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ACMEM130

investigate the different kinds of samples; for example, systematic samples, self-selected samples, simple random samples

ACMEM131

investigate the advantages and disadvantages of these kinds of samples; for example, comparing simple random samples with self-selected samples.

ACMMM172

discuss sources of bias in samples, and procedures to ensure randomness

ACMMM175

examine the approximate normality of the distribution of \(\widehat p\) for large samples

ACMMM180

use simulation to illustrate variations in confidence intervals between samples and to show that most but not all confidence intervals contain \(p\)

ACMSM142

use simulation to illustrate variations in confidence intervals between samples and to show that most but not all confidence intervals contain \(\mu\)

ACMMM173

use graphical displays of simulated data to investigate the variability of random samples from various types of distributions, including uniform, normal and Bernoulli.

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 \(\widehat p\)

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

ACMSM139

simulate repeated random sampling, from a variety of distributions and a range of sample sizes, to illustrate the approximate standard normality of \(\frac{\overline X-\mu}{s/\sqrt[{}]n}\) for large samples \(\left(n\geq30\right)\), where \(s\) is the …

ACMEM118

work with the concepts of angle of elevation and angle of depression

ACMSM138

simulate repeated random sampling, from a variety of distributions and a range of sample sizes, to illustrate properties of the distribution of \(\overline X\;\) across samples of a fixed size \(n\), including its mean \(\mu\), its standard deviation …

Unit 4 Mathematical Methods

The calculus in this unit deals with derivatives of logarithmic functions. In probability and statistics, continuous random variables and their applications are introduced and the normal distribution is used in a variety of contexts. The study of statistical …

Unit 4 | Mathematical Methods | Mathematics | Senior secondary curriculum

Structure of Essential Mathematics Essential Mathematics

Essential Mathematics has four units each of which contains a number of topics. It is intended that the topics be taught in a context relevant to students’ needs and interests. In Essential Mathematics, students use their knowledge and skills to investigate …

Structure of Essential Mathematics | Essential Mathematics | Mathematics | Senior secondary curriculum

Structure of General Mathematics General Mathematics

General Mathematics is organised into four units. The topics in each unit broaden students’ mathematical experience and provide different scenarios for incorporating mathematical arguments and problem solving. The units provide a blending of algebraic, …

Structure of General Mathematics | General Mathematics | 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

Structure of Specialist Mathematics Specialist Mathematics

Specialist Mathematics is structured over four units. The topics in Unit 1 broaden students’ mathematical experience and provide different scenarios for incorporating mathematical arguments and problem solving. The unit provides a blending of algebraic …

Structure of Specialist Mathematics | Specialist Mathematics | Mathematics | Senior secondary curriculum

Unit 1 Essential Mathematics

This unit provides students with the mathematical skills and understanding to solve problems relating to calculations, applications of measurement, the use of formulas to find an unknown quantity, and the interpretation of graphs. Teachers are encouraged …

Unit 1 | Essential Mathematics | Mathematics | Senior secondary curriculum

Unit 2 Essential Mathematics

This unit provides students with the mathematical skills and understanding to solve problems related to representing and comparing data, percentages, rates and ratios, the mathematics of finance, and time and motion. Teachers are encouraged to apply the …

Unit 2 | Essential Mathematics | Mathematics | Senior secondary curriculum

Unit 3 Essential Mathematics

This unit provides students with the mathematical skills and understanding to solve problems related to measurement, scales, plans and models, drawing and interpreting graphs, and data collection. Teachers are encouraged to apply the content of the four …

Unit 3 | Essential Mathematics | Mathematics | Senior secondary curriculum

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