Board Endorsed December 07 - Amended December 2013
Mathematical
Applications
Type 2
Written under the:
Accredited from:
Mathematics Framework
2006
1 January /2008 – 31 December 2012 Extended to 2016
Amended October 2013
(includes Assessment Task Types
approved August 2013)
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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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Type 2 Course Accreditation/Adoption Form
B S S S
AUSTRALIAN CAPITAL TERRITORY
Choose one of the following:
 accreditation of Type 2 course
 adoption of Type 2 course from
College
 small changes from Written Evaluation of Type 2 course
 modification of Type 2 course
 extension of Type 2 course
College:
Course Title: Mathematical Applications
Classification:  A  T  M  R
Unit Title(s)
Course Code
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
0.5
MA Matrices, Sequences & Mensuration
MA Matrices, Sequences & Series
MA Mensuration
MA Modelling, Matrices and Networks
MA Modelling
MA Matrices and Networks
MA Financial Modelling and Trigonometry
MA Financial Modelling
MA Trigonometry
MA Statistics and Probability
MA Statistics
MA Probability
Maths for Apprenticeships
Dates of Course Accreditation:
Length
Unit Codes
S
Q
Q
S
Q
Q
S
Q
Q
S
Q
Q
Q
31 / 12 / 2016
01 / 01 / 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:
/
From
/
/
/
/
/
Endorsement of Final Version:
Principal:
Panel Chair:
/
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Type 2 Course Accreditation/Adoption Supporting Statement
Provides support for information on the Course Accreditation/Adoption Form
B S S S
Written Evaluation for small changes, or reasons for Modification or Adoption of
a Type 2 course
AUSTRALIAN CAPITAL TERRITORY
College:
Course Title: Mathematical Applications
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.
College:
Course Code
Course Title: Mathematical Applications
Provision for Continuing Students:
This course is intended for Yr11 students commencing College 2008. Students in Year 12 in 2008 will
complete the old course
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Table of Contents
Course Name .............................................................................................................................. 6
Course Classification ................................................................................................................... 6
Course Framework ..................................................................................................................... 6
Course Developers...................................................................................................................... 6
Evaluation of Previous Course .................................................................................................... 6
Course Length and Composition ................................................................................................ 7
Implementation Guidelines ........................................................................................................ 7
Subject Rationale ........................................................................................................................ 9
Goals ......................................................................................................................................... 10
Student Group .......................................................................................................................... 10
Content ..................................................................................................................................... 11
Teaching and Learning Strategies............................................................................................. 13
Assessment ............................................................................................................................... 14
Unit Grades ............................................................................................................................... 17
Moderation ............................................................................................................................... 19
Bibliography .............................................................................................................................. 20
Resources.................................................................................................................................. 21
Proposed Evaluation Procedures ............................................................................................. 22
MA Matrices, Sequences & Mensuration Value 1.0 .............................................................. 23
MA Matrices, Sequences & Series Value 0.5 ........................................................................ 26
MA Mensuration Value 0.5 ................................................................................................... 29
MA Modelling, Matrices and Networks Value 1.0 ................................................................ 31
MA Modelling Value 0.5 ....................................................................................................... 34
MA Matrices and Networks Value 0.5................................................................................... 36
MA Financial Modelling and Trigonometry Value 1.0 ......................................................... 38
MA Financial Modelling Value 0.5 ....................................................................................... 42
MA Trigonometry Value 0.5 .................................................................................................. 45
MA Statistics and Probability Value 1.0 ................................................................................ 47
MA Statistics
Value 0.5 ....................................................................................................... 51
MA Probability
Value 0.5 ................................................................................................... 54
Maths for Apprenticeships Value 0.5 ..................................................................................... 56
Modelling & Maths for Apprenticeships Value 1.0 ............................................................... 61
Matrices & Networks & Maths for Apprenticeships Value 1.0 ............................................. 67
Appendix 1 – Industry Feedback .............................................................................................. 74
Appendix 2 – Apprenticeship skills by workplace .................................................................... 75
Appendix 3 – Trade requirements ............................................................................................ 78
Appendix 4 - Selected Unit Resources ...................................................................................... 81
Appendix 5 - Australian Curriculum Achievement Standards for General Mathematics (T) ... 83
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Course Name
Mathematical Applications
Course Classification
T
Course Framework
This course is presented under the 2006 Mathematics Course Framework.
Course Developers
Name
Qualifications
Jenny Budd
BSc (ANU), Dip Ed (UC)
Lynda Chubb
BSc Grad Dip Ed (Sydney)
Anna Hyslop
BSc (UTAS) Dip Ed (UC)
Julie Hedditch
BA (Sydney) Dip Ed (UC)
Peter Holmes
BSc (ANU) Dip Ed (UNE)
Tom Klekner
BSc (ANU) Dip Ed (UC)
This group gratefully acknowledges the work of previous developers.
Evaluation of Previous Course
This Course is proposed to replace the Mathematical Applications Type 2 course that has been accredited
until end 2008.
The previous structure of Mathematics courses was established in 2004. Since then there have been
several developments impacting on the teaching of mathematics in the ACT:
All ACT Mathematics courses will need to be re-written for the start of 2008 in line with the new
Mathematics framework.
To enable a major in a Specialist course and movement between all Mathematics courses as students find
their correct course in College, the Applications course needs to be modified accordingly.
There is a wider range of resources available
Technology is now strongly embedded in all Mathematics courses
This Type 2 course was developed out of the new Mathematics Course Framework. Much content from
the previous Type 2 course have been included in this document.
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Course Length and Composition
Unit Title
MA Matrices, Sequences & Series and Mensuration
MA Matrices, Sequences & Series
MA Mensuration
MA Modelling, Matrices and Networks
MA Modelling
MA Matrices and Networks
MA Financial Modelling and Trigonometry
MA Financial Modelling
MA Trigonometry
MA Statistics and Probability
MA Statistics
MA Probability
Maths for Apprenticeships
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
0.5
Available course patterns
This course is offered as a minor or major only.
(delete any course patterns which are not applicable at your college)
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 Mathematical Applications can comprise any combination of the following units
 MA Matrices, Sequences & Series and Mensuration or MM Numbers, Patterns, Relations, Functions –
(but not both);
 MA Modelling, Matrices and Networks or MM Introductory & Differential Calculus – (but not both)
recognising that this does not constitute a Calculus course
 Students may change from Mathematical Methods to Mathematical Applications during or at the end
of Year 11.
 Students may change from MA Matrices Sequences & Series and Mensuration to MM Number,
Patterns, Relations & Functions and MM Introduction to Calculus at the discretion of the Executive
Teacher of Mathematics but not to MM Differential Calculus.
Maths for Apprenticeships 0.5
It is envisaged that this unit be an optional 0.5 unit that would be offered in the last term of year 12. It
would replace the Probability unit, 0.5, for some students. It is specifically designed to prepare students for
transition into apprenticeships or vocational based course (eg CIT courses)
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Compulsory units
There are no compulsory units.
Prerequisites for the course or units within the course
There are no formal prerequisites for this course.
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Arrangements for students who are continuing to study a course in this subject
Students who studied the previous course Mathematical Applications course in Year 11 may take MA
Financial Modelling and Trigonometry and MA Statistics and Probability in Year 12.
Units from other courses
See “relationship with other courses”
Negotiated Units
Nil
Relationship with other courses
Mathematical Methods
The first unit of this course, MA Matrices, Sequences & Series and Mensuration, has common content with
the first unit of Mathematical Methods Number, Patterns, Relations and Functions. MM Number, Patterns,
Relations and Functions and MM Introductory and Differential Calculus can be included in a Mathematical
Applications course.
Under this structure, it is intended that, subject to other relevant BSSS policies, students will be certificated
in only one Mathematics course. It is envisaged that students will have identified their appropriate course
by the end of Year 11. Where students change courses during their study of Mathematics, they should be
certificated in the course in which they conclude their study, according to BSSS requirements.
Suggested Implementation Patterns
Implementation Pattern
Minor
Major
Units Involved
MA Matrices, Sequences & Series and Mensuration,
MA Modelling, Matrices and Networks
MA Matrices, Sequences & Series and Mensuration,
MA Modelling, Matrices and Networks,
MA Financial Modelling and Trigonometry,
MA Statistics and Probability
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.
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
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.
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 as a suitable preparation for general tertiary entry or for students intending
tertiary study in areas where mathematical content is not emphasised. The course is intended to present
mathematics as an organised body of useful knowledge and provides students with the skills and
confidence necessary to apply this knowledge to practical situations. The content, therefore, need not be
prescriptive but does need to develop the students’ ability to think logically and communicate succinctly.
Students enrolling in this course should have demonstrated success in their studies of Year 10
Mathematics at a minimum of an Intermediate Level or its equivalent.
This course is written under the Mathematics Course Framework. It aims to achieve a balance between
concept development, engagement in processes and the presentation of content. Adequate opportunity
for students to construct their personal mathematical understandings is allowed through investigations
and applications.
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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.
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.
Mensuration
Mensuration 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 mensuration.
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.
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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.
Essential skills
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.
Mensuration
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.
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.
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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.
Teaching and Learning Strategies
Teaching 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:

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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Assessment
This collection of evidence enables a comparison of achievement within and across colleges, through
moderation processes. This enables valid, fair and equitable reporting of student achievement on the ACT
Year 12 Certificate.
Assessment tasks elicit responses that demonstrate the degree to which students have achieved the goals
of a unit (and the course as a whole).
Assessment Task Types (with weightings) group assessment tasks in ways that reflect agreed shared
practice in the subject area and facilitate the comparison of student work across different assessment
tasks.
Assessment Criteria (the dimensions of quality that teachers look for in evaluating student work) provide a
common and agreed basis for judgement of performance against unit and course goals, within and across
colleges. Over a course, teachers use all of these criteria to assess students’ performance, but do not
necessarily use all criteria on each task. Assessment criteria are to be used holistically on a given task and
in determining the unit grade.
Assessment Rubrics draw on the general course framework criteria to develop assessment criteria for a
task type and a continuum which indicates levels of student performance against each criterion.
Colleges may find rubrics useful in assessing and providing feedback to students on individual assessment
tasks. A variety of rubrics, which could be used as models, have been developed in various colleges.
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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
-
Short answer
-
Extended questions
40-75%
Non-Test Tasks (in-class):
-
For example:
-
Validation activities
-
Modelling
-
Investigations
-
Problem solving
-
Journals
-
Portfolios
-
Presentations
-
Practical activities
0-60%
25-60%
Take Home Tasks:
- For example:
-
Modelling
-
Investigations
-
Portfolios
-
Practical activities
0-30%
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.
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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.
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.
Enterprising problem-solvers
Students will be provided with opportunities to demonstrate initiative and resourcefulness in using
appropriate technologies to develop solutions to a variety of problems. This may involve collaborative
tasks or projects that require the development of unique solutions to problems.
Skilled and empathetic communicators
Students will be challenged to express themselves using a variety of media and applying appropriate
mathematical language.
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.
Environmentally and culturally aware citizens
Students will be encouraged to examine and analyse information and use this evidence as the basis of
judgements and decisions.
Confident and capable users of technologies
Students are expected to use a range of appropriate technologies in collecting, processing and analysing
information.
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.
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Unit Grades
Grade descriptors provide a guide for teacher judgement of students’ achievement, based on the
assessment criteria, over a unit of work in this subject. Grades are organized on an A-E basis and represent
standards of achievement.
Grades are awarded on the proviso that the assessment requirements have been met. Teachers will
consider, when allocating grades, the degree to which students demonstrate their ability to complete and
submit tasks within a specified time frame.
The following descriptors are consistent with the system grade descriptors.
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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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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.
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 non-written 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
Version 2 October 2009
- 19 -
Board Endorsed December 07 - Amended December 2013

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
Student texts
It is anticipated the student text will be:
Nolan, J et al Jacaranda Maths Quest 11 General Mathematics, Wiley, Brisbane 2000
Nolan, J et al Jacaranda Maths Quest 12 Further Mathematics, Wiley, Brisbane
(Most Schools have already purchased these texts and the purchase of new editions would involve a substantial financial
outlay)
The following books will be used as resources throughout the course:
Important notice re Copyright
Jacaranda, the publisher of the QUEST series of texts, has agreed in principle that when colleges purchase class sets of books,
an arrangement can be made with regard to resourcing supplementary materials from their other titles and CDs. If you are
concerned about exceeding the 10% limit on photocopying, please contact your sales consultant at Jacaranda publishing or the
Assessment Executive Officer at BSSS.
Texts written for Victoria Senior Mathematics Courses
Mathematical Applications
Nolan, J et al , Jacaranda Maths Quest 11 General Mathematics, Wiley, Brisbane 2000, 2005 edition,
9780731402533
Nolan, J et al , Jacaranda Maths Quest 12 Further Mathematics, Wiley, Brisbane z/e, 9780731402557
Jones, P; Evans, M and Lipson, K, Essential Further Mathematics, Cambridge University Press, Melbourne
2001, 3rd Edition, 9780521613286
Evans, M and Avery, S, Essential Further Mathematics solution supplement, Cambridge University Press,
Melbourne 2001, 9780521609166
Jones, P; Evans, M and Lipson, K, Essential General Mathematics, Cambridge University Press, Melbourne
2001, 2005 edition, 9780521672603
Avery, S, 2000Essential General Mathematics solution supplement, Cambridge University Press, Melbourne
2000, 2005 edition, 9780521612548
Mathematical Methods
Nolan, J et al, Jacaranda Maths Quest 11 Mathematical Methods 1 and 2, Wiley, Brisbane 2000, Z/E
9780731402236
Nolan, J et al, Jacaranda Maths Quest 12 Mathematical Methods 3 and 4, Wiley, Brisbane 2000, Z/E
9780731402557
Texts written for Queensland Senior Mathematics Courses
Maths A
Brodie, R and Swift, S, New Q Maths 11A, Nelson, Melbourne 2002, 9780170103817
Brodie, R and Swift, S, New Q Maths 12A, Nelson, Melbourne 2002, 9780170103794
Elms, L & Simpson, N, Jacaranda Maths Quest 11A for Queensland, Brisbane, 2001, 9780701636241
Elms, L & Simpson, N, Jacaranda Maths Quest 12A for Queensland, Brisbane, 9780701636258
Shield, M et al, Mathematics for Queensland 11A, Oxford, Melbourne, 2001, 9780195508505
Shield, M et al, Mathematics for Queensland 12A, Oxford, Melbourne, 2002, 9780170103794
Version 2 October 2009
- 20 -
Board Endorsed December 07 - Amended December 2013
Maths B
Brodie, R and Swift, S , New Q Maths 11B, Nelson, Melbourne, 2002, 9780170103794
Brodie, R and Swift, S , New Q Maths 12B, Nelson, Melbourne, 2002, 9780170104876
Bolger, K et al, Mathematics for Queensland 11B, Oxford, Melbourne, 2001, 9780195508529
Bolger, K et al, Mathematics for Queensland 12B, Oxford, Melbourne, 2002, 978019550553x
Porter, J and Walton, J, Queensland Senior Mathematics, Heinemann, Melbourne 1993
Simpson, N & Rowland, R, Jacaranda Maths Quest 11B for Queensland, Nelson, Brisbane, 2000,
9780701636265
Simpson, N & Rowland, R, Jacaranda Maths Quest 12B for Queensland, Nelson, Brisbane, 2002,
9780701636272
Texts written for New South Wales Senior Mathematics Courses
General Mathematics
Ley, J and Fuller, M, Insight General Mathematics Preliminary Course, Oxford, Melbourne, 2001,
9780195508222
Ley, J and Fuller, M, Insight General Mathematics HSC Course, Oxford, Melbourne, 2001, 9780195508208
Brown, A, et al, General Mathematics Year 11, Cambridge, Melbourne, 2000, 9780521643788
Thomas, A et al, General Mathematics Year 12, Cambridge, Melbourne, 2000,9780521643771
Rowland, R, Jacaranda Maths Quest General Mathematics Preliminary Course, Wiley, Brisbane, 2000, new
Edition in September, 9780734105701
Rowland, R, Jacaranda Maths Quest General Mathematics HSC Course, Wiley, Brisbane, 2000, Z/E
9780731405695
Yen, R and Willard, M, New Century Maths 11 General Preliminary Course, Nelson, Melbourne, 2000,
9780170101721
Yen, R and Willard, M, New Century Maths 12 General HSC Course, Nelson, Melbourne, 2001,
97801701027635
These were accurate at the time of publication.
Resources
The college will supply students with texts that are appropriate to this course, together with additional
reference books for the purposes of carrying out projects and investigations. All students studying this
course require a graphics calculator. Laptops with appropriate software (eg Autograph, Mathcad,
Graphmatica) are required for classroom demonstrations and classes will be expected to have some access
to computer laboratories.
A focal point for ideas and resources for all courses developed under the ACT Mathematics Framework can
be found at www.bsss.act.gov.au  select Resources and Publications.
These were accurate at the time of publication.
Version 2 October 2009
- 21 -
Board Endorsed December 07 - Amended December 2013
Proposed Evaluation Procedures
A course adopted from this document should be reviewed at the end of each semester by reference to the
views of students and staff.
Students, teachers and others should, as appropriate, evaluate:

whether the course and course framework are still consistent;

whether the goals were achieved;

the success of the course content;

the success of the teaching strategies used;

the success of the across curriculum perspectives in, for example, including students with special
needs or addressing information access skills of students or fulfilling the statements made in this
section in the course document;

the success of the assessment program;

whether the needs of the students have been met;

the relevance of the course;

the number of students completing the course in each of the years of accreditation;

the need for improvements in the course.
Version 2 October 2009
- 22 -
Board Endorsed December 07 - Amended December 2013
MA Matrices, Sequences & Mensuration
Value 1.0
This unit combines MA Matrices, Sequences & Series 0.5 and MA Mensuration 0.5.
Prerequisites
Nil
The first unit in Mathematical Applications is very similar to the first unit in Mathematical Methods. The
Mathematical Methods unit, however, involves a significant amount of algebra revision which is not
required in the Mathematical Applications unit. The opportunity for substantial overlap in assessment
items between these two units provides a strong basis for moderation between the two courses. The use
of technology in this course is clearly indicated. Teaching practice should encourage students to take
personal responsibility for mastering the technology which is a supporting tool.
The second half of this unit provides students with an opportunity to review and extend measurement
concepts taught in high school.
Specific Unit Goals
This unit should enable students to:

use technology to explore the concepts of this unit

understand matrix representations and simple applications

recognise the importance of number sequences and series in our everyday lives

use number sequences and series in a range of realistic situations

use length, area and volume measurement techniques in practical situations

understand and apply the fundamentals of trigonometry
Content (SS – Spreadsheet, GC – Graphics Calculator)
Content
Matrix Manipulations (16 hours)
Teaching Guidelines

Introduction and notation

Matrix Operations

Applications
Representation of information as a rectangular array of
numbers.
Egs. summarising information for processing in a
computer; economic and biological applications.
Addition, subtraction, scalar multiplication, matrix
multiplication, inverses, solve simple equations. Restrict
manual calculations to 2 × 2. Use of GC for higher order
matrices.
These are restricted to solving simultaneous equations
and organising data. (Further matrix applications are
treated later in the course)
Use data from a range of financial and non-financial
contexts such as lending and borrowing, bouncing balls
and stacking cans in a supermarket to develop concepts
of sequences and series.
Introduce general concepts common to all sequences
and series; consider a range of types other than APs and
GPs.
Sequences and Series (16 hours)

General sequences and series
Version 2 October 2009
- 23 -
Board Endorsed December 07 - Amended December 2013
Content
 Arithmetic and Geometric sequences
and series: nth term, sum to n terms,
infinite sum of a geometric series
where r  1
Mensuration (12 hours)


Pythagoras’ theorem in three
dimensions
Perimeter and area including sectors
and arc lengths
Total surface area (use of nets)

Volume (prisms and pyramids)

Applied Trigonometry (12 hours)
 Right angled triangle ratios
 Sine and Cosine rule

Areas of triangles
Teaching Guidelines
Students should appreciate the particular properties of
APs and GPs and be able to recognise them readily.
Consider sequences and series numerically and
graphically, using SS and GC.
Determine whether a sequence is arithmetic, geometric
or neither from both context and numerical data sets.
Use contexts such as art and design, architecture,
navigation and construction.
Use practical contexts to calculate: prisms, cylinders,
cones, composite figures.
Include cylinders, spheres and cones – consider a
variety of items -storage containers, roofing materials
etc.
Incorporate decision-making in the comparison of
volumes of different shaped solids.
Emphasis on accuracy and terminology.
Include both decimal and dms (, ´, ´´) but not radians
Consider the ambiguous case and offer a number of
real-life examples to consolidate.
Consider Heron’s rule as an alternative to
A
1
abSinC
2

Applications of trigonometry
Applications involving angles of elevation and
depression, and bearings.
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
 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
Version 2 October 2009
- 24 -
Board Endorsed December 07 - Amended December 2013
Assessment
Refer to pages 13-15.
Student Capabilities
Evidence could be in:
Student Capabilities
Goals
Content
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

Teaching



Assessment









Specific Unit Resources
Books
Selected Unit Resources from VCE Text: Matrices
VCE Quest 11
General Maths
VCE Quest 12
Further Maths
Ch19 (CDRom)
VCE Quest 2ndEd
General Maths A
VCE Quest 2ndEd
Further Maths
Cambridge
Essential Standard
General
Mathematics 1st Ed
Cambridge
Essential Further
Mathematics 3rd
Ed
Ch1 Ch3
Ch16
Ch 11
Ch 26,27
Selected Unit Resources from VCE Text: Sequences & Series
VCE Quest 11
General Maths
VCE Quest 12
Further Maths
VCE Quest 2ndEd
General Maths A
VCE Quest 2ndEd
Further Maths
Cambridge Essential
Standard General
Mathematics 1st Ed
Cambridge
Essential Further
Mathematics 3rd
Ed
Ch 5 : challenging
Ch 6: suitable
Ch 3: challenging
Ch 5 suitable
Ch 8
Ch9
Selected Unit Resources from VCE Text: Mensuration
VCE Quest 11
General Maths
VCE Quest 12
Further Maths
Ch 11
VCE Quest 2ndEd
General Maths A
VCE Quest 2ndEd
Further Maths
Ch13
Cambridge Essential
Standard General
Mathematics 1st Ed
Ch 5
See the bibliography in this document for other suggested resources.
Other
www.bsss.act.gov.au and select Resources and Publications
These were accurate at the time of publication.
Version 2 October 2009
- 25 -
Cambridge
Essential Further
Mathematics 3rd
Ed
Board Endorsed December 07 - Amended December 2013
MA Matrices, Sequences & Series
Value 0.5
Prerequisites
Nil
The first unit in Mathematical Applications is very similar to the first unit in Mathematical Methods. The
Mathematical Methods unit, however, involves a significant amount of algebra revision which is not
required in the Mathematical Applications unit. The opportunity for substantial overlap in assessment
items between these two units provides a strong basis for moderation between the two courses. The use
of technology in this course is clearly indicated. Teaching practice should encourage students to take
personal responsibility for mastering the technology which is a supporting tool.
Specific Unit Goals
This unit should enable students to:

use technology to explore the concepts of this unit

understand matrix representations and simple applications

recognise the importance of number sequences and series in our everyday lives

use number sequences and series in a range of realistic situations
Content (SS – Spreadsheet, GC – Graphics Calculator)
Content
Matrix Manipulations (16 hours)
Teaching Guidelines

Introduction and notation

Matrix Operations

Applications
Representation of information as a rectangular array of
numbers.
Egs. summarising information for processing in a
computer; economic and biological applications.
Addition, subtraction, scalar multiplication, matrix
multiplication, inverses, solve simple equations. Restrict
manual calculations to 2 × 2. Use of GC for higher order
matrices.
These are restricted to solving simultaneous equations
and organising data. (Further matrix applications are
treated later in the course)
Use data from a range of financial and non-financial
contexts such as lending and borrowing, bouncing balls
and stacking cans in a supermarket to develop concepts
of sequences and series.
Introduce general concepts common to all sequences
and series; consider a range of types other than APs and
GPs.
Students should appreciate the particular properties of
APs and GPs and be able to recognise them readily.
Sequences and Series (16 hours)

General sequences and series

Arithmetic and Geometric sequences
and series: nth term, sum to n terms,
infinite sum of a geometric series
where r  1
Consider sequences and series numerically and
graphically, using SS and GC.
Determine whether a sequence is arithmetic, geometric
or neither from both context and numerical data sets.
Version 2 October 2009
- 26 -
Board Endorsed December 07 - Amended December 2013
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
 development of student prepared summaries/glossaries
 use of appropriate technology to aid concept development and as a tool for problem solving
 sequenced investigations to scaffold learning
Assessment
Refer to pages 13-15.
Student Capabilities
Evidence could be in:
Student Capabilities
Goals
Content
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

Version 2 October 2009
- 27 -
Teaching



Assessment









Board Endorsed December 07 - Amended December 2013
Specific Unit Resources
Books
Selected Unit Resources from VCE Text: Matrices
VCE Quest 11
General Maths
VCE Quest 12
Further Maths
Ch19 (CDRom)
VCE Quest 2ndEd
General Maths A
VCE Quest 2ndEd
Further Maths
Cambridge
Essential Standard
General
Mathematics 1st Ed
Cambridge
Essential Further
Mathematics 3rd
Ed
Ch1 Ch3
Ch16
Ch 11
Ch 26,27
Selected Unit Resources from VCE Text: Sequences & Series
VCE Quest 11
General Maths
VCE Quest 12
Further Maths
VCE Quest 2ndEd
General Maths A
VCE Quest 2ndEd
Further Maths
Cambridge Essential
Standard General
Mathematics 1st Ed
Cambridge
Essential Further
Mathematics 3rd
Ed
Ch 5 : challenging
Ch 6: suitable
Ch 3: challenging
Ch 5 suitable
Ch 8
Ch9
See the bibliography in this document for suggested student resources.
Other
www.bsss.act.gov.au and select Resources and Publications
These were accurate at the time of publication.
Version 2 October 2009
- 28 -
Board Endorsed December 07 - Amended December 2013
MA Mensuration
Value 0.5
Prerequisites
Nil
This unit provides students with an opportunity to review and extend measurement concepts taught in
high school.
Specific Unit Goals
This unit should enable students to:

use length, area and volume measurement techniques in practical situations

understand and apply the fundamentals of trigonometry
Content
Content
Mensuration (12 hours)


Pythagoras’ theorem in three
dimensions
Perimeter and area including sectors
and arc lengths
Total surface area (use of nets)

Volume (prisms and pyramids)

Applied Trigonometry (12 hours)
 Right angled triangle ratios
 Sine and Cosine rule

Areas of triangles
Teaching Guidelines
Use contexts such as art and design, architecture,
navigation and construction.
Use practical contexts to calculate: prisms, cylinders,
cones, composite figures.
Include cylinders, spheres and cones – consider a
variety of items -storage containers, roofing materials
etc.
Incorporate decision-making in the comparison of
volumes of different shaped solids.
Emphasis on accuracy and terminology.
Include both decimal and dms (, ´, ´´) but not radians
Consider the ambiguous case and offer a number of
real-life examples to consolidate.
Consider Heron’s rule as an alternative to
A
1
abSinC
2

Applications of trigonometry
Applications involving angles of elevation and
depression, and bearings.
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
 longer-term activities such as investigative, research and project tasks
 development of student prepared summaries/glossaries
 use of appropriate technology to aid concept development and as a tool for problem solving
 appropriate practical work
Version 2 October 2009
- 29 -
Board Endorsed December 07 - Amended December 2013
Assessment
Refer to pages 13-15.
Student Capabilities
Evidence could be in:
Student Capabilities
Goals
Content
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

Teaching



Assessment









Specific Unit Resources
Books
Selected Unit Resources from VCE Text: Mensuration
VCE Quest 11
General Maths
VCE Quest 12
Further Maths
Ch 11
VCE Quest 2ndEd
General Maths A
VCE Quest 2ndEd
Further Maths
Ch13
Cambridge Essential
Standard General
Mathematics 1st Ed
Cambridge
Essential Further
Mathematics 3rd
Ed
Ch 5
Selected Unit Resources from VCE Text: Trigonometry
VCE Quest 11
General Maths
VCE Quest 12
Further Maths
Ch 15
VCE Quest 2ndEd
General Maths A
VCE Quest 2ndEd
Further Maths
Ch 16
(not radians)
Cambridge Essential
Standard General
Mathematics 1st Ed
Ch 7
See the bibliography in this document for suggested student resources.
Other
www.bsss.act.gov.au and select Resources and Publications
These were accurate at the time of publication.
Version 2 October 2009
- 30 -
Cambridge
Essential Further
Mathematics 3rd
Ed
Board Endorsed December 07 - Amended December 2013
MA Modelling, Matrices and Networks
Value 1.0
This unit combines MA Linear Modelling 0.5 with MA Matrices and Networks 0.5.
Prerequisites
Nil
The first part of this unit presents to the student realistic and applicable problems that require the use of
mathematical models and algorithms to develop the optimum solution.
The second half of the unit aims to have them aware of some techniques of modelling and their application
to real life situations as it applies to matrices and networks. It involves network analysis, modelling of
activities and their relationships.
Specific Unit Goals
This unit should enable students to:

describe the key features of linear graphs and their use in modelling real life situations.

recognising the shape of non linear graphs from their equations and investigating their applications
in modelling

analyse and solve problems using matrices to representing data

represent and analyse relationships between nodes of a network in a range of formats

apply network theory to practical situations
Content
Linear modelling (12 hours)
 Sketching straight line graphs
Teaching guidelines
Use data from a range of contexts to develop the concept
of a linear relationship. Step graphs (eg taxi fares and
mobile phone charges) can also be included. Include a
discussion of dependent and independent variables and
GC sketching to emphasise features such as intercepts
and gradients and the use of domain and range in
practical situations.
Finding the gradient of a straight line given two points.
Equations of the form y = mx + b and ax +by +c = 0


Simultaneous equations
Applications of linear modelling
Linear programming (10 hours)
The optimisation process and its
components considered in a range of
contexts
 Linear inequalities
 Constraints, feasible region, corner
point
Non linear models. (8 hours)
Investigating Parabolic and Exponential
Relationships
Matrix Applications (12 hours)
Version 2 October 2009
given gradient and y intercept; given the gradient and
any point; given two points.
Use of GC to find solutions.
Eg Breakeven, relate to the success or failure of
businesses. Use GC to find breakeven point
Focus on students acquiring a working knowledge of the
linear programming process.
Students should be given experiences in interpreting a
given situation, formulating an objective function,
constructing and drawing the inequations and applying
the corner point method to the objective function.
Focus on interpreting the general shape of the graph
given the equations.
Examples may include projectile paths, cooling, of hot
water, population growth and decline, radioactive decay
These may include: Transformations on the plane,
- 31 -
Board Endorsed December 07 - Amended December 2013
Content
 A selection of Matrix applications
Graphs and Networks (14 hours)
 Terminology and representation
(including matrix representation)
 Planar graphs

Directed Graphs and Networks
Teaching guidelines
Dominance Matrices, Simple Markov chains (Transition
matrices) and coding. It is not intended to teach Matrix
Arithmetic again.
Relate to maps, plans, systems and relationships.
Euler paths and circuits, Hamiltonian paths and circuits,
minimum and maximum spanning trees. Examples such
as orienteering courses, telephone networks, airline
routes, considering distance, time or cost.
Critical path analysis, project management, network flow
and assignment problems.
Use examples from construction, manufacturing and
transport industries.
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
 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 13-15.
Student Capabilities
Evidence could be in:
Student Capabilities
Goals
Content
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

Version 2 October 2009
- 32 -
Teaching








Assessment





Board Endorsed December 07 - Amended December 2013
Specific Unit Resources
Books
See the bibliography in this document for suggested student resources.
Other
www.bsss.act.gov.au and select Resources and Publications
Selected Unit Resources from VCE Text: modelling (+ Linear programming)
VCE Quest 11
General Maths
VCE Quest 12
Further Maths
Ch 6,7 (9 12,)
VCE Quest 2ndEd
General Maths A
VCE Quest
2ndEd
Further Maths
Ch9, 11 (7,15)
Cambridge Essential
Standard General
Mathematics 1st Ed
Cambridge
Essential Further
Mathematics 3rd
Ed
Ch 3,9
Selected Unit Resources from VCE Text: Matrix Applications
VCE Quest 11
General Maths
VCE Quest 12
Further Maths
VCE Quest 2ndEd
General Maths A
VCE Quest 2ndEd
Further maths
Ch19-CD Rom
transformations
Cambridge
Essential Standard
General
Mathematics 1st
Ed
Cambridge
Essential Further
Mathematics 3rd
Ed
Ch11 Coding
Ch27 Transition
matrices
Additional useful sources
1. NewQMaths 11C Ch5- harder but can be adapted
Selected Unit Resources from VCE Text: Networks
VCE Quest 11
General Maths
VCE Quest 12
Further Maths
Ch 21 (CDRom)
(some)
Ch 16 , 17
(CDRom)better
VCE Quest
2ndEd
General Maths A
These were accurate at the time of publication.
Version 2 October 2009
- 33 -
VCE Quest
2ndEd
Further maths
Cambridge
Essential Standard
General
Mathematics 1st Ed
Cambridge
Essential Further
Mathematics 3rd
Ed
Ch 14, 15
Ch 10
23,24
Board Endorsed December 07 - Amended December 2013
MA Modelling
Value 0.5
Prerequisites
Nil
This unit presents to the student realistic and applicable problems that require the use of mathematical
models and algorithms to develop the optimum solution.
Specific Unit Goals
This unit should enable students to:

describe the key features of linear graphs and their use in modelling real life situations.

recognising the shape of non linear graphs from their equations and investigating their applications
in modelling
Content
Linear modelling (12 hours)
 Sketching straight line graphs
Teaching guidelines
Use data from a range of contexts to develop the concept
of a linear relationship. Step graphs (eg taxi fares and
mobile phone charges) can also be included. Include a
discussion of dependent and independent variables and
GC sketching to emphasise features such as intercepts
and gradients and the use of domain and range in
practical situations.
Finding the gradient of a straight line given two points.
Equations of the form y = mx + b and ax +by +c = 0


Simultaneous equations
Applications of linear modelling
Linear programming (10 hours)
The optimisation process and its
components considered in a range of
contexts
 Linear inequalities
 Constraints, feasible region, corner
point
Non linear models. (8 hours)
Investigating Parabolic and Exponential
Relationships
Version 2 October 2009
given gradient and y intercept; given the gradient and
any point; given two points.
Use of GC to find solutions.
Eg Break-even, relate to the success or failure of
businesses. Use GC to find break-even point
Focus on students acquiring a working knowledge of the
linear programming process.
Students should be given experiences in interpreting a
given situation, formulating an objective function,
constructing and drawing the inequations and applying
the corner point method to the objective function.
Focus on interpreting the general shape of the graph
given the equations.
Examples may include projectile paths, cooling, of hot
water, population growth and decline, radioactive decay
- 34 -
Board Endorsed December 07 - Amended December 2013
Teaching and Learning Strategies
May include:
 discussion between teacher and students, and between students
 teacher – guided learning: modelling the use of the appropriate technology
 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
 appropriate practical work
Assessment
Refer to pages 13-15.
Student Capabilities
Evidence could be in:
Student Capabilities
Goals
Content
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

Teaching








Assessment





Specific Unit Resources
Books
See the bibliography in this document for suggested student resources.
Other
www.bsss.act.gov.au and select Resources and Publications
Selected Unit Resources from VCE Text: modelling (+ Linear programming)
VCE Quest 11
General Maths
VCE Quest 12
Further Maths
Ch 6,7 (9 12,)
VCE Quest 2ndEd
General Maths A
Ch9, 11 (7,15)
Cambridge Essential
Standard General
Mathematics 1st Ed
Ch 3,9
These were accurate at the time of publication.
Version 2 October 2009
VCE Quest
2ndEd
Further Maths
- 35 -
Cambridge
Essential Further
Mathematics 3rd
Ed
Board Endorsed December 07 - Amended December 2013
MA Matrices and Networks
Value 0.5
Prerequisites
Nil
This unit aims to have them aware of some techniques of modelling and their application to real life
situations as it applies to matrices and networks. It involves network analysis, modelling of activities and
their relationships.
Specific Unit Goals
This unit should enable students to:

analyse and solve problems using matrices to representing data

represent and analyse relationships between nodes of a network in a range of formats

apply network theory to practical situations
Content
Matrix Applications (12 hours)
 A selection of Matrix applications
Graphs and Networks (14 hours)
 Terminology and representation
(including matrix representation)
 Planar graphs

Directed Graphs and Networks
Teaching guidelines
These may include: Transformations on the plane,
Dominance Matrices, Simple Markov chains (Transition
matrices) and coding. It is not intended to teach Matrix
Arithmetic again.
Relate to maps, plans, systems and relationships.
Euler paths and circuits, Hamiltonian paths and circuits,
minimum and maximum spanning trees. Examples such
as orienteering courses, telephone networks, airline
routes, considering distance, time or cost.
Critical path analysis, project management, network flow
and assignment problems.
Use examples from construction, manufacturing and
transport industries.
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
 longer-term activities such as investigative, research and project tasks
 development of student prepared summaries/glossaries
 appropriate practical work
 sequenced investigations to scaffold learning
Version 2 October 2009
- 36 -
Board Endorsed December 07 - Amended December 2013
Assessment
Pages 13-15.
Student Capabilities
Evidence could be in:
Student Capabilities
Goals
Content
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

Teaching








Assessment





Specific Unit Resources
Books
See the bibliography in this document for suggested student resources.
Other
www.bsss.act.gov.au and select Resources and Publications
Selected Unit Resources from VCE Text: Matrix Applications
VCE Quest 11
General Maths
VCE Quest 12
Further Maths
VCE Quest 2ndEd
General Maths A
VCE Quest 2ndEd
Further maths
Ch19-CD Rom
transformations
Cambridge
Essential Standard
General
Mathematics 1st
Ed
Cambridge
Essential Further
Mathematics 3rd
Ed
Ch11 Coding
Ch27 Transition
matrices
Additional useful sources
1. NewQMaths 11C Ch5- harder but can be adapted
Selected Unit Resources from VCE Text: Networks
VCE Quest 11
General Maths
VCE Quest 12
Further Maths
Ch 21 (CDRom)
(some)
Ch 16 , 17
(CDRom)better
VCE Quest
2ndEd
General Maths A
Additional useful sources
1. New Q maths 12 ch 8,17
These were accurate at the time of publication.
Version 2 October 2009
- 37 -
VCE Quest
2ndEd
Further maths
Cambridge
Essential Standard
General
Mathematics 1st Ed
Cambridge
Essential Further
Mathematics 3rd
Ed
Ch 14, 15
Ch 10
23,24
Board Endorsed December 07 - Amended December 2013
MA Financial Modelling and Trigonometry
Value 1.0
This unit combines MA Financial Modelling 0.5 with MA Trigonometry 0.5
Prerequisites
Nil
The first half of this unit aims to build a firm understanding of the concepts underlying many financial
transactions. The many applications studied will give students a greater awareness of future financial
choices.
The second half will then introduce various strategies to extend the concepts previously learnt by students
in the first unit on mensuration. This will include applying students’ trigonometric skills and techniques to
problems involving bearings, triangulation and navigation. Students will then consider geometry relating to
the earth (contour maps and measurement around the Earth).
Specific Unit Goals
This unit should enable students to:

use arithmetic in personal finance contexts

examine the role of interest rates in the context of consumer earnings, spending and investment

investigate break-even analyses

apply an understanding of ratio and proportion to practical situations

apply geometric and trigonometric procedures in real-life contexts
Content
Teaching Guidelines
Financial Arithmetic ( 4 hours)
This should be a brief introduction only and the aim is
to focus on financial situations students could
experience now or in the future. Use a Case Study
format:
Encourage students to make informed decisions as
consumers and be aware of their entitlements.

Implications of spending



Income/Tax
Budgeting
Cost of services
Interest and Depreciation (12 hours)
 Credit cards and other “buy now, pay
later” schemes – interest calculations
 Simple and compound interest

Depreciation
Version 2 October 2009
Personal and/or family budgeting.
Use of ACT service bills and exploration of the costs
involved in specific situations, (family home, shared
housing, apartment living etc).
Focus on impact/significance of interest
Relate to students’ experiences.
Recognise simple and compound interest in different
contexts.
Explore graphically the difference in rates of growth of
simple and compound interest investments. Encourage
exploration of various options. Use technology to model
compound interest as an exponential growth function.
Students should note that depreciation of assets is a
component of both financial statement and budget
preparation for companies and is therefore an
important application of mathematics. Compare flat
rate, increasing/reducing balance and unit cost
methods
- 38 -
Board Endorsed December 07 - Amended December 2013
Content
Teaching Guidelines

Relate to the success or failure of businesses. Use GC to
find the break-even point.
Use current data from financial institutions.
Consider both mortgages and personal loans in contexts
relevant to students. Discuss the implications for
borrowers of the decisions they make.
Calculate the amount owing at any time, and the
proportion of capital to interest in any repayment.
Identify the limitation of this process.
Develop skills of
a) using the formula
b) using the formula in a spreadsheet treatment
c) using the formula and/or GC to calculate the
balance at any given time, the number of
remaining repayments on a loan and the effect
of changing the amount of repayment or their
frequency or the rate.
Break-even analysis
Reducing Balance Loans (16 hours)
 Reducing-interest loans

Loan schedules

Annuities

Comparing reducing balance and flat
rate loans
Use contexts which allow students to identify the
financial benefits of the reducing balance loan.
This is not meant to be treated in depth.
Ratio and Proportion ( 4 hours)

Similar figures including triangles

Enlargement factors
Applications of Geometry and
Trigonometry ( 20 hours)
 Review right-angled and non rightangled triangles.
 Bearings and Backbearings – specifying
location
 Triangulation
 Traverse and radial surveying
 Interpreting contour maps

Earth Geometry and Time Zones
Version 2 October 2009
Scale factors: apply to scale drawings, relate to maps
and plans in construction and design contexts.
Focus on applications of the techniques in contexts
where direct measurement is not feasible
e.g. shadow reckoning.
Applications to maps, scales, conversions, scale factors
and similar figures including area and volume contexts.
Practical experiences in areas such as Civil Engineering,
Surveying, Navigation and/or Orienteering.
Review bearings. Applications to navigation, including
non right-angled triangles.
Applying skills to calculate remote distances and angles.
Create and interpret surveyors’ notes.
Conversion of contours to profiles, and the reverse. Use
examples from orienteering, hiking and road
construction to calculate distance and slope.
Extend study of land, air and sea navigation, to include
from: shortest distances between two places on
different latitudes and longitudes, nautical miles, using
a compass, cross bearing fixes, transit fixes, running
fixes, dead reckoning, and time zones.
- 39 -
Board Endorsed December 07 - Amended December 2013
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
 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 13-15.
Student Capabilities
Evidence could be in:
Student Capabilities
Goals
Content
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

Version 2 October 2009
- 40 -
Teaching








Assessment



Board Endorsed December 07 - Amended December 2013
Specific Unit Resources
Books
See the bibliography in this document for suggested student resources.
Other
www.bsss.act.gov.au and select Resources and Publications
Great Circle Mapper: http://gc.kls2.com;
http://greenwichengland.com
Selected Unit Resources from VCE Text: Finance
VCE Quest 11
General Maths
VCE Quest 12
Further Maths
VCE Quest 2ndEd
General Maths A
ch 13,14,15
VCE Quest 2ndEd
Further maths
Cambridge
Essential Standard
General
Mathematics 1st
Ed
Ch 12,13
Cambridge
Essential Further
Mathematics 3rd
Ed
20,21
Selected Unit Resources from VCE Text: Trigonometry & Earth geometry
VCE Quest 11
General Maths
VCE Quest 12
Further Maths
VCE Quest 2ndEd
General Maths A
Ch 9(review) 10
VCE Quest 2ndEd
Further maths
Ch8(review) .9
Additional useful sources
1. Maths Quest general mathematics ch 13 spherical geometry
2. New Century Maths 12 General ch7
3. New Q Maths 11 ch 7,10
4. New Q Maths 12 ch 2
5. Cambridge General Mathematics y12 ch 14
These were accurate at the time of publication
Version 2 October 2009
- 41 -
Cambridge
Essential Standard
General
Mathematics 1st
Ed
Cambridge
Essential Further
Mathematics 3rd
Ed
Ch14
Board Endorsed December 07 - Amended December 2013
MA Financial Modelling
Value 0.5
Prerequisites
Nil
This unit aims to build a firm understanding of the concepts underlying many financial transactions. The
many applications studied will give students a greater awareness of future financial choices.
Specific Unit Goals
This unit should enable students to:

use arithmetic in personal finance contexts

examine the role of interest rates in the context of consumer earnings, spending and investment

investigate break-even analyses
Content
Teaching Guidelines
Financial Arithmetic ( 4 hours)
This should be a brief introduction only and the aim is
to focus on financial situations students could
experience now or in the future. Use a Case Study
format:
Encourage students to make informed decisions as
consumers and be aware of their entitlements.

Implications of spending



Income/Tax
Budgeting
Cost of services
Interest and Depreciation (12 hours)
 Credit cards and other “buy now, pay
later” schemes – interest calculations
 Simple and compound interest

Depreciation

Break-even analysis
Reducing Balance Loans (16 hours)
 Reducing-interest loans

Loan schedules
Version 2 October 2009
Personal and/or family budgeting.
Use of ACT service bills and exploration of the costs
involved in specific situations, (family home, shared
housing, apartment living etc).
Focus on impact/significance of interest
Relate to students’ experiences.
Recognise simple and compound interest in different
contexts.
Explore graphically the difference in rates of growth of
simple and compound interest investments. Encourage
exploration of various options. Use technology to model
compound interest as an exponential growth function.
Students should note that depreciation of assets is a
component of both financial statement and budget
preparation for companies and is therefore an
important application of mathematics. Compare flat
rate, increasing/reducing balance and unit cost
methods
Relate to the success or failure of businesses. Use GC to
find the break-even point.
Use current data from financial institutions.
Consider both mortgages and personal loans in contexts
relevant to students. Discuss the implications for
borrowers of the decisions they make.
Calculate the amount owing at any time, and the
proportion of capital to interest in any repayment.
Identify the limitation of this process.
- 42 -
Board Endorsed December 07 - Amended December 2013
Content
Teaching Guidelines

Annuities
Develop skills of
a) using the formula
b) using the formula in a spreadsheet treatment
c) using the formula and/or GC to calculate the
balance at any given time, the number of
remaining repayments on a loan and the effect
of changing the amount of repayment or their
frequency or the rate.

Comparing reducing balance and flat
rate loans
Use contexts which allow students to identify the
financial benefits of the reducing balance loan.
This is not meant to be treated in depth.
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
 development of student prepared summaries/glossaries
 use of appropriate technology to aid concept development and as a tool for problem solving
 sequenced investigations to scaffold learning
Assessment
Refer to pages 13-15.
Student Capabilities
Student Capabilities
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
Version 2 October 2009
Evidence could be in:
Goals
Content














- 43 -
Teaching








Assessment



Board Endorsed December 07 - Amended December 2013
Specific Unit Resources
Books
See the bibliography in this document for suggested student resources.
Other
www.bsss.act.gov.au and select Resources and Publications
Selected Unit Resources from VCE Text: Finance
VCE Quest 11
General Maths
VCE Quest 12
Further Maths
VCE Quest 2ndEd
General Maths A
ch 13,14,15
Ch 12,13
These were accurate at the time of publication
Version 2 October 2009
VCE Quest 2ndEd
Further maths
- 44 -
Cambridge
Essential Standard
General
Mathematics 1st
Ed
Cambridge
Essential Further
Mathematics 3rd
Ed
20,21
Board Endorsed December 07 - Amended December 2013
MA Trigonometry
Value 0.5
Prerequisites
Nil
This unit introduces various strategies to extend the concepts previously learnt by students in the first unit
on mensuration. This will include applying students’ trigonometric skills and techniques to problems
involving bearings, triangulation and navigation. Students will then consider geometry relating to the earth
(contour maps and measurement around the Earth).
Specific Unit Goals
This unit should enable students to:

apply an understanding of ratio and proportion to practical situations

apply geometric and trigonometric procedures in real-life contexts
Content
Teaching Guidelines
Ratio and Proportion ( 4 hours)

Similar figures including triangles

Enlargement factors
Applications of Geometry and
Trigonometry ( 20 hours)
 Review right-angled and non rightangled triangles.
 Bearings and Backbearings – specifying
location
 Triangulation
 Traverse and radial surveying
 Interpreting contour maps

Earth Geometry and Time Zones
Scale factors: apply to scale drawings, relate to maps
and plans in construction and design contexts.
Focus on applications of the techniques in contexts
where direct measurement is not feasible
e.g. shadow reckoning.
Applications to maps, scales, conversions, scale factors
and similar figures including area and volume contexts.
Practical experiences in areas such as Civil Engineering,
Surveying, Navigation and/or Orienteering.
Review bearings. Applications to navigation, including
non right-angled triangles.
Applying skills to calculate remote distances and angles.
Create and interpret surveyors’ notes.
Conversion of contours to profiles, and the reverse. Use
examples from orienteering, hiking and road
construction to calculate distance and slope.
Extend study of land, air and sea navigation, to include
from: shortest distances between two places on
different latitudes and longitudes, nautical miles, using
a compass, cross bearing fixes, transit fixes, running
fixes, dead reckoning, and time zones.
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
Version 2 October 2009
- 45 -
Board Endorsed December 07 - Amended December 2013
 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
 appropriate practical work.
Assessment
Refer to pages 13-15.
Student Capabilities
Evidence could be in:
Student Capabilities
Goals
Content
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

Teaching








Assessment



Specific Unit Resources
Books
See the bibliography in this document for suggested student resources.
Other
www.bsss.act.gov.au and select Resources and Publications
Great Circle Mapper: http://gc.kls2.com;
http://greenwichengland.com
Selected Unit Resources from VCE Text: Trigonometry & Earth geometry
VCE Quest 11
General Maths
VCE Quest 12
Further Maths
VCE Quest 2ndEd
General Maths A
Ch 9(review) 10
VCE Quest 2ndEd
Further maths
Ch8(review) .9
Additional useful sources
6. Maths Quest general mathematics ch 13 spherical geometry
7. New Century Maths 12 General ch7
8. New Q Maths 11 ch 7,10
9. New Q Maths 12 ch 2
10. Cambridge General Mathematics y12 ch 14
These were accurate at the time of publication
Version 2 October 2009
- 46 -
Cambridge
Essential Standard
General
Mathematics 1st
Ed
Cambridge
Essential Further
Mathematics 3rd
Ed
Ch14
Board Endorsed December 07 - Amended December 2013
MA Statistics and Probability
Value 1.0
This unit combines MA Statistics 0.5 with MA Probability 0.5.
Prerequisites
Nil
In the first half of this unit students will develop an understanding of data analysis as an important tool in
our modern society. Statistical and other numerical methods are necessary in making policy decisions in
many areas such as business, research, industry, agriculture and government. All students should be able
to critically interpret and analyse statistical claims presented to them by the media and other lobbyists.
The aims of the probability section are to enable students to use mathematics to analyse random events,
to introduce concepts that will prove useful in further studies of probability.
Specific Unit Goals
This unit should enable students to:
display and analyse data
make informed decisions about data based on a range of display and calculation techniques
analyse and interpret patterns in bivariate data from the real world using regression models
analyse and interpret trends in time series data from the real world using a range of techniques
 understand and apply concepts relating to the laws of chance
 explore ways of grouping and arranging objects
 use permutation and combination methods in calculating probabilities
Content
Teaching Guidelines
Univariate data (12 hours)
Use real data from the Australian Bureau of Statistics
and other sources.
Distinguish between categorical and numerical data;
consider how each may be analysed and their relevance
in given contexts.
Use examples which students can process to obtain a
variety of types of information
e.g. display using cumulative frequency histograms
and/or cumulative frequency polygons and identify
percentiles
Offer contexts which show the relevance or otherwise
of each measure and/or how each measure can be used
to justify an opinion or argument. Consider the
significance of outliers and their effect on the statistics.
5 figure summary on GC. Include treatment of grouped
data.
Histograms, stem and leaf plots and boxplots. Compare
two or more sets of data.
Place particular emphasis on symmetry, skewness and
outliers and what these factors tell us about the data.
Solve problems associated with standardised scores.. (A
brief explanation based on z score = (raw – mean)/sd
so students can correctly interpret their unit scores in
terms of their approximate position in the cohort.)

Categorical and numerical data

Cumulative data


Measures of central tendency and
dispersion – mean, median, mode,
range, interquartile range, standard
deviation.
Summary statistics

Displaying univariate data

Describing distributions

Normal distributions
Version 2 October 2009
- 47 -
Board Endorsed December 07 - Amended December 2013
Content
Teaching Guidelines
Bivariate data (4 hours)

Scatterplots
Correlation and regression (8 hours)
 Correlation and Causality
 Linear modelling:
 Predictions - interpolation and
extrapolation
 Regression analysis
Possible extensions include – Residual
analysis and modelling non linear data
Smoothing – Forecasting Models (8
hours)

Classifying trend patterns

Predicting from a linear trend

Smoothing

Seasonal adjustment
Probability (10 hours)
 Events, sample space and probability
of events
 Simulations


Simple and compound events:
independent events, mutually
exclusive events, overlapping events
Conditional probability
Combinatorics (8 hours)
 Permutations and factorial notation
 Combinations
Binomial Distribution (6 hours)
 Determine probabilities of given
numbers of successes
 Confidence intervals for a proportion
Version 2 October 2009
Describing relationships
Introduce q correlation coefficient as a means of
quantifying the relationship
Noting the effect of outliers
Plot and find equation of the line of best fit by eye
Discuss the reliability of the prediction.
Use of technology to find Pearsons correlation
coefficient ( r ) and the least squares regression
equation. Investigate the effect of outliers.
Determine the “quality” of the linearity and calculate
the residuals. The emphasis is on GC use
Identify whether a trend is secular, seasonal, cyclic or
random.
Construct trend lines by eye and least squares
regression.
Use to remove random or cyclic fluctuations and
present a clearer picture of the underlying trend.. ( 3point moving median/averages. Consider both odd and
even numbers of points. )
Use for deseasonalising. Calculate seasonal indices. And
the effect of this form of adjustment
Consolidate basic probability concepts with familiar
examples including cards and dice.
Use simulation to compare experimental and
theoretical probabilities.
Use technology for investigations, including web-based
simulations
Use tree diagrams and Venn diagrams to determine
outcomes.
Include with/without replacement
Calculate conditional probabilities from tree diagrams
or a reduced sample space.
Use nPr notation
Use nCr notation and link with terms in Pascal’s triangle
Use Pascal’s Triangle to determine coefficients.
Consider the sizing of samples; use political polling as an
example.
- 48 -
Board Endorsed December 07 - Amended December 2013
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
 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 13-15.
Student Capabilities
Evidence could be in:
Student Capabilities
Goals
Content
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

Version 2 October 2009
- 49 -
Teaching








Assessment




Board Endorsed December 07 - Amended December 2013
Specific Unit Resources
Books
See the bibliography in this document for suggested student resources.
Maths Quest 12A for Queensland has supplementary material on games of chance.
Other
www.bsss.act.gov.au and select Resources and Publications
Selected Unit Resources from VCE Text: Statistics
VCE Quest 11
General Maths
VCE Quest 12
Further Maths
VCE Quest 2ndEd
General Maths A
Ch 1,2,3,4,
VCE Quest 2ndEd
Further maths
Cambridge
Essential Standard
General
Mathematics 3rdt
Ed
Ch 1,2,3,4
Cambridge
Essential Further
Mathematics 3rd
Ed
1- 8
Selected Unit Resources from VCE Text: Probability
VCE Quest 11
General Maths
VCE Quest 12
Further Maths
VCE Quest 2ndEd
General Maths A
Ch 23,24
(CD Rom)
Additional useful sources
1. New Century Maths 11 ch9
2. New Century Maths 12 General ch6
3. New Q Maths 12 ch 6,9, 12
4. Cambridge General Mathematics y12 ch 4, 13
These were accurate at the time of publication.
Version 2 October 2009
- 50 -
VCE Quest 2ndEd
Further maths
Cambridge
Essential Standard
General
Mathematics 1st
Ed
Cambridge
Essential Further
Mathematics 3rd
Ed
Board Endorsed December 07 - Amended December 2013
MA Statistics
Value 0.5
Prerequisites
Nil
In this unit students will develop an understanding of data analysis as an important tool in our modern
society. Statistical and other numerical methods are necessary in making policy decisions in many areas
such as business, research, industry, agriculture and government. All students should be able to critically
interpret and analyse statistical claims presented to them by the media and other lobbyists.
Specific Unit Goals
This unit should enable students to:

display and analyse data

make informed decisions about data based on a range of display and calculation techniques

analyse and interpret patterns in bivariate data from the real world using regression models

analyse and interpret trends in time series data from the real world using a range of techniques
Content
Univariate data (12 hours)

Categorical and numerical data

Cumulative data


Measures of central tendency and
dispersion – mean, median, mode,
range, interquartile range, standard
deviation.
Summary statistics

Displaying univariate data

Describing distributions

Normal distributions
Teaching Guidelines
Use real data from the Australian Bureau of Statistics
and other sources.
Distinguish between categorical and numerical data;
consider how each may be analysed and their relevance
in given contexts.
Use examples which students can process to obtain a
variety of types of information
e.g. display using cumulative frequency histograms
and/or cumulative frequency polygons and identify
percentiles
Offer contexts which show the relevance or otherwise
of each measure and/or how each measure can be used
to justify an opinion or argument. Consider the
significance of outliers and their effect on the statistics.
5 figure summary on GC. Include treatment of grouped
data.
Histograms, stem and leaf plots and boxplots. Compare
two or more sets of data.
Place particular emphasis on symmetry, skewness and
outliers and what these factors tell us about the data.
Solve problems associated with standardised scores. (A
brief explanation based on z score = (raw – mean)/sd
so students can correctly interpret their unit scores in
terms of their approximate position in the cohort.)
Bivariate data (4 hours)

Scatterplots
Correlation and regression (8 hours)
 Correlation and Causality
 Linear modelling:
 Predictions - interpolation and
extrapolation
 Regression analysis
Version 2 October 2009
Describing relationships
Introduce q-correlation coefficient as a means of
quantifying the relationship
Noting the effect of outliers
Plot and find equation of the line of best fit by eye
Discuss the reliability of the prediction.
Use of technology to find Pearsons correlation
- 51 -
Board Endorsed December 07 - Amended December 2013
Content
Possible extensions include - Residual
analysis and modelling non linear data
Smoothing – Forecasting Models (8
hours)

Classifying trend patterns

Predicting from a linear trend

Smoothing

Seasonal adjustment
Teaching Guidelines
coefficient ( r ) and the least squares regression
equation. Investigate the effect of outliers.
Determine the “quality” of the linearity and calculate
the residuals. The emphasis is on GC use
Identify whether a trend is secular, seasonal, cyclic or
random.
Construct trend lines by eye and least squares
regression.
Use to remove random or cyclic fluctuations and
present a clearer picture of the underlying trend. ( 3point moving median/averages. Consider both odd and
even numbers of points. )
Use for deseasonalising. Calculate seasonal indices. And
the effect of this form of adjustment
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
 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/glossaries
 use of appropriate technology to aid concept development and as a tool for problem solving
 appropriate practical work
Assessment
Refer to pages 13-15.
Student Capabilities
Evidence could be in:
Student Capabilities
Goals
Content
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

Version 2 October 2009
- 52 -
Teaching








Assessment




Board Endorsed December 07 - Amended December 2013
Specific Unit Resources
Books
See the bibliography in this document for suggested student resources.
Maths Quest 12A for Queensland has supplementary material on games of chance.
Other
www.bsss.act.gov.au and select Resources and Publications
Selected Unit Resources from VCE Text: Statistics
VCE Quest 11
General Maths
VCE Quest 12
Further Maths
VCE Quest 2ndEd
General Maths A
Ch 1,2,3,4,
Ch 1,2,3,4
These were accurate at the time of publication.
Version 2 October 2009
VCE Quest 2ndEd
Further maths
- 53 -
Cambridge
Essential Standard
General
Mathematics 3rd
Ed
Cambridge
Essential Further
Mathematics 3rd
Ed
Ch 1- 8
Board Endorsed December 07 - Amended December 2013
MA Probability
Value 0.5
Prerequisites
Nil
The aims of the probability section are to enable students to use mathematics to analyse random events,
to introduce concepts that will prove useful in further studies of probability.
Specific Unit Goals
This unit should enable students to:

understand and apply concepts relating to the laws of chance

explore ways of grouping and arranging objects

use permutation and combination methods in calculating probabilities
Content
Probability (10 hours)
 Events, sample space and probability
of events
 Simulations


Simple and compound events:
independent events, mutually
exclusive events, overlapping events
Conditional probability
Combinatorics (8 hours)
 Permutations and factorial notation
 Combinations
Binomial Distribution (6 hours)
 Determine probabilities of given
numbers of successes
 Confidence intervals for a proportion
Teaching Guidelines
Consolidate basic probability concepts with familiar
examples including cards and dice.
Use simulation to compare experimental and
theoretical probabilities.
Use technology for investigations, including web-based
simulations
Use tree diagrams and Venn diagrams to determine
outcomes.
Include with/without replacement
Calculate conditional probabilities from tree diagrams
or a reduced sample space.
Use nPr notation
Use nCr notation and link with terms in Pascal’s triangle
Use Pascal’s Triangle to determine coefficients.
Consider the sizing of samples; use political polling as an
example.
Teaching and Learning Strategies
May include:

discussion between teacher and students, and between students

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

development of student prepared summaries/glossaries

use of appropriate technology to aid concept development and as a tool for problem solving

appropriate practical work
Version 2 October 2009
- 54 -
Board Endorsed December 07 - Amended December 2013

sequenced investigations to scaffold learning
Assessment
Refer to pages 13-15.
Student Capabilities
Evidence could be in:
Student Capabilities
Goals
Content
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

Teaching








Assessment




Specific Unit Resources
Books
See the bibliography in this document for suggested student resources.
Maths Quest 12A for Queensland has supplementary material on games of chance.
Other
www.bsss.act.gov.au and select Resources and Publications
Selected Unit Resources from VCE Text: Probability
VCE Quest 11
General Maths
VCE Quest 12
Further Maths
VCE Quest 2ndEd
General Maths A
Ch 23,24
(CD Rom)
Additional useful sources
1. New Century Maths 11 ch9
2. New Century Maths 12 General ch6
3. New Q Maths 12 ch 6,9, 12
4. Cambridge General Mathematics y12 ch 4, 13
These were accurate at the time of publication.
Version 2 October 2009
- 55 -
VCE Quest 2ndEd
Further maths
Cambridge
Essential Standard
General
Mathematics 1st
Ed
Cambridge
Essential Further
Mathematics 3rd
Ed
Board Endorsed December 07 - Amended December 2013
Maths for Apprenticeships
Value 0.5
It is envisaged that this unit be an optional 0.5 unit that would be offered in the last term of year 12. It
would replace the Probability unit, 0.5, for some students. It is specifically designed to prepare students for
transition into apprenticeships or vocational based course (eg CIT courses)
Prerequisites
Nil
Specific Unit Goals
This unit should allow students to:

Consolidate numeracy skills and mathematical understandings

Solve problems in context

Develop the skills and experience required in entrance tests

Acquire the mathematical skills to successfully commence an apprenticeship/vocational course
Content
These skills have been endorsed by employers and trade trainers as vital for students entering
trades/apprenticeships or vocational courses. See appendix for details.
Revision of skills acquired over their schooling is vital at this time as many entrance tests require this
knowledge to be current. Many of these tests have strict time limits that require students to perform these
skills quickly and accurately.
It is recommended that teachers embed the Proficiency Skills with regular practice across the term rather
than in a block.
Practice entrance tests for various apprenticeships and vocational courses are available (see resource list)
and the student should experience these and improve their skills throughout this unit.
:
Proficiency Skills requiring continuous revision
Without calculators
Number, Squares, Fractions, Decimals, rounding, ratio,
proportion arrow percentage
With calculators
Percentage, time, , measurement(units conversion, perimeter,
area, volume, angle) Pythagoras, scientific notation (including 1 mamp
= 10-3 amp) Trigonometry ( bearings, elevation, sine and cosine rule)
Time
7 hours
Algebra
Solving equations eg 2(3x – 1) = 7(x – 1) – 4
x/2 + 7 = (2x – 1)/3
Substitution into formula then solving eg
Find a if T = , V = a = 3TV/2 T = sqrt( 5aV + 2)
Transposing formula eg Find Q if A = M ( 2Q + 6)
S = ut^2 + 0.5t Q^2
Estimation and costing eg brick estimation (50 per m^2, pacing,
painters (hand spans)
6 hours
Version 2 October 2009
- 56 -
2 hours
Board Endorsed December 07 - Amended December 2013
Geometry
Site plans, angles, perspective drawings, building elevations (eg plan to
west elevation), creating scale drawings from measurements
Ratio/rates
Mixing amounts eg hair dyes, fertilisers, paint
3 components (a:b:c)- finding total and individual amounts eg
concrete, bread
drug dosages
portions eg hospitality
adjusting amounts eg recipes from 4 tom9 , staff/student ratios for
childcare)
Accuracy in measurements
Absolute error
% error
limits + or - ..
Mechanical reasoning
Pulleys, lifting weights, Cogs/gears
4 hours
4
2 hours
2 hours
Practice Tests
www.acer.edu.au/tests/vet
www.staltd.com.au/state_associations/sa/resources/pa_assessment
Automotive, building and constructing, electrical, engineering, hospitality, plumbing
www.ulmitb.com.au/preapprenticeshippracticetest
www.bcit.ca/tlc/pretest/samples.shtme
BCIT Practice Tests for Upgrading
http://www.bcit.ca/admission/upgrading/testoptions.shtml
www.camsin.ca/services/assessment/sample
CNC Student Success Centre
http://www.cnc.bc.ca <http://www.cnc.bc.ca/>
http://www.psychometric-success.com/
http://www.queendom.com Tests include time management, meticulousness, IQ and management style
http://www.gtaltd.com.au/state_associations/sa/resources/pa_assessment.html
Camosun College Assessment Centre
http://camosun.ca/services/assessment/sample.html
<http://www.camosun.bc.ca/assessment/tradesmathtest.php>
Electrical Industry Practice Aptitude Assessment
These assessments are intended to prepare people who may be required to sit an aptitude test as part of an interview and
assessment process for a job vacancy, such as an apprenticeship.
http://www.grouptraining.com.au/state_associations/sa/resources/pa_assessment.html
Sample on-line test
This test is designed to help you determine whether you are suited to a career in the Electrotechnology
industry.
http://www.electrotecfutures.com.au/content.cfm?section_id=4&ss_id=0
Version 2 October 2009
- 57 -
Board Endorsed December 07 - Amended December 2013
Teaching and Learning Strategies
Teachers should emphasise what workplace the skills in this unit are relevant for. See appendix 1 and 2 .
Teaching strategies may include:
 all examples/exercise must relate to trades
 revisiting skills, no calculator section
 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
Assessment
Refer to pages 13-15.
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
√
Version 2 October 2009
- 58 -
Assessment
√
√
√
Board Endorsed December 07 - Amended December 2013
Specific Unit Resources
Books
Kenman Sandra, Maths at Work Bks 1& 2 EDServe (www.edserve.com.au)2006
Vize Anne, Maths Skills for Working, Phoenix Education, 2005.
Spencer Andrew, 2009, Pre-apprenticeship series (student handbook) Nelson Cengage Learning 2008
- hospitality
- electrical
- retail
- automotive
- plumbing
- building and carpentry
Web sites
http://www.bbc.co.uk/skillswise Worksheets, quizzes and games to improve your numeracy & literacy.
http://www.bluecirclesoutherncement.com.au/Docs/Howto/PackagedProducts/HowTo_Packaged_180706
_111800.asp?AUD=bcsc_packagedproducts&site=BCSC
http://www.dest.gov.au/archive/ty/litnet/numeracy/home/nh_0000.htm
- automotive, distribution and transport
- business, financial and property services
- community services and safety
- construction, utilities and telecommunications
- food, wholesale and retail
- forests, rural and mining
- manufacturing and engineering
- tourism, sport and recreation
http://www.micron.com/k12/math/numop/index
http://www.vetassess.com.au/index.cfm?menu=1.4#link6A
Dealing with fractions
If an object is cut into smaller parts, it's useful to be able to express this mathematically. For example, cut a
pie into two equal pieces so that there are two halves. The two halves make up the whole pie. You can
write this mathematically as: + = 1. This is what fractions are.
http://tle.tafevc.com.au/toolbox/items/2d69b838-2ebc-3956-095fd85585f1be2a/1/ViewScorm.jsp?backto=close
Calculations - Perform simple algebraic expressions
Transposition of formulae is extremely useful in engineering. It sounds more complicated than it really is
because, for example, some calculations done in your head are actually transpositions. When transposing,
do the same to both sides of an equation. If you add, subtract, multiply or divide on one side of the equals
sign you must do it on the other. …
http://tle.tafevc.com.au/toolbox/items/a1e40507-8c43-7258-5ec81de7b909944d/1/ViewScorm.jsp?backto=close
Version 2 October 2009
- 59 -
Board Endorsed December 07 - Amended December 2013
Round off numbers
Numbers are rounded off when they are simplified so that they become whole numbers, or close to whole
numbers. Whether performing a calculation by hand or using a calculator, do not round off during the
calculation process. Wait until the end of the calculation and round off the answer.
http://tle.tafevc.com.au/toolbox/items/c2dc46b5-e006-dbbc-b0040af10b1cc60c/1/ViewScorm.jsp?backto=close
Perform four basic rules mathematical calculations
Understanding how to do calculations is important when measuring and marking out lengths of material
for specific jobs. Trying to reduce waste and cost is always necessary. To do any simple calculations there
are four main rules that you need to follow.
http://tle.tafevc.com.au/toolbox/items/0c7db17f-9408-7367-061f9e1cf14af365/1/ViewScorm.jsp?backto=close
Calculate length, perimeter, area and volume
Accuracy is critical because manufactured parts must fit and do exactly what they are designed to do, eg, a
piston must fit exactly into the cylinder bore for an engine to work properly. It is important that all drawing
measurements are accurate. To work out the perimeter, circumference, area and volume of the
components, a range of calculations will be …
http://tle.tafevc.com.au/toolbox/items/ee2534dd-e04d-6fac-cdc017ea863308f2/1/ViewScorm.jsp?backto=close
Algebra Equals
These exercises have been created specifically for apprentice electricians and people considering a job or
career in Electrotechnology.
http://www.nateeqsba.com/algebra/index.htm
These were accurate at the time of publication.
Version 2 October 2009
- 60 -
Board Endorsed December 07 - Amended December 2013
Modelling & Maths for Apprenticeships
Value 1.0
Prerequisites
Nil
This unit presents to the student realistic and applicable problems that require the use of mathematical
models and algorithms to develop the optimum solution.
It is envisaged that this unit be an optional 0.5 unit that would be offered in the last term of year 12. It
would replace the Probability unit, 0.5, for some students. It is specifically designed to prepare students for
transition into apprenticeships or vocational based course (eg CIT courses)
Specific Unit Goals
This unit should enable students to:

describe the key features of linear graphs and their use in modelling real life situations.

recognising the shape of non linear graphs from their equations and investigating their applications
in modelling

consolidate numeracy skills and mathematical understandings

solve problems in context

develop the skills and experience required in entrance tests

acquire the mathematical skills to successfully commence an apprenticeship/vocational course
Content
Linear modelling (12 hours)
 Sketching straight line graphs
Teaching guidelines
Use data from a range of contexts to develop the concept
of a linear relationship. Step graphs (eg taxi fares and
mobile phone charges) can also be included. Include a
discussion of dependent and independent variables and
GC sketching to emphasise features such as intercepts
and gradients and the use of domain and range in
practical situations.
Finding the gradient of a straight line given two points.
Equations of the form y = mx + b and ax +by +c = 0


Simultaneous equations
Applications of linear modelling
Linear programming (10 hours)
The optimisation process and its
components considered in a range of
contexts
 Linear inequalities
 Constraints, feasible region, corner
point
Non linear models. (8 hours)
Investigating Parabolic and Exponential
Relationships
Version 2 October 2009
given gradient and y intercept; given the gradient and
any point; given two points.
Use of GC to find solutions.
Eg Break-even, relate to the success or failure of
businesses. Use GC to find break-even point
Focus on students acquiring a working knowledge of the
linear programming process.
Students should be given experiences in interpreting a
given situation, formulating an objective function,
constructing and drawing the inequations and applying
the corner point method to the objective function.
Focus on interpreting the general shape of the graph
given the equations.
Examples may include projectile paths, cooling, of hot
water, population growth and decline, radioactive decay
- 61 -
Board Endorsed December 07 - Amended December 2013
Content
Proficiency Skills requiring continuous
revision
Without calculators
Number, Squares, Fractions, Decimals,
rounding, ratio, proportion arrow
percentage
With calculators
Percentage, time, , measurement(units
conversion, perimeter, area, volume,
angle) Pythagoras, scientific notation
(including 1 mamp = 10-3 amp)
Trigonometry ( bearings, elevation, sine
and cosine rule)
Teaching guidelines
7 hours
Algebra
Solving equations
eg 2(3x – 1) = 7(x – 1) – 4
x/2 + 7 = (2x – 1)/3
Substitution into formula then solving
eg Find a if T = , V = a = 3TV/2 T =
sqrt( 5aV + 2)
Transposing formula
eg Find Q if A = M ( 2Q + 6)
S = ut^2 + 0.5t Q^2
Estimation and costing
eg brick estimation (50 per m^2,
pacing, painters (hand spans)
Geometry
Site plans, angles, perspective drawings,
building elevations (eg plan to west
elevation), creating scale drawings from
measurements
Ratio/rates
Mixing amounts
eg hair dyes, fertilisers, paint
3 components (a:b:c)- finding total and
individual amounts
eg concrete, bread
drug dosages
portions eg hospitality
adjusting amounts
eg recipes from 4 tom9 , staff/student
ratios for childcare)
Accuracy in measurements
Absolute error
% error
limits + or - ..
Mechanical reasoning
Pulleys, lifting weights, Cogs/gears
6 hours
2 hours
4 hours
4
2 hours
2 hours
Practice Tests
www.acer.edu.au/tests/vet
www.staltd.com.au/state_associations/sa/resources/pa_assessment
Automotive, building and constructing, electrical, engineering, hospitality, plumbing
Version 2 October 2009
- 62 -
Board Endorsed December 07 - Amended December 2013
www.ulmitb.com.au/preapprenticeshippracticetest
www.bcit.ca/tlc/pretest/samples.shtme
BCIT Practice Tests for Upgrading
http://www.bcit.ca/admission/upgrading/testoptions.shtml
www.camsin.ca/services/assessment/sample
CNC Student Success Centre
http://www.cnc.bc.ca <http://www.cnc.bc.ca/>
http://www.psychometric-success.com/
http://www.queendom.com Tests include time management, meticulousness, IQ and management style
http://www.gtaltd.com.au/state_associations/sa/resources/pa_assessment.html
Camosun College Assessment Centre
http://camosun.ca/services/assessment/sample.html
<http://www.camosun.bc.ca/assessment/tradesmathtest.php>
Electrical Industry Practice Aptitude Assessment
These assessments are intended to prepare people who may be required to sit an aptitude test as part of an interview and
assessment process for a job vacancy, such as an apprenticeship.
http://www.grouptraining.com.au/state_associations/sa/resources/pa_assessment.html
Sample on-line test
This test is designed to help you determine whether you are suited to a career in the Electrotechnology
industry.
http://www.electrotecfutures.com.au/content.cfm?section_id=4&ss_id=0
Teaching and Learning Strategies
May include:
 discussion between teacher and students, and between students
 teacher – guided learning: modelling the use of the appropriate technology
 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
 appropriate practical work
 all examples/exercise must relate to trades
 revisiting skills, no calculator section
 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
Version 2 October 2009
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Board Endorsed December 07 - Amended December 2013
 longer-term activities such as investigative, research and project tasks
Assessment
Refer to pages 13-15.
Student Capabilities
Evidence could be in:
Student Capabilities
Goals
Content
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

Teaching








Assessment





Specific Unit Resources
Books
Kenman Sandra, Maths at Work Bks 1& 2 EDServe (www.edserve.com.au)2006
Spencer Andrew, 2009, Pre-apprenticeship series (student handbook) Nelson Cengage Learning 2008
- hospitality
- electrical
- retail
- automotive
- plumbing
- building and carpentry
Vize Anne, Maths Skills for Working, Phoenix Education, 2005.
See the bibliography in this document for suggested student resources.
Selected Unit Resources from VCE Text: modelling (+ Linear programming)
VCE Quest 11
General Maths
VCE Quest 12
Further Maths
Ch 6,7 (9 12,)
VCE Quest 2ndEd
General Maths A
Ch9, 11 (7,15)
VCE Quest
2ndEd
Further Maths
Cambridge Essential
Standard General
Mathematics 1st Ed
Cambridge
Essential Further
Mathematics 3rd
Ed
Ch 3,9
Web sites
http://www.bbc.co.uk/skillswise Worksheets, quizzes and games to improve your numeracy & literacy.
http://www.bluecirclesoutherncement.com.au/Docs/Howto/PackagedProducts/HowTo_Packaged_180706
_111800.asp?AUD=bcsc_packagedproducts&site=BCSC
http://www.bsss.act.gov.au and select Resources and Publications
http://www.dest.gov.au/archive/ty/litnet/numeracy/home/nh_0000.htm
- automotive, distribution and transport
- business, financial and property services
- community services and safety
- construction, utilities and telecommunications
Version 2 October 2009
- 64 -
Board Endorsed December 07 - Amended December 2013
- food, wholesale and retail
- forests, rural and mining
- manufacturing and engineering
- tourism, sport and recreation
http://www.micron.com/k12/math/numop/index
http://www.vetassess.com.au/index.cfm?menu=1.4#link6A
Dealing with fractions
If an object is cut into smaller parts, it's useful to be able to express this mathematically. For example, cut a
pie into two equal pieces so that there are two halves. The two halves make up the whole pie. You can
write this mathematically as: + = 1. This is what fractions are.
http://tle.tafevc.com.au/toolbox/items/2d69b838-2ebc-3956-095fd85585f1be2a/1/ViewScorm.jsp?backto=close
Calculations - Perform simple algebraic expressions
Transposition of formulae is extremely useful in engineering. It sounds more complicated than it really is
because, for example, some calculations done in your head are actually transpositions. When transposing,
do the same to both sides of an equation. If you add, subtract, multiply or divide on one side of the equals
sign you must do it on the other. …
http://tle.tafevc.com.au/toolbox/items/a1e40507-8c43-7258-5ec81de7b909944d/1/ViewScorm.jsp?backto=close
Round off numbers
Numbers are rounded off when they are simplified so that they become whole numbers, or close to whole
numbers. Whether performing a calculation by hand or using a calculator, do not round off during the
calculation process. Wait until the end of the calculation and round off the answer.
http://tle.tafevc.com.au/toolbox/items/c2dc46b5-e006-dbbc-b0040af10b1cc60c/1/ViewScorm.jsp?backto=close
Perform four basic rules mathematical calculations
Understanding how to do calculations is important when measuring and marking out lengths of material
for specific jobs. Trying to reduce waste and cost is always necessary. To do any simple calculations there
are four main rules that you need to follow.
http://tle.tafevc.com.au/toolbox/items/0c7db17f-9408-7367-061f9e1cf14af365/1/ViewScorm.jsp?backto=close
Calculate length, perimeter, area and volume
Accuracy is critical because manufactured parts must fit and do exactly what they are designed to do, eg, a
piston must fit exactly into the cylinder bore for an engine to work properly. It is important that all drawing
measurements are accurate. To work out the perimeter, circumference, area and volume of the
components, a range of calculations will be …
http://tle.tafevc.com.au/toolbox/items/ee2534dd-e04d-6fac-cdc017ea863308f2/1/ViewScorm.jsp?backto=close
Algebra Equals
These exercises have been created specifically for apprentice electricians and people considering a job or
career in Electrotechnology.
http://www.nateeqsba.com/algebra/index.htm
Version 2 October 2009
- 65 -
Board Endorsed December 07 - Amended December 2013
These were accurate at the time of publication.
Version 2 October 2009
- 66 -
Board Endorsed December 07 - Amended December 2013
Matrices & Networks & Maths for Apprenticeships
Value 1.0
Prerequisites
Nil
This unit aims to have them aware of some techniques of modelling and their application to real life
situations as it applies to matrices and networks. It involves network analysis, modelling of activities and
their relationships.
It is envisaged that this unit be an optional 0.5 unit that would be offered in the last term of year 12. It
would replace the Probability unit, 0.5, for some students. It is specifically designed to prepare students for
transition into apprenticeships or vocational based course (eg CIT courses)
Specific Unit Goals
This unit should enable students to:

analyse and solve problems using matrices to representing data

represent and analyse relationships between nodes of a network in a range of formats

apply network theory to practical situations

consolidate numeracy skills and mathematical understandings

solve problems in context

develop the skills and experience required in entrance tests

acquire the mathematical skills to successfully commence an apprenticeship/vocational course
Content
Matrix Applications (12 hours)
 A selection of Matrix applications
Graphs and Networks (14 hours)
 Terminology and representation
(including matrix representation)
 Planar graphs

Directed Graphs and Networks
Proficiency Skills requiring continuous
revision
Without calculators
Number, Squares, Fractions, Decimals,
rounding, ratio, proportion arrow
percentage
With calculators
Percentage, time, , measurement(units
conversion, perimeter, area, volume,
angle) Pythagoras, scientific notation
(including 1 mamp = 10-3 amp)
Version 2 October 2009
Teaching guidelines
These may include: Transformations on the plane,
Dominance Matrices, Simple Markov chains (Transition
matrices) and coding. It is not intended to teach Matrix
Arithmetic again.
Relate to maps, plans, systems and relationships.
Euler paths and circuits, Hamiltonian paths and circuits,
minimum and maximum spanning trees. Examples such
as orienteering courses, telephone networks, airline
routes, considering distance, time or cost.
Critical path analysis, project management, network flow
and assignment problems.
Use examples from construction, manufacturing and
transport industries.
7 hours
- 67 -
Board Endorsed December 07 - Amended December 2013
Content
Trigonometry ( bearings, elevation, sine
and cosine rule)
Teaching guidelines
Algebra
Solving equations eg 2(3x – 1) = 7(x – 1) –
4
x/2 + 7 = (2x – 1)/3
Substitution into formula then solving eg
Find a if T = , V = a = 3TV/2 T
= sqrt( 5aV + 2)
Transposing formula eg Find Q if A = M (
2Q + 6)
S = ut^2 +
0.5t Q^2
Estimation and costing eg brick estimation
(50 per m^2, pacing, painters (hand
spans)
Geometry
Site plans, angles, perspective drawings,
building elevations (eg plan to west
elevation), creating scale drawings from
measurements
Ratio/rates
Mixing amounts eg hair dyes, fertilisers,
paint
3 components (a:b:c)- finding total and
individual amounts eg concrete, bread
drug dosages
portions eg hospitality
adjusting amounts eg recipes from 4 tom9 ,
staff/student ratios for childcare)
Accuracy in measurements
Absolute error
% error
limits + or - ..
Mechanical reasoning
Pulleys, lifting weights, Cogs/gears
6 hours
2 hours
4 hours
4
2 hours
2 hours
These skills have been endorsed by employers and trade trainers as vital for students entering
trades/apprenticeships or vocational courses. See appendix for details.
Revision of skills acquired over their schooling is vital at this time as many entrance tests require this
knowledge to be current. Many of these tests have strict time limits that require students to perform these
skills quickly and accurately.
It is recommended that teachers embed the Proficiency Skills with regular practice across the term rather
than in a block.
Practice entrance tests for various apprenticeships and vocational courses are available (see resource list)
and the student should experience these and improve their skills throughout this unit.
Practice Tests
www.acer.edu.au/tests/vet
www.staltd.com.au/state_associations/sa/resources/pa_assessment
Version 2 October 2009
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Board Endorsed December 07 - Amended December 2013
Automotive, building and constructing, electrical, engineering, hospitality, plumbing
www.ulmitb.com.au/preapprenticeshippracticetest
www.bcit.ca/tlc/pretest/samples.shtme
BCIT Practice Tests for Upgrading
http://www.bcit.ca/admission/upgrading/testoptions.shtml
www.camsin.ca/services/assessment/sample
CNC Student Success Centre
http://www.cnc.bc.ca <http://www.cnc.bc.ca/>
http://www.psychometric-success.com/
http://www.queendom.com Tests include time management, meticulousness, IQ and management style
http://www.gtaltd.com.au/state_associations/sa/resources/pa_assessment.html
Camosun College Assessment Centre
http://camosun.ca/services/assessment/sample.html
<http://www.camosun.bc.ca/assessment/tradesmathtest.php>
Electrical Industry Practice Aptitude Assessment
These assessments are intended to prepare people who may be required to sit an aptitude test as part of an interview and
assessment process for a job vacancy, such as an apprenticeship.
http://www.grouptraining.com.au/state_associations/sa/resources/pa_assessment.html
Sample on-line test
This test is designed to help you determine whether you are suited to a career in the Electrotechnology
industry.
http://www.electrotecfutures.com.au/content.cfm?section_id=4&ss_id=0
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
 longer-term activities such as investigative, research and project tasks
 development of student prepared summaries/glossaries
 appropriate practical work
 sequenced investigations to scaffold learning
 all examples/exercise must relate to trades
 revisiting skills, no calculator section
 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
Version 2 October 2009
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Board Endorsed December 07 - Amended December 2013
 opportunities to develop modelling or problem solving skills in practical contexts
 longer-term activities such as investigative, research and project tasks
Assessment
Refer to pages 13-15.
Student Capabilities
Evidence could be in:
Student Capabilities
Goals
Content
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

Teaching








Assessment





Specific Unit Resources
Books
Kenman Sandra, Maths at Work Bks 1& 2 EDServe (www.edserve.com.au)2006
Spencer Andrew, 2009, Pre-apprenticeship series (student handbook) Nelson Cengage Learning 2008
- hospitality
- electrical
- retail
- automotive
- plumbing
- building and carpentry
Vize Anne, Maths Skills for Working, Phoenix Education, 2005.
See the bibliography in this document for suggested student resources.
Selected Unit Resources from VCE Text: Matrix Applications
VCE Quest 11
General Maths
VCE Quest 12
Further Maths
VCE Quest 2ndEd
General Maths A
VCE Quest 2ndEd
Further maths
Ch19-CD Rom
transformations
Cambridge
Essential Standard
General
Mathematics 1st
Ed
Cambridge
Essential Further
Mathematics 3rd
Ed
Ch11 Coding
Ch27 Transition
matrices
Additional useful sources
1. NewQMaths 11C Ch5- harder but can be adapted
Selected Unit Resources from VCE Text: Networks
VCE Quest 11
General Maths
VCE Quest 12
Further Maths
Ch 21 (CDRom)
(some)
Ch 16 , 17
(CDRom)better
Version 2 October 2009
VCE Quest
2ndEd
General Maths A
- 70 -
VCE Quest
2ndEd
Further maths
Cambridge
Essential Standard
General
Mathematics 1st Ed
Cambridge
Essential Further
Mathematics 3rd
Ed
Ch 14, 15
Ch 10
23,24
Board Endorsed December 07 - Amended December 2013
Additional useful sources
2. New Q maths 12 ch 8,17
Version 2 October 2009
- 71 -
Board Endorsed December 07 - Amended December 2013
Web sites
http://www.bbc.co.uk/skillswise Worksheets, quizzes and games to improve your numeracy & literacy.
http://www.bluecirclesoutherncement.com.au/Docs/Howto/PackagedProducts/HowTo_Packaged_180706
_111800.asp?AUD=bcsc_packagedproducts&site=BCSC
http://www.bsss.act.gov.au and select Resources and Publications
http://www.dest.gov.au/archive/ty/litnet/numeracy/home/nh_0000.htm
- automotive, distribution and transport
- business, financial and property services
- community services and safety
- construction, utilities and telecommunications
- food, wholesale and retail
- forests, rural and mining
- manufacturing and engineering
- tourism, sport and recreation
http://www.micron.com/k12/math/numop/index
http://www.vetassess.com.au/index.cfm?menu=1.4#link6A
Dealing with fractions
If an object is cut into smaller parts, it's useful to be able to express this mathematically. For example, cut a
pie into two equal pieces so that there are two halves. The two halves make up the whole pie. You can
write this mathematically as: + = 1. This is what fractions are.
http://tle.tafevc.com.au/toolbox/items/2d69b838-2ebc-3956-095fd85585f1be2a/1/ViewScorm.jsp?backto=close
Calculations - Perform simple algebraic expressions
Transposition of formulae is extremely useful in engineering. It sounds more complicated than it really is
because, for example, some calculations done in your head are actually transpositions. When transposing,
do the same to both sides of an equation. If you add, subtract, multiply or divide on one side of the equals
sign you must do it on the other. …
http://tle.tafevc.com.au/toolbox/items/a1e40507-8c43-7258-5ec81de7b909944d/1/ViewScorm.jsp?backto=close
Round off numbers
Numbers are rounded off when they are simplified so that they become whole numbers, or close to whole
numbers. Whether performing a calculation by hand or using a calculator, do not round off during the
calculation process. Wait until the end of the calculation and round off the answer.
http://tle.tafevc.com.au/toolbox/items/c2dc46b5-e006-dbbc-b0040af10b1cc60c/1/ViewScorm.jsp?backto=close
Perform four basic rules mathematical calculations
Understanding how to do calculations is important when measuring and marking out lengths of material
for specific jobs. Trying to reduce waste and cost is always necessary. To do any simple calculations there
are four main rules that you need to follow.
http://tle.tafevc.com.au/toolbox/items/0c7db17f-9408-7367-061f9e1cf14af365/1/ViewScorm.jsp?backto=close
Version 2 October 2009
- 72 -
Board Endorsed December 07 - Amended December 2013
Calculate length, perimeter, area and volume
Accuracy is critical because manufactured parts must fit and do exactly what they are designed to do, eg, a
piston must fit exactly into the cylinder bore for an engine to work properly. It is important that all drawing
measurements are accurate. To work out the perimeter, circumference, area and volume of the
components, a range of calculations will be …
http://tle.tafevc.com.au/toolbox/items/ee2534dd-e04d-6fac-cdc017ea863308f2/1/ViewScorm.jsp?backto=close
Algebra Equals
These exercises have been created specifically for apprentice electricians and people considering a job or
career in Electrotechnology.
http://www.nateeqsba.com/algebra/index.htm
These were accurate at the time of publication.
Version 2 October 2009
- 73 -
Board Endorsed December 07 - Amended December 2013
Appendix 1 – Industry Feedback
The following is a list of the skills that employers and training providers would like students to have:















An understanding of volume and expressing it in the correct units
Ability to do the 4 basic operations
Understanding of dimensions
Area and expressing it in the correct units
Basic algebra
The principles of trigonometry (some comments that this is done pretty well)
Need to be able to do mental arithmetic – there is not always mobile coverage on all sites
Estimation skills
Ratio
Fractions
Basic geometry – Pythagoras
Ability to put the theory into a practical context
Literacy – ability to read and comprehend the problem
It is important that they understand the principles behind maths
Need to show all calculations
The following additional skills were identified in the Electro trade:
 Formula transpositions – understanding the principles – moving things around in formulas
 Units and unit conversions (mms and metres)
 Scientific notation
 Putting numbers into formula – working out what the question is asking
 Basic physics – Ohms law
 Mechanical spatial – need practical experience
Version 2 October 2009
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Appendix 2 – Apprenticeship skills by workplace
Measuring
Reading &
following
written
instructions
Reading &
understanding
Basic addition,
subtraction & division
Skills
Hospitality
Workplace
Sport & Recreation
Workplace
Your Own
Business
Automotive
Workplace
Adding up the cost
of a bill for a
customer.
Taking money &
giving change.
Using fractions to
divide food such as
cakes or slices into
equal portions.
Using fractions as part of
games such as football,
hockey and soccer.
Adding up the cost of
running events such as
sporting carnivals by adding
staff, equipment & other
costs.
Adding up the costs of
being in business (e.g.
advertising, equipment
purchases, repairs,
debts that are not paid).
Adding up income over
a period of time &
calculating profits
made.
Adding up the bill &
additional costs for a
customer.
The steps in a
recipe.
The prices on a
menu.
Tables & graphs of sporting
results or team
performances.
Tables & charts of
money going into & out
of your business.
The steps in a
recipe accurately.
Reading
instructions to
follow workplace
procedures.
Fitness programs.
Reading and following
instructions (e.g. setting
up equipment)
The odometer of a car to
know how far it has travelled.
Dials & instruments to
diagnose faults in cars.
Using ratios, rates & simple
formulas such as kilometres
per hour.
Alternative or unfamiliar
forms of measurement such
as miles per hour.
Instruction on a job card.
Instruction in a service
manual.
Dry ingredients for
a recipe using
grams or kilograms.
Wet ingredients
using millilitres or
litres.
Measuring & recording
personal information such
as height, weight and waist
measurements.
Using formal measuring
equipment such as stop
watches, scales & tape
measures.
Heart rate using beats per
minute.
Changes in fitness or
performance for a player
over-time.
Taking measurements
(this will be dependent
on the type of business)
Using equipment such as
pressure gauges.
Page 75
Childcare Workplace
Retail
Workplace
Adding up bills for
equipment, daily supplies &
food that has been bought
by the childcare centre.
Counting & checking
equipment such as toys or
books.
Using ratios to decide how
many staff are needed for a
particular group sizes.
Playing games with children
to help them develop their
own maths skills, such as
puzzles, blocks & sorting
games.
Reading & measuring out
medication for children.
Counting coins &
notes given by a
customer.
Calculating & giving
change to a
customer.
Reading & measuring out
medication for children.
The height of the play
equipment to check it is
safe for children to use.
The dimensions of nursery
furniture to see if it suits
the relevant standards &
requirements.
Weighing children to see if
they can travel in a car seat
or booster seat.
Recognising all the
coins & notes.
Reading prices on
price tags &
receipts. Matching
written values with
actual notes &
coins.
Timesheets &
rosters.
Reading and
following written
direction about
workplace
procedures. (e.g.
using the cash
register)
Manufacturing
Workplace
Building
Adding up
measurements &
weights of various
objects & areas.
Finding & fixing
mistakes in your
own work, as well as
other peoples work.
Orders places by
customers.
Checking
information such as
names, addresses &
phone numbers.
Following written
directions on work
orders &
procedures.
Weighing &
measuring products.
Plans for houses
& buildings.
Drawing plans for
cupboards,
vanities & other
items.
On a list for
cutting board or
timber.
Regarding
measurements &
information given
on a house plan.
Height, width or
length of
cupboards,
windows or
doors.
Supplies & stock
Organising
Altering
measurements
or calculations
Calculating
Estimating &
accurately
calculating
Measurin
g&
calculatin
g
Skills
Hospitality
Workplace
Sport & Recreation
Workplace
Your Own
Business
Automotive
Workplace
Childcare Workplace
The correct quantities Using simple formulas to
for a mixed drink or
calculate (e.g. calculating
cocktail.
body mass index)
Estimating & allowing
sufficient time for
preparing & cooking a
meal.
The perimeter & area of play
spaces.
The price you will need
to charge for services
or products.
The amount of food
required & what
portions for each
customer.
Calculating individual and
team statistics associated
with different sports.(e.g.
run rate in cricket)
Making alterations to
an order made by a
customer.
Making alterations to
a recipe to increase
or decrease the
amount of food
required.
Organising a roster
to meet expected
demand.
Checking & altering the
weights on a machine for a
client doing a fitness
program in a gym.
Checking that equipment is
set up correctly (e.g. the
height of hurdles or the
length of a running track).
Managing time to meet
clients needs
Ordering food
Checking and maintaining
supplies for a kitchen. supply and stock records.
Ordering stationary and
equipment.
Reading and checking
invoices from suppliers.
Retail
Workplace
How much to charge a
customer for particular
services.
Percentages for
discounts given to
customers.
Managing time using a
calendar or diary so
that jobs are booked in
& completed in a
reasonable time
frame.
Booking services or
products from other
people.
Checking invoices or
supply statements
given to you by a
supplier.
Manufacturing
Workplace
Checking that weights The perimeter of blocks of land
& volumes are within or building sites.
a certain range.
The area of shapes such as
rooms within a house
Estimating stock
requirements.
Estimating required
float for days trading.
Using percentage to
calculate the commission
paid on a car & the
discounts given to
customers.
Understanding and using
ratios, rates and simple
formulas
Building
Fees to be paid for childcare
Entering values into a
services.
cash register or
Using ratios to decide how many
calculator accurately.
staff are needed for particular group Percentage of dollar
sizes,
values for sales or
Using ratios to decide how many
discounts.
children can come into a group with
the number of staff available
Understanding &
correcting errors
related to money
handling.
Estimating and accurately
calculating the amount of
material that will be needed for
a job (e.g. number of bricks,
length of timber).
Estimating the number of hours
or days needed to complete a
job.
The amount of hours or days
needed to complete a job.
The cost of employing other
trades to work on the job.
Changing measurements or
calculations on a plan or order.
Managing time using a
calendar or diary so that
jobs are booked in &
completed in a
reasonable time frame.
Entering information onto a
calendar.
Preparing a daily schedule of
activities
Organising a roster to Materials in a
meet expected
warehouse.
demand.
Tradespeople to work on a
building site at a suitable time.
Reading & checking
invoices from suppliers.
Paying invoices &
managing a bank
account.
Checking & maintaining
records of stock in an
automotive shop.
Checking and maintaining supply
and stock records.
(e.g. cleaning supplies)
Checking and
Packing orders.
maintaining supply Matching stock with
and stock records.
order sheets.
Reading and checking
invoices from
suppliers.
Checking invoices & supply
statements from trades &
businesses.
Page 76
Hospitality
Workplace
Sport &
Recreation
Workplace
Your Own
Business
Automotive Workplace
Childcare
Workplace
Taking down a
customer order in a
restaurant, deli or fast
food store.
Scores for games or
events.
Measuring & recording
personal information such
as height, weight & waist
measurements.
Changes in fitness levels
using appropriate
measuring tools & results.
Reading & understanding
timesheets & rosters.
Following workplace
timetables & procedures.
Checking payslip details.
Keeping track of stock or
equipment you have
bought for your business.
Keeping good records of
work you have done on a
weekly, monthly or yearly
basis.
Mathematical information
accurately & transferring numbers
from one place to another.
Details of problems found in cars.
Making records of goods or
equipment sold to customers.
Taking payments from customers
& recording the details.
Information about
children such as dates
of birth & the phone
numbers & addresses
of contact people.
Maintaining accurate
information about the
children in the centre.
Recording end of day
sales, percentages and
other various amounts
into business log books.
Accounting for time
spent on activities.
Recording supply costs
and accounting for
time spent on
activities.
Reading & understanding
timesheets & rosters.
Preparing workplace
timetables & procedures.
Preparing and checking
payslip details.
Reading & understanding
timesheets & rosters.
Following workplace timetables &
procedures.
Checking payslip details.
Following timetables
for daily & weekly
activities.
Filling in & checking
timesheets & payslip
information.
Reading & understanding
timesheets & rosters.
Checking payslip details.
Following workplace
timetables & procedures.
Reading &
understanding
timesheets & rosters.
Following workplace
timetables &
procedures.
Checking payslip details.
Reading &
understanding
timesheets & rosters.
Following workplace
timetables &
procedures.
Checking payslip
details.
Setting up equipment
Setting up equipment (e.g. for
taking measurements)
Reading
written
numbers
Reading written
numbers such as those
on a customer bill &
saying them out loud to
a customer.
Setting up equipment
accurately (e.g. the height
of hurdles or the length of
a running track).
Read written numbers
such as those on a
scoreboard or fitness plan
Reading written numbers
(e.g. profit and loss
statements)
Reading written number such as
those needed to order parts or on
a customer bill and saying them
out loud.
Reading numbers on
price tags and receipts.
Matching written values
with actual notes and
coins.
Picking orders according
to written information.
Numbers written on
plans
Compari
ng
Using fractions to divide
food such as cakes or
slices into equal
portions
Scores for individuals or
teams.
Performances between
players or teams.
Comparing income and
workloads over time.
Playing games with
children to help them
develop their own
maths skills, such as
puzzles, blocks &
sorting games.
Using ratios to decide
how many staff are
needed for particular
group sizes.
Filling out forms to
order food and supplies
Filling out forms to record
results (e.g. progress
through a fitness program
or game score sheets)
Filing out forms for the
tax office or bank.
Writing out invoices for customers.
Filling out forms.
Reading and filling out
forms to comply with
building approval
procedures
Reading graphs and
table to follow
workplace procedures
Reading, creating &
interpreting graphs &
tables of team or players
performances.
Making graphs of profits,
income, expenses or work
completed.
Reading graphs and table to follow
workplace procedures
Timetables &
procedures
The time or
temperature on an
oven.
Graphs
&
tables
Forms
Reading &
understanding
timesheets & rosters.
Following workplace
timetables &
procedures.
Checking payslip details.
Settin
g
Recording
Skills
Page 77
Filling in forms to
maintain accurate
records and children
in the childcare
centre
Retail Workplace Manufacturing
Workplace
Prices & using phrases
such as greater than, less
than & equal to in
relation to prices &
values.
Filling out inventories &
forms related to stock
numbers.
Filling out forms about
the value of stock in a
store.
Reading graphs & tables
relating to sales of items
& values of items sold in
a retail store.
Creating graphs &
tables of data.
Reading graphs &
tables.
Building
Appendix 3 – Trade requirements
x
x
x
x
x
x
x
x
x
x
x
x
x
xxx
x
x
x
x
x
xx
x
xx
x
x
x
x
xx
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
Page 78
No of grps
x
x
x
x
x
EectroGrp
xx
?
x
x
xx
GTA Auto
x
x
GTA chippie
GTA Chef
GTA Plumb
x
x
GTA Engin
x
x
x
GTA Elect
Sample
EnergAust
alg (x-2)(3x-3)
alg subst formula
algebra - transpose
area circles
area idea
area rect
area triangle
average + halfway
best buy
BODMAS
cogs & gears
comp areas
cost of 'n' things
decimal 4 ops
decimal div (by .5)
equn 2 step
est meas.
estimate answer
estimate meas
fraction between
fraction division
fraction multiply
fractions +, fractions simplify
geom angle props
graph conversion
1
2
4
4
1
3
3
5
2
3
3
2
2
4
2
1
1
2
4
1
1
1
5
5
3
1
indices
x
integers 4 ops
invoices
meas accuracy
Ordering
p% - what %
p% discounts
p% inc/decr
p% of
p% profit
p%,D,F
patterns
perimeter
perimeter compound
prob solving
pythagoras
rates
ratio
Rounding
salary to wkly etc
Scientific notation
shapes
speed calc
sq & sq rt
time diff
totals dec money
unitary meth
units convert
units correct
units reln L, cu m
volume calc
volume idea
wages
wages overtime
words -> nos.
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
xx
x
x
x
x
x
xx
x
x
x
x
x
x
x
x
x
x
x
x
xxxxxx
x
x
xx
xxxx
x
x
x
xx
x
x
x
x
x
xxx
x
x
xxxx
x
x
x
x
x
x
x
x
xx
x
x
x
x
x
x
x
x
x
x
xx
x
x
x
x
x
x
x
x
xxx
x
x
x
x
x
x
x
x
x
x
x
x
x
x
Page 79
1
2
2
2
5
2
3
5
5
3
4
1
1
2
7
1
4
5
4
2
3
2
5
2
1
6
4
4
3
1
2
1
4
1
3
Spelling
x
Comprehension
x
Alphbetical
x
Gen Knowledge
Spatial Reasoning
MechanicalReasoning
EnOz
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
Sam
ple
GTAEl
ec
GTAEn
g
Plumb
Chef
chip
Auto
Page 80
ElGrp
No
Appendix 4 - Selected Unit Resources
Selected Unit Resources from VCE Text: Matrices
VCE Quest 11
General Maths
VCE Quest 12
Further Maths
Ch19 (CDRom)
VCE Quest 2ndEd
General Maths A
VCE Quest 2ndEd
Further Maths
Cambridge
Essential Standard
General
Mathematics 1st Ed
Cambridge
Essential Further
Mathematics 3rd
Ed
Ch1 Ch3
Ch16
Ch 11
Ch 26,27
Selected Unit Resources from VCE Text: Sequences & Series
VCE Quest 11
General Maths
VCE Quest 12
Further Maths
VCE Quest 2ndEd
General Maths A
VCE Quest 2ndEd
Further Maths
Cambridge Essential
Standard General
Mathematics 1st Ed
Cambridge
Essential Further
Mathematics 3rd
Ed
Ch 5 : challenging
Ch 6: suitable
Ch 3: challenging
Ch 5 suitable
Ch 8
Ch9
Cambridge Essential
Standard General
Mathematics 1st Ed
Cambridge
Essential Further
Mathematics 3rd
Ed
Selected Unit Resources from VCE Text: Mensuration
VCE Quest 11
General Maths
VCE Quest 12
Further Maths
Ch 11
VCE Quest 2ndEd
General Maths A
VCE Quest 2ndEd
Further Maths
Ch13
Ch 5
Selected Unit Resources from VCE Text: Trigonometry
VCE Quest 11
General Maths
VCE Quest 12
Further Maths
Ch 15
VCE Quest 2ndEd
General Maths A
VCE Quest 2ndEd
Further Maths
Ch 16
(not radians)
Cambridge Essential
Standard General
Mathematics 1st Ed
Cambridge
Essential Further
Mathematics 3rd
Ed
Ch 7
Selected Unit Resources from VCE Text: Linear modelling (+ Linear programming)
VCE Quest 11
General Maths
VCE Quest 12
Further Maths
Ch 6,7 (9 12,)
VCE Quest 2ndEd
General Maths A
VCE Quest 2ndEd
Further Maths
Ch9, 11 (7,15)
Cambridge Essential
Standard General
Mathematics 1st Ed
Cambridge
Essential Further
Mathematics 3rd
Ed
Ch 3,9
Selected Unit Resources from VCE Text: Networks
VCE Quest 11
General Maths
VCE Quest 12
Further Maths
VCE Quest 2ndEd
General Maths A
Ch 21 (CDRom)
Ch 16 , 17
(some)
(CDRom)better
Additional useful sources
1. New Q Maths 12 ch 8,17
Page 81
VCE Quest 2ndEd
Further maths
Cambridge Essential
Standard General
Mathematics 1st Ed
Cambridge
Essential Further
Mathematics 3rd
Ed
Ch 14, 15
Ch 10
23,24
Selected Unit Resources from VCE Text: Finance
VCE Quest 11
General Maths
VCE Quest 12
Further Maths
VCE Quest 2ndEd
General Maths A
ch 13,14,15
VCE Quest 2ndEd
Further maths
Cambridge Essential
Standard General
Mathematics 1st Ed
Ch 12,13
Cambridge Essential
Further
Mathematics 3rd Ed
20,21
Selected Unit Resources from VCE Text: Trigonometry & Earth geometry
VCE Quest 11
General Maths
VCE Quest 12
Further Maths
VCE Quest 2ndEd
General Maths A
Ch 9(review) 10
VCE Quest 2ndEd
Further maths
Cambridge Essential
Standard General
Mathematics 1st Ed
Ch8(review) .9
Cambridge Essential
Further
Mathematics 3rd Ed
Ch14
Additional useful sources
11. Maths Quest general mathematics ch 13 spherical geometry
12. New Century Maths 12 General ch7
13. New Q Maths 11 ch 7,10
14. New Q Maths 12 ch 2
15. Cambridge General Mathematics y12 ch 14
Selected Unit Resources from VCE Text: Statistics
VCE Quest 11
General Maths
VCE Quest 12
Further Maths
VCE Quest 2ndEd
General Maths A
Ch 1,2,3,4,
VCE Quest 2ndEd
Further maths
Cambridge Essential
Standard General
Mathematics 3rdt
Ed
Ch 1,2,3,4
Cambridge Essential
Further
Mathematics 3rd Ed
1- 8
Selected Unit Resources from VCE Text: Probability
VCE Quest 11
General Maths
VCE Quest 12
Further Maths
VCE Quest 2ndEd
General Maths A
VCE Quest 2ndEd
Further maths
Ch 23,24
(CD Rom)
Additional useful sources
1. New Century Maths 11 ch9
2. New Century Maths 12 General ch6
3. New Q Maths 12 ch 6,9, 12
4. Cambridge General Mathematics y12 ch 4, 13
Page 82
Cambridge Essential
Standard General
Mathematics 1st Ed
Cambridge Essential
Further
Mathematics 3rd Ed
Board Endorsed December 07 - Amended December 2013
Reasoning and Communication
Concepts and Techniques
Appendix 5 - Australian Curriculum Achievement Standards for General Mathematics (T)
Units 1 and 2
A student who achieves an A grade
typically
A student who achieves a B grade
typically
A student who achieves a C grade
typically
 demonstrates knowledge of
A student who achieves a D
grade typically
 demonstrates knowledge of
 demonstrates knowledge of concepts of
 demonstrates knowledge of concepts
consumer arithmetic, algebra and matrices,
linear equations, geometry and trigonometry,
and statistics, in routine and non-routine
problems in a variety of contexts
of consumer arithmetic, algebra and
matrices, linear equations, geometry and
trigonometry, and statistics, in routine
and non-routine problems
 selects and applies techniques in
 selects and applies techniques in
mathematics and statistics to solve routine
and non-routine problems in a variety of
contexts
 develops, selects and applies mathematical
and statistical models to solve routine and
non-routine problems in a variety of contexts
mathematics and statistics to solve
routine and non-routine problems
concepts of consumer arithmetic,
algebra and matrices, linear
equations, geometry and
trigonometry, and statistics, that
apply to routine problems
 selects and applies techniques in
mathematics and statistics to solve
routine problems
concepts of consumer
arithmetic, algebra and
matrices, linear equations,
geometry and trigonometry,
and statistics
 uses simple techniques in
mathematics and statistics in
routine problems
familiarity with simple concepts
of consumer arithmetic, algebra
and matrices, linear equations,
geometry and trigonometry, and
statistics
 uses simple techniques in a
structured context
 selects and applies mathematical and
 applies mathematical and
 demonstrates familiarity with
 demonstrates limited
statistical models to routine and nonroutine problems
statistical models to routine
problems
mathematical and statistical
models
familiarity with mathematical or
statistical models
 uses digital technologies effectively to
 uses digital technologies appropriately
 uses digital technologies to graph,
 uses digital technologies to
 uses digital technologies for
graph, display and organise mathematical
and statistical information to solve a range of
routine and non-routine problems in a variety
of contexts
 represents mathematical and statistical
information in numerical, graphical and
symbolic form in routine and non-routine
problems in a variety of contexts
to graph, display and organise
mathematical and statistical information
to solve a range of routine and nonroutine problems
 represents mathematical and
statistical information in numerical,
graphical and symbolic form in routine
and non-routine problems
display and organise mathematical
and statistical information to solve
routine problems
display some mathematical and
statistical information in
routine problems
arithmetic calculations and to
display limited mathematical and
statistical information
 represents mathematical and
 represents simple
 represents simple
statistical information in numerical,
graphical and symbolic form in
routine problems
mathematical or statistical
information in a structured
context
 communicates mathematical and statistical
 communicates mathematical and
 communicates mathematical and
judgments and arguments which are succinct
and reasoned using appropriate language
statistical arguments using
appropriate language
routine problems in a variety of contexts
statistical judgments and arguments
which are clear and reasoned using
appropriate language
 interprets the solutions to routine and
non-routine problems
problems
mathematical and statistical
information in numerical,
graphical or symbolic form in
routine problems
 communicates simple
mathematical and statistical
information using appropriate
language
 describes solutions to routine
problems
 explains the reasonableness of the results
 explains the reasonableness of results
 describes the reasonableness of
 describes the
 demonstrates limited
and solutions to routine and non-routine
problems in a variety of contexts
and solutions to routine and non-routine
problems
results and solutions to routine
problems
appropriateness of the results
of calculations
 identifies and explains the validity and
 identifies and explains limitations of
 identifies limitations of models
 identifies limitations of
familiarity with the
appropriateness of the results of
calculations
 identifies simple models
limitations of models used when developing
solutions to routine and non-routine
problems
models used when developing solutions
to routine problems
used when developing solutions to
routine problems
simple models
 interprets the solutions to routine and non-
 interprets the solutions to routine
Page 83
A student who achieves an E
grade typically
 demonstrates limited
 communicates simple
mathematical or statistical
information
 identifies solutions to routine
problems
Board Endorsed December 07 - Amended December 2013
Australian Curriculum Achievement Standards for General Mathematics (T) for Units 3 and 4
Reasoning and Communication
Concepts and Techniques
A student who achieves an A grade
typically
 demonstrates knowledge of concepts of
A student who achieves a B grade
typically
 demonstrates knowledge of
statistics, growth and decay in sequences,
graphs and networks, and financial
mathematics in routine and non-routine
problems in a variety of contexts
concepts of statistics, growth and
decay in sequences, graphs and
networks, and financial mathematics in
routine and non-routine problems
 selects and applies techniques in
 selects and applies techniques in
mathematics and statistics to solve routine
and non-routine problems in a variety of
contexts
 develops, selects and applies
mathematical and statistical models to
routine and non-routine problems in a
variety of contexts
 uses digital technologies effectively to
graph, display and organise mathematical
and statistical information to solve a range of
routine and non-routine problems in a
variety of contexts
 represents mathematical and statistical
information in numerical, graphical and
symbolic form in routine and non-routine
problems in a variety of contexts
A student who achieves a C
grade typically
A student who achieves a D
grade typically
 demonstrates knowledge of
 demonstrates knowledge of
concepts of statistics, growth
and decay in sequences, graphs
and networks, and financial
mathematics
mathematics and statistics to solve
routine and non-routine problems
concepts of statistics, growth and
decay in sequences, graphs and
networks, and financial
mathematics that apply to routine
problems
 selects and applies techniques in
mathematics and statistics to solve
routine problems
 selects and applies mathematical
 applies mathematical and
 demonstrates familiarity with
and statistical models to routine and
non-routine problems
statistical models to routine
problems
mathematical and statistical
models
 uses digital technologies
 uses digital technologies to
 uses digital technologies to
appropriately to graph, display and
organise mathematical and statistical
information to solve a range of routine
and non-routine problems
 represents mathematical and
statistical information in numerical,
graphical and symbolic form in routine
and non-routine problems
graph, display and organise
mathematical and statistical
information to solve routine
problems
 represents mathematical and
statistical information in numerical,
graphical and symbolic form in
routine problems
display some mathematical and
statistical information in routine
problems
 communicates mathematical and
 communicates mathematical and
 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
statistical judgments and arguments
which are clear and reasoned using
appropriate language
 interprets the solutions to routine
and non-routine problems
statistical arguments using
appropriate language
 explains the reasonableness of the results
and solutions to routine and non-routine
problems in a variety of contexts
 uses simple techniques in
mathematics and statistics in
routine problems
A student who achieves an E
grade typically
 demonstrates limited
familiarity with simple concepts
of statistics, growth and decay in
sequences, graphs and
networks, and financial
mathematics
 uses simple techniques in a
structured context
 demonstrates limited
familiarity with mathematical or
statistical models
 uses digital technologies for
arithmetic calculations and to
display limited mathematical and
statistical information
 represents simple
 represents simple
mathematical or statistical
information in a structured
context
routine problems
mathematical and statistical
information in numerical,
graphical or symbolic form in
routine problems
 communicates simple
mathematical and statistical
information using appropriate
language
 describes solutions to routine
problems
 explains the reasonableness of the
 describes the reasonableness of
 describes the appropriateness
 demonstrates limited
results and solutions to routine and
non-routine problems
the results and solutions to routine
problems
of the results of calculations
 identifies and explains the validity and
 identifies and explains limitations of
 identifies limitations of models
 identifies limitations of simple
familiarity with the
appropriateness of the results of
calculations
 identifies simple models
limitations of models used when developing
solutions to routine and non-routine
problems
models used when developing
solutions to routine problems
used when developing solutions to
routine problems
models
 interprets the solutions to
Page 84
 communicates simple
mathematical or statistical
information
 identifies solutions to routine
problems
Board Endorsed December 07 - Amended December 2013
Page 85