extend to three dimensions including introducing the unit vectors i, j and k.

ACSCH028

Nanomaterials are substances that contain particles in the size range 1–100 nm and have specific properties relating to the size of these particles

ACMMM178

use the approximate confidence interval \(\left(\widehat p-z\sqrt[{}]{(\widehat p(1-\widehat p)/n},\;\;\widehat p+z\sqrt[{}]{(\widehat p(1-\widehat p)/n}\right),\) as an interval estimate for \(p\), where \(z\) is the appropriate quantile for the standard …

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