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Specialist Mathematics Units 3 and 4 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

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Authorised and published by the Victorian Curriculum and Assessment Authority. Level 1 2 Lonsdale Street Melbourne VIC 3000, Accredited by the Victorian Registration and Qualifications Authority. Level 4 2 Lonsdale Street Melbourne VIC 3000,ISBN 978 1 922082 72 5. Victorian Curriculum and Assessment Authority 2015. No part of this publication may be reproduced except as specified under the Copyright Act 1968. or by permission from the VCAA For more information go to. www vcaa vic edu au Footer Pages Copyright aspx, The VCAA provides the only official up to date versions of VCAA publications Details of updates. can be found on the VCAA website www vcaa vic edu au. This publication may contain copyright material belonging to a third party Every effort has. been made to contact all copyright owners If you believe that material in this publication is an. infringement of your copyright please email the Copyright Officer. vcaa copyright edumail vic gov au, Copyright in materials appearing at any sites linked to this document rests with the copyright. owner s of those materials subject to the Copyright Act The VCAA recommends you refer to. copyright statements at linked sites before using such materials. The VCAA logo is a registered trademark of the Victorian Curriculum and Assessment Authority. Contents VCE Mathematics 2016 2021 3,Important information 5.

Introduction 6,Scope of study 6,Rationale 6,Structure 6. Duration 8,Changes to the study design 8,Monitoring for quality 8. Safety and wellbeing 9,Employability skills 9,Legislative compliance 9. Assessment and reporting 10,Satisfactory completion 10. Levels of achievement 10,Authentication 11,Foundation Mathematics Units 1 and 2 12.

Areas of study 12,Outcomes 14,Assessment 17,General Mathematics Units 1 and 2 18. Areas of study 18,Outcomes 23,Assessment 30,Mathematical Methods Unit 1 31. Areas of study 31,Outcomes 33,Assessment 36,Mathematical Methods Unit 2 37. Areas of study 37,Outcomes 39,Assessment 41,Specialist Mathematics Units 1 and 2 42. Prescribed topics 42,Areas of study 42,Other topics 44.

Areas of study 44,Outcomes 47,Assessment 52,Contents VCE Mathematics 2016 2021 4. Further Mathematics Units 3 and 4 54,Area of Study 1 Unit 3 54. Outcomes 57,Area of Study 2 Unit 4 60,Outcomes 63,School based assessment 67. External assessment 69,Mathematical Methods Units 3 and 4 71. Areas of study 71,Outcomes 74,School based assessment 77.

External assessment 79,Specialist Mathematics Units 3 and 4 81. Areas of study 81,Outcomes 85,School based assessment 87. External assessment 89,Important information VCE Mathematics 2016 2021 5. Important information,Accreditation period,Units 1 4 1 January 2016 31 December 2021. Implementation of this study commences in January 2016. Sources of information, The VCAA Bulletin VCE VCAL and VET is the only official source of changes to regulations and accredited studies.

The VCAA Bulletin also regularly includes advice on VCE studies It is the responsibility of each VCE teacher to. refer to each issue of the VCAA Bulletin The VCAA Bulletin is available as an e newsletter via free subscription on. the VCAA s website at www vcaa vic edu au, To assist teachers in developing courses the VCAA publishes online the Advice for teachers which includes. teaching and learning activities for Units 1 4 and advice on assessment tasks and performance criteria for School. assessed Coursework in Units 3 and 4, The current VCE and VCAL Administrative Handbook contains essential information on assessment processes. and other procedures,VCE providers, Throughout this study design the term school is intended to include both schools and other VCE providers. VCE schools may reproduce parts of this study design for use by teachers The full VCAA Copyright Policy is. available at www vcaa vic edu au Footer Pages Copyright aspx. Introduction VCE Mathematics 2016 2021 6,Introduction. Scope of study, Mathematics is the study of function and pattern in number logic space and structure and of randomness.

chance variability and uncertainty in data and events It is both a framework for thinking and a means of symbolic. communication that is powerful logical concise and precise Mathematics also provides a means by which people. can understand and manage human and natural aspects of the world and inter relationships between these. Essential mathematical activities include conjecturing hypothesising and problem posing estimating calculating. and computing abstracting proving refuting and inferring applying investigating modelling and problem solving. 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. This study enables students to, develop mathematical concepts knowledge and skills. apply mathematics to analyse investigate and model a variety of contexts and solve practical and theoretical. problems in situations that range from well defined and familiar to open ended and unfamiliar. use technology effectively as a tool for working mathematically. The study is made up of the following units,Foundation Mathematics Units 1 and 2. General Mathematics Units 1 and 2,Mathematical Methods Units 1 and 2. Specialist Mathematics Units 1 and 2,Further Mathematics Units 3 and 4. Mathematical Methods Units 3 and 4,Specialist 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 A glossary. defining mathematical terms and notations used across Units 1 to 4 in the VCE Mathematics Study Design is. included in a companion document Advice for teachers. Introduction VCE Mathematics 2016 2021 7, Foundation Mathematics Units 1 and 2 are completely prescribed and provide for the continuing mathematical. development of students entering VCE In general these students would not intend to undertake Unit 3 and 4. studies in VCE Mathematics in the following year However students who do well in these units and undertake. some supplementary study of selected topics could proceed to Further Mathematics Units 3 and 4. General Mathematics Units 1 and 2 provide for a range of courses of study involving non calculus based. topics for a broad range of students and may be implemented in various ways to reflect student interests in and. applications of mathematics They incorporate topics that provide preparation for various combinations of studies. at Units 3 and 4 and cover assumed knowledge and skills for those units. 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, Specialist Mathematics Units 1 and 2 comprise a combination of prescribed and selected non calculus based. topics and provide courses of study for students interested in advanced study of mathematics with a focus on. mathematical structure and reasoning They incorporate topics that in conjunction with Mathematical Methods. Units 1 and 2 provide preparation for Specialist Mathematics Units 3 and 4 and cover assumed knowledge and. skills for those units, 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, 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, Specialist Mathematics Units 3 and 4 are designed to be taken in conjunction with Mathematical Methods.

Units 3 and 4 or following previous completion of Mathematical Methods Units 3 and 4 The areas of study extend. content from Mathematical Methods Units 3 and 4 to include rational and other quotient functions as well as other. advanced mathematics topics such as complex numbers vectors differential equations mechanics and statistical. inference Study of Specialist Mathematics Units 3 and 4 assumes concurrent study or previous completion of. Mathematical Methods Units 3 and 4,Introduction VCE Mathematics 2016 2021 8. Combinations of Mathematics units,Units 1 and 2 Units 3 and 4. Foundation Mathematics Further Mathematics,General Mathematics Further Mathematics. Mathematical Methods Mathematical Methods or Further Mathematics. General Mathematics and Mathematical Methods Mathematical Methods and or Further Mathematics. Mathematical Methods Mathematical Methods and Specialist Mathematics. Mathematical Methods and General Mathematics Mathematical Methods and Specialist Mathematics. Mathematical Methods and Specialist Mathematics Mathematical Methods and Specialist Mathematics. General Mathematics or Specialist Mathematics and Further Mathematics Mathematical Methods and Specialist. Mathematical Methods Mathematics, For this combination of units students wishing to progress to Further Mathematics Units 3 and 4 will need to undertake some supplementary. study with respect to assumed knowledge and skills for Area of Study 1. For this combination of units students will need to undertake some supplementary study with respect to assumed knowledge and skills for. Specialist Mathematics Units 3 and 4, 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 There. are no restrictions on the number of units students may obtain credit towards satisfactory completion of the VCE. Each unit involves at least 50 hours of scheduled classroom instruction over the duration of a semester. Changes to the study design, During its period of accreditation minor changes to the study will be announced in the VCAA Bulletin VCE VCAL and. VET The VCAA Bulletin is the only source of changes to regulations and accredited studies It is the responsibility. of each VCE teacher to monitor changes and advice about VCE studies published in the VCAA Bulletin. Monitoring for quality, As part of ongoing monitoring and quality assurance the VCAA undertakes an audit of VCE Mathematics to ensure. the study is being taught and assessed as accredited The details of the audit procedures and requirements are. published annually in the VCE and VCAL Administrative Handbook Schools will be notified if they are required to. submit material to be audited,Introduction VCE Mathematics 2016 2021 9. Safety and wellbeing, It is the responsibility of the school to ensure that duty of care is exercised in relation to the health and safety of. all students undertaking the study,Employability skills.

This study offers a number of opportunities for students to develop employability skills The Advice for teachers. companion document provides specific examples of how students can develop employability skills during learning. activities and assessment tasks,Legislative compliance. When collecting and using information the provisions of privacy and copyright legislation such as the Victorian. Privacy and Data Protection Act 2014 and Health Records Act 2001 and the federal Privacy Act 1988 and. Copyright Act 1968 must be met, Assessment and reporting VCE Mathematics 2016 2021 10. Assessment and reporting,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 1 and 2, Procedures for the assessment of levels of achievement in Units 1 and 2 are a matter for school decision Assessment. of levels of achievement for these units will not be reported to the VCAA Schools may choose to report levels of. achievement using grades descriptive statements or other indicators. 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 To receive a study score the student must achieve two or more graded assessments. and receive S for both Units 3 and 4 The study score is reported on a scale of 0 50 it is a measure of how well. the student performed in relation to all others who took the study Teachers should refer to the current VCE and. VCAL Administrative Handbook for details on graded assessment and calculation of the study score 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,Mathematical Methods.

Unit 3 School assessed Coursework 17 per cent,Unit 4 School assessed Coursework 17 per cent. Units 3 and 4 Examination 1 22 per cent,Units 3 and 4 Examination 2 44 per cent. Assessment and reporting VCE Mathematics 2016 2021 11. Specialist Mathematics,Unit 3 School assessed Coursework 17 per cent. Unit 4 School assessed Coursework 17 per cent,Units 3 and 4 Examination 1 22 per cent. Units 3 and 4 Examination 2 44 per cent, Examination 1 for Mathematical Methods and Examination 1 for Specialist Mathematics are technology free.

examinations Examinations 1 and 2 for Further Mathematics Examination 2 for Mathematical Methods and. Examination 2 for Specialist Mathematics assume student access to VCAA approved technology Details of the. assessment program are described in the sections for Units 3 and 4 in this study design. Authentication, Work related to the outcomes of each unit will be accepted only if the teacher can attest that to the best of their. knowledge all unacknowledged work is the student s own Teachers need to refer to the current VCE and VCAL. Administrative Handbook for authentication procedures. Foundation Mathematics Units 1 and 2 VCE Mathematics 2016 2021 12. Foundation Mathematics Units 1 and 2, Foundation Mathematics provides for the continuing mathematical development of students entering VCE and who. do not necessarily intend to undertake Unit 3 and 4 studies in VCE Mathematics in the following year This course is. designed to complement General Mathematics and Mathematical Methods Students completing this course would. need to undertake additional targeted mathematical study in order to attempt Further Mathematics Units 3 and 4. In Foundation Mathematics there is a strong emphasis on the use of mathematics in practical contexts. encountered in everyday life in the community at work and at study The areas of study for Units 1 and 2 of. Foundation Mathematics are Space shape and design Patterns and number Data and Measurement. All four areas of study are to be completed over the two units The content should be developed using contexts. present in students other studies work and personal or other familiar situations. 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 equations and graphs. 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. Area of Study 1,Space shape and design, In this area of study students cover the geometric properties of lines and curves and shapes and objects and their. graphical and diagrammatic representations with attention to scale and drawing conventions used in domestic. societal industrial and commercial plans maps and diagrams. This area of study includes, geometric conventions and properties of shapes and objects. interpretation and use of plans elevations maps models and diagrams. application and use of similarity and symmetry,enlargement and reduction of diagrams and models.

interpretation and use of location distance direction and scale on diagrams maps and plans. application of Pythagoras theorem in practical situations. Area of Study 2,Patterns and number, In this area of study students cover estimation the use and application of different forms of numbers and calculations. and the representation of patterns and generalisations in number including formulas and other algebraic expressions. in everyday contexts,This area of study includes, application of integers decimals fractions ratios proportions percentages and rates to solve practical. estimation approximation and reasonableness of results. Foundation Mathematics Units 1 and 2 VCE Mathematics 2016 2021 13. use and interpretation of formulas and algebraic expressions to describe relationships between variables and. to model patterns, manipulation and solution of expressions and equations to solve problems including predicting a required. quantity or finding a break even point,Area of Study 3. In this area of study students cover collection presentation and analysis of gathered and provided data from. community work recreation and media contexts including consideration of suitable forms of representation and. This area of study includes, features conventions and terminology used when representing information in diagrammatic graphical and.

tabular forms, collection and representation of data in diagrammatic tabular and graphical forms. interpretation of diagrams charts tables and graphs. use of measures of central tendency averages and spread to summarise and interpret data. comparison and interpretation of data sets,Area of Study 4. Measurement, In this area of study students cover the use and application of the metric system and related measurement in a. variety of domestic societal industrial and commercial contexts including consideration of accuracy. This area of study includes, application and use of metric units and measures including derived measures. interpretation of scales on digital and analogue instruments. solution of personal societal and workplace problems involving metric measurement with consideration of. error required accuracy and tolerances,estimation and approximation strategies.

interpretation and use of time and duration including time and date specifications conventions schedules. timetables and time zones, Foundation Mathematics Units 1 and 2 VCE Mathematics 2016 2021 14. For each unit the student is required to demonstrate achievement of all three outcomes As a set these outcomes. encompass all of the selected areas of study for each unit For each of Unit 1 and Unit 2 the outcomes apply to. the content from the areas of study selected for that unit. On completion of this unit the student should be able to use and apply a range of mathematical concepts skills and. procedures from selected areas of study to solve problems based on a range of everyday and real life contexts. Space shape and design, To achieve this outcome the student will draw on knowledge and skills outlined in Area of Study 1. Key knowledge, the names and properties of common geometric shapes and objects. the language symbols and conventions for the representation of geometric objects including point line ray. angle diagonal edge curve face and vertex, the language symbols and labelling and drawing conventions for diagrams maps plans and models including. key scale direction distance coordinates and grid reference and elevation. transformations symmetry and similarity,Pythagoras theorem.

Key skills, interpret and describe objects using accurate and appropriate geometric language and conventions. create and modify diagrams plans maps and designs using drawing equipment and digital drawing packages. develop three dimensional models for objects and produce two dimensional representations. interpret diagrams plans maps and models and evaluate their accuracy. interpret information on maps to plan and describe travel routes including use of navigational software and. apply similarity symmetry and Pythagoras theorem to problems in art design and measurement. Patterns and number, To achieve this outcome the student will draw on knowledge and skills outlined in Area of Study 2. Key knowledge, integers decimals fractions ratios proportions percentages and rates. place value rounding leading digit approximation and order of magnitude as powers of 10. numerals and symbols number facts and operations and strategies for calculation. concepts of constant variable and formula,Key skills. form estimates and carry out relevant calculations using mental and by hand methods. use technology effectively for accurate reliable and efficient calculation. solve practical problems which require the use and application of a range of numerical computations involving. integers decimals fractions ratios proportions percentages rates powers and roots. solve practical problems using constants variables formulas and algebra. check for accuracy and reasonableness of results, Foundation Mathematics Units 1 and 2 VCE Mathematics 2016 2021 15.

To achieve this outcome the student will draw on knowledge and skills outlined in Area of Study 3. Key knowledge,categorical and numerical data,methods of data collection and organisation. the key terminology features and conventions of diagrams charts tables and graphs. the purposes for using different forms of data representation and types of data scales categorical and numerical. the common measures of central tendency averages and spread. characteristics and properties of data sets and their distributions. the terminology for comparison and analysis of data sets graphs and summary statistics. Key skills, collect organise collate and represent categorical and numerical data. accurately read and interpret diagrams charts tables and graphs. summarise statistical data and calculate commonly used measures of central tendency and spread. describe compare and analyse data sets and any limitations. Measurement, To achieve this outcome the student will draw on knowledge and skills outlined in Area of Study 4. Key knowledge, the metric units for length area volume capacity time mass temperature and common derived units. the meaning and conventions of different metric units relative scale and conversions including International. System of Units SI, digital and analogue tools and instruments and scales.

the formulas for calculating length area surface area volume and capacity. concepts of tolerance and error,Key skills, identify and use common metric and other relevant measurements. convert between a range of metric and other relevant units. estimate and accurately measure different quantities using appropriate tools. calculate and interpret length area surface area volume capacity and duration. solve a broad range of personal societal or workplace measurement problems with consideration of error. required accuracy and tolerances estimation rounding and approximation strategies.

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