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Is this the right maths for me?
Is this the right maths for me?
Watch the following brief video that explains all of the different mathematics subjects and suggests some possible mathematical pathways for you to consider before making your final choice.
Further Mathematics - Units 3 & 4
Further Mathematics - Units 3 & 4
Rationale
Rationale
This study is designed to provide access to worthwhile and challenging mathematical learning in a way which takes into account the interests, needs, dispositions and aspirations of a wide range of students, and introduces them to key aspects of the discipline. It is also designed to promote students’ awareness of the importance of mathematics in everyday life in a technological society, and to develop confidence and the disposition to make effective use of mathematical concepts, processes and skills in practical and theoretical contexts.
Structure
Structure
The study is made up of the following units:
Further Mathematics Units 3 and 4
Each unit deals with specific content contained in areas of study and is designed to enable students to achieve a set of three outcomes for that unit. Each outcome is described in terms of key knowledge and key skills.
Further Mathematics Units 3 and 4 are designed to be widely accessible and comprise a combination of non-calculus based content from a prescribed core and a selection of two from four possible modules across a range of application contexts. They provide general preparation for employment or further study, in particular where data analysis, recursion and number patterns are important. The assumed knowledge and skills for the Further Mathematics Units 3 and 4 prescribed core are covered in specified topics from General Mathematics Units 1 and 2. Students who have done only Mathematical Methods Units 1 and 2 will also have had access to assumed knowledge and skills to undertake Further Mathematics but may also need to undertake some supplementary study of statistics content.
Entry
Entry
There are no prerequisites for entry to Units 1, 2 and 3. Students must undertake Unit 3 prior to undertaking Unit 4. Units 1 to 4 are designed to a standard equivalent to the final two years of secondary education. All VCE studies are benchmarked against comparable national and international curriculum.
Further Mathematics Units 3 and 4
Further Mathematics Units 3 and 4
Further Mathematics consists of two areas of study, a compulsory Core area of study to be completed in Unit 3 and an Applications area of study to be completed in Unit 4. The Core comprises ‘Data analysis’ and ‘Recursion and financial modelling’. The Applications comprises two modules to be completed in their entirety, from a selection of four possible modules: ‘Matrices’, ‘Networks and decision mathematics’, ‘Geometry and measurement’ and ‘Graphs and relations’. ‘Data analysis’ comprises 40 per cent of the content to be covered, ‘Recursion and financial modelling’ comprises 20 per cent of the content to be covered, and each selected module comprises 20 per cent of the content to be covered.
At St Augustine's College, the modules studied are: Matrices and Graphs and relations.
Assumed knowledge and skills for the Core are contained in the General Mathematics Units 1 and 2 topics: ‘Computation and practical arithmetic’, ‘Investigating and comparing data distributions’, ‘Investigating relationships between two numerical variables’, ‘Linear graphs and modelling’, ‘Linear relations and equations’, and ‘Number patterns and recursion’. For each module there are related topics in General Mathematics Units 1 and 2.
In undertaking these units, students are expected to be able to apply techniques, routines and processes involving rational and real arithmetic, sets, lists and tables, diagrams and geometric constructions, algebraic manipulation, equations, and graphs. They should have a facility with relevant mental and by-hand approaches to estimation and computation. The use of numerical, graphical, geometric, symbolic, financial and statistical functionality of technology for teaching and learning mathematics, for working mathematically, and in related assessment, is to be incorporated throughout each unit as applicable.
Resources
Resources
Area of Study 1 – Unit 3
Core
Data analysis
Investigating
data distributions
associations between two variables
and modelling linear associations
and modelling time series data
Area of Study 1 – Unit 3
Core
Recursion and financial modelling
Depreciation of assets
Compound interest investments and loans
Reducing balance loans
Annuities and perpetuities
Compound interest investment with periodic and equal additions to the principal
Area of Study 2 – Unit 4
Applications
Matrices
Matrices and their applications
Transition matrices
Area of Study 2 – Unit 4
Applications
Graphs and relations
Construction and interpretation of graphs
Linear programming
Outcome 1
On completion of this unit the student should be able to define and explain key concepts as specified in the content from Area of Study 1 & 2, and apply related mathematical techniques and models in routine contexts.
Outcome 2
On completion of this unit the student should be able to select and apply the mathematical concepts, models and techniques from Area of Study 1 & 2 in a range of contexts of increasing complexity.
Outcome 3
On completion of this unit the student should be able to select and appropriately use numerical, graphical, symbolic and statistical functionalities of technology to develop mathematical ideas, produce results and carry out analysis in situations requiring problem-solving, modelling or investigative techniques or approaches.
Assessment
Assessment
Satisfactory completion
The award of satisfactory completion for a unit is based on the teacher’s decision that the student has demonstrated achievement of the set of outcomes specified for the unit. Demonstration of achievement of outcomes and satisfactory completion of a unit are determined by evidence gained through the assessment of a range of learning activities and tasks. Teachers must develop courses that provide appropriate opportunities for students to demonstrate satisfactory achievement of outcomes. The decision about satisfactory completion of a unit is distinct from the assessment of levels of achievement. Schools will report a student’s result for each unit to the VCAA as S (Satisfactory) or N (Not Satisfactory).
Levels of achievement
Units 3 and 4
The VCAA specifies the assessment procedures for students undertaking scored assessment in Units 3 and 4. Designated assessment tasks are provided in the details for each unit in the VCE study designs. The student’s level of achievement in Units 3 and 4 will be determined by School-assessed Coursework (SACs) and/or School-assessed Tasks (SATs) as specified in the VCE study designs, and external assessment. The VCAA will report the student’s level of achievement on each assessment component as a grade from A+ to E or UG (ungraded). Percentage contributions to the study score in VCE Mathematics are as follows:
Further Mathematics
Unit 3 School-assessed Coursework: 20 per cent
Unit 4 School-assessed Coursework: 14 per cent
Units 3 and 4 Examination 1: 33 per cent
Units 3 and 4 Examination 2: 33 per cent
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