Mathematics General - Stage 6 Syllabus 2012

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MathematicsGeneralStage 6Syllabus2012

2012 Board of Studies NSW for and on behalf of the Crown in right of the State of New South Wales.This document contains Material prepared by the Board of Studies NSW for and on behalf of the Stateof New South Wales. The Material is protected by Crown copyright.All rights reserved. No part of the Material may be reproduced in Australia or in any other country by anyprocess, electronic or otherwise, in any material form or transmitted to any other person or stored electronicallyin any form without the prior written permission of the Board of Studies NSW, except as permitted by theCopyright Act 1968. School students in NSW and teachers in schools in NSW may copy reasonable portionsof the Material for the purposes of bona fide research or study.When you access the Material you agree: to use the Material for information purposes only to reproduce a single copy for personal bona fide study use only and not to reproduce any major extractor the entire Material without the prior permission of the Board of Studies NSW to acknowledge that the Material is provided by the Board of Studies NSW not to make any charge for providing the Material or any part of the Material to another person or in anyway make commercial use of the Material without the prior written consent of the Board of Studies NSWand payment of the appropriate copyright fee to include this copyright notice in any copy made not to modify the Material or any part of the Material without the express prior written permission of theBoard of Studies NSW.The Material may contain third-party copyright materials such as photos, diagrams, quotations, cartoonsand artworks. These materials are protected by Australian and international copyright laws and may notbe reproduced or transmitted in any format without the copyright owner‟s specific permission. Unauthorisedreproduction, transmission or commercial use of such copyright materials may result in prosecution.The Board of Studies has made all reasonable attempts to locate owners of third-party copyright material andinvites anyone from whom permission has not been sought to contact the Copyright Officer, ph (02) 9367 8289,fax (02) 9279 1482.Published byBoard of Studies NSWGPO Box 5300Sydney NSW 2001AustraliaTel: (02) 9367 8111Fax: (02) 9367 8484Internet: 7620130276

Contents1The Higher School Certificate Program of Study.52Rationale.53Continuum of Learning for Stage 6 Mathematics General Students .74Mathematics in Stage 6.84.1Courses.84.2Statistics in the Mathematics General Syllabus .115Aim .126Objectives .127Objectives and Outcomes .138Preliminary Mathematics General/HSC Mathematics General 2 Pathway .15910*8.1Pathway Structure.158.2Employability Skills .168.3Use of Technology .168.4Course Requirements .178.5Presentation of Content .17Preliminary Mathematics General Course Content* .21Strand:Financial Mathematics.22Strand:Data and Statistics .30Strand:Measurement .38Strand:Probability.46Strand:Algebra and Modelling.50Focus Study:Mathematics and Communication .56Focus Study:Mathematics and Driving .62HSC Mathematics General 2 Course Content .71Strand:Financial Mathematics.72Strand:Data and Statistics .78Strand:Measurement .86Strand:Probability.94Strand:Algebra and Modelling.98Focus Study:Mathematics and Health.106Focus Study:Mathematics and Resources.114Satisfactory completion of the Preliminary Mathematics General course may be followed bystudy of either the HSC Mathematics General 2 course or the HSC Mathematics General 1course. (Note: The HSC Mathematics General 2 course is a Board Developed Course(examined at the HSC), while the HSC Mathematics General 1 course is a Content EndorsedCourse (not examined at the HSC)).3

Mathematics General Stage 6 Syllabus11HSC Mathematics General 2: Assessment and Reporting .12212Preliminary Mathematics General/HSC Mathematics General 1 Pathway .12312.1Pathway Structure.12312.2Employability Skills .12412.3Use of Technology .12412.4Course Requirements .12512.5Presentation of Content .12513Preliminary Mathematics General Course Content (see Section 9).12814HSC Mathematics General 1 Course Content.1291516Strand:Financial Mathematics.130Strand:Data and Statistics .134Strand:Measurement .142Strand:Probability.146Strand:Algebra and Modelling.150Focus Study:Mathematics and Design.156Focus Study:Mathematics and Household Finance .162Focus Study:Mathematics and the Human Body .168Focus Study:Mathematics and Personal Resource Usage .176HSC Mathematics General 1: Assessment and Reporting .18415.1Requirements and Advice.18415.2Assessment of Stage 6 Content Endorsed Courses.18415.3Assessment Components, Weightings and Tasks.185Post-school Opportunities.1874

Mathematics General Stage 6 Syllabus1The Higher School Certificate Program of StudyThe purpose of the Higher School Certificate program of study is to: provide a curriculum structure that encourages students to completesecondary education foster the intellectual, social and moral development of students, in particulardeveloping their: knowledge, skills, understanding and attitudes in the fields of study they choose capacity to manage their own learning desire to continue learning in formal or informal settings after school capacity to work together with others respect for the cultural diversity of Australian societyprovide a flexible structure within which students can prepare for: further education and training employment full and active participation as citizens provide formal assessment and certification of students’ achievements provide a context within which schools also have the opportunity to foster students’physical and spiritual development.2RationaleMathematics is deeply embedded in modern society. From the numeracy skills requiredto manage personal finances, to making sense of data in various forms, to leading-edgetechnologies in the sciences and engineering, mathematics provides the framework forinterpreting, analysing and predicting, and the tools for effective participation in anincreasingly complex society.The need to interpret the large volumes of data made available through technology drawson skills in logical thought and skills in checking claims and assumptions in a systematicway. Mathematics is the appropriate training ground for the development of these skills.The thinking required to enhance further the power and usefulness of technology in real-worldapplications requires advanced mathematical training. The rapid advances in technologyexperienced in recent years have driven, and been driven by, advances in the disciplineof mathematics.The development of mathematics throughout history has been catalysed by its utility inexplaining real-world phenomena and its inherent beauty. In this way, the discipline hascontinued to evolve through a process of observation, conjecture, proof and application.Effective participation in a changing society is enhanced by the development of mathematicalcompetence in contextualised problem-solving. Experience in such problem-solving is gainedby students gathering, analysing and interpreting mathematical information, and applyingmathematics to model situations.5

Mathematics General Stage 6 SyllabusThe opportunities for creative thinking, communication and contextualised problem-solvingwithin the Preliminary Mathematics General course, the HSC Mathematics General 2 courseand the HSC Mathematics General 1 course assist students in finding solutions for the broadrange of problems encountered in life beyond secondary schooling.The purpose of the courses is to provide an appropriate mathematical background forstudents who wish to enter occupations that require the use of a variety of mathematicaland statistical techniques. As well as introducing some new mathematical content, thevarious Focus Studies within the courses give students the opportunity to apply, and developfurther, the knowledge, skills and understanding initially developed in the various Strands:Financial Mathematics, Data and Statistics, Measurement, Probability, and Algebra andModelling. Through the Focus Studies, students develop the capacity to integrate theirknowledge, skills and understanding across the Strands in contemporary contexts chosenfor their ongoing relevance to the students’ everyday lives and likely vocational pathways.The Preliminary Mathematics General course, the HSC Mathematics General 2 courseand the HSC Mathematics General 1 course are highly contextualised. The PreliminaryMathematics General course contains the five Strands as well as two Focus Studies:Mathematics and Communication, and Mathematics and Driving. It is structured to provideappropriate pathways to both the HSC Mathematics General 2 course and the HSCMathematics General 1 course.Preliminary Mathematics General provides an appropriate course of study for students whohave demonstrated competence in mathematics up to and including at least Stage 5.1 by theend of Year 10. The two Focus Studies within the course have been designed for one-thirdof the course time.The HSC Mathematics General 2 course has been written on the assumption that studentshave demonstrated a high level of competence in the Preliminary Mathematics Generalcourse. The two Focus Studies within the course – Mathematics and Health, andMathematics and Resources – have been designed for one-third of the course time.The course provides students with the opportunity to develop an understanding of andcompetence in further aspects of mathematics through a large variety of real-worldapplications for a range of concurrent HSC studies, such as in the life sciences, thehumanities and business studies. The course also provides a strong foundation forvocational pathways, in the workforce and in further training, and for university coursesin the humanities, nursing and paramedical sciences.The HSC Mathematics General 1 course has been written to meet the needs of studentswho have demonstrated competence in the Preliminary Mathematics General course.The four Focus Studies within the course – Mathematics and Design, Mathematics andHousehold Finance, Mathematics and the Human Body, and Mathematics and PersonalResource Usage – have been designed for two-thirds of the course time. The courseprovides students with the opportunity to develop an understanding of and competencein further aspects of mathematics through a large variety of real-world applications forconcurrent HSC studies, such as in vocational education and training courses, otherpractically oriented courses, and some humanities courses, and for vocational pathways,in the workforce or in further training.6

Mathematics General Stage 6 Syllabus3Continuum of Learning for Stage 6Mathematics General Experienceinproblem- os.nsw.edu.au.7

Mathematics General Stage 6 Syllabus4Mathematics in Stage 64.1CoursesFor the Higher School Certificate, there are three Board Developed mathematics courses forstudy as Preliminary Year courses: (in increasing order of difficulty) Preliminary MathematicsGeneral, Preliminary Mathematics (‘2 Unit’), and Preliminary Mathematics Extension. Thereare four Board Developed Courses and one Content Endorsed Course (CEC) for studyas HSC Year courses: (in increasing order of difficulty) Mathematics General 1 (CEC),Mathematics General 2, Mathematics (‘2 Unit’), Mathematics Extension 1, and MathematicsExtension 2.Students of the two Mathematics General pathways study the preliminary course, PreliminaryMathematics General, followed by either the HSC Mathematics General 2 course or theHSC Mathematics General 1 course.Mathematics (‘2 Unit’) consists of the courses Preliminary Mathematics (‘2 Unit’) and HSCMathematics (‘2 Unit’). Students studying one or both Extension courses study the course,Preliminary Mathematics Extension, before undertaking the study of HSC MathematicsExtension 1, or HSC Mathematics Extension 1 and HSC Mathematics Extension 2.The following assumptions and recommendations regarding Stage 5 Mathematics, typicallyundertaken by students in Years 9 and 10, are provided in relation to the suite of Stage 6Mathematics courses.The Preliminary Mathematics General course has been constructed on the assumptionthat students have studied the content and achieved the outcomes of the MathematicsYears 7–10 Syllabus (2002) up to, and including, the content and outcomes of Stage 5.1.For students who intend to study the HSC Mathematics General 2 course, it is recommendedthat they experience at least some of the Stage 5.2 content, particularly the Patterns andAlgebra topics and Trigonometry, if not all of the content.The Mathematics (‘2 Unit’) course has been constructed on the assumption that studentshave studied the content and achieved the outcomes of the Mathematics Years 7–10Syllabus (2002) up to, and including, the content and outcomes of Stage 5.2. Wherepossible, it is recommended that they also experience the topics Real Numbers, AlgebraicTechniques and Coordinate Geometry, as well as at least some of Trigonometry fromStage 5.3 (identified by §), if not all of the content.The Preliminary Mathematics Extension and HSC Mathematics Extension 1 courses havebeen constructed on the assumption that students have studied the content and achieved theoutcomes of the Mathematics Years 7–10 Syllabus (2002) up to, and including, the contentand outcomes of Stage 5.3. Where possible, it is recommended that they also experience theoptional topics (identified by #) Curve Sketching and Polynomials, Functions and Logarithms,and Circle Geometry.The Mathematics Extension 2 course consists of an HSC course (only) and may beundertaken following completion of the Preliminary Mathematics (‘2 Unit’) and PreliminaryMathematics Extension courses. Students may study the Mathematics Extension 2 courseconcurrently with, or following completion of, the HSC Mathematics Extension 1 course.The preliminary and HSC courses undertaken by students who study the PreliminaryMathematics General/HSC Mathematics General 1 pathway, the Preliminary MathematicsGeneral/HSC Mathematics General 2 pathway, or Mathematics (‘2 Unit’), and by studentswho study mathematics in Stage 6 to Mathematics Extension 1 or Mathematics Extension 2level, are illustrated on the following pages.8

Mathematics General Stage 6 SyllabusPreliminary Mathematics General/HSC Mathematics General 1 pathwayPreliminaryMathematics General*HSCMathematics General 1Units: 2Indicative hours: 120Units: 2Indicative hours: 120Total indicative hours: 240Preliminary Mathematics General/HSC Mathematics General 2 pathwayPreliminaryMathematics General*HSCMathematics General 2Units: 2Indicative hours: 120Units: 2Indicative hours: 120Total indicative hours: 240Mathematics (‘2 Unit’)HSCMathematics (‘2 Unit’)PreliminaryMathematics (‘2 Unit’)Units: 2Indicative hours: 120Units: 2Indicative hours: 120Total indicative hours: 240*Satisfactory completion of the Preliminary Mathematics General course may be followed bystudy of either the HSC Mathematics General 2 course or the HSC Mathematics General 1course. (Note: The HSC Mathematic

as HSC Year courses: (in increasing order of difficulty) Mathematics General 1 (CEC), Mathematics General 2, Mathematics (‘2 Unit’), Mathematics Extension 1, and Mathematics Extension 2. Students of the two Mathematics General pathways study the preliminary course, Preliminary Mathematics General, followed by either the HSC Mathematics .