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Mathematics involves observation, representation, investigation and comparison of patterns and relationships in social and physical phenomena. It allows the creative solution of problems and is also a powerful, precise and concise means of communication. At an everyday level, it is concerned with practical applications in many branches of human activity. At a higher level, it involves abstraction and generalisation. As such, it has been integral to most of the scientific and technological advances made in Australia and elsewhere.
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General
Mathematics
Stage 6
Syllabus
Original published version updated:
September 1999 – Board Bulletin/Official Notices Vol 8 No 7 (BOS 54/99)
April 2000 – Board Bul etin/Official Notices Vol 9 No 2 (BOS 13/00)
The Board of Studies owns the copyright on all syllabuses. Schools may reproduce this
syllabus in part or in full for bona fide study or classroom purposes only. Acknowledgement
of the Board of Studies copyright must be included on any reproductions. Students may
copy reasonable portions of the syllabus for the purpose of research or study. Any other
use of this syllabus must be referred to the Copyright Officer, Board of Studies NSW.
Ph: (02) 9367 8111; fax: (02) 9279 1482.
Material on p 5 from Securing Their Future © NSW Government 1997.
© Board of Studies NSW 1999
Published by
Board of Studies NSW
GPO Box 5300
Sydney NSW 2001
Australia
Tel: (02) 9367 8111
Internet: http://www.boardofstudies.nsw.edu.au
ISBN 0 7313 4370 0
99342B
Contents
1
The Higher School Certificate Program of Study.................................................... 5
2
Rationale for General Mathematics in the Stage 6 Curriculum ........................... 6
3
Continuum of Learning for Stage 6 General Mathematics Students .................. 7
4
Aim .................................................................................................................................. 8
5
Objectives ...................................................................................................................... 8
6
Course Structure........................................................................................................... 9
7
Objectives and Outcomes.........................................................................................10
7.1
Table of Objectives and Outcomes..............................................................10
7.2
Key Competencies..........................................................................................12
8
Preliminary Course Content .....................................................................................15
8.1
Financial Mathematics....................................................................................16
8.2
Data Analysis ...................................................................................................24
8.3
Measurement ...................................................................................................32
8.4
Probability.........................................................................................................40
8.5
Algebraic Modelling........................................................................................44
9
HSC Course Content .................................................................................................49
9.1
Financial Mathematics....................................................................................50
9.2
Data Analysis ...................................................................................................58
9.3
Measurement ...................................................................................................64
9.4
Probability.........................................................................................................70
9.5
Algebraic Modelling........................................................................................74
10
Course Requirements................................................................................................79
11
Post-school Opportunities.........................................................................................80
12
Assessment and Reporting.......................................................................................81
12.1 Requirements and Advice .............................................................................81
12.2 Internal Assessment........................................................................................82
12.3 External Examination......................................................................................82
12.4 Board Requirements for the Internal Assessment Mark in Board Developed
Courses
83
12.5 Assessment Components, Weightings and Tasks....................................84
12.6 Summary of Internal and External Assessment .........................................85
12.7 HSC External Examination Specifications..................................................86
12.8 Reporting Student Performance Against Standards.................................87
General Mathematics Stage 6 Syllabus
1
The Higher School Certificate Program of Study
The purpose of the Higher School Certificate program of study is to:
• provide a curriculum structure that encourages students to complete secondary
education;
• foster the intellectual, social and moral development of students, in particular developing
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 beyond school
– capacity to work together with others
– respect for the cultural diversity of Australian society;
• provide 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.
5
General Mathematics Stage 6 Syllabus
2
Rationale for General Mathematics in the Stage 6 Curriculum
Mathematics involves observation, representation, investigation and comparison of patterns
and relationships in social and physical phenomena. It allows the creative solution of
problems and is also a powerful, precise and concise means of communication. At an
everyday level, it is concerned with practical applications in many branches of human activity.
At a higher level, it involves abstraction and generalisation. As such, it has been integral to
most of the scientific and technological advances made in Australia and elsewhere.
Effective participation in a changing society is enhanced by the development of mathematical
competence in contextualised problem-solving. Experience in such problem-solving is
gained by students by:
(i)
gathering, interpreting and analysing mathematical information and
(ii)
applying mathematics to model situations.
The opportunities for creative thinking, communication and contextualised problem-solving
provided by this course, assist students to find positive solutions for the broad range of
problems encountered in life and work beyond school.
General Mathematics supports the other Stage 6 mathematics courses in catering for the
wide variation in students’ mathematical competence at the conclusion of Year 10, and
provides opportunities for continuing mathematical growth.
The purpose of General Mathematics is to provide an appropriate mathematical background
for students who wish to enter occupations which require the use of basic mathematical and
statistical techniques. The direction taken by the course, in focusing on mathematical skills
and techniques that have direct application to everyday activity, contrasts with the more
abstract approach taken by the other Stage 6 mathematics courses.
The study of General Mathematics provides students with valuable support in a range of
concurrent Stage 6 subjects, in fostering development of mathematical skills and techniques
that assist students who undertake associated research and projects. The course provides a
strong foundation for vocational pathways, either in the workforce or in further vocational
training studies, and for university courses in the areas of business, the humanities, nursing
and paramedical sciences.
6
General Mathematics Stage 6 Syllabus
3
Continuum of Learning for Stage 6 General Mathematics
Students
Stages 1–3
Experience in problem-solving and modelling as a result of involvement in courses in the
K–6 Mathematics
Stage 4
Mathematics
Mathematics Learning Area
Stage 5
Mathematics courses that provide relevant
experiences for General Mathematics Stage 6:
• Intermediate Mathematics
• Standard Mathematics
Stage 6
General Mathematics
Preliminary and HSC
Workplace
University
TAFE
Other
(selected courses)
7
General Mathematics Stage 6 Syllabus
4
Aim
General Mathematics is designed to promote the development of skills, knowledge and
understanding in areas of mathematics that have direct application to the broad range of
human activity. Students will learn to use a range of techniques and tools to develop
solutions to a wide variety of problems related to their present and future needs and
aspirations.
5
Objectives
Students will develop:
• appreciation of the relevance of mathematics
• the ability to apply mathematical skills and techniques to interpret practical situations
• the ability to communicate mathematics in written and/or verbal form
• skills, knowledge and understanding in financial mathematics
• skills, knowledge and understanding in data analysis
• skills, knowledge and understanding in measurement
• skills, knowledge and understanding in probability
• skills, knowledge and understanding in algebraic modelling.
8
General Mathematics Stage 6 Syllabus
6
Course Structure
The following schematic view provides an overview of the arrangement and relationship
between components of the Preliminary course and HSC course for General Mathematics
Stage 6.
Preliminary Course
HSC Course
Financial Mathematics
Financial Mathematics
• FM1: Earning money
• FM4: Credit and borrowing
• FM2: Investing money
• FM5: Annuities and loan
• FM3: Taxation
repayments
• FM6: Depreciation
Data Analysis
Data Analysis
• DA1: Statistics and society
(A) DA5: Interpreting sets of data
• DA2: Data collection and sampling
(B) DA6: The normal distribution
• DA3: Displaying single data sets
(C) DA7: Correlation
• DA4: Summary statistics
Measurement
Measurement
• M1: Units of measurement
• M5: Further applications of area
• M2: Applications of area and volume
and volume
• M3: Similarity of two-dimensional
• M6: Applications of trigonometry
figures
• M7: Spherical geometry
• M4: Right-angled triangles
Probability
Probability
• PB1: The language of chance
P1.1 PB3: Multi-stage events
• PB2: Relative frequency and
P1.1 PB4: Applications of probability
probability
Algebraic Modelling
Algebraic Modelling
• AM1: Basic algebraic skills
• AM3: Algebraic skills and
• AM2: Modelling linear relationships
techniques
• AM4: Modelling linear and non-
linear relationships
9
General Mathematics Stage 6 Syllabus
7
Objectives and Outcomes
7.1
Table of Objectives and Outcomes
Objectives
Preliminary Outcomes
HSC Outcomes
Students will develop:
A student:
A student:
• appreciation of the
P1
H1
relevance of mathematics develops a positive attitude to
appreciates the importance
mathematics and appreciates
of mathematics in her/his
its capacity to provide
own life and its usefulness in
enjoyment and recreation
contributing to society
• the ability to apply
P2
H2
mathematical skills and
applies mathematical
integrates mathematical
techniques to interpret
knowledge and skills to
knowledge and skills from
practical situations
solving problems within
different content areas in
familiar contexts
exploring new situations
P3
H3
develops rules to represent
develops and tests a general
patterns arising from
mathematical relationship
numerical and other sources
from observed patterns
• skills, knowledge and
P4
H4
understanding in
represents information in
analyses representations of
algebraic modelling
symbolic, graphical and
data in order to make
tabular forms
inferences, predictions and
conclusions
P5
H5
represents the relationships
makes predictions about the
between changing quantities
behaviour of situations based
in algebraic and graphical
on simple models
form
• skills, knowledge and
P6
H6
understanding in
performs calculations in
analyses two-dimensional
measurement
relation to two-dimensional
and three-dimensional
and three-dimensional figures
models to solve practical and
mathematical problems
P7
H7
determines the degree of
interprets the results of
accuracy of measurements
measurements and
and calculations
calculations and makes
judgements about
reasonableness
10
Mathematics
Stage 6
Syllabus
Original published version updated:
September 1999 – Board Bulletin/Official Notices Vol 8 No 7 (BOS 54/99)
April 2000 – Board Bul etin/Official Notices Vol 9 No 2 (BOS 13/00)
The Board of Studies owns the copyright on all syllabuses. Schools may reproduce this
syllabus in part or in full for bona fide study or classroom purposes only. Acknowledgement
of the Board of Studies copyright must be included on any reproductions. Students may
copy reasonable portions of the syllabus for the purpose of research or study. Any other
use of this syllabus must be referred to the Copyright Officer, Board of Studies NSW.
Ph: (02) 9367 8111; fax: (02) 9279 1482.
Material on p 5 from Securing Their Future © NSW Government 1997.
© Board of Studies NSW 1999
Published by
Board of Studies NSW
GPO Box 5300
Sydney NSW 2001
Australia
Tel: (02) 9367 8111
Internet: http://www.boardofstudies.nsw.edu.au
ISBN 0 7313 4370 0
99342B
Contents
1
The Higher School Certificate Program of Study.................................................... 5
2
Rationale for General Mathematics in the Stage 6 Curriculum ........................... 6
3
Continuum of Learning for Stage 6 General Mathematics Students .................. 7
4
Aim .................................................................................................................................. 8
5
Objectives ...................................................................................................................... 8
6
Course Structure........................................................................................................... 9
7
Objectives and Outcomes.........................................................................................10
7.1
Table of Objectives and Outcomes..............................................................10
7.2
Key Competencies..........................................................................................12
8
Preliminary Course Content .....................................................................................15
8.1
Financial Mathematics....................................................................................16
8.2
Data Analysis ...................................................................................................24
8.3
Measurement ...................................................................................................32
8.4
Probability.........................................................................................................40
8.5
Algebraic Modelling........................................................................................44
9
HSC Course Content .................................................................................................49
9.1
Financial Mathematics....................................................................................50
9.2
Data Analysis ...................................................................................................58
9.3
Measurement ...................................................................................................64
9.4
Probability.........................................................................................................70
9.5
Algebraic Modelling........................................................................................74
10
Course Requirements................................................................................................79
11
Post-school Opportunities.........................................................................................80
12
Assessment and Reporting.......................................................................................81
12.1 Requirements and Advice .............................................................................81
12.2 Internal Assessment........................................................................................82
12.3 External Examination......................................................................................82
12.4 Board Requirements for the Internal Assessment Mark in Board Developed
Courses
83
12.5 Assessment Components, Weightings and Tasks....................................84
12.6 Summary of Internal and External Assessment .........................................85
12.7 HSC External Examination Specifications..................................................86
12.8 Reporting Student Performance Against Standards.................................87
General Mathematics Stage 6 Syllabus
1
The Higher School Certificate Program of Study
The purpose of the Higher School Certificate program of study is to:
• provide a curriculum structure that encourages students to complete secondary
education;
• foster the intellectual, social and moral development of students, in particular developing
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 beyond school
– capacity to work together with others
– respect for the cultural diversity of Australian society;
• provide 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.
5
General Mathematics Stage 6 Syllabus
2
Rationale for General Mathematics in the Stage 6 Curriculum
Mathematics involves observation, representation, investigation and comparison of patterns
and relationships in social and physical phenomena. It allows the creative solution of
problems and is also a powerful, precise and concise means of communication. At an
everyday level, it is concerned with practical applications in many branches of human activity.
At a higher level, it involves abstraction and generalisation. As such, it has been integral to
most of the scientific and technological advances made in Australia and elsewhere.
Effective participation in a changing society is enhanced by the development of mathematical
competence in contextualised problem-solving. Experience in such problem-solving is
gained by students by:
(i)
gathering, interpreting and analysing mathematical information and
(ii)
applying mathematics to model situations.
The opportunities for creative thinking, communication and contextualised problem-solving
provided by this course, assist students to find positive solutions for the broad range of
problems encountered in life and work beyond school.
General Mathematics supports the other Stage 6 mathematics courses in catering for the
wide variation in students’ mathematical competence at the conclusion of Year 10, and
provides opportunities for continuing mathematical growth.
The purpose of General Mathematics is to provide an appropriate mathematical background
for students who wish to enter occupations which require the use of basic mathematical and
statistical techniques. The direction taken by the course, in focusing on mathematical skills
and techniques that have direct application to everyday activity, contrasts with the more
abstract approach taken by the other Stage 6 mathematics courses.
The study of General Mathematics provides students with valuable support in a range of
concurrent Stage 6 subjects, in fostering development of mathematical skills and techniques
that assist students who undertake associated research and projects. The course provides a
strong foundation for vocational pathways, either in the workforce or in further vocational
training studies, and for university courses in the areas of business, the humanities, nursing
and paramedical sciences.
6
General Mathematics Stage 6 Syllabus
3
Continuum of Learning for Stage 6 General Mathematics
Students
Stages 1–3
Experience in problem-solving and modelling as a result of involvement in courses in the
K–6 Mathematics
Stage 4
Mathematics
Mathematics Learning Area
Stage 5
Mathematics courses that provide relevant
experiences for General Mathematics Stage 6:
• Intermediate Mathematics
• Standard Mathematics
Stage 6
General Mathematics
Preliminary and HSC
Workplace
University
TAFE
Other
(selected courses)
7
General Mathematics Stage 6 Syllabus
4
Aim
General Mathematics is designed to promote the development of skills, knowledge and
understanding in areas of mathematics that have direct application to the broad range of
human activity. Students will learn to use a range of techniques and tools to develop
solutions to a wide variety of problems related to their present and future needs and
aspirations.
5
Objectives
Students will develop:
• appreciation of the relevance of mathematics
• the ability to apply mathematical skills and techniques to interpret practical situations
• the ability to communicate mathematics in written and/or verbal form
• skills, knowledge and understanding in financial mathematics
• skills, knowledge and understanding in data analysis
• skills, knowledge and understanding in measurement
• skills, knowledge and understanding in probability
• skills, knowledge and understanding in algebraic modelling.
8
General Mathematics Stage 6 Syllabus
6
Course Structure
The following schematic view provides an overview of the arrangement and relationship
between components of the Preliminary course and HSC course for General Mathematics
Stage 6.
Preliminary Course
HSC Course
Financial Mathematics
Financial Mathematics
• FM1: Earning money
• FM4: Credit and borrowing
• FM2: Investing money
• FM5: Annuities and loan
• FM3: Taxation
repayments
• FM6: Depreciation
Data Analysis
Data Analysis
• DA1: Statistics and society
(A) DA5: Interpreting sets of data
• DA2: Data collection and sampling
(B) DA6: The normal distribution
• DA3: Displaying single data sets
(C) DA7: Correlation
• DA4: Summary statistics
Measurement
Measurement
• M1: Units of measurement
• M5: Further applications of area
• M2: Applications of area and volume
and volume
• M3: Similarity of two-dimensional
• M6: Applications of trigonometry
figures
• M7: Spherical geometry
• M4: Right-angled triangles
Probability
Probability
• PB1: The language of chance
P1.1 PB3: Multi-stage events
• PB2: Relative frequency and
P1.1 PB4: Applications of probability
probability
Algebraic Modelling
Algebraic Modelling
• AM1: Basic algebraic skills
• AM3: Algebraic skills and
• AM2: Modelling linear relationships
techniques
• AM4: Modelling linear and non-
linear relationships
9
General Mathematics Stage 6 Syllabus
7
Objectives and Outcomes
7.1
Table of Objectives and Outcomes
Objectives
Preliminary Outcomes
HSC Outcomes
Students will develop:
A student:
A student:
• appreciation of the
P1
H1
relevance of mathematics develops a positive attitude to
appreciates the importance
mathematics and appreciates
of mathematics in her/his
its capacity to provide
own life and its usefulness in
enjoyment and recreation
contributing to society
• the ability to apply
P2
H2
mathematical skills and
applies mathematical
integrates mathematical
techniques to interpret
knowledge and skills to
knowledge and skills from
practical situations
solving problems within
different content areas in
familiar contexts
exploring new situations
P3
H3
develops rules to represent
develops and tests a general
patterns arising from
mathematical relationship
numerical and other sources
from observed patterns
• skills, knowledge and
P4
H4
understanding in
represents information in
analyses representations of
algebraic modelling
symbolic, graphical and
data in order to make
tabular forms
inferences, predictions and
conclusions
P5
H5
represents the relationships
makes predictions about the
between changing quantities
behaviour of situations based
in algebraic and graphical
on simple models
form
• skills, knowledge and
P6
H6
understanding in
performs calculations in
analyses two-dimensional
measurement
relation to two-dimensional
and three-dimensional
and three-dimensional figures
models to solve practical and
mathematical problems
P7
H7
determines the degree of
interprets the results of
accuracy of measurements
measurements and
and calculations
calculations and makes
judgements about
reasonableness
10
Document Outline
- General Mathematics Stage 6 Syllabus
- Contents
- 1 The Higher School Certificate Program of Study
- 2 Rationale for General Mathematics in the Stage 6 Curriculum
- 3 Continuum of Learning for Stage 6 General Mathematics Students
- 4 Aim
- 5 Objectives
- 6 Course Structure
- 7 Objectives and Outcomes
- 7.1 Table of Objectives and Outcomes
- 7.2 Key Competencies
- 8 Preliminary Course Content
- 8.1 Financial Mathematics
- 8.2 Data Analysis
- 8.3 Measurement
- 8.4 Probability
- 8.5 Algebraic Modelling
- 9 HSC Course Content
- 9.1 Financial Mathematics
- 9.2 Data Analysis
- 9.3 Measurement
- 9.4 Probability
- 9.5 Algebraic Modelling
- 10 Course Requirements
- 11 Post-school Opportunities
- 12 Assessment and Reporting
- 12.1 Requirements and Advice
- 12.2 Internal Assessment
- 12.3 External Examination
- 12.4 Board Requirements for the Internal Assessment Mark In Board Developed Courses
- 12.5 Assessment Components, Weightings and Tasks
- 12.6 Summary of Internal and External Assessment
- 12.7 HSC External Examination Specifications
- 12.8 Reporting Student Performance Against Standards
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