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
ACMEM130
investigate the different kinds of samples; for example, systematic samples, self-selected samples, simple random samples
ACMEM130 | Content Descriptions | Unit 3 | Essential Mathematics | Mathematics | Senior secondary curriculum
ACMEM131
investigate the advantages and disadvantages of these kinds of samples; for example, comparing simple random samples with self-selected samples.
ACMEM131 | Content Descriptions | Unit 3 | Essential Mathematics | Mathematics | Senior secondary curriculum
ACMMM172
discuss sources of bias in samples, and procedures to ensure randomness
ACMMM172 | Content Descriptions | Unit 4 | Mathematical Methods | Mathematics | Senior secondary curriculum
ACMMM175
examine the approximate normality of the distribution of \(\widehat p\) for large samples
ACMMM175 | Content Descriptions | Unit 4 | Mathematical Methods | Mathematics | Senior secondary curriculum
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
ACSCH028 | Content Descriptions | Unit 1 | Chemistry | Science | Senior secondary curriculum
ACMMM180
use simulation to illustrate variations in confidence intervals between samples and to show that most but not all confidence intervals contain \(p\)
ACMMM180 | Content Descriptions | Unit 4 | Mathematical Methods | Mathematics | Senior secondary curriculum
ACMSM142
use simulation to illustrate variations in confidence intervals between samples and to show that most but not all confidence intervals contain \(\mu\)
ACMSM142 | Content Descriptions | Unit 4 | Specialist Mathematics | 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
ACMMM020 | Content Descriptions | Unit 1 | Mathematical Methods | Mathematics | Senior secondary curriculum
ACMMM173
use graphical displays of simulated data to investigate the variability of random samples from various types of distributions, including uniform, normal and Bernoulli.
ACMMM173 | Content Descriptions | Unit 4 | Mathematical Methods | Mathematics | Senior secondary curriculum
ACMSM121
integrate expressions of the form \(\frac{\pm1}{\sqrt[{}]{a^2-x^2}}\) and \(\frac a{a^2+x^2}\)
ACMSM121 | Content Descriptions | Unit 4 | Specialist Mathematics | Mathematics | Senior secondary curriculum
ACSPH025
Energy transfers and transformations in mechanical systems (for example, internal and external combustion engines, electric motors) always result in some heat loss to the environment, so that the usable energy is reduced and the system cannot be 100 percent …
ACSPH025 | Content Descriptions | Unit 1 | Physics | Science | Senior secondary curriculum
ACMSM063
prove irrationality by contradiction for numbers such as \(\sqrt[{}]2\) and \(\log_25\)
ACMSM063 | Content Descriptions | Unit 2 | Specialist Mathematics | Mathematics | Senior secondary curriculum
ACMMM174
understand the concept of the sample proportion \(\widehat p\) as a random variable whose value varies between samples, and the formulas for the mean \(p\) and standard deviation \(\sqrt[{}]{(p(1-p)/n}\) of the sample proportion \(\widehat p\)
ACMMM174 | Content Descriptions | Unit 4 | Mathematical Methods | 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
ACMEM001
solve practical problems requiring basic number operations
ACMEM001 | Content Descriptions | Unit 1 | Essential Mathematics | Mathematics | Senior secondary curriculum
ACMEM008
evaluate decimal fractions to the required number of decimal places
ACMEM008 | Content Descriptions | Unit 1 | Essential Mathematics | Mathematics | Senior secondary curriculum
ACMEM058
complete a five number summary for different datasets
ACMEM058 | Content Descriptions | Unit 2 | Essential Mathematics | Mathematics | Senior secondary curriculum
ACMEM059
construct box plots using a five number summary
ACMEM059 | Content Descriptions | Unit 2 | Essential Mathematics | Mathematics | Senior secondary curriculum
ACMMM011
recognise features of the graph of the general quadratic \(y=ax^2+bx+c\)
ACMMM011 | Content Descriptions | Unit 1 | Mathematical Methods | Mathematics | Senior secondary curriculum