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Mathematical Methods
Mathematical Methods
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:
Mathematical Methods Units 1 and 2
Mathematical Methods 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.
Mathematical Methods Units 1 and 2 are completely prescribed and provide an introductory study of simple elementary functions, algebra, calculus, probability and statistics and their applications in a variety of practical and theoretical contexts. They are designed as preparation for Mathematical Methods Units 3 and 4 and cover assumed knowledge and skills for those units.
Mathematical Methods Units 3 and 4 are completely prescribed and extend the study of simple elementary functions to include combinations of these functions, algebra, calculus, probability and statistics, and their applications in a variety of practical and theoretical contexts. They also provide background for further study in, for example, science, humanities, economics and medicine.
Entry
Entry
There are no prerequisites for entry to Units 1, 2 and 3; however, students undertaking Mathematical Methods Units 1 and 2 or Specialist Mathematics Units 1 and 2 are assumed to have a sound background in number, algebra, function, geometry, probability and statistics. 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. Enrolment in Specialist Mathematics Units 3 and 4 assumes a current enrolment in, or previous completion of, Mathematical Methods Units 3 and 4.
At St Augustine's College, students planning to undertake Mathematical Methods should be working at level 10A while they are in Year 10 and should speak to their current Maths teacher regarding this to ensure they are preparing appropriately.
Units 1 - 4 Topics:
Units 1 - 4 Topics:
Area of study 1 - Functions, relations and graphs
Area of study 2 - Algebra, number & structure
Area of study 3 - Calculus
Area of study 4 - Data analysis, probability & statistics
Mathematical investigation
Mathematical investigation
This comprises one to two weeks of investigation into one or two practical or theoretical contexts or scenarios based on content from areas of study and application of key knowledge and key skills for the outcomes.
Investigation is to be incorporated in the development of concepts, skills and processes for the unit, and can be used to assess the outcomes.
There are three components to mathematical investigation:
There are three components to mathematical investigation:
Formulation
Exploration
Communication
Unit 1: Mathematical Methods
Mathematical Methods Units 1 and 2 provide an introductory study of simple elementary functions of a single real variable, algebra, calculus, probability and statistics and their applications in a variety of practical and theoretical contexts. The units are designed as preparation for Mathematical Methods Units 3 and 4 and contain assumed knowledge and skills for these units.
The focus of Unit 1 is the study of simple algebraic functions, and the areas of study are ‘Functions, relations and graphs’, ‘Algebra, number and structure’, ‘Calculus’ and ‘Data analysis, probability and statistics’. At the end of Unit 1, students are expected to have covered the content outlined in each area of study, with the exception of ‘Algebra, number and structure’ which extends across Units 1 and 2. This content should be presented so that there is a balanced and progressive development of skills and knowledge from each of the four areas of study with connections between and across the areas of study being developed consistently throughout both Units 1 and 2.
In undertaking this unit, 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, algorithms, algebraic manipulation, equations, graphs and differentiation, with and without the use of technology. They should have facility with relevant mental and by-hand approaches to estimation and computation. The use of numerical, graphical, geometric, symbolic and statistical functionality of technology for teaching and learning mathematics, for working mathematically, and in related assessment, is to be incorporated throughout the unit as applicable.
Assessment
The award of satisfactory completion for a unit is based on whether the student has demonstrated achievement of the set of outcomes specified for the unit. Teachers should use a variety of learning activities and assessment tasks that provide a range of opportunities for students to demonstrate the key knowledge and key skills in the outcomes.
The areas of study and the key knowledge and key skills listed for the outcomes, should be used for course design and the development of learning activities and assessment tasks. Assessment must be a part of the regular teaching and learning program and should be completed mainly in class and within a limited timeframe.
All assessments at Units 1 and 2 are school-based. Procedures for assessment of levels of achievement in Units 1 and 2 are a matter for school decision.
For this unit students are required to demonstrate achievement of three outcomes. As a set these outcomes encompass the areas of study in the unit.
Suitable tasks for assessment in this unit may be selected from the following.
Demonstration of achievement of Outcome 1 should be based on the student's performance on a selection of the following assessment tasks:
assignments
tests
solutions to sets of worked questions
summary notes or review notes.
Demonstration of achievement of Outcome 2 should be based on the student's performance on mathematical investigations and a selection of modelling or problem-solving tasks.
Demonstration of achievement of Outcome 3 should be based on the student’s performance on aspects of tasks completed in demonstrating achievement of Outcomes 1 and 2 that incorporate opportunity for computational thinking and the effective and appropriate use of technology.
Where teachers allow students to choose between tasks, they must ensure that the tasks they set are of comparable scope and demand.
Unit 2: Mathematical Methods
The focus of Unit 2 is the study of simple transcendental functions, the calculus of polynomial functions and related modelling applications. The areas of study are ‘Functions, relations and graphs’, ‘Algebra, number and structure’, ‘Calculus’ and ‘Data analysis, probability and statistics’. At the end of Unit 2, students are expected to have covered the content outlined in each area of study.
Material from the areas of study should be organised so that there is a clear progression of skills and knowledge from Unit 1 to Unit 2 in each area of study.
In undertaking this unit, 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, algorithms, algebraic manipulation, equations, graphs, differentiation and anti-differentiation, with and without the use of technology. They should have facility with relevant mental and by-hand approaches to estimation and computation. The use of numerical, graphical, geometric, symbolic and statistical functionality of technology for teaching and learning mathematics, for working mathematically, and in related assessment,
is to be incorporated throughout the unit as applicable.
Assessment
The award of satisfactory completion for a unit is based on whether the student has demonstrated achievement of the set of outcomes specified for the unit. Teachers should use a variety of learning activities and assessment tasks that provide a range of opportunities for students to demonstrate the key knowledge and key skills in the outcomes.
The areas of study and the key knowledge and key skills listed for the outcomes, should be used for course design and the development of learning activities and assessment tasks. Assessment must be a part of the regular teaching and learning program and should be completed mainly in class and within a limited timeframe.
All assessments at Units 1 and 2 are school-based. Procedures for assessment of levels of achievement in Units 1 and 2 are a matter for school decision.
For this unit students are required to demonstrate achievement of three outcomes. As a set these outcomes encompass the areas of study in the unit.
Suitable tasks for assessment in this unit may be selected from the following.
Demonstration of achievement of Outcome 1 should be based on the student's performance on a selection of the following assessment tasks:
assignments
tests
solutions to sets of worked questions
summary notes or review notes.
Demonstration of achievement of Outcome 2 should be based on the student's performance on mathematical investigations and a selection of modelling or problem-solving tasks.
Demonstration of achievement of Outcome 3 should be based on the student’s performance on aspects of tasks completed in demonstrating achievement of Outcomes 1 and 2 that incorporate opportunity for computational thinking and the effective and appropriate use of technology.
Where teachers allow students to choose between tasks, they must ensure that the tasks they set are of comparable scope and demand.
Units 3 and 4: Mathematical Methods
Mathematical Methods Units 3 and 4 extend the introductory study of simple elementary functions of a single real variable, to include combinations of these functions, algebra, calculus, probability and statistics, and their applications in a variety of practical and theoretical contexts. Units 3 and 4 consist of the areas of study ‘Algebra, number and structure’, ‘Data analysis, probability and statistics’, ‘Calculus’, and ‘Functions, relations and graphs’, which must be covered in progression from Unit 3 to Unit 4, with an appropriate selection of content for each of Unit 3 and Unit 4. Assumed knowledge and skills for Mathematical Methods Units 3 and 4 are contained in Mathematical Methods Units 1 and 2, and will be drawn on, as applicable, in the development of related content from the areas of study, and key knowledge and key skills for the outcomes of Mathematical Methods Units 3 and 4.
For Unit 3 a selection of content would typically include the areas of study ‘Functions, relations and graphs’ and ‘Algebra, number and structure’, applications of derivatives and differentiation, and identifying and analysing key features of the functions and their graphs from the ‘Calculus’ area of study. For Unit 4, a corresponding selection of content would typically consist of remaining content from ‘Functions, relations and graphs’, ‘Algebra, number and structure’ and ‘Calculus’ areas of study, and the study of random variables, discrete and continuous probability distributions, and the distribution of sample proportions from the ‘Data analysis, probability and statistics’ area of study. For Unit 4, the content from the ‘Calculus’ area of study would be likely to include the treatment of anti-differentiation, integration, the relation between integration and the area of regions specified by lines or curves described by the rules of functions, and simple applications of this content, including to probability distributions of continuous random variables.
The selection of content from the areas of study should be constructed so that there is a development in the complexity and sophistication of problem types and mathematical processes used (modelling, transformations, graph sketching and equation solving) in application to contexts related to these areas of study. There should be a clear progression of skills and knowledge from Unit 3 to Unit 4 in an area of study.
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, algorithms, algebraic manipulation, equations, graphs, differentiation, anti-differentiation, integration and inference, with and without the use of technology. They should have facility with relevant mental and by-hand approaches to estimation and computation. The use of numerical, graphical, geometric, symbolic 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.
External assessment
The level of achievement for Units 3 and 4 is also assessed by two end-of-year examinations.
Contribution to final assessment
Examination 1 will contribute 20 per cent to the study score and Examination 2 will contribute 40 per cent to the study score.
End-of-year examinations
Description
The examinations will be set by a panel appointed by the VCAA. All of the content from the areas of study and the key knowledge and key skills that underpin the outcomes in Units 3 and 4 are examinable.
Examination 1
This examination comprises short-answer and some extended-answer questions covering all areas of study in relation to Outcome 1. It is designed to assess students’ knowledge of mathematical concepts, their skills in carrying out mathematical algorithms without the use of technology and their ability to apply concepts and skills.
Conditions
The examination will be completed under the following conditions:
Duration: 1 hour.
No technology (calculators or software) or notes of any kind are permitted. A sheet of formulas will be provided with the examination.
Date: end-of-year, on a date to be published annually by the VCAA.
VCAA examination rules will apply. Details of these rules are published annually in the VCE and VCAL Administrative Handbook.
The examination will be marked by assessors appointed by the VCAA.
Examination 2
This examination comprises multiple-choice questions and extended-answer questions covering all areas of the study in relation to all three outcomes, with an emphasis on Outcome 2. The examination is designed to assess students’ ability to understand and communicate mathematical ideas, and to interpret, analyse and solve both routine and non-routine problems.
Conditions
The examination will be completed under the following conditions:
Duration: 2 hours.
Student access to an approved technology with numerical, graphical, symbolic and statistical functionality will be assumed.
One bound reference text (which may be annotated) or lecture pad may be brought into the examination.
Date: end-of-year, on a date to be published annually by the VCAA.
VCAA examination rules will apply. Details of these rules are published annually in the VCE and VCAL Administrative Handbook.
The examination will be marked by assessors appointed by the VCAA.
Casio Classpad
Casio Classpad
FX-CP 400
Click on the link to take you to the VCAA site.
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