Board Endorsed December 07- Amended December 2013
Mathematical Methods
Type 2
T Course
Written under the
Mathematics Framework
2006
Accredited from
1 January 2008 – 31 December 2012
Extended to 2016
Amended October 2013
(includes Assessment Task Types
approved August 2013)
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Board Endorsed December 07- Amended December 2013
Student Capabilities
The Student Capabilities (Year 11-12), as shown below, can be mapped to the essential
Learning achievements in the Curriculum Renewal (P-10) showing a strong relationship.
Student capabilities are supported through course and unit content and through pedagogical
and assessment practices.
All programs of study for the ACT Year 12 Certificate should enable students to become:
 creative and critical thinkers
 enterprising problem-solvers
 skilled and empathetic communicators
 informed and ethical decision-makers
 environmentally and culturally aware citizens
 confident and capable users of technologies
 independent and self-managing learners
 collaborative team members
and provide students with:
 a comprehensive body of specific knowledge, principles and concepts
 a basis for self-directed and lifelong learning
 personal attributes enabling effective participation in society
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Board Endorsed December 07- Amended December 2013
Type 2 Course Accreditation/Adoption Form
B S S S
AUSTRALIAN CAPITAL TERRITORY
Choose one of the following:
 adoption of Type 2 course
 small changes from Written Evaluation of Type 2 course
 extension of Type 2 course or units
 modification of Type 2 course
 adoption of additional units for a Type 2 course
Scope: The college is entered on the National Register to award Certificates delivered by this course
 Yes  No (Adoption of V courses only)
College:
Course Title:Mathematical Methods
Classification:  A  T  M  V
Unit Title(s)
Course Code
MM Numbers, Patterns, Relations, Functions
MM Numbers and Patterns
MM Relations and Functions
MM Introductory & Differential Calculus
MM Introduction to Calculus
MM Differential Calculus
MM Integral Calculus & Special Functions
MM Integral Calculus
MM Special Functions
MM Probability, Statistics & Applications
MM Probability and Statistics
MM Further Applications
Dates of Course Accreditation:
From
Value
(1.0/0.5)
1.0
0.5
0.5
1.0
0.5
0.5
1.0
0.5
0.5
1.0
0.5
0.5
Length
Unit Codes
Q/S/Y
Q/S/Y
Q/S/Y
Q/S/Y
Q/S/Y
Q/S/Y
Q/S/Y
Q/S/Y
Q/S/Y
Q/S/Y
Q/S/Y
Q/S/Y
31 / 12 / 2016
1 / 1 / 2008 To
Accreditation: The course and units named above are consistent with the goals of the Course
Framework and are signed on behalf of the BSSS.
Course Development Coordinator:
Panel Chair:
/
/
/
/
OR (delete box that does not apply)
Adoption/Alteration: The adopting College has the human and physical resources to implement the
course. Written Evaluation for small changes, and details of and reasons for Adoptions, Extensions,
and addition of units are outlined on the Supporting Statement.
Principal:
College Board Chair:
/
/
/
/
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Board Endorsed December 07- Amended December 2013
Type 2 Course Accreditation/Adoption Supporting Statement
Provides support for information on the Course Accreditation/Adoption Form
B S S S
AUSTRALIAN CAPITAL TERRITORY
College:
Course Title:
Written Evaluation for small changes, reasons for Modification or Adoption
of a Type 2 course, or Addition of units to a Type 2 course
For V courses indicate the certificate the college will award.
Course Code
Course Length and Composition
Number and Length of Units
Which units will your college deliver?
Available Course Patterns
Must be consistent with Table 1.1 in the Guidelines.
Implementation Guidelines
Must be consistent with the original course document.
Compulsory Units
Must remain the same as original document.
Prerequisites for the course or units within the course
Must remain the same as original document.
Arrangements for students who are continuing to study a course in this subject
The adopting college may customize this to suit their individual needs.
Units from other courses
If the original course allows the adopting college must indicate which units can be added. These will be
forwarded to the panel chair for approval.
Additional Units
The adopting college may write additional units to suit their individual needs but within policy 2.3.9.1
and with panel approval. The course should have coherence between units of study (Policy 2.3.9.1).
Suggested Implementation Patterns
This must be in line with the original course document.
Please indicate any specific needs for your college when adopting this course.
For example – if you intend to deliver the course in any delivery time structure other than the way it
has been written (ie 1.0 units instead of 0.5 units) then these must be submitted with this adoption
form.
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Board Endorsed December 07- Amended December 2013
Contents
Course Name .........................................................................................................6
Course Classification ..............................................................................................6
Course Framework .................................................................................................6
Course Developers .................................................................................................6
Evaluation of Previous Course ................................................................................6
Course Length and Composition .............................................................................7
Subject Rationale ...................................................................................................9
Goals ................................................................................................................... 10
Student Group ..................................................................................................... 10
Content ............................................................................................................... 11
Teaching and Learning Strategies ......................................................................... 14
Assessment.......................................................................................................... 15
Student Capabilities ............................................................................................. 16
Unit Grades................................................................. Error! Bookmark not defined.
Moderation ......................................................................................................... 19
Bibliography ........................................................................................................ 20
Resources ............................................................................................................ 20
Proposed Evaluation Procedures .......................................................................... 21
MM Numbers, Patterns, Relations, Functions
Value 1.0 ................................. 22
MM Numbers and Patterns Value 0.5 .............................................................. 27
MM Relations and Functions
Value 0.5 ............................................................ 31
MM Introductory & Differential Calculus
Value 1.0....................................... 36
MM Introduction to Calculus
Value 0.5 ........................................................... 41
MM Differential Calculus
Value: 0.5 ............................................................... 45
MM Integral Calculus & Special Functions
Value 1.0 ...................................... 48
MM Integral Calculus
Value 0.5 ...................................................................... 53
MM Special Functions
Value 0.5 ..................................................................... 55
MM Probability, Statistics & Applications
Value 1.0 ....................................... 57
MM Probability and Statistics
Value 0.5 .......................................................... 61
MM Further Applications
Value 0.5 ................................................................. 66
Appendix A – Australian Curriculum Achievement Standards for Mathematical
Methods (T) ......................................................................................................... 87
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Board Endorsed December 07- Amended December 2013
Course Name
Mathematical Methods
Course Classification
T
Course Framework
This course is presented under the Mathematics Course Framework, 2006.
Course Developers
Name
Qualifications
College
Margaret Rowlands
B.A., Dip. Ed., M.Ed.
Lake Tuggeranong College
Evelyn Ashcroft
B.A., NSW Teacher’s Certificate
Erindale College
Jan Bentley
BA. Dip. Ed.
Dickson College
Clare Byrne
B. Sc., Grad. Dip. Ed
Narrabundah College
Mark Carroll
B Ed.
Hawker College
Alfred Del-Pin
B Ed (Secondary Mathematics)
Lake Tuggeranong College
Julie Rasmus
B A (Hons) Dip Ed.
St Clare’s College
Simon Olivero
B.Sc., Grad. Dip. Ed.
Hawker College
Tom Mutton
B. Sc., Grad. Dip. Ed.
Daramalan College
Phil Rasmus
B. Sc., Grad. Dip. Ed.
Lake Ginninderra College
This group gratefully acknowledges the work of previous developers.
Evaluation of Previous Course
A new Course Framework was endorsed by BSSS in 2006. This necessitates the
rewriting of all Mathematics course for implementation in 2008.
Concerns were also raised during the implementation of the previous framework and
course, in particular the sequencing and crowded nature of the content. Several
reviews of all the courses during their accreditation period tried to address the
situation. There was also evidence to indicate that the previous structure did not
allow the Specialist Mathematics students to be sufficiently discriminated from the
Mathematical Methods students at the course level. This course is written under the
new Framework which allows students in Mathematical Methods to be separated
from those students studying Specialist Mathematics. The content and sequencing of
the new course accommodates this major change and the earlier issues raised during
the previous courses’ period of accreditation.
Mathematics teaching is dynamic and the courses continue to encourage the
incorporation of new technologies where appropriate.
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Board Endorsed December 07- Amended December 2013
The previous course program encouraged a broad range of assessment tasks and this
has been further clarified under the new framework whilst increasing the flexibility
of the task types.
The course continues to be relevant to the needs of those students requiring entry to
tertiary studies where a sound and broad knowledge of mathematics is required.
Students intending quantitative courses such as Engineering, Physics, Astronomy,
Meteorology, Actuarial Studies etc., would be advised to select a Specialist
Mathematics course of study.
Course Length and Composition
Unit Title
MM Numbers, Patterns, Relations, Functions
MM Numbers and Patterns
MM Relations and Functions
MM Introductory & Differential Calculus
MM Introduction to Calculus
MM Differential Calculus
MM Integral Calculus & Special Functions
MM Integral Calculus
MM Special Functions
MM Probability, Statistics & Applications
MM Probability and Statistics
MM Further Applications
Unit Value
1.0
0.5
0.5
1.0
0.5
0.5
1.0
0.5
0.5
1.0
0.5
0.5
Available course patterns
Course
Number of standard units to meet course requirements
Minor
Minimum of 2 units
Major
Minimum of 3.5 units
Major Minor
Minimum of 5.5 units
Double Major
Minimum of 7 units
Implementation Guidelines
A course in Mathematics Methods can comprise any combination of the following
units
MA Matrices, Sequences & Series and Measurement or MM Numbers, Patterns,
Relations & Functions or SM Numbers, Patterns and Religion- (but not any two);
MM Introduction & Differential calculus or SM Trigonometry and Derivitives– (but not
any two)
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Board Endorsed December 07- Amended December 2013
Students may change from Specialist Maths to Mathematical Methods by the end of
Year 11 or at the discretion of the Executive Teacher of Mathematics as per BSSS
requirements.
Students may change from MA Matrices Sequences & Series and Measurement to
MM Numbers, Patterns, Relations & Functions at the discretion of the Executive
Teacher of Mathematics as per BSSS requirements.
Compulsory units
There are no compulsory units. However, it is recommended that students complete
the units in the order as shown in the suggested implementation pattern below.
Prerequisites for the course or units within the course
There are no formal prerequisites for this course although it is recommended that.
students enrolling in this course should demonstrate a reasonable grasp of Year 10
Mathematics at Advanced Level or its equivalent. Students who have not satisfied
this requirement may be enrolled following consultation with the Executive Teacher
of Mathematics.
Arrangements for students who are continuing to study a course in this subject
Students who studied the previous Mathematical Methods course in Year 11 may
take MM Integral Calculus & Special Functions, MM Probability, and Statistics&
Applications from this course in Year 12, to complete their major.
Units from other courses
Under the new 2006 Course Framework, subject to other relevant BSSS policies,
students will be certified in only one Mathematics Course. It is envisaged that
students will have identified an appropriate course by the end of Year 11. Where
students change courses during their study of Mathematics, they should be certified
in the course in which they conclude their study according to BSSS requirements.
Negotiated Units
There are no negotiated units.
Suggested Implementation Patterns
Implementation Pattern
Minor
Major
Units Involved
MM Number, Patterns, Relations, Functions 1.0
MM Introductory & Differential Calculus 1.0
MM Number, Patterns, Relations& Functions 1.0
MM Introductory & Differential Calculus 1.0
MM Integral Calculus & Special Functions 1.0
MM Probability and Statistics 0.5
MM Further Applications (where relevant) 0.5
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Board Endorsed December 07- Amended December 2013
Subject Rationale
‘Mathematics involves observing, representing and investigating patterns and
relationships in social and physical phenomena and between mathematical objects
themselves. Mathematics is the science of patterns. The mathematician seeks
patterns in number, in space, in science, in computers, and in imagination.
Mathematical theories explain the relation between patterns…Applications of
mathematics use these patterns to explain and predict natural phenomena.’
(National Statement on Mathematics for Australian Schools 1991 p4)
 Mathematics is a way of thinking that encourages learners to reflect critically
and reason logically.
 Mathematics employs a vital, concise and unambiguous form of
communication that represents and explains by means of a symbolic system
with written, spoken and visual aspects.
 Mathematics is thus a powerful tool with wide ranging applications, which
include: solving quantitative problems, analysing relations among patterns
and structures and explaining and predicting natural phenomena.
 Mathematics is also a creative activity with its own intrinsic value involving
invention, intuition, imagination and exploration.
 Mathematics is a pervasive feature of modern society. A sound knowledge
and appreciation of the subject are essential for informed citizenship.
A senior secondary education in Mathematics aims to enable students to deal
successfully with the future mathematical demands of their work, further study, and
personal life. It should:
 promote the development of mathematical knowledge, concepts and skills
 provide students with a variety of applications and problem solving contexts
 contribute to the development of those distinctive logical, quantitative and
relational thought processes that assist people in becoming rational decision
makers
 encourage students to develop proficiency in communicating mathematics
 provide students with opportunities for success in mathematics in a
challenging and supportive learning environment
 incorporate the changes in knowledge and skills which the continuing growth
in technology has brought to mathematics
 acknowledge and build upon the individual mathematical experiences
brought to the classroom by each student
 promote an awareness and understanding of the uses, significance and value
of mathematics within various contexts – social, scientific, technological,
environmental, economic, cultural, political, and historical.
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Board Endorsed December 07- Amended December 2013
Goals
This course should enable students to:






select critically and use effectively mathematical language, concepts,
processes and skills in a variety of contexts and applications at an appropriate
level
display the confidence to use mathematics in making informed decisions,
both at work and in their personal lives
communicate mathematical ideas effectively and creatively to diverse
audiences
be competent in the use of appropriate technology in the learning and
application of mathematics
recognise and evaluate the influence and importance of mathematics in
modern society
work both independently and co-operatively in modelling, investigating and
solving mathematical problems.
Student Group
This T course is designed for students who intend subsequent tertiary study in
disciplines in which a sound and broad knowledge of mathematics is required, such
as the behavioural sciences, the social sciences, applied sciences, business. Students
intending quantitative courses such as Engineering, Physics, Astronomy,
Meteorology, Actuarial Studies etc., would be advised to select a Specialist
Mathematics course of study.
This course emphasises the acquisition and understanding of abstract mathematical
concepts, relationships and techniques, incorporating practical explorations and
meaningful applications. Students are provided with opportunities to analyse and
solve real world problems, and to communicate their reasoning through logical
arguments.
Students enrolling in this course should demonstrate a reasonable grasp of Year 10
Mathematics at Advanced Level or its equivalent.
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Board Endorsed December 07- Amended December 2013
Content
The content of the following section has been adapted from material on the website
of the National Council of Teachers of Mathematics, at the time of publication.
All courses developed under this Framework will be based on the essential concepts
and skills inherent in the subject area, as outlined below. All courses should enable
students to understand these concepts and acquire these skills at an appropriate
level.
Students studying T courses in Mathematics should be able to fully integrate the use
of graphics calculator technology – or equivalent technologies – into their
mathematics learning.
The essential concepts of Mathematics include the following:
Number and Operations
Number pervades all areas of mathematics. Students should understand:
 the different kinds of numbers
 the different ways of representing numbers
 the different operations that can be applied to numbers and how these
operations relate to each other.
Geometry
Geometry offers ways for understanding and reflecting on our physical environment
and is an essential tool in the study of many other topics in mathematics. Students
should understand:
 the characteristics and properties of two- and three- dimensional geometrical
objects
 the use of coordinate geometry and/or representational systems to specify
locations and describe spatial relationships.
Pattern and Symmetry
Pattern and symmetry are central concepts in mathematics. Students should
understand:
 the different kinds of patterns and symmetries, both numerical and
geometrical, that arise in various mathematical contexts.
Measurement
Measurement is a key mathematical concept due both to its usefulness in everyday
life and its vital role in the physical and social sciences. Students should understand:
 the distinction between a qualitative and quantitative approach to
investigations
 the measurable attributes of objects and the units and systems of
measurement.
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Board Endorsed December 07- Amended December 2013
Representation
Representation is crucial to the organisation and communication of mathematical
ideas. Students should understand:
 the different ways of representing mathematical concepts and relationships –
graphical, diagrammatic, symbolic
 the power and utility of clear and concise representations for the gaining of
mathematical knowledge and insight
 that the range of representations used in mathematics is not fixed but is
constantly expanding as part of the process of mathematical discovery.
Connections
Mathematics is a highly integrated field of study. It should be seen and experienced
as a connected whole rather than as a collection of isolated skills and arbitrary rules.
Students should understand:
 the many and varied connections among mathematical ideas
 that recognising such connections is invaluable for deepening one’s
knowledge of mathematics
 that mathematics can be applied to a wide range of contexts outside of the
mathematics classroom.
The essential skills inherent in Mathematics include the following:
Computational fluency
Students should be able to:
 employ efficient and accurate methods of calculation
 confidently use computational technology
 make reasonable estimates.
Measurement
Students should be able to:
 employ appropriate techniques and a variety of technologies , tools and
formulae to determine measurements in various contexts to suitable degrees
of accuracy.
Reasoning and Proof
Students (particularly those studying T courses developed under this Framework)
should be able to:
 recognise that verification and justification are fundamental aspects of
mathematics
 develop and evaluate various types of mathematical arguments and proofs at
appropriate levels of rigour
 make and investigate mathematical conjectures.
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Board Endorsed December 07- Amended December 2013
Problem Solving
Students should be able to:
 formulate different kinds of mathematical problems ( open-ended/closed,
pure/applied) by various means – including extensions of existing problems
 apply and adapt a variety of strategies ( e.g. using diagrams, searching for
patterns, trying special values or cases ) to solve problems
 monitor and reflect systematically on the problem solving process,
recognising the dynamic and cyclic nature of mathematical problem solving.
Modelling
Students should be able to:
 identify situations in which a mathematical model would be appropriate and
useful
 select and use suitable representations to model physical, social and
mathematical phenomena
 explore a model mathematically and interpret the results in terms of the
original situation
 validate a model, identifying its assumptions, strengths and limitations.
Communication
Students should be able to:
 communicate their mathematical thinking coherently and clearly to peers,
teachers and others
 use appropriate representations to express their mathematical ideas
precisely.
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Board Endorsed December 07- Amended December 2013
Teaching and Learning Strategies
Teaching strategies that are particularly relevant and effective in Mathematics
recognise that students in their final years of secondary schooling need to:
 discover their own individual optimal learning style
 form positive attitudes towards the value of mathematics and look forward
to opportunities for further study
 develop a capacity for independent learning.
Such strategies include:
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






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discussion between teacher and students, and between students
teacher – guided learning
appropriate practical work
consolidation and practice of fundamental skills and routines
sequenced investigations to scaffold learning
participation in group activities
individual problem solving, including the application of mathematics to
everyday situations
opportunities to develop modelling or problem solving skills in practical
contexts
longer-term activities such as investigative, research and project tasks
development of student prepared summaries to be used in supervised
assessment tasks (reducing the need to memorise formulas and procedures).
This allows equity of access, especially for students whose first language is
not English
use of appropriate technology to aid concept development and as a tool for
problem solving. All courses should incorporate the appropriate use of
suitable technology to facilitate the learning and teaching of mathematics.
This could include the use of some of the following technologies: graphics
calculators, spreadsheets, graphing packages, dynamic geometry systems,
statistical analysis packages and computer algebra systems.
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Board Endorsed December 07- Amended December 2013
Assessment
Assessment Tasks Types
Across the course, the recommended task types and weightings are:
Assessment for T Courses
Task Type
Weighting for 1.0 and 0.5 units
Tests:
-
For example:
-
Multiple choice
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Short answer
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Extended questions
40-75%
Non-Test Tasks (in-class):
- For example:
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Validation activities
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Modelling
-
Investigations
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Problem solving
-
Journals
-
Portfolios
-
Presentations
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Practical activities
0-60%
25-60%
Take Home Tasks:
- For example:
-
Modelling
-
Investigations
-
Portfolios
-
Practical activities
0-30%
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Board Endorsed December 07- Amended December 2013
Additional Assessment Advice for T Courses

For a standard 1.0 unit, a minimum of three and a maximum of five
assessment items.

For a half-standard 0.5 unit, minimum of two and a maximum of three
assessment items.

Each unit (standard 1.0 or half standard 0.5) should include at least two
different types of tasks. It is recommended that, in standard 1.0 units, no
assessment item should carry a weighting of greater than 45% of the unit
assessment.

Where possible, for tasks completed in unsupervised circumstances, validation
of the students’ work should be undertaken.

It is recommended that students undertake a take home task. It may be worth
0% and lead into a non-zero weighted in-class validation.

It is desirable that students studying at tertiary level investigate Mathematics
beyond the classroom and this should be reflected in the task type.
Assessment Criteria
Technology, its selection and appropriate use, is an integral part of all the following
criteria. Students will be assessed on the degree to which they demonstrate:
 Knowledge – knowledge of mathematical facts, techniques and formulae
presented in the unit
 Application – appropriate selection and application of mathematical skills in
mathematical modelling and problem solving
 Reasoning – ability to use reasoning to support solutions and conclusions (in T
courses only)
 Communication – interpretation and communication of mathematical ideas
in a form appropriate for a given use or audience.
Additional Assessment Advice
Where possible, for tasks completed in unsupervised circumstances, validation of the
students’ work should be undertaken.
Course developers should not have too many assessment items that count towards a
unit grade or score, as this detracts from assessing depth of knowledge and skill.
Student Capabilities
Creative and Critical Thinkers
Students will be given opportunities to demonstrate their ability to think creatively
and critically. They will be provided with tasks that develop their ability to think
laterally, employ analytical and evaluative skills that require them to generate and
synthesise ideas in order to solve problems. Tasks may involve exploring,
researching, understanding and applying information, collecting, analysing and
classifying data, evaluating, communicating ideas, understanding and applying
mathematical techniques.
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Board Endorsed December 07- Amended December 2013
Enterprising Problem Solvers
Students will be expected to show initiative and resourcefulness in posing,
identifying and clarifying problems. They will be expected to utilise practical,
theoretical and innovative approaches to problem solving and to apply the use of
appropriate technologies. Students will be exposed to situations which will require
both individual and collaborative work to achieve a solution.
Skilled and Empathetic Communicators
Students will be expected to demonstrate oral and written skills using
communication relevant to their audience and purpose. Students will be challenged
to express themselves using a variety of media, and applying appropriate
mathematical language to communicate meaning.
Informed and Ethical Decision Makers
Students will be provided with the opportunity to formulate opinions with regard to
relevant social and ethical issues. They will be encouraged to share their opinions
with others, and to critically analyse and evaluate a range of diverse opinions.
Students should be able to find information which supports their decision making
and develop an awareness of different perspectives. The process of decision making
should encourage students to reflect critically on their own values and judgements.
Environmentally and Culturally Aware Citizens
Students will be encouraged to consider the implications of problem solutions on the
natural and constructed world and the society around them.
Confident and Capable Users of Technologies
Having a range of IT capabilities, students will be expected to access information,
design their responses and communicate by using appropriate technologies and
show a willingness to learn new skills.
Independent and Self-managing Learners
Students will be encouraged in the utilisation of time and resource management
skills in the completion of tasks within the context of class activities, assessment
tasks and projects. Students will also be encouraged to be flexible and resilient in
their approach to problem solving.
Collaborative Team members.
The opportunity to work as a member of a team in collaborative projects or class
work will be provided to students to enable them to demonstrate their ability to
effectively and efficiently sustain and develop strategies to satisfy group outcomes.
They should be able to contribute to the effectiveness of a group, the trust within a
group and be prepared to take on varying roles in a group situation. They will be
encouraged to use skills in negotiation and be prepared to be resilient in accepting a
reasonable compromise to achieve group goals.
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Board Endorsed December 07- Amended December 2013
Unit Grades for T Courses
Communication
Reasoning
Application
Knowledge
Technology, its selection and appropriate use, is an integral part of all the following descriptors.
A student who achieves the
grade A typically
 Demonstrates very high
level of proficiency in the
use of mathematical facts,
techniques and formulae.
A student who achieves the
grade B typically
 Demonstrates high level of
proficiency in the use of
mathematical facts,
techniques and formulae.
A student who achieves the
grade C typically
 Demonstrates some
proficiency in the use of
mathematical facts,
techniques and formulae
studied.
A student who achieves the
grade D typically
 Demonstrates limited use
of mathematical facts,
techniques and formulae
studied.
A student who achieves the
grade E typically
 Demonstrates very limited
use of mathematical facts,
techniques and formulae
studied.
 Selects, extends and
 Selects and applies
 With direction, applies a
 Solves some mathematical
 Solves some mathematical
applies appropriate
mathematical modelling and
problem solving techniques.
appropriate mathematical
modelling and problem
solving techniques.
mathematical model. Solves
most problems.
problems independently.
problems with guidance.
 Uses mathematical
 Uses mathematical
 Uses some mathematical
 Uses some mathematical
 Uses limited reasoning to
reasoning to develop logical
arguments in support of
conclusions, results and/or
decisions; justifies
procedures.
 Is consistently accurate
and appropriate in
presentation of
mathematical ideas in
different contexts.
reasoning to develop logical
arguments in support of
conclusions, results and/or
decisions.
reasoning to develop logical
arguments.
reasoning to develop simple
logical arguments.
justify conclusions.
 Is generally accurate and
 Presents mathematical
 Presents some
 Presents some
appropriate in presentation
of mathematical ideas in
different contexts.
ideas in different contexts.
mathematical ideas.
mathematical ideas with
guidance.
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Board Endorsed December 07- Amended December 2013
Moderation
Moderation is a system designed and implemented to:
 provide comparability in the system of school-based assessment
 form the basis for valid and reliable assessment in senior secondary schools
 involve the ACT Board of Senior Secondary Studies and colleges in
cooperation and partnership
 maintain the quality of school-based assessment and the credibility, validity
and acceptability of Board certificates
Moderation commences within individual colleges. Teachers develop assessment
programs and instruments, apply assessment criteria, and allocate Unit Grades,
according to the relevant Course Framework. Teachers within course teaching
groups conduct consensus discussions to moderate marking or grading of individual
assessment instruments and unit grade decisions.
The Moderation Model
Moderation within the ACT encompasses structured, consensus-based peer review
of Unit Grades for all accredited courses, as well as statistical moderation of course
scores, including small group procedures, for T courses.
Moderation by Structured, Consensus-based Peer Review
Review is a subcategory of moderation, comprising the review of standards and the
validation of Unit Grades. In the review process, Unit Grades, determined for Year 11
and Year 12 student assessment portfolios that have been assessed in schools by
teachers under accredited courses, are moderated by peer review against system
wide criteria and standards. This is done by matching student performance with the
criteria and standards outlined in the unit grade descriptors as stated in the Course
Framework. Advice is then given to colleges to assist teachers with, and/or reassure
them on, their judgments.
Preparation for Structured, Consensus-based Peer Review
Each year, teachers teaching a Year 11 class are asked to retain originals or copies of
student work completed in Semester 2. Similarly, teachers teaching a Year 12 class
should retain originals or copies of student work completed in Semester 1. Colleges
not on a semester structure will negotiate with BSSS on work required. Assessment
and other documentation required by the Office of the BSSS should also be kept.
Year 11 work from Semester 2 of the previous year is presented for review at
Moderation Day 1 in March, and Year 12 work from Semester 1 is presented for
review at Moderation Day 2 in August.
In the lead up to Moderation Day, a College Course Presentation (comprised of a
document folder and a set of student portfolios) is prepared for each A and T course
offered by the school, and is sent in to the Office of the BSSS.
- 19 -
Board Endorsed December 07- Amended December 2013
The College Course Presentation
The package of materials (College Course Presentation) presented by a college for
review on moderation days in each course area will comprise the following:
 a folder containing supporting documentation as requested by the Office of
the Board through memoranda to colleges
 a set of student portfolios containing marked and/or graded written and nonwritten assessment responses and completed criteria and standards feedback
forms. Evidence of all assessment responses on which the unit grade decision
has been made is to be included in the student review portfolios. Specific
requirements for subject areas and types of evidence to be presented for
each moderation day will be outlined by the Office of the BSSS through
memoranda and Information Papers
Bibliography
Books
Nolan, J et al
Maths Quest 11 Mathematical Methods 1 and 2, Wiley, Jacaranda, Brisbane 2000
Nolan, J et al
Maths Quest 12 Mathematical Methods 3 and 4, Wiley, Jacaranda, Brisbane 2000
Rehill & McCauliffe GS
General Maths Macmillan
Rehill & McCauliffe GS
Maths Methods 1 & 2 Macmillan
Pendler, Bill, Sadler, O, Shee, J, Ward,
D
Cambridge Maths 2 Unit, Cambridge University Press 1999
Pendler, Bill, Sadler, O, Shee, J, Ward,
D
Cambridge Maths 3 Unit, Cambridge University Press 1999
Brodie, R & Swift, S
New Q Maths 11B, Thomson Nelson, 2002
Brodie, R & Swift, S
New Q Maths 11C Thomson Nelson, 2002
Brodie, R & Swift, S
New Q Maths 12 B Thomson Nelson, 2002
Brodie, R & Swift, S
New Q Maths 12 C Thomson Nelson, 2002
Rowland, P
Maths Q 11C Thomson Nelson, 1994
Rowland, P
Maths Q 12 B Thomson Nelson, 1994
Rowland, P
Maths Q 12 C Thomson Nelson, 1994
Resources
All students studying this course are expected to have access to a personal graphics
calculator.
Classes should be able to access computer laboratories, where appropriate.
Appropriate software (eg Autograph, Mathcad, Graphmatica ) should be available for
classroom demonstrations and student use.
Access to electronic whiteboards and/or data projectors would be highly desirable.
Individual access to computers and the net for projects, assignments and other
resources.
These were accurate at the time of publication.
- 20 -
Board Endorsed December 07- Amended December 2013
Proposed Evaluation Procedures










Are the course and Course Framework still consistent?
Were the goals achieved?
Was the course content appropriate?
Were the teaching strategies used successful?
Was the assessment program appropriate?
Have the needs of the students been met?
Was the course relevant?
How many students completed the course in each of the years of
accreditation?
What improvements need to be made to the course?
When, where and with whom will the evaluation be done?
The evaluation procedures which have been found valuable have included:





Unit and course evaluation by completing students (questionnaires and
discussions).
Course evaluation by students who have subsequently gone on to post
secondary studies in this area.
Inter-college discussion at the teacher level including structured discussion at
Moderation Days in General Maths and informal discussions between at
other times.
Discussions with lecturers at post secondary institutions.
Discussions with accreditation panel members.
- 21 -
Board Endorsed December 07- Amended December 2013
MM Numbers, Patterns, Relations, Functions
Value 1.0
This unit combines MM Numbers and Patterns 0.5 and MM Relations and Functions
0.5.
Prerequisites
Satisfactory completion of Year 10 Mathematics at Advanced Level or its equivalent.
Students who have not satisfied this requirement may be enrolled following
consultation with the Executive Teacher of Mathematics.
This first unit in Mathematical Methods is very similar to the first Mathematical
Applications unit, MA Matrices, Sequences and Series. However, a significant
amount of algebra revision has been included in MM Numbers and Patterns to
ensure adequate preparation for later units.
The opportunity for substantial overlap in assessment items between these two
units provides a strong basis for moderation between the two courses.
The importance of the appropriate use of technology in this course is clearly
indicated in this unit. Teaching practice should encourage students to take personal
responsibility for mastering the technology which is a supporting tool. The students
should provide algebraic justification as required.
Specific Unit Goals
This unit should enable students to:
 understand the structure, properties and behaviour of real numbers and
matrices
 be competent in basic manipulations of real numbers (including surds),
matrices and algebra
 understand and apply arithmetic and geometric sequences and series
 understand the concepts of relations and functions
 understand the inter-connectivity of the written, graphical and algebraic
forms of relations
 develop mathematical models with various functions
 use algebraic methods and graphing software to identify the key features of
linear and quadratic functions.
- 22 -
Board Endorsed December 07- Amended December 2013
Content
Topics
Guidelines
Detail
Real Numbers



Structure
Field laws
Surds
Definitions; notation; sets/subsets
Terminology; counter-examples
Laws; basic operations with numeric egs;
simplifying; monic rationalising denominator
6 hours
Algebra Review


Time Allocation
4 hours
expanding, factorising, simplifying, indices
equations: linear, simultaneous, quadratic
Matrices


Introduction and notation
Matrix Operations
o addition
o subtraction
o scalar multiplication
o matrix multiplication
 Determinants
 Inverse
 Simple Matrix equations
o Solving systems of linear equations:
representing as a matrix equation
10 hours
Representation of information as a
rectangular array of numbers
Briefly consider field laws as they apply to
matrices
Variety of dimensions
Matrix multiplication by hand, 2x2 only
M .M 1 = I. 2x 2 by hand, others by GC.
Consider types such as A+X=B and AX=B using
field law properties. 2 x 2 by hand others by
GC.
Include systems of equations: no solution, a
unique solution and an infinite solution set,
supported by GC.
 Applications
Sequences & Series
eg Cost equations, etc words to matrix form.

Patterns, general
Introduce general concepts common to all
sequences and series; consider a range of
types other than APs and GPs.

 notation


Arithmetic: nth term, sum to n terms
Geometric: nth term, sum to n terms, limiting
sum
Applications
10 hours
Students should be able to recognise and use
properties of APs and GPs.
Properties should be developed and
expressed algebraically and also represented
graphically. SS or GC
(a wide range including simple and compound
interest and population growth)
Functions & Relations

Curve recognition

Reciprocal

Modelling
8 hours
Contextual approach (Mary Barnes, Shell
Centre, Curric Corp) Matching graph shapes
with equations
Introduction to asymptotes
Using GC: linear, quad, cubic, hyperbola;
circle, semi-circle, exponential (not log)
- 23 -
Board Endorsed December 07- Amended December 2013
o
Definitions; vertical line test; notation;
domain & range
o Modelling/applications
Linear Functions





Review
y = mx+c; general form;
Parallel, perpendicular;
Forms of straight lines
Simultaneous equations to find point(s) of
intersection
Quadratic Functions
 y = ax2 + bx + c
 graph/features, axis of symmetry
( x = -b/2a), vertex
 factorising expressions and solving equations:
quadratic formula and completing the square
 Forms: y-a = (x-b)2
 Discriminant
 Simultaneous solutions between a quadratic and a
linear function.
 Modelling
Real life examples and applications
8 hours
Grad-intercept; pt-grad form
Using GC
12 hours
Only to be used to determine the number of
roots for graphical implications
Including maximum and minimum problems.
Teaching and Learning Strategies
May include:











discussion between teacher and students, and between students
teacher – guided learning: modelling the use of the appropriate technology
consolidation and practice of relevant algebra and technological skills and
routines
participation in group activities
individual problem solving, including the application of mathematics to
everyday situations
opportunities to develop modelling or problem solving skills in practical
contexts
longer-term activities such as investigative, research and project tasks eg
Dominance Matrices
development of student prepared summaries/glossaries.
use of appropriate technology to aid concept development and as a tool for
problem solving.
appropriate practical work
sequenced investigations to scaffold learning
Assessment
Refer to pages 14-15.
For examples of assessment see cLc page on BSSS website: www.bsss.act.edu.au
Student Capabilities
- 24 -
Board Endorsed December 07- Amended December 2013
Evidence could be in:
Student Capabilities
Goals
Content Teaching



creative and critical thinkers



enterprising problem-solvers


skilled and empathetic communicators


informed and ethical decision-makers


environmentally and culturally aware citizens



confident and capable users of technologies



independent and self-managing learners


collaborative team members
Assessment





Specific Unit Resources
Chapter
Cambridge
Yr 11 2 unit
Cambridge
Yr 12 2 unit
Maths
Quest 11
Maths
Quest 12
New Q
Maths
11C
New Q
Maths
11B
New Q
Maths
12B
10.2
3.2
Numbers
and
Patterns
Algebra Review
 Expanding, factorising,
simplifying, indices
 Equations: linear,
simultaneous, quadratic
Matrices
 Introduction and notation
 Matrix Operations
 Addition, subtraction,
scalar multiplication, matrix
multiplication
 Determinants
 Inverse
 Simple Matrix equations
 Solving systems of linear
equations: representing as
a matrix equation
 Applications
2A
2B
2A
2B
4A
4B
1J
2C
2D1,4
1A
1F
2D
See
general
year 11
1A
1B
1C
1D
1E
1F
1G
1H
1.1
1.2
1.3
1.2
1.3
1.4
1.5
1.6
1.4
1.5
1.2
3.1
3.2
3.4
3.3 q 411
Sequences & Series
 Patterns, general
  notation
 Arithmetic: nth term, sum to
n terms
 Geometric: nth term, sum to
n terms, limiting sum
Applications (a wide range
including simple and compound
interest and population growth,
cite text refs)
4.1
4.5
4.6
4.2
4.3
6
C,D,E,F,G,H,I
,J,K
5A,B,C,D
8-12
14-19
- 25 -
Board Endorsed December 07- Amended December 2013
Chapter
Relations
and
Functions
Cambridge
Yr 11 2 unit
Cambridge
Yr 12 2 unit
Maths
Quest 11
Maths
Quest 12
New Q
Maths
11C
New Q
Maths
11B
New Q
Maths
12B
10.1
9.4
9.5
Functions & Relations
 Curve recognition
26
F,G,H,J,Q7
6A, B, C, D,
E, H
 Reciprocal (asymptotes)
4.3
4.4
 Modelling
o Definitions; vertical line
test; notation; domain &
range
o Modelling/applications
Linear Functions





Review
y = mx+c; general form;
parallel, perpendicular;
grad-intercept; pt-grad form;
simultaneous equations to
find point(s) of intersection
Quadratic Functions
 y = ax2 + bx + c
 graph/features, axis of
symmetry
( x = -b/2a), vertex
 factorising expressions and
solving equations: quadratic
formula and completing the
square
 Forms: y-a = (x-b)2
 Discriminant to determine
the number of roots for
graphical implications.
 Simultaneous solutions
between a quadratic and a
linear function.
 Modelling including
maximum and minimum
problems.
5 C,D,F
1H
3E
1C
1D
1E
1G
1H
4.1
4.2
4.7
4.8
4.10
8 A,B,C,D,E,F
1 G, I
2H
2I
2J
2C
2E
2F
2G
2K
7.1
7.4
7.2
7.5
7.6
7.3
These were accurate at the time of publication.
- 26 -
Board Endorsed December 07- Amended December 2013
MM Numbers and Patterns
Value 0.5
Prerequisites
Satisfactory completion of Year 10 Mathematics at Advanced Level or its equivalent..
Students who have not satisfied this requirement may be enrolled following
consultation with the Executive Teacher of Mathematics.
This first unit in Mathematical Methods is very similar to the first Mathematical
Applications unit, MA Matrices, Sequence Series. However a significant amount of
algebra revision has been included in MM Number and Pattern to ensure adequate
preparation for later units.
The opportunity for substantial overlap in assessment items between these two
units provides a strong basis for moderation between the two courses.
The importance of the appropriate use of technology in this course is clearly
indicated in this unit. Teaching practice should encourage students to take personal
responsibility for mastering the technology which is a supporting tool. The students
should provide algebraic justification as required.
Specific Unit Goals
This unit should enable students to:
 understand the structure, properties and behaviour of real numbers and
matrices
 be competent in basic manipulations of real numbers (including surds),
matrices and algebra
 understand and apply arithmetic and geometric sequences and series
Topics
Guidelines
Detail
Real Numbers



Structure
Field laws
Surds
Definitions; notation; sets/subsets
Terminology; counter-examples
Laws; basic operations with numeric egs;
simplifying; monic rationalising denominator
6 hours
Algebra Review


expanding, factorising, simplifying, indices
equations: linear, simultaneous, quadratic
Matrices


Time Allocation
4 hours
Introduction and notation
Matrix Operations
o addition
o subtraction
o scalar multiplication
o matrix multiplication
10 hours
Representation of information as a
rectangular array of numbers
Briefly consider field laws as they apply to
matrices
Variety of dimensions
Matrix multiplication by hand, 2x2 only
- 27 -
Board Endorsed December 07- Amended December 2013



Determinants
Inverse
Simple Matrix equations
o Solving systems of linear equations:
representing as a matrix equation
M .M 1 = I. 2x 2 by hand, others by GC.
Consider types such as A+X=B and AX=B using
field law properties. 2 x 2 by hand others by
GC.
Include systems of equations: no solution, a
unique solution and an infinite solution set,
supported by GC.
eg Cost equations, etc words to matrix form.
 Applications
Sequences & Series

Patterns, general

 notation


Arithmetic: nth term, sum to n terms
Geometric: nth term, sum to n terms, limiting
sum
Applications
10 hours
Introduce general concepts common to all
sequences and series; consider a range of
types other than Aps and GPs.
Students should be able to recognise and use
properties of APs and GPs.
Properties should be developed and
expressed algebraically and also represented
graphically. SS or GC
(a wide range including simple and compound
interest and population growth)
Teaching and Learning Strategies
May include:











discussion between teacher and students, and between students
teacher – guided learning: modelling the use of the appropriate technology
consolidation and practice of relevant algebra and technological skills and
routines
participation in group activities
individual problem solving, including the application of mathematics to
everyday situations
opportunities to develop modelling or problem solving skills in practical
contexts
longer-term activities such as investigative, research and project tasks eg
Dominance Matrices
development of student prepared summaries/glossaries.
use of appropriate technology to aid concept development and as a tool for
problem solving.
appropriate practical work
sequenced investigations to scaffold learning
- 28 -
Board Endorsed December 07- Amended December 2013
Assessment
Refer to pages 14-15.
Student Capabilities
Evidence could be in:
Student Capabilities
Goals
Content Teaching



creative and critical thinkers



enterprising problem-solvers

skilled and empathetic communicators

informed and ethical decision-makers

environmentally and culturally aware citizens



confident and capable users of technologies


independent and self-managing learners

collaborative team members
Assessment




- 29 -
Board Endorsed December 07- Amended December 2013
Specific Unit Resources
Chapter
Cambridge
Yr 11 2 unit
Cambridge
Yr 12 2 unit
Maths
Quest 11
Quest
Further
Maths
New Q
Maths
11C
New Q
Maths
11B
New Q
Maths
12B
10.2
3.2
Numbers
and
Patterns
Algebra Review
 Expanding,
factorising,
simplifying, indices
 Equations: linear,
simultaneous,
quadratic
Matrices
 Introduction and
notation
 Matrix Operations

Addition,
subtraction, scalar
multiplication,
matrix
multiplication
 Determinants
 Inverse
 Simple Matrix
equations
 Solving systems of
linear equations:
representing as a
matrix equation
 Applications
2A
2B
2A
2B
4A
4B
1J
2C
2D1,4
1.4
1.5
1.2
1A
1F
2D
See
general
year 11
1A
1B
1C
1D
1E
1F
1G
1H
1.2
1.3
1.4
1.5
1.6
3.1
3.2
3.4
3.3 q 411
Sequences & Series
 Patterns, general
  notation
 Arithmetic: nth term,
sum to n terms
 Geometric: nth term,
sum to n terms,
limiting sum
Applications (a wide
range including simple
and compound interest
and population
growth, cite text refs)
1.1
1.2
1.3
Ch 6
4.1
4.5
4.6
4.2
4.3
6
C,D,E,F,G,H,I
,J,K
5A,B,C,D
8-12
14-19
These were accurate at the time of publication.
- 30 -
Board Endorsed December 07- Amended December 2013
MM Relations and Functions
Value 0.5
Prerequisites


Satisfactory completion of MM Numbers and Patterns or equivalent.
Students who have not satisfied this requirement may be enrolled following
consultation with the Executive Teacher of Mathematics.
Specific Unit Goals
This unit should enable students to:
 understand the concepts of relations and functions;
 understand the inter-connectivity of the written, graphical and algebraic
forms of relations;
 develop mathematical models using various functions;
 use algebraic methods and graphing software to identify the key features of
linear and quadratic functions.
Content
Topics
Guidelines
Detail
Functions & Relations
 Curve recognition
 Reciprocal
 Modelling
o Definitions; vertical line
test; notation; domain &
range
o Modelling/applications
Linear Functions





Review
y = mx+c; general form;
Parallel, perpendicular;
Forms of straight lines
Simultaneous equations to find
point(s) of intersection
Time Allocation
8 hours
Contextual approach (Mary Barnes,
Shell Centre stuff, Curric Corp)
Matching graph shapes with equations
Introduction to asymptotes
Using GC: linear, quad, cubic,
hyperbola; circle, semi-circle,
exponential (not log)
Real life examples and applications
Grad-intercept; pt-grad form
Using GC
8 hours
- 31 -
Board Endorsed December 07- Amended December 2013
Quadratic Functions
 y = ax2 + bx + c
 graph/features, axis of
symmetry
( x = -b/2a), vertex
 factorising expressions and
solving equations: quadratic
formula and completing the
square
 Forms: y-a = (x-b)2
 Discriminant
 Simultaneous solutions
between a quadratic and a
linear function.
 Modelling
12 hours
Only to be used to determine the
number of roots for graphical
implications
Including maximum and minimum
problems.
Teaching and Learning Strategies:
May include:











discussion between teacher and students, and between students
teacher – guided learning: modelling the use of the appropriate technology
consolidation and practice of relevant algebra and technological skills and
routines
participation in group activities
individual problem solving, including the application of mathematics to
everyday situations
opportunities to develop modelling or problem solving skills in practical
contexts
longer-term activities such as investigative, research and project tasks eg
Dominance Matrices
development of student prepared summaries/glossaries.
use of appropriate technology to aid concept development and as a tool for
problem solving.
appropriate practical work
sequenced investigations to scaffold learning
- 32 -
Board Endorsed December 07- Amended December 2013
Assessment
Refer to pages 14-15
Student Capabilities
Evidence could be in:
Student Capabilities
Goals
Content Teaching

creative and critical thinkers



enterprising problem-solvers


skilled and empathetic communicators

informed and ethical decision-makers

environmentally and culturally aware citizens



confident and capable users of technologies



independent and self-managing learners


collaborative team members
Assessment





- 33 -
Board Endorsed December 07- Amended December 2013
Specific Unit Resources
Chapter
Relations
and
Functions
Cambridge
Yr 11 2 unit
Cambridge
Yr 12 2 unit
Maths
Quest 11
Maths
Quest 12
New Q
Maths
11C
New Q
Maths
11B
New Q
Maths
12B
10.1
9.4
9.5
Functions & Relations
 Curve recognition
26
F,G,H,J,Q7
6A, B, C,
D, E, H
 Reciprocal
(asymptotes)
4.3
4.4
 Modelling
o Definitions;
vertical line
test; notation;
domain & range
o Modelling/appli
cations
Linear Functions
 Review
 y = mx+c; general
form;
 parallel,
perpendicular;
 grad-intercept; ptgrad form;
 simultaneous
equations to find
point(s) of
intersection
Quadratic Functions
 y = ax2 + bx + c
 graph/features, axis
of symmetry
( x = -b/2a), vertex
 factorising
expressions and
solving equations:
quadratic formula
and completing the
square
 Forms: y-a = (x-b)2
 Discriminant to
determine the
number of roots for
graphical
implications.
 Simultaneous
solutions between a
quadratic and a
linear function.
 Modelling including
maximum and
minimum problems.
5 C,D,F
1H
3E
1C
1D
1E
1G
1H
4.1
4.2
4.7
4.8
4.10
8 A,B,C,D,E,F
1 G, I
2H
2I
2J
2C
2E
2F
2G
2K
7.1
7.4
7.2
7.5
7.6
7.3
- 34 -
Board Endorsed December 07- Amended December 2013
These were accurate at the time of publication
- 35 -
Board Endorsed December 07- Amended December 2013
MM Introductory & Differential Calculus
Value 1.0
This unit combines MM Introduction to Calculus 0.5 and MM Differential Calculus 0.5.
Prerequisites


Satisfactory completion of MM Numbers, Patterns, Relations, Functions or
equivalent.
Students who have not satisfied this requirement may be enrolled following
consultation with the Executive Teacher of Mathematics.
Specific Unit Goals
This unit should enable students to:
 use algebraic methods and graphing software to identify the key features of
polynomial, rational and trigonometric functions;
 develop mathematical models using the above functions;
 understand the concept of rates of change;
 develop an intuitive understanding of limits and differentiation from first
principles;
 differentiate polynomial and simple rational functions;
 apply chain, product and quotient rules for finding derivatives;
 use the second derivative to investigate changes in concavity;
 use calculus to confirm critical features of the graphs of polynomial and
simple rational functions;
 solve problems using differential calculus.
Content
Topics
Polynomials
 Graphs (cubic, quartic)
Rational Functions
 Graphs/features, behaviour
Guidelines
Detail
Graphing various powers from factored form, other forms,
does not include remainder theorem
-Shape/intercepts
- y = axn (n odd & even)
-Modelling/applications
Time
Allocation
4 hours
3 hours
c
c
- by observation checking with
;
ax  b ( x  b)( x  d )
GC
 Asymptotic behaviour
Rates of Change
 Constant, variable, average and
instantaneous

x →+∞, -∞, checking with GC
- Include interpretation of graphs illustrating these
-Intuitive understanding as required for developing
differentiation from first principles – no formal proof
required
4 hours
Limits, notation
- 36 -
Board Endorsed December 07- Amended December 2013
Trigonometry
 Review ratios
Include complementary, reciprocals, exact values
10 hours
Unit circle definition; boundary angles;

Angles of any magnitude

Radians

Simple trigonometric equations
Simple trigonometric equations (as needed for modelling,
finding intercepts)

6 basic trigonometric graphs and
transformations for sin, cos and tan
Graphs, including domain, range, period, amplitude and
phase shift eg. Asinb(x+c)+D
Definition as required for graphing functions.
 Modelling/Applications
Introduction to Differentiation
 Tangent as the limiting position of a
secant
 Gradient of tangent as instantaneous
rate of change
 Notation and historical context
 Differentiation from first principles
Differential Calculus
 Polynomials and rational functions
Trigonometric relationships eg tides, ferris wheels etc
Differentiation of y= xn by rule; notations
2 hours

Rules
First derivative including chain, product and quotient rules.
Second derivative
10 hours

Equations of tangents and normals
6 hours
Simple polynomials to develop the rule
4 hours

Stationary pts
Nature of stationary points using first derivative and second
derivative. Concavity and inflections

Applications
Sketching Graphs
Sketching graphs including roots, stationary points and
points of infection, asymptotes. Use technology as a
supporting tool.
Modelling
Related rates
Including maximum and minimum problems
Basic ideas
10 hours
Teaching and Learning Strategies
May include:
 appropriate practical work
 consolidation and practice of fundamental skills and routines
 discussion between teacher and students, and between students
 individual problem solving, including the application of mathematics to
everyday situations
 longer-term activities such as investigative, research and project tasks
 opportunities to develop modelling or problem solving skills in practical
contexts
- 37 -
Board Endorsed December 07- Amended December 2013




participation in group activities
sequenced investigations to scaffold learning
teacher – guided learning: modelling the use of the appropriate technology
use of appropriate technology to aid concept development and as a tool for
problem solving.
Assessment
Each unit (standard 1.0 or half standard 0.5) should include at least 2 different types
of tasks. It is recommended that, in standard units, no assessment item should carry
a
weighting of less than 5% or greater than 45% of the unit assessment.
Task Type
Tests:
For example:
-
Weighting
40-75%
Multiple Choice
Short Answer
Extended Questions
Non-Test Tasks:
For example:
- Modelling
- Investigations
- Problem solving
- Journals
- Portfolios
- Presentations
- Practical activities
25-60%
For examples of assessment see Myclasses page on BSSS website:
www.bsss.act.edu.au/maths_methods
Student Capabilities
Evidence could be in:
Student Capabilities
Goals
Content Teaching



creative and critical thinkers



enterprising problem-solvers

skilled and empathetic communicators

informed and ethical decision-makers

environmentally and culturally aware citizens



confident and capable users of technologies



independent and self-managing learners
Assessment






- 38 -
Board Endorsed December 07- Amended December 2013

collaborative team members

Specific Unit Resources
Books
Chapter
Introduction to
Calculus
Cambridge
Yr 11 2 unit
Polynomials
Cambridge
Yr 12 2 unit
3 C, G
 Graphs (cubic,
quartic)
Rational Functions
 Graphs/features,
behaviour
 Asymptotic
behaviour
Trigonometry
 Review ratios
 Angles of any
magnitude
 Radians
 Simple trigonometric
equations
 6 basic trigonometric
graphs and
transformations for
sin, cos and tan
 Modelling/Applicatio
ns
Rates of Change:
 constant, variable,
average and
instantaneous
 Limits, notation
Maths
Quest 11
Maths
Quest 12
3I
3J
1G
New Q
Maths
11C
New Q
Maths
11B
New Q
Maths
12B
1.2
Q3,4
9.3
8A
8B
4 A, C, D, G
3C
7B
5A
5B
5C
5D
5F
5G
5H
5I
7A
7B
7C
7D
7E
9.2
9.1
9.3
6.1
6.2
6.3
6.4
6.5
6.6
8.1
- 39 -
Board Endorsed December 07- Amended December 2013
Chapter
Differential
Calculus
Cambridge
Yr 11 2 unit
Introduction to
Differentiation
 Tangent as the
limiting position of
a secant
 Gradient of tangent
as instantaneous
rate of change
Notation and
historical context
 Differentiation from
first principles for
simple polynomials
to develop the rule
Differential Calculus
 Polynomials and
rational functions
 Techniques
 Stationary pts
 Applications
Cambridge
Yr 12 2 unit
7 B, C, D, H, I
Maths
Quest 11
Maths
Quest 12
New Q
Maths
11C
New Q
Maths
11B
New Q
Maths
12B
8C
6.7
6.7
8.2
7 C, D, E, F,
G
10 A, B, C, D,
E, G
8D
5 A, B, E
4
7C
7D
9B
9C
8.4
8.5
8.7
8.8
8.9
These were accurate at the time of publication.
- 40 -
Board Endorsed December 07- Amended December 2013
MM Introduction to Calculus
Value 0.5
Prerequisites


Satisfactory completion of MM Number, Patterns, Relations, Functions or
equivalent.
Students who have not satisfied this requirement may be enrolled following
consultation with the mathematics coordinator.
Specific Unit Goals
This unit should enable students to:
 use algebraic methods and graphing software to identify the key features of
polynomial, rational and trigonometric functions
 develop mathematical models using the above functions
 understand the concept of rates of change
 develop an intuitive understanding of limits and differentiation from first
principles
 differentiate polynomial and simple rational functions
Topics
Polynomials
 Graphs (cubic, quartic)
Rational Functions
 Graphs/features, behaviour
Guidelines
Detail
Graphing various powers from factored form, other forms,
does not include remainder theorem
-Shape/intercepts
- y = axn (n odd & even)
-Modelling/applications
Time
Allocation
4 hours
3 hours
c
c
- by observation checking with
;
ax  b ( x  b)( x  d )
GC
 Asymptotic behaviour
Rates of Change
 Constant, variable, average and
instantaneous
 Limits, notation
Trigonometry
 Review ratios
x →+∞, -∞, checking with GC
- Include interpretation of graphs illustrating these
-Intuitive understanding as required for developing
differentiation from first principles – no formal proof
required
4 hours
Include complementary, reciprocals, exact values
10 hours
Unit circle definition; boundary angles;
 Angles of any magnitude
 Radians
Definition as required for graphing functions.
Simple trigonometric equations (as needed for modelling,
finding intercepts)
 Simple trigonometric equations
- 41 -
Board Endorsed December 07- Amended December 2013
 6 basic trigonometric graphs and
transformations for sin, cos and tan
Graphs, including domain, range, period, amplitude and
phase shift eg. Asinb(x+c)+D
 Modelling/Applications
Introduction to Differentiation
 Tangent as the limiting position of a
secant
 Gradient of tangent as instantaneous
rate of change
 Notation and historical context
 Differentiation from first principles
Trigonometric relationships eg tides, ferris wheels etc
6 hours
Simple polynomials to develop the rule
Teaching and Learning Strategies
May include:
 appropriate practical work
 consolidation and practice of fundamental skills and routines
 discussion between teacher and students, and between students
 individual problem solving, including the application of mathematics to
everyday situations
 longer-term activities such as investigative, research and project tasks
 opportunities to develop modelling or problem solving skills in practical
contexts
 participation in group activities
 sequenced investigations to scaffold learning
 teacher – guided learning: modelling the use of the appropriate technology
 use of appropriate technology to aid concept development and as a tool for
problem solving.
- 42 -
Board Endorsed December 07- Amended December 2013
Assessment
Refer to pages 14-15.
Student Capabilities
Evidence could be in:
Student Capabilities
Goals
Content Teaching



creative and critical thinkers



enterprising problem-solvers

skilled and empathetic communicators

informed and ethical decision-makers

environmentally and culturally aware citizens



confident and capable users of technologies



independent and self-managing learners


collaborative team members
Assessment





Specific Unit Resources
Books
Chapter
Introduction to
Calculus
Cambridge
Yr 11 2 unit
Polynomials
 Graphs (cubic,
quartic)
Rational Functions
 Graphs/features,
behaviour
 Asymptotic
behaviour
3 C, G
Cambridge
Yr 12 2 unit
Maths
Quest 11
Maths
Quest 12
3I
3J
1G
New Q
Maths
11C
New Q
Maths
11B
New Q
Maths
12B
1.2
Q3,4
9.3
8A
8B
7A
7B
7C
7D
7E
- 43 -
Board Endorsed December 07- Amended December 2013
Chapter
Cambridge
Yr 11 2 unit
Trigonometry
 Review ratios
 Angles of any
magnitude
 Radians
 Simple trigonometric
equations
 6 basic trigonometric
graphs and
transformations for
sin, cos and tan
 Modelling/Applicatio
ns
Rates of Change:
 constant, variable,
average and
instantaneous
 Limits, notation
Cambridge
Yr 12 2 unit
4 A, C, D, G
3C
Maths
Quest 11
5A
5B
5C
5D
5F
5G
5H
5I
7B
Maths
Quest 12
New Q
Maths
11C
New Q
Maths
11B
New Q
Maths
12B
9.2
9.1
9.3
6.1
6.2
6.3
6.4
6.5
6.6
8.1
Introduction to
Differentiation
 Tangent as the
limiting position of
a secant
 Gradient of tangent
as instantaneous
rate of change
Notation and
historical context
 Differentiation from
first principles for
simple polynomials
to develop the rule
7 B, C, D, H, I
8C
6.7
6.7
8.2
These were accurate at the time of publication.
- 44 -
Board Endorsed December 07- Amended December 2013
MM Differential Calculus
Value: 0.5
Prerequisites


Satisfactory completion of MM Introduction to Calculus or equivalent.
Students who have not satisfied this requirement may be enrolled following
consultation with the mathematics coordinator.
Specific Unit Goals
This unit should enable students to:
 differentiate polynomial and simple rational functions;
 apply chain, product and quotient rules for finding derivatives;
 use the second derivative to investigate changes in concavity;
 use calculus to confirm critical features of the graphs of polynomial and
simple rational functions;
 solve problems using differential calculus
Content
Topic
Details
Time
Allocation
Differential Calculus
 Polynomials and rational functions
Differentiation of y= xn by rule; notations
2 hours
First derivative including chain, product and quotient rules.
Second derivative
10 hours
 Stationary pts
Nature of stationary points using first derivative and second
derivative. Concavity and inflections
4 hours
 Applications
Sketching Graphs
Sketching graphs including roots, stationary points and
points of infection, asymptotes. Use technology as a
supporting tool.
10 hours
 Rules
 Equations of tangents and normals
Modelling
Related rates
Including maximum and minimum problems
Basic ideas
- 45 -
Board Endorsed December 07- Amended December 2013
Teaching and Learning Strategies
May include:
 appropriate practical work
 consolidation and practice of fundamental skills and routines
 discussion between teacher and students, and between students
 individual problem solving, including the application of mathematics to
everyday situations
 longer-term activities such as investigative, research and project tasks
 opportunities to develop modelling or problem solving skills in practical
contexts
 participation in group activities
 sequenced investigations to scaffold learning
 teacher – guided learning: modelling the use of the appropriate technology
 use of appropriate technology to aid concept development and as a tool for
problem solving.
Assessment
Refer to pages 14-15.
- 46 -
Board Endorsed December 07- Amended December 2013
Student Capabilities
Evidence could be in:
Student Capabilities
Goals
Content Teaching



creative and critical thinkers



enterprising problem-solvers


skilled and empathetic communicators

informed and ethical decision-makers

environmentally and culturally aware citizens



confident and capable users of technologies



independent and self-managing learners


collaborative team members
Assessment






Specific Unit Resources
Differential
Calculus
Differential Calculus
 Polynomials and
rational functions
 Techniques
 Stationary pts
 Applications
7 C, D, E, F,
G
10 A, B, C, D,
E, G
8D
5 A, B, E
4
7C
7D
9B
9C
8.4
8.5
8.7
8.8
8.9
These were accurate at the time of publication.
- 47 -
Board Endorsed December 07- Amended December 2013
MM Integral Calculus & Special Functions
Value 1.0
This unit combines MM Integral Calculus 0.5 and MM Special Functions 0.5
Prerequisites


Satisfactory completion of MM Introductory & Differential Calculus or
equivalent.
Students who have not satisfied this requirement may be enrolled following
consultation with the Executive Teacher of Mathematics.
Specific Unit Goals
This unit should enable students to:
 use upper and lower rectangles to investigate areas enclosed by functions to
develop the fundamental theorem of calculus
 find indefinite and definite integrals
 use integral calculus to find areas enclosed by functions
 use integral calculus to find volumes of solids of revolution
 use the logarithm, its laws and algebra to solve indicial and logarithmic
equations to any base, including e
 differentiate exponential, logarithmic and trigonometric functions
 integrate exponential, trigonometric and appropriate rational functions
 use differential and integral calculus to solve problems
 use trigonometric, exponential and logarithmic functions in modelling.
- 48 -
Board Endorsed December 07- Amended December 2013
Content
Topics
Guidelines
Detail



Differentiation
Anti-differentiation
Exploring approximations of area
under curves
Integration
 Fundamental theorem &
approximation
 Definite integrals

Review as studied in previous unit
Restrict to fitting upper and lower rectangles as a lead into
integration as a summative process (not Simpson’s Rule or
Trapezoidal rule)
Intuitive approach to Fundamental Theorem rather than
detailed proof
Only those functions identified in previous calculus units
Time
Allocation
3 hours
3 hours
28 hours
2 hours
3 hours
Indefinite integrals
6 hours


Areas
Volumes

Applications
Special Functions
 Definition of logarithm:
 Log laws
 The logarithmic function and
logarithmic and exponential graphs
 Calculus of trigonometric, exponential
and logarithmic functions

Modelling and applications of these
functions including growth and decay
Areas under and between curves with respect to x and y
axes
Volumes generated by rotation of one function about the x
and y axes
Further applications could include kinematics, economic
applications.
3 hours
4 hours
28 hours
4 hours
Manipulation of log expressions using log laws
Investigate graphs of ex and logex
Differentiating and integratingAlso includes exponentials in
the form y= ax, ex and ef(x).
Restrict calculus of trigonometric functions to sin, cos, tan
Include growth and decay
4 hours
12 hours
8 hours
Teaching and Learning Strategies
May include:
 discussion between teacher and students, and between students
 teacher – guided learning: modelling the use of the appropriate technology
 appropriate practical work
 consolidation and practice of fundamental skills and routines
 sequenced investigations to scaffold learning
 participation in group activities
 individual problem solving, including the application of mathematics to
everyday situations
 opportunities to develop modelling or problem solving skills in practical
contexts. This could provide an excellent opportunity for an open-ended
assessment task.
 longer-term activities such as investigative, research and project tasks
- 49 -
Board Endorsed December 07- Amended December 2013

use of appropriate technology to aid concept development and as a tool for
problem solving, for example, 3D graphic software.
- 50 -
Board Endorsed December 07- Amended December 2013
Assessment
Refer to pages 14-15.
For examples of assessment see cLc page on BSSS website: www.bsss.act.edu.au/
Student Capabilities
Evidence could be in:
Student Capabilities
Goals
Content Teaching



creative and critical thinkers



enterprising problem-solvers

skilled and empathetic communicators

informed and ethical decision-makers

environmentally and culturally aware citizens



confident and capable users of technologies



independent and self-managing learners


collaborative team members
Assessment






Specific Unit Resources
Chapter
Introduction
to Calculus
Cambridge
Yr 11 2 unit
Polynomials
 Graphs (cubic,
quartic)
Rational Functions
 Graphs/features,
behaviour
 Asymptotic
behaviour
3 C, G
Cambridge
Yr 12 2 unit
Maths
Quest 11
Maths
Quest 12
3I
3J
1G
New Q
Maths
11C
New Q
Maths
11B
New Q
Maths
12B
1.2
Q3,4
9.3
8A
8B
7A
7B
7C
7D
7E
- 51 -
Board Endorsed December 07- Amended December 2013
Chapter
Cambridge
Yr 11 2 unit
Rates of Change:
 constant, variable,
average and
instantaneous
 Limits, notation
Cambridge
Yr 12 2 unit
Maths
Quest 11
7B
Maths
Quest 12
New Q
Maths
11C
New Q
Maths
11B
6.1
6.2
6.3
6.4
6.5
6.6
New Q
Maths
12B
8.1
Trigonometry
 Review ratios
 Angles of any
magnitude
 Radians
 Simple trigonometric
equations
 6 basic trigonometric
graphs and
transformations for
sin, cos and tan
 Modelling/Applicatio
ns
Introduction to
Differentiation
 Tangent as the
limiting position of
a secant
 Gradient of tangent
as instantaneous
rate of change
Notation and
historical context
 Differentiation from
first principles for
simple polynomials
to develop the rule
4 A, C, D, G
3C
7 B, C, D, H, I
5A
5B
5C
5D
5F
5G
5H
5I
9.2
9.1
9.3
8C
6.7
6.7
8.2
These were accurate at the time of publication
- 52 -
Board Endorsed December 07- Amended December 2013
MM Integral Calculus
Value 0.5
Prerequisites

Satisfactory completion of MM Introductory & Differential Calculus or
equivalent.
Specific Unit Goals
This unit should enable students to:
 use upper and lower rectangles to investigate areas enclosed by functions to
develop the fundamental theorem of calculus
 find indefinite and definite integrals
 use integral calculus to find areas enclosed by functions
 use integral calculus to find volumes of solids of revolution
Content
Topics
Guidelines
Detail
 Differentiation
 Anti-differentiation
 Exploring approximations of area under
curves
Review as studied in previous unit
Restrict to fitting upper and lower rectangles as a lead into
integration as a summative process (not Simpson’s Rule or
Trapezoidal rule)
Time
Allocation
4 hours
4 hours
Integration
 Fundamental theorem & approximation
 Definite integrals
Intuitive approach to Fundamental Theorem rather than
detailed proof
 Indefinite integrals
Only those functions identified in previous calculus units
3 hours
 Areas
 Volumes
Areas under and between curves with respect to x and y
axes
Volumes generated by rotation of one function about the x
and y axes
6 hours
3 hours
 Applications
18 hours
2 hours
4 hours
Further applications could include kinematics, economic
applications.
Teaching and Learning Strategies
May include:
 discussion between teacher and students, and between students
 teacher – guided learning: modelling the use of the appropriate technology
 appropriate practical work
 consolidation and practice of fundamental skills and routines
 sequenced investigations to scaffold learning
- 53 -
Board Endorsed December 07- Amended December 2013





participation in group activities
individual problem solving, including the application of mathematics to
everyday situations
opportunities to develop modelling or problem solving skills in practical
contexts. This could provide an excellent opportunity for an open-ended
assessment task.
longer-term activities such as investigative, research and project tasks
use of appropriate technology to aid concept development and as a tool for
problem solving, for example, 3D graphic software.
Assessment
Refer to pages 14-15.
Student Capabilities
Evidence could be in:
Student Capabilities
Goals
Content Teaching



creative and critical thinkers



enterprising problem-solvers

skilled and empathetic communicators

informed and ethical decision-makers

environmentally and culturally aware citizens



confident and capable users of technologies



independent and self-managing learners


collaborative team members
Assessment






Specific Unit Resources
Chapter
Differential
Calculus
Cambridge
Yr 11 2 unit
Differential Calculus
 Polynomials and
rational functions
 Techniques
 Stationary pts
 Applications
Cambridge
Yr 12 2 unit
7 C, D, E, F,
G
10 A, B, C, D,
E, G
5 A, B, E
4
Maths
Quest 11
Maths
Quest 12
8D
7C
7D
9B
9C
New Q
Maths
11C
New Q
Maths
11B
8.4
8.5
8.7
8.8
8.9
These were accurate at the time of publication
- 54 -
New Q
Maths
12B
Board Endorsed December 07- Amended December 2013
MM Special Functions
Value 0.5
Prerequisites


Satisfactory completion of MM Introductory & Differential Calculus or
equivalent.
Students who have not satisfied this requirement may be enrolled following
consultation with the mathematics coordinator.
Specific Unit Goals
This unit should enable students to:
 use the logarithm, its laws and algebra to solve indicial and logarithmic
equations to any base, including e
 differentiate exponential, logarithmic and trigonometric functions
 integrate exponential, trigonometric and appropriate rational functions
 use differential and integral calculus to solve problems
 use trigonometric, exponential and logarithmic functions in modelling.
Content
Special Functions
 Definition of logarithm:
 Log laws
 The logarithmic function and
logarithmic and exponential graphs
 Calculus of trigonometric, exponential
and logarithmic functions
 Modelling and applications of these
functions including growth and decay
28 hours
4 hours
Manipulation of log expressions using log laws
Investigate graphs of ex and logex
Differentiating and integrating. Also includes exponentials
in the form y= ax, ex and ef(x).
Restrict calculus of trigonometric functions to sin, cos, tan
Include growth and decay
4 hours
12 hours
8 hours
Teaching and Learning Strategies
May include:
 discussion between teacher and students, and between students
 teacher – guided learning: modelling the use of the appropriate technology
 appropriate practical work
 consolidation and practice of fundamental skills and routines
 sequenced investigations to scaffold learning
 participation in group activities
 individual problem solving, including the application of mathematics to
everyday situations
 opportunities to develop modelling or problem solving skills in practical
contexts. This could provide an excellent opportunity for an open-ended
assessment task.
 longer-term activities such as investigative, research and project tasks
- 55 -
Board Endorsed December 07- Amended December 2013

use of appropriate technology to aid concept development and as a tool for
problem solving, for example, 3D graphic software.
Assessment
Refer to pages 14-15.
Student Capabilities
Evidence could be in:
Student Capabilities
Goals
Content Teaching



creative and critical thinkers



enterprising problem-solvers

skilled and empathetic communicators

informed and ethical decision-makers

environmentally and culturally aware citizens



confident and capable users of technologies



independent and self-managing learners


collaborative team members
Assessment






Specific Unit Resources
Chapter
Special
Functions
Cambridge
Yr 11 2 unit
Special Functions
 Definition of
logarithm: laws
and algebra
 The logarithmic
function and
logarithmic and
exponential graphs
 Calculus of
trigonometric,
exponential and
logarithmic
functions
 Modelling and
applications of
these functions
including growth
and decay
6 A, B
Cambridge
Yr 12 2
unit
2A
3 E, F, G, H
Maths
Quest 11
Maths
Quest 12
4E
4F
4D
4G
3B
3D
3E
3F
4A
4C
4D
7E
7F
7G
7H
7I
New Q
Maths
11C
New Q
Maths
11B
New Q
Maths
12B
10.3
10.1
3.2
3.7
3.8
3.3
3.4
3.5 Q2
10.1
10.5
These were accurate at the time of publication.
- 56 -
2.6
3.9
3.10
Board Endorsed December 07- Amended December 2013
MM Probability, Statistics & Applications
Value 1.0
This unit combines MM Probability and Statistics 0.5 and MM Further Applications
0.5.
Prerequisites


Satisfactory completion of MM Integral Calculus & Special Functions or
equivalent.
Students who have not satisfied this requirement may be enrolled following
consultation with the Executive Teacher of Mathematics.
Specific Unit Goals
This unit should enable students to:
 develop and apply the concepts of combinatorics
 calculate the probability of events
 analyse univariate data for central tendency and dispersion
 analyse bivariate data for correlation and regression
and
 apply matrices in a variety of practical situations
 use technology to facilitate the solution of problems involving matrices
or
Business Applications
 use a variety of mathematical processes to interpret financial applications
 use linear programming techniques to solve appropriate real life situations
 use knowledge of graphs to interpret modelling involving variation
or
Further Statistics and Probability
 describe the features of a probability distribution
 apply the binomial and normal distributions to calculate probabilities
or
Geometry
 develop skills of Euclidean geometry
 develop skills to solve problems through use of vectors
 develop further skills of analytical geometry to solve problems in both 2D and
3D situations
or
Further Trigonometry
 develop skills of proof through the use of Pythagorean identities
 develop skills in the measurement of sectors
 further develop skills for calculus applications
- 57 -
Board Endorsed December 07- Amended December 2013

further develop approximation techniques to find area under curves
Content
Topics
Guidelines
Detail
Time
Allocation
28 hours
Probability and Statistics
 Measures of central tendency
 Measures of dispersion
 Normal distribution
 Correlation, regression
 Counting techniques
o permutations
o factorial notation
o combinations
Review: Mean, mode and median.
Cover the strengths and weaknesses of the three measures
of central tendency. Discuss the effect of outliers on each of
them.
Review: Range, IQ range and standard deviation. Include
stem plots and box plots. Discuss skewness.
Standard Deviation: Students should be aware of the
formula for standard deviation but should only be asked to
find it using technology.
Stress the difference between sample and population
standard deviations
Use a variety of visual representations of data; focus on use
of GC or other technologies
As related to percentages associated with the standard
deviations.
Focus on interpretation of correlation and regressions
rather than method used in calculation
Discussion of interpolation and extrapolation, association
and causality
Variety of strategies including:
n
Use of, but not restricted to, Pr notation and include
restrictions such as several identical objects, set positioning
and arrangements in a circle.
n
Use of, but not restricted to, C r notation and highlight
link between Pascal’s triangle and combinations
Include tree diagrams and Venn diagrams,
Include applications of counting techniques
 Probability
o
o
o
o
o
o
randomness
experimental and
theoretical
independent events
combining via addition,
multiplication
mutually exclusive
events
conditional probability
/dependent events
Conditional probability based on examples with restricted
and unrestricted domains
- 58 -
Board Endorsed December 07- Amended December 2013
Select two of the four options below. Within each option there is scope for further
depth of study if so desired by concentrating on one or two topics, or taking a
broader approach.
Options
Guidelines
Business Applications
Further Statistics
Topics
 Financial maths
 Linear programming
 Variation
 Inequations/regions
Time Allocation
14-16 hours on each of the two
options chosen – within an option
topic schools may elect some, but not
all, of the suggestions

Derivation of E(X) and Var(X) for
Binomial Dist. is beyond the scope of
this course







Geometry
Simple discrete probability distributions to
illustrate expectation (and variance)
The Binomial distribution
Continuous probability functions (pdf)
Normal distribution
Normal approximation to the binomial
Euclidean
Vectors
Analytical geometry 2D, 3D
Matrix Applications
 2 x 2 Transformation matrices:
linear, homogeneous, rotation, reflection, dilation,
shear
 Markov chains
 Leontief in Economics
 Leslie matrices
 Graph Theory
 Networks
Further Trigonometry




including expectation and variance
Use of GC and/or tables
Proof using Pythagorean identities
Arc length; areas of sectors
Calculus applications eg complex areas and
volumes
Approximation techniques eg Simpson’s Rule?
Teaching and Learning Strategies
May include:
 discussion between teacher and students, and between students
 teacher – guided learning: modelling the use of the appropriate technology
 appropriate practical work
 consolidation and practice of fundamental skills and routines
 sequenced investigations to scaffold learning
- 59 -
Board Endorsed December 07- Amended December 2013






participation in group activities
individual problem solving, including the application of mathematics to
everyday situations
opportunities to develop modelling or problem solving skills in practical
contexts
longer-term activities such as investigative, research and project tasks
use of appropriate technology to aid concept development and as a tool for
problem solving.
statistical information from the public domain should be used wherever
possible
Assessment
Refer tp [ages 14-15.
For examples of assessment see cLc page on BSSS website: www.bsss.act.edu.au/
Student Capabilities
Evidence could be in:
Student Capabilities
Goals
Content Teaching



creative and critical thinkers



enterprising problem-solvers

skilled and empathetic communicators


informed and ethical decision-makers

environmentally and culturally aware citizens



confident and capable users of technologies



independent and self-managing learners


collaborative team members
Assessment






Specific Unit Resources
Chapter
Probability
and Statistics
Cambridge
Yr 11 2 unit
Probability and
Statistics
 Counting,
Permutations,
Combinations
 Independent/depen
dent variables and
restrictions
 Review measures of
central tendency
and dispersion
 Correlation,
regression
 Probability
o randomness
o experimental
and theoretical
o independent
Cambridge
Yr 12 2 unit
Maths
Quest 11
7
10B
10D
10G
11A
11B
11D
11E
11F
11G
11H
Maths
Quest 12
New Q
Maths
11C
New Q
Maths
11B
10.1
10.2
10.3
11.1
11.2
- 60 -
New Q
Maths
12B
Board Endorsed December 07- Amended December 2013
Chapter
Cambridge
Yr 11 2 unit
Cambridge
Yr 12 2 unit
events
combining via
addition,
multiplication
o mutually
exclusive
events
o conditional
probability
/dependent
events
Simple discrete
probability
distributions to
illustrate
expectation (and
variance)
The Binomial
distribution
The Continuous
probability
distribution
including
expectation and
variance
Normal distribution
Use of GC and/or
tables
Maths
Quest 11
Maths
Quest 12
New Q
Maths
11C
New Q
Maths
11B
New Q
Maths
12B
o





Further
Applications
Business Applications
Geometry
Matrix Applications
Further Trigonometry
5.2
10A
10B
10C
11A
11B
11C
11.3
5.3
5.4
13A
13B
13C
5.5
1F
3 A, E, F
6
These were accurate at the time of publication.
MM Probability and Statistics
Value 0.5
Prerequisites


Satisfactory completion of MM Integral Calculus & Special Functions or
equivalent.
Students who have not satisfied this requirement may be enrolled following
consultation with the mathematics coordinator.
Specific Unit Goals
- 61 -
Board Endorsed December 07- Amended December 2013
This unit should enable students to:
 develop and apply the concepts of combinatorics
 calculate the probability of events
 analyse univariate data for central tendency and dispersion
 analyse bivariate data for correlation and regression
Content
Topics
Guidelines
Detail
Time
Allocation
28 hours
Probability and Statistics
 Measures of central tendency
 Measures of dispersion
 Normal distribution
 Correlation, regression
 Counting techniques
o permutations
o factorial notation
o combinations
Review: Mean, mode and median.
Cover the strengths and weaknesses of the three measures
of central tendency. Discuss the effect of outliers on each of
them.
Review: Range, IQ range and standard deviation. Include
stem plots and box plots. Discuss skewness.
Standard Deviation: Students should be aware of the
formula for standard deviation but should only be asked to
find it using technology.
Stress the difference between sample and population
standard deviations
Use a variety of visual representations of data; focus on use
of GC or other technologies
As related to percentages associated with the standard
deviations.
Focus on interpretation of correlation and regressions
rather than method used in calculation
Discussion of interpolation and extrapolation, association
and causality
Variety of strategies including:
n
Use of, but not restricted to, Pr notation and include
restrictions such as several identical objects, set positioning
and arrangements in a circle.
n
Use of, but not restricted to, C r notation and highlight
link between Pascal’s triangle and combinations
Include tree diagrams and Venn diagrams,
Include applications of counting techniques
 Probability
o
o
o
o
o
randomness
experimental and
theoretical
independent events
combining via addition,
multiplication
mutually exclusive
- 62 -
Board Endorsed December 07- Amended December 2013
o
events
conditional probability
/dependent events
Conditional probability based on examples with restricted
and unrestricted domains
Teaching and Learning Strategies
May include:
 discussion between teacher and students, and between students
 teacher – guided learning: modelling the use of the appropriate technology
 appropriate practical work
 consolidation and practice of fundamental skills and routines
 sequenced investigations to scaffold learning
 participation in group activities
 individual problem solving, including the application of mathematics to
everyday situations
 opportunities to develop modelling or problem solving skills in practical
contexts
 longer-term activities such as investigative, research and project tasks
 use of appropriate technology to aid concept development and as a tool for
problem solving.
 statistical information from the public domain should be used wherever
possible
- 63 -
Board Endorsed December 07- Amended December 2013
Assessment
Refer to pages 14-15.
Student Capabilities
Evidence could be in:
Student Capabilities
Goals
Content Teaching



creative and critical thinkers



enterprising problem-solvers

skilled and empathetic communicators

informed and ethical decision-makers

environmentally and culturally aware citizens



confident and capable users of technologies



independent and self-managing learners


collaborative team members
Assessment






Specific Unit Resources
Chapter
Probability and
Statistics
Cambrid
ge Yr 11
2 unit
Probability and
Statistics
 Counting,
Permutations,
Combinations
 Independent/depen
dent variables and
restrictions
 Review measures of
central tendency
and dispersion
 Correlation,
regression
 Probability
o randomness
o experimental
and theoretical
o independent
events
o combining via
addition,
multiplication
o mutually
exclusive
events
o conditional
probability
/dependent
events
Camb
ridge
Yr 12
2 unit
Maths
Quest 11
7
10B
10D
10G
11A
11B
11D
11E
11F
11G
11H
Maths
Quest 12
Quest
General
Maths
New Q
Maths
11C
Ne
wQ
Mat
hs
11B
10.1
10.2
10.3
Ch 2 & 3
11.
1
11.
2
- 64 -
New Q
Maths
12B
Board Endorsed December 07- Amended December 2013
Chapter
Cambrid
ge Yr 11
2 unit
Camb
ridge
Yr 12
2 unit
Maths
Quest 11
 Simple discrete
probability
distributions to
illustrate
expectation (and
variance)
 The Binomial
distribution
 The Continuous
probability
distribution
including
expectation and
variance
 Normal distribution
 Use of GC and/or
tables
Maths
Quest 12
Quest
General
Maths
New Q
Maths
11C
Ne
wQ
Mat
hs
11B
New Q
Maths
12B
5.2
10A
10B
10C
11A
11B
11C
5.3
11.
3
13A
13B
13C
5.4
5.5
These were accurate at the time of publication.
- 65 -
Board Endorsed December 07- Amended December 2013
MM Further Applications
Value 0.5
Prerequisites


Satisfactory completion of MM Integral Calculus & Special Functions or
equivalent.
Students who have not satisfied this requirement may be enrolled following
consultation with the mathematics coordinator.
Specific Unit Goals
This unit should enable students to:
 apply matrices in a variety of practical situations;
 use technology to facilitate the solution of problems involving matrices
and
Business Applications
 use a variety of mathematical processes to interpret financial applications
 use linear programming techniques to solve appropriate real life situations
 use knowledge of graphs to interpret modelling involving variation
or
Further Statistics and probability
 describe the features of a probability distribution
 apply the binomial and normal distributions to calculate probabilities
or
Geometry
 develop skills of Euclidean geometry
 develop skills to solve problems through use of vectors
 develop further skills of analytical geometry to solve problems in both 2D and
3D situations
or
Further Trigonometry
 develop skills of proof through the use of Pythagorean identities
 develop skills in the measurement of sectors
 further develop skills for calculus applications
 further develop approximation techniques to find area under curves
- 66 -
Board Endorsed December 07- Amended December 2013
Content
Select two of the four options below. Within each option there is scope for further
depth of study if so desired by concentrating on one or two topics, or taking a
broader approach.
Options
Guidelines
Business Applications
Further Statistics
Geometry
Topics
 Financial maths
 Linear programming
 Variation
 Inequations/regions
Time Allocation
14-16 hours on each of the two
options chosen – within an option
topic schools may elect some, but not
all, of the suggestions
 Simple discrete probability distributions to illustrate
expectation (and variance)
 The Binomial distribution
Derivation of E(X) and Var(X) for
Binomial Dist. is beyond the scope of
this course






including expectation and variance
Use of GC and/or tables
Continuous probability functions (pdf)
Normal distribution
Normal approximation to the binomial
Euclidean
Vectors
Analytical geometry 2D, 3D
Matrix Applications
 2 x 2 Transformation matrices:
linear, homogeneous, rotation, reflection, dilation,
shear
 Markov chains
 Leontief in Economics
 Leslie matrices
 Graph Theory
 Networks
Further Trigonometry




Proof using Pythagorean identities
Arc length; areas of sectors
Calculus applications eg complex areas and volumes
Approximation techniques eg Simpson’s Rule
Teaching and Learning Strategies
Having selected two options from the four available, students can explore the subtopics in a number of ways which may include individual or group research projects
and presentations or more traditional strategies.
May include:
 discussion between teacher and students, and between students
 teacher – guided learning: modelling the use of the appropriate technology
 appropriate practical work
 consolidation and practice of fundamental skills and routines
 sequenced investigations to scaffold learning
- 67 -
Board Endorsed December 07- Amended December 2013






participation in group activities
individual problem solving, including the application of mathematics to
everyday situations
opportunities to develop modelling or problem solving skills in practical
contexts
longer-term activities such as investigative, research and project tasks
use of appropriate technology to aid concept development and as a tool for
problem solving.
statistical information from the public domain should be used wherever
possible
Assessment
Refer to pages 14-15.
Student Capabilities
Evidence could be in:
Student Capabilities
Goals
Content Teaching



creative and critical thinkers



enterprising problem-solvers

skilled and empathetic communicators

informed and ethical decision-makers

environmentally and culturally aware citizens



confident and capable users of technologies



independent and self-managing learners


collaborative team members
Assessment






Specific Unit Resources
- 68 -
Board Endorsed December 07- Amended December 2013
Chapter
Further
Applications
Macmillan
General
Maths
(RMG)
Business
Applications
 Financial
maths
 Linear
programming
 Variation
 Inequations/r
egions
Geometry
 Euclidean
 Vectors
 Analytical
geometry,
2D, 3D
Cambridge
Yr 11 2 unit
Cambridge
Yr 12 2 unit
Maths
Quest 11
6
Ch 3
Ch 13, 14,
15
Ch 7
Ch 12
1F
3 A, E, F
Maths
Quest 12
New Q
Maths
11C
New Q
Maths
11B
New Q
Maths
12B
New Q
maths
12c
Ch 8
Ch 10
Ch 5
Ch 4
Ch 7
Ch 13
Ch 12
- 69 -
Board Endorsed December 07- Amended December 2013
Matrix
Applications
 2x2
Transformati
on matrices:
linear,
homogeneou
s, rotation,
reflection,
dilation,
shear
 Markov
chains
 Network
representatio
n
 Leontief in
Economics
 Leslie
matrices
 Graph Theory
 Networks
Ch 19
Ex 5.2
Ch 16 (CD)
Ex
13.4
Ex 5.1
Ch 16/17
(CD)
- 70 -
Board Endorsed December 07- Amended December 2013
Further
Trigonometry
 Algebra of
trig/Pythagor
ean identities
 Arc length;
areas of
sectors
 Calculus
applications
 Approximatio
n techniques
Ex 7.07
Ex
10.4
Ex 3.1,
4.7
ch 7
Ch 14
These were accurate at the time of publication.
- 71 -
Board Endorsed December 07- Amended December 2013
Chapte
r
Macmillan
General
Maths
(RMG)
Macmill
an
Maths
Methods
(RMM)
Quest
Gener
al
maths
CD
Camb
ridge
Yr 11
2 unit
Cambri
dge Yr
12 2
unit
Maths
Quest 11
Maths
Quest 12
Quest
Further
maths
New Q
Maths
11C
New
Q
Math
s 11B
New
Q
Math
s 12B
Q
ma
ths
12
B
Numbe
rs and
Pattern
s
- 72 -
Q
ma
ths
12
C
Board Endorsed December 07- Amended December 2013
Chapte
r
Macmillan
General
Maths
(RMG)
Real Numbers
Macmill
an
Maths
Methods
(RMM)
Quest
Gener
al
maths
CD
Camb
ridge
Yr 11
2 unit
Cambri
dge Yr
12 2
unit
Maths
Quest 11
Maths
Quest 12
Quest
Further
maths
New Q
Maths
11C
New
Q
Math
s 11B
New
Q
Math
s 12B
10.2
3.2
Q
ma
ths
12
B
18

Structure
o definitions;
notation;
sets/subsets
 Field laws
o terminology;
counterexamples
 Surds
o laws; basic
operations with
numeric egs;
simplifying;
monic
rationalising
denominator
Algebra Review


Expanding,
factorising,
simplifying, indices
Equations: linear,
simultaneous,
quadratic
- 73 -
Q
ma
ths
12
C
Board Endorsed December 07- Amended December 2013
Chapte
r
Macmillan
General
Maths
(RMG)
Matrices








Introduction and
notation
Matrix Operations
Addition,
subtraction, scalar
multiplication,
matrix multiplication
Determinants
Inverse
Simple Matrix
equations
Solving systems of
linear equations:
representing as a
matrix equation
Applications
Macmill
an
Maths
Methods
(RMM)
Quest
Gener
al
maths
CD
Camb
ridge
Yr 11
2 unit
Ch 19
2A
2B
1J
2C
2D1,4
1A
1B
1C
1D
1E
1F
1G
1H
Cambri
dge Yr
12 2
unit
Maths
Quest 11
2A
2B
4A
4B
1A
1F
2D
See general
year 11
Maths
Quest 12
Quest
Further
maths
New Q
Maths
11C
1.1
1.2
1.3
1.4
1.5
1.2
New
Q
Math
s 11B
New
Q
Math
s 12B
Q
ma
ths
12
B
1.2
1.3
1.4
1.5
1.6
3.1
3.2
3.4
3.3 q 4-11
- 74 -
Q
ma
ths
12
C
Board Endorsed December 07- Amended December 2013
Chapte
r
Macmillan
General
Maths
(RMG)
Macmill
an
Maths
Methods
(RMM)
Quest
Gener
al
maths
CD
Camb
ridge
Yr 11
2 unit
Cambri
dge Yr
12 2
unit
Sequences & Series
 Patterns, general
  notation
 Arithmetic: nth term,
sum to n terms
 Geometric: nth term,
sum to n terms,
limiting sum
Applications (a wide
range including simple
and compound interest
and population growth)
Maths
Quest 11
Maths
Quest 12
Quest
Further
maths
New Q
Maths
11C
New
Q
Math
s 11B
4.1
4.5
4.6
New
Q
Math
s 12B
Q
ma
ths
12
B
Ch 6
4.2
4.3
6
C,D,E,F,
G,H,I,J,
K
5A,B,C,D
8-12
14-19
- 75 -
Q
ma
ths
12
C
Board Endorsed December 07- Amended December 2013
Chapte
r
Relatio
ns and
Functio
ns
Macmillan
General
Maths
(RMG)
Macmill
an
Maths
Methods
(RMM)
Quest
Gener
al
maths
CD
Camb
ridge
Yr 11
2 unit
Cambri
dge Yr
12 2
unit
Maths
Quest 11
Maths
Quest 12
Quest
Further
maths
New Q
Maths
11C
New
Q
Math
s 11B
New
Q
Math
s 12B
10.1
9.4
9.5
Q
ma
ths
12
B
Functions & Relations

Curve recognition

Reciprocal
(asymptotes)

Modelling
o Definitions;
vertical line test;
notation; domain
& range
o Modelling/applic
ations
26
F,G,H,J,
Q7
6A, B, C, D,
E, H
4.3
4.4
- 76 -
Q
ma
ths
12
C
Board Endorsed December 07- Amended December 2013
Chapte
r
Macmillan
General
Maths
(RMG)
Macmill
an
Maths
Methods
(RMM)
Quest
Gener
al
maths
CD
Camb
ridge
Yr 11
2 unit
Cambri
dge Yr
12 2
unit
Maths
Quest 11
Maths
Quest 12
Quest
Further
maths
New Q
Maths
11C
New
Q
Math
s 11B
New
Q
Math
s 12B
Q
ma
ths
12
B
Linear Functions





Review
y = mx+c; general
form;
parallel,
perpendicular;
grad-intercept; ptgrad form;
simultaneous
equations to find
point(s) of
intersection
5 C,D,F
1H
3E
1C
1D
1E
1G
1H
4.1
4.2
4.7
4.8
4.10
- 77 -
Q
ma
ths
12
C
Board Endorsed December 07- Amended December 2013
Chapte
r
Macmillan
General
Maths
(RMG)
Quadratic Functions
 y = ax2 + bx + c
 graph/features, axis of
symmetry
( x = -b/2a), vertex
 factorising expressions
and solving equations:
quadratic formula and
completing the square
 Forms: y-a = (x-b)2
 Discriminant to
determine the number
of roots for graphical
implications.
 Simultaneous
solutions between a
quadratic and a linear
function.
 Modelling including
maximum and
minimum problems.
Macmill
an
Maths
Methods
(RMM)
Quest
Gener
al
maths
CD
Camb
ridge
Yr 11
2 unit
8
A,B,C,D
,E,F
1 G, I
Cambri
dge Yr
12 2
unit
Maths
Quest 11
2H
2I
2J
2C
2E
2F
2G
2K
Maths
Quest 12
Quest
Further
maths
New Q
Maths
11C
New
Q
Math
s 11B
New
Q
Math
s 12B
Q
ma
ths
12
B
7.1
7.4
7.2
7.5
7.6
7.3
- 78 -
Q
ma
ths
12
C
Board Endorsed December 07- Amended December 2013
Chapte
r
Macmillan
General
Maths
(RMG)
Introdu Polynomials
ction to  Graphs (cubic,
quartic)
Calculu
s
Rational Functions
 Graphs/features,
behaviour
 Asymptotic
behaviour
Macmill
an
Maths
Methods
(RMM)
Quest
Gener
al
maths
CD
Camb
ridge
Yr 11
2 unit
3 C, G
Cambri
dge Yr
12 2
unit
Maths
Quest 11
Maths
Quest 12
3I
3J
1G
Quest
Further
maths
New Q
Maths
11C
New
Q
Math
s 11B
New
Q
Math
s 12B
Q
ma
ths
12
B
1.2
Q3,4
9.3
8A
8B
7A
7B
7C
7D
7E
- 79 -
Q
ma
ths
12
C
Board Endorsed December 07- Amended December 2013
Chapte
r
Macmillan
General
Maths
(RMG)
Trigonometry
 Review ratios
 Angles of any
magnitude
 Radians
 Simple trigonometric
equations
 6 basic trigonometric
graphs and
transformations for
sin, cos and tan
 Modelling/Applicatio
ns
Rates of Change:
 constant, variable,
average and
instantaneous
 Limits, notation
Macmill
an
Maths
Methods
(RMM)
Quest
Gener
al
maths
CD
Camb
ridge
Yr 11
2 unit
Cambri
dge Yr
12 2
unit
4 A, C,
D, G
3C
7B
Maths
Quest 11
5A
5B
5C
5D
5F
5G
5H
5I
Maths
Quest 12
Quest
Further
maths
New Q
Maths
11C
New
Q
Math
s 11B
New
Q
Math
s 12B
Q
ma
ths
12
B
9.2
9.1
9.3
6.1
6.2
6.3
6.4
6.5
6.6
8.1
- 80 -
Q
ma
ths
12
C
Board Endorsed December 07- Amended December 2013
Chapte
r
Differe
ntial
Calculu
s
Macmillan
General
Maths
(RMG)
Introduction to
Differentiation
 Tangent as the
limiting position of a
secant
 Gradient of tangent
as instantaneous
rate of change
Notation and
historical context
 Differentiation from
first principles for
simple polynomials
to develop the rule
Differential Calculus
 Polynomials and
rational functions
 Techniques
 Stationary pts
 Applications
Macmill
an
Maths
Methods
(RMM)
Quest
Gener
al
maths
CD
Camb
ridge
Yr 11
2 unit
Cambri
dge Yr
12 2
unit
7 B, C,
D, H, I
Maths
Quest 11
Maths
Quest 12
Quest
Further
maths
New Q
Maths
11C
New
Q
Math
s 11B
New
Q
Math
s 12B
Q
ma
ths
12
B
8C
6.7
6.7
8.2
7 C, D,
E, F, G
10 A, B,
C, D, E,
G
8D
5 A, B, E
4
7C
7D
9B
9C
8.4
8.5
8.7
8.8
8.9
- 81 -
Q
ma
ths
12
C
Board Endorsed December 07- Amended December 2013
Chapte
r
Macmillan
General
Maths
(RMG)
Integral Review calculus
Calculu  Differentiation
 Anti-differentiation
s

Macmill
an
Maths
Methods
(RMM)
Quest
Gener
al
maths
CD
Camb
ridge
Yr 11
2 unit
Cambri
dge Yr
12 2
unit
10 H
1 A, B
Maths
Quest 11
Maths
Quest 12
8E
8F
1 B, C, D,
E, F
1 G, H, I
New Q
Maths
11C
New
Q
Math
s 11B
New
Q
Math
s 12B
Q
ma
ths
12
B
12.1
12.4
12.5
Exploring
approximations of
area under curves
Integration
 Fundamental
theorem &
approximation
 Definite integrals
 Indefinite integrals
 Areas
 Volumes
 Applications
Quest
Further
maths
9D
some 9E
some 9C
some 9I
some 9G
some 9H
some 9I
4.4
4.3
4.5
4.6
4.7
- 82 -
Q
ma
ths
12
C
Board Endorsed December 07- Amended December 2013
Chapte
r
Special
Functio
ns
Probab
ility
and
Statisti
cs
Macmillan
General
Maths
(RMG)
Special Functions
 Definition of
logarithm: laws and
algebra
 The logarithmic
function and
logarithmic and
exponential graphs
 Calculus of
trigonometric,
exponential and
logarithmic functions
 Modelling and
applications of these
functions including
growth and decay
Probability and
Statistics
 Counting,
Permutations,
Combinations
 Independent/depen
dent variables and
restrictions
 Review measures of
Macmill
an
Maths
Methods
(RMM)
Quest
Gener
al
maths
CD
Camb
ridge
Yr 11
2 unit
Cambri
dge Yr
12 2
unit
Maths
Quest 11
Maths
Quest 12
6 A, B
2A
3 E, F, G,
H
4E
4F
4D
4G
3B
3D
3E
3F
4A
4C
4D
7E
7F
7G
7H
7I
Quest
Further
maths
New Q
Maths
11C
New
Q
Math
s 11B
10B
10D
10G
11A
11B
11D
11E
11F
11G
Q
ma
ths
12
B
10.3
10.1
3.2
3.7
3.8
3.3
3.4
3.5 Q2
10.1
10.5
7
New
Q
Math
s 12B
2.6
3.9
3.10
10.1
10.2
10.3
- 83 -
Q
ma
ths
12
C
Board Endorsed December 07- Amended December 2013
Chapte
r
Macmillan
General
Maths
(RMG)





central tendency and
dispersion
Correlation,
regression
Probability
o randomness
o experimental and
theoretical
o independent
events
o combining via
addition,
multiplication
o mutually
exclusive events
o conditional
probability
/dependent
events
Simple discrete
probability
distributions to
illustrate expectation
(and variance)
The Binomial
distribution
The Continuous
Macmill
an
Maths
Methods
(RMM)
Quest
Gener
al
maths
CD
Camb
ridge
Yr 11
2 unit
Cambri
dge Yr
12 2
unit
Maths
Quest 11
Maths
Quest 12
Quest
Further
maths
New Q
Maths
11C
New
Q
Math
s 11B
New
Q
Math
s 12B
Q
ma
ths
12
B
11H
Ch 2 &
3
11.1
11.2
5.2
10A
11.3
5.3
- 84 -
Q
ma
ths
12
C
Board Endorsed December 07- Amended December 2013
Chapte
r
Macmillan
General
Maths
(RMG)


Further
Applica
tions
Macmill
an
Maths
Methods
(RMM)
Quest
Gener
al
maths
CD
Camb
ridge
Yr 11
2 unit
Cambri
dge Yr
12 2
unit
Maths
Quest 11
probability
distribution including
expectation and
variance
Normal distribution
Use of GC and/or
tables
Business Applications
 Financial maths
 Linear programming
 Variation
 Inequations/regions
Geometry
 Euclidean
 Vectors
 Analytical geometry,
2D, 3D
1F
3 A, E,
F
Ch 10
6
Ch 3
Ch 7
Ch 4
Ch 7
Maths
Quest 12
Quest
Further
maths
New Q
Maths
11C
New
Q
Math
s 11B
New
Q
Math
s 12B
10B
10C
11A
11B
11C
5.4
13A
13B
13C
5.5
Ch 13, 14,
15
Ch 12
Q
ma
ths
12
B
Q
ma
ths
12
C
Ch
8
Ch
5
Ch 13
Ch 12
- 85 -
Board Endorsed December 07- Amended December 2013
Chapte
r
Macmillan
General
Maths
(RMG)
Matrix Applications
 2 x 2 Transformation
matrices: linear,
homogeneous,
rotation, reflection,
dilation, shear
 Markov chains
 Network
representation
 Leontief in Economics
 Leslie matrices
 Graph Theory
 Networks
Further Trigonometry
 Algebra of
trig/Pythagorean
identities
 Arc length; areas of
sectors
 Calculus applications
 Approximation
techniques
Macmill
an
Maths
Methods
(RMM)
Quest
Gener
al
maths
CD
Camb
ridge
Yr 11
2 unit
Cambri
dge Yr
12 2
unit
Maths
Quest 11
Maths
Quest 12
Quest
Further
maths
New Q
Maths
11C
New
Q
Math
s 11B
New
Q
Math
s 12B
Q
ma
ths
12
B
Q
ma
ths
12
C
Ch 19
Ex 5.2
Ch 16 (CD)
Ex 13.4
Ex 5.1
Ch 16/17
(CD)
Ex 7.07
Ex
10.
4
Ch
14
Ex
3.1
4.7
ch
7
- 86 -
Board Endorsed December 07
Appendix A – Australian Curriculum Achievement Standards for Mathematical Methods (T)
for Units 1 and 2
Reasoning and Communication
Concepts and Techniques
A student who achieves an A grade
typically
 demonstrates knowledge of
concepts of functions, calculus and
statistics in routine and non-routine
problems in a variety of contexts
 selects and applies techniques in
functions, calculus and statistics to
solve routine and non-routine
problems in a variety of contexts
 develops, selects and applies
mathematical and statistical models in
routine and non-routine problems in a
variety of contexts
 uses digital technologies effectively
to graph, display and organise
mathematical and statistical
information and to solve a range of
routine and non-routine problems in a
variety of contexts
 represents functions, calculus and
statistics in numerical, graphical and
symbolic form in routine and nonroutine problems in a variety of
contexts
 communicates mathematical and
statistical judgments and arguments,
which are succinct and reasoned, using
appropriate language
 interprets the solutions to routine
and non-routine problems in a variety
of contexts
 explains the reasonableness of the
results and solutions to routine and
non-routine problems in a variety of
contexts
 identifies and explains the validity
and limitations of models used when
developing solutions to routine and
non-routine problems
A student who achieves a B
grade typically
 demonstrates knowledge of
concepts of functions, calculus
and statistics in routine and nonroutine problems
 selects and applies techniques
in functions, calculus and
statistics to solve routine and
non-routine problems
 selects and applies
mathematical and statistical
models in routine and nonroutine problems
 uses digital technologies
appropriately to graph, display
and organise mathematical and
statistical information and to
solve a range of routine and nonroutine problems
 represents functions, calculus
and statistics in numerical,
graphical and symbolic form in
routine and non-routine problems
A student who achieves a C
grade typically
 demonstrates knowledge of
concepts of functions, calculus
and statistics that apply to
routine problems
 selects and applies techniques
in functions, calculus and
statistics to solve routine
problems
 applies mathematical and
statistical models in routine
problems
A student who achieves a D
grade typically
 demonstrates knowledge of
concepts of simple functions,
calculus and statistics
 demonstrates familiarity
mathematical and statistical
models
 demonstrates limited
familiarity with mathematical or
statistical models
 uses digital technologies to
graph, display and organise
mathematical and statistical
information to solve routine
problems
 uses digital technologies to
display some mathematical
and statistical information in
routine problems
 uses digital technologies for
arithmetic calculations and to
display limited mathematical
and statistical information
 represents functions, calculus
and statistics in numerical,
graphical and symbolic form in
routine problems
 represents simple functions
and distributions in numerical,
graphical or symbolic form in
routine problems
 represents limited
mathematical or statistical
information in a structured
context
 communicates mathematical
and statistical judgments and
arguments, which are clear and
reasoned, using appropriate
language
 interprets the solutions to
routine and non-routine problems
 communicates mathematical
and statistical arguments using
appropriate language
 communicates simple
mathematical and statistical
information using appropriate
language
 communicates simple
mathematical and statistical
information
 interprets the solutions to
routine problems
 describes solutions to routine
problems
 identifies solutions to routine
problems
 explains the reasonableness of
the results and solutions to routine
and non-routine problems
 describes the reasonableness
of results and solutions to routine
problems
 describes the appropriateness
of the result of calculations
 describes with limited
familiarity the appropriateness of
the results of calculations
 identifies and explains the
limitations of models used when
developing solutions to routine
problems
 identifies the limitations of
models used when developing
solutions to routine problems
 identifies the limitations of
simple models used
 identifies simple models
 uses simple techniques in
functions, calculus and
statistics in routine problems
A student who achieves an E
grade typically
 demonstrates limited
familiarity with concepts of
simple functions, calculus and
statistics
 uses simple techniques in a
structured context
- 87 -
Board Endorsed December 07
Reasoning and Communication
Concepts and Techniques
Achievement Standards for Mathematical Methods (T) for Units 3 and 4
A student who achieves an A grade
typically
 demonstrates knowledge of concepts
of functions, integration and
distributions in routine and non-routine
problems in a variety of contexts
 selects and applies techniques in
functions, integration and distributions
to solve routine and non-routine
problems in a variety of contexts
 develops, selects and applies
mathematical and statistical models in
routine and non-routine problems in a
variety of contexts
 uses digital technologies effectively
to graph, display and organise
mathematical and statistical
information and to solve a range of
routine and non-routine problems in a
variety of contexts
 represents functions, integration and
distributions in numerical, graphical
and symbolic form in routine and nonroutine problems in a variety of
contexts
 communicates mathematical and
statistical judgments and arguments,
which are succinct and reasoned, using
appropriate language
 interprets the solutions to routine
and non-routine problems in a variety
of contexts
 explains the reasonableness of the
results and solutions to routine and
non-routine problems in a variety of
contexts
 identifies and explains the validity
and limitations of models used when
developing solutions to routine and
non-routine problems
A student who achieves a B
grade typically
 demonstrates knowledge of
concepts of functions, integration
and distributions in routine and
non-routine problems
 selects and applies techniques in
functions, integration and
distributions to solve routine and
non-routine problems
 selects and applies
mathematical and statistical
models in routine and non-routine
problems
 uses digital technologies
appropriately to graph, display and
organise mathematical and
statistical information and to solve
a range of routine and non-routine
problems
 represents functions, integration
and distributions in numerical,
graphical and symbolic form in
routine and non-routine problems
A student who achieves a C
grade typically
 demonstrates knowledge of
concepts of functions, integration
and distributions that apply to
routine problems
 selects and applies techniques
in functions, integration and
distributions to solve routine
problems
 applies mathematical and
statistical models in routine
problems
A student who achieves a D
grade typically
 demonstrates knowledge of
concepts of simple functions,
integration and distributions
 demonstrates familiarity with
mathematical and statistical
models
 demonstrates limited
familiarity with mathematical or
statistical models
 uses digital technologies to
graph, display and organise
mathematical and statistical
information to solve routine
problems
 uses digital technologies to
display some mathematical and
statistical information in routine
problems
 uses digital technologies for
arithmetic calculations and to
display limited mathematical and
statistical information
 represents functions,
integration and distributions in
numerical, graphical and symbolic
form in routine problems
 represents simple functions
and distributions in numerical,
graphical or symbolic form in
routine problems
 represents limited
mathematical or statistical
information in a structured
context
 communicates mathematical
and statistical judgments and
arguments, which are clear and
reasoned, using appropriate
language
 interprets the solutions to
routine and non-routine problems
 communicates mathematical
and statistical arguments using
appropriate language
 communicates simple
mathematical and statistical
information using appropriate
language
 communicates simple
mathematical and statistical
information
 interprets the solutions to
routine problems
 describes solutions to routine
problems
 identifies solutions to routine
problems
 explains the reasonableness of
the results and solutions to routine
and non-routine problems
 describes the reasonableness of
results and solutions to routine
problems
 describes the appropriateness
of the result of calculations
 identifies and explains the
limitations of models used when
developing solutions to routine
problems
 identifies the limitations of
models used when developing
solutions to routine problems
 identifies limitations of simple
models used
 demonstrates limited
familiarity with the
appropriateness of the results of
calculations
 identifies simple models
 uses simple techniques in
functions, integration and
distributions in routine problems
A student who achieves an E
grade typically
 demonstrates limited
familiarity with concepts of
simple functions, integration and
distributions
 uses simple techniques in a
structured context
- 88 -
Board Endorsed December 07
- 89 -