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MathematicsGeneralStage 6Syllabus2012

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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 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)).9

Mathematics General Stage 6 SyllabusStage 6 Mathematics to Mathematics Extension 1 levelPreliminaryMathematics (‘2 Unit’)HSCMathematics (‘2 Unit’)Units: 2Indicative hours: 120Units: 2Indicative hours: tension 1Units: 1Indicativehours: 60Units: 1Indicativehours: 60Total indicative hours: 360Stage 6 Mathematics to Mathematics Extension 2 levelPreliminaryMathematics (‘2 Unit’)HSCMathematics (‘2 Unit’)Units: 2Indicative hours: 120Units: 2Indicative hours: tension 1Units: 1Indicativehours: 60Units: 1Indicativehours: 60HSCMathematicsExtension 2Units: 1Indicativehours: 60Total indicative hours: 42010

Mathematics General Stage 6 Syllabus4.2Statistics in the Mathematics General SyllabusThe study of Statistics in the Preliminary Mathematics General course, the HSC MathematicsGeneral 2 course and the HSC Mathematics General 1 course in Stage 6 recognisesthe need for people in contemporary society to develop competence in understanding,interpreting and analysing information, or ‘data’, displayed in tabular or graphical forms.Such competence, often described as ‘statistical literacy’, has become more and moreimportant with advances in technology and the resulting increases in the availability oflarge amounts of data. Students need to recognise that while such data is very oftenused scrupulously and with high levels of accuracy as a means of persuasion to aparticular point of view, it can also be used in a deliberately misleading manner inorder to deliver false conclusions.Statistics in the Mathematics General syllabus builds on the Data strand in the MathematicsK–6 Syllabus (2002) and the Mathematics Years 7–10 Syllabus (2002). The strand extendsfrom Early Stage 1 to Stage 5.2 and provides students with the opportunity to developknowledge, skills and understanding in the collection, organisation, display and analysisof data. Students should be aware that mathematics and statistics are different fields ofstudy, but that various aspects of mathematics are fundamental to the design and applicationof statistical techniques. They should also develop an understanding that mathematics isconcerned with describing patterns and relationships and developing generalisations insituations of certainty, whereas Statistics is concerned with describing patterns andrelationships in situations of uncertainty, and developing generalisations without anassurance of complete accuracy.The principal focus of Statistics as a practical discipline is the application of techniquesfor the detection and interpretation of systematic patterns in data drawn from the realworld. The discipline can be divided into Descriptive Statistics and Inferential Statistics.The study of Statistics within the Mathematics General syllabus aims to develop furtherstudents’ knowledge, skills and understanding in Descriptive Statistics. Study of InferentialStatistics, which has foundations in Descriptive Statistics and Probability, is beyond thescope of the syllabus.Mathematical models of real-world situations are a key feature of each of the Stage 6Mathematics courses. Many of these models are of a ‘deterministic’ nature, ie either theyare models that represent situations that are certain, or they are models that representuncertain situations where the uncertainty is not taken into account. They are called‘deterministic’ models because the values assigned to a model’s inputs completelydetermine the model’s output: there is no influence from chance events.However, there are many real-world situations where the use of such models isinappropriate. Sometimes it is possible to gather data only from a small sample of a largerpopulation in order to make predictions about the behaviour of the population. At othertimes, the situation being studied involves behaviour that is random in nature, eg the motionof molecules in a gas. In such cases, the use of methods drawn from the study of Statisticsis often an appropriate way of extracting usable information from the data gathered.The study of topics in Descriptive Statistics complements the study of the other componentsof the Preliminary Mathematics General course, the HSC Mathematics General 2 course andthe HSC Mathematics General 1 course, because it provides a foundation for extending thetypes of practical situations with which these courses are concerned to situations where theimpact of uncertainty is recognised.11

Mathematics General Stage 6 Syllabus5AimThe Preliminary Mathematics General course, the HSC Mathematics General 2 courseand the HSC Mathematics General 1 course are designed to promote the developmentof knowledge, skills and understanding in areas of mathematics that have direct applicationto the broad range of human activity, including a range of post-school pathways requiringa variety of mathematical and statistical techniques.Students will learn to use a range of techniques and tools, including relevant technologies,in order to develop solutions to a wide variety of problems relating to their present and futureneeds and aspirations.The HSC Mathematics General 2 course provides a strong foundation for a broad rangeof vocational pathways, as well as for a range of university courses. The HSC MathematicsGeneral 1 course provides an appropriate foundation for a range of such vocationalpathways, either in the workforce or in further training.6ObjectivesKnowledge, skills and understandingStudents will develop the ability to: apply reasoning, and the use of appropriate language, in the evaluation and constructionof arguments and the interpretation and use of models based on mathematical andstatistical concepts use concepts and apply techniques to the solution of problems in algebra and modelling,measurement, financial mathematics, data and statistics, and probability use mathematical skills and techniques, aided by appropriate technology, to organiseinformation and interpret practical situations interpret and communicate mathematics in a variety of written and verbal forms,including diagrams and statistical graphs.Values and attitudesStudents will develop: appreciation of the relevance of mathematics.12

Mathematics General Stage 6 Syllabus7Objectives and OutcomesKnowledge, skills and understandingHSCMathematics General 2OutcomesHSCMathematics General 1OutcomesA student:A student:A student:apply reasoning,and the useof appropriatelanguage, in theevaluation andconstruction ofarguments andthe interpretationand use of modelsbased onmathematical andstatistical conceptsMGP-1uses mathematics andstatistics to comparealternative solutionsto contextual problemsMG2H-1uses mathematics andstatistics to evaluate andconstruct arguments ina range of familiar andunfamiliar contextsMG1H-1uses mathematics andstatistics to evaluate andconstruct arguments in arange of familiar contextsMGP-2represents informationin symbolic, graphicaland tabular formMG2H-2analyses representationsof data in order to makeinferences, predictionsand conclusionsMG1H-2analyses representationsof data in order to makepredictionsuse concepts andapply techniquesto the solution ofproblems in algebraand modelling,measurement,financialmathematics,data and statistics,and probabilityMGP-3represents the relationshipsbetween changingquantities in algebraicand graphical formMG2H-3makes predictions aboutsituations based onmathematical models,including those involvingcubic, hyperbolic orexponential functionsMG1H-3makes predictions abouteveryday situations basedon simple mathematicalmodelsMGP-4performs calculationsin relation totwo-dimensional andthree-dimensional figuresMG2H-4analyses two-dimensionaland three-dimensionalmodels to solve practicalproblems, including thoseinvolving spheres andnon-right-angled trianglesMG1H-4analyses simpletwo-dimensional andthree-dimensional modelsto solve practical problemsMGP-5demonstrates awarenessof issues in practicalmeasurement, includingaccuracy, and the choiceof relevant unitsMG2H-5interprets the resultsof measurements andcalculations and makesjudgements aboutreasonableness, includingthe degree of accuracyof measurements andcalculations and theconversion to appropriateunitsMG1H-5interprets the resultsof measurements andcalculations and makesjudgements aboutreasonableness,including the conversionto appropriate unitsMGP-6models financial situationsrelevant to the student’scurrent life usingappropriate toolsMG2H-6makes informed decisionsabout financial situations,including annuities and loanrepaymentsMG1H-6makes informed decisionsabout financial situationslikely to be encounteredpost-schoolMGP-7determines an appropriateform of organisationand representationof collected dataMG2H-7answers questions requiringstatistical processes,including the use of thenormal distribution, and thecorrelation of bivariate dataMG1H-7develops and carries outsimple statistical processesto answer questions posedMGP-8performs simplecalculations in relationto the likelihood offamiliar eventsMG2H-8solves problems involvingcounting techniques,multistage events andexpectationMG1H-8solves problems involvinguncertainty using basiccounting techniquesObjectivesStudents willdevelop theability to:PreliminaryMathematics GeneralOutcomes13

Mathematics General Stage 6 SyllabusHSCMathematics General 2OutcomesHSCMathematics General 1OutcomesA student:A student:A student:use mathematicalskills andtechniques, aidedby appropriatetechnology, toorganise informationand interpretpractical situationsMGP-9uses appropriatetechnology to organiseinformation from a limitedrange of practical andeveryday contextsMG2H-9chooses and usesappropriate technologyto locate and organiseinformation from a rangeof contextsMG1H-9chooses and usesappropriate technologyto organise informationfrom a range of practicaland everyday

The HSC Mathematics General 1 course has been written to meet the needs of students who have demonstrated competence in the Preliminary Mathematics General course. The four Focus Studies within the course - Mathematics and Design, Mathematics and Household Finance, Mathematics and the Human Body, and Mathematics and Personal