ACMGM067
use recursion to generate an arithmetic sequence
ACMGM067 | Content Descriptions | Unit 3 | General Mathematics | Mathematics | Senior secondary curriculum
ACMGM071
use recursion to generate a geometric sequence
ACMGM071 | Content Descriptions | Unit 3 | General Mathematics | Mathematics | Senior secondary curriculum
Overview of the senior secondary Australian Curriculum
ACARA has developed a senior secondary Australian Curriculum for English, Mathematics, Science and Humanities and Social Sciences. The senior secondary Australian Curriculum specifies content and achievement standards for each senior secondary subject. …
Overview of the senior secondary Australian Curriculum | Mathematics | Senior secondary curriculum
ACMGM069
deduce a rule for the nth term of a particular arithmetic sequence from the pattern of the terms in an arithmetic sequence, and use this rule to make predictions
ACMGM069 | Content Descriptions | Unit 3 | General Mathematics | Mathematics | Senior secondary curriculum
ACMGM073
deduce a rule for the nth term of a particular geometric sequence from the pattern of the terms in the sequence, and use this rule to make predictions
ACMGM073 | Content Descriptions | Unit 3 | General Mathematics | Mathematics | Senior secondary curriculum
ACMMM071
establish and use the formula for the sum of the first \(n\) terms of an arithmetic sequence.
ACMMM071 | Content Descriptions | Unit 2 | Mathematical Methods | Mathematics | Senior secondary curriculum
ACMGM075
use a general first-order linear recurrence relation to generate the terms of a sequence and to display it in both tabular and graphical form
ACMGM075 | Content Descriptions | Unit 3 | General Mathematics | Mathematics | Senior secondary curriculum
ACMMM068
recognise and use the recursive definition of an arithmetic sequence: \(t_{n+1}=t_n+d\)
ACMMM068 | Content Descriptions | Unit 2 | Mathematical Methods | Mathematics | Senior secondary curriculum
ACMMM072
recognise and use the recursive definition of a geometric sequence:\(t_{n+1}=rt_n\)
ACMMM072 | Content Descriptions | Unit 2 | Mathematical Methods | Mathematics | Senior secondary curriculum
ACMMM073
use the formula \(t_n=r^{n-1}t_1\) for the general term of a geometric sequence and recognise its exponential nature
ACMMM073 | Content Descriptions | Unit 2 | Mathematical Methods | Mathematics | Senior secondary curriculum
ACMMM075
establish and use the formula \(S_n=t_1\frac{r^n-1}{r-1}\) for the sum of the first \(n\) terms of a geometric sequence
ACMMM075 | Content Descriptions | Unit 2 | 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
ACMGM068
display the terms of an arithmetic sequence in both tabular and graphical form and demonstrate that arithmetic sequences can be used to model linear growth and decay in discrete situations
ACMGM068 | Content Descriptions | Unit 3 | General Mathematics | Mathematics | Senior secondary curriculum
ACMGM072
display the terms of a geometric sequence in both tabular and graphical form and demonstrate that geometric sequences can be used to model exponential growth and decay in discrete situations
ACMGM072 | Content Descriptions | Unit 3 | General Mathematics | Mathematics | Senior secondary curriculum
ACMGM076
recognise that a sequence generated by a first-order linear recurrence relation can have a long term increasing, decreasing or steady-state solution
ACMGM076 | Content Descriptions | Unit 3 | General Mathematics | Mathematics | Senior secondary curriculum
ACMMM069
use the formula \(t_n=t_1+\left(n-1\right)d\) for the general term of an arithmetic sequence and recognise its linear nature
ACMMM069 | Content Descriptions | Unit 2 | Mathematical Methods | Mathematics | Senior secondary curriculum
ACMMM074
understand the limiting behaviour as \(n\rightarrow\infty\) of the terms \(t_n\) in a geometric sequence and its dependence on the value of the common ratio \(r\)
ACMMM074 | Content Descriptions | Unit 2 | Mathematical Methods | Mathematics | Senior secondary curriculum