STAGE 2 MATHEMATICS PATHWAYS
FOLIO TASK
Critical path analysis
Topic:
Optimisation
Subtopics from the Stage 2 Mathematical Applications Subject Outline:
5.1 – Network Problems
A completed investigation should include:
 an introduction that outlines the problem to be explored, including it significance, its features,
and the context
 the method required to find a solution, in terms of the mathematical model or strategy to be
used
 the appropriate application of the mathematical model or strategy, including
- the generation or collection of relevant data and/or information, with details of the process
of collection
- mathematical calculations and results, and appropriate representations
- the analysis and interpretation of results
- reference to the limitations of the original problem
 a statement of the results and conclusions in the context of the original problem
 appendices and a bibliography, as appropriate.
Learning Requirements
1.
2.
3.
4.
5.
6.
Assessment Design Criteria
Capabilities
Demonstrate an understanding
of mathematical concepts and
relationships.
Mathematical Knowledge and Skills and Their
Application
Communication
Identify, collect, and organise
mathematical information
relevant to investigating and
finding solutions to
questions/problems.

MKSA1 Knowledge of content and understanding
of mathematical concepts and relationships.

MKSA2 Use of mathematical algorithms and
techniques (implemented electronically where
appropriate) to find solutions to routine and
complex questions.
Recognise and apply the
mathematical techniques
needed when analysing and
finding a solution to a
question/problem in context.
Make informed use of
electronic technology to aid
and enhance understanding.
Interpret results, draw
conclusions, and reflect on the
reasonableness of these in the
context of the
question/problem.
Communicate mathematical
ideas and reasoning using
appropriate language and
representations.
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The specific features are as follows:

Citizenship
Personal
Development
Work
Learning
MKSA3 Application of knowledge and skills to
answer questions in applied contexts.
Mathematical Modelling and Problem-solving
The specific features are as follows:

MMP1 Application of mathematical models.

MMP2 Development of mathematical results for
problems set in applied contexts.

MMP3 Interpretation of the mathematical results in
the context of the problem.

MMP4 Understanding of the reasonableness and
possible limitations of the interpreted results, and
recognition of assumptions made..
Communication of Mathematical Information
The specific features are as follows:

CMI1 Communication of mathematical ideas and
reasoning to develop logical arguments.

CMI2 Use of appropriate mathematical notation,
representations, and terminology.
Stage 2 Mathematics Pathways Optimisation task
Ref: A203779 (revised February 2016)
© SACE Board of South Australia 2010
PERFORMANCE STANDARDS FOR STAGE 2 MATHEMATICS PATHWAYS
Mathematical Knowledge and
Skills and Their Application
A
Comprehensive knowledge of
content and understanding of
concepts and relationships.
Appropriate selection and use of
mathematical algorithms and
techniques (implemented
electronically where appropriate) to
find efficient solutions to complex
questions.
Highly effective and accurate
application of knowledge and skills
to answer questions set in applied
contexts.
B
Some depth of knowledge of
content and understanding of
concepts and relationships.
Use of mathematical algorithms
and techniques (implemented
electronically where appropriate) to
find some correct solutions to
complex questions.
Accurate application of knowledge
and skills to answer questions set
in applied contexts.
C
Generally competent knowledge of
content and understanding of
concepts and relationships.
Use of mathematical algorithms
and techniques (implemented
electronically where appropriate) to
find mostly correct solutions to
routine questions.
Generally accurate application of
knowledge and skills to answer
questions set in applied contexts.
D
Basic knowledge of content and
some understanding of concepts
and relationships.
Some use of mathematical
algorithms and techniques
(implemented electronically where
appropriate) to find some correct
solutions to routine questions.
Sometimes accurate application of
knowledge and skills to answer
questions set in applied contexts.
E
Limited knowledge of content.
Attempted use of mathematical
algorithms and techniques
(implemented electronically where
appropriate) to find limited correct
solutions to routine questions.
Attempted application of knowledge
and skills to answer questions set
in applied contexts, with limited
effectiveness.
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Mathematical Modelling and Problemsolving
Development and effective application of
mathematical models.
Complete, concise, and accurate solutions to
mathematical problems set in applied contexts.
Concise interpretation of the mathematical results
in the context of the problem.
Communication of
Mathematical Information
Highly effective communication of
mathematical ideas and reasoning
to develop logical arguments.
Proficient and accurate use of
appropriate notation,
representations, and terminology.
In-depth understanding of the reasonableness and
possible limitations of the interpreted results, and
recognition of assumptions made.
Attempted development and appropriate application
of mathematical models.
Mostly accurate and complete solutions to
mathematical problems set in applied contexts.
Complete interpretation of the mathematical results
in the context of the problem.
Effective communication of
mathematical ideas and reasoning
to develop mostly logical
arguments.
Mostly accurate use of
appropriate notation,
representations, and terminology.
Some depth of understanding of the
reasonableness and possible limitations of the
interpreted results, and recognition of assumptions
made.
Appropriate application of mathematical models.
Some accurate and generally complete solutions to
mathematical problems set in applied contexts.
Generally appropriate interpretation of the
mathematical results in the context of the problem.
Some understanding of the reasonableness and
possible limitations of the interpreted results, and
some recognition of assumptions made.
Application of a mathematical model, with partial
effectiveness.
Partly accurate and generally incomplete solutions
to mathematical problems set in applied contexts.
Attempted interpretation of the mathematical results
in the context of the problem.
Appropriate communication of
mathematical ideas and reasoning
to develop some logical
arguments.
Use of generally appropriate
notation, representations, and
terminology, with some
inaccuracies.
Some appropriate communication
of mathematical ideas and
reasoning.
Some attempt to use appropriate
notation, representations, and
terminology, with occasional
accuracy.
Some awareness of the reasonableness and
possible limitations of the interpreted results.
Attempted application of a basic mathematical
model.
Limited accuracy in solutions to one or more
mathematical problems set in applied contexts.
Limited attempt at interpretation of the
mathematical results in the context of the problem.
Attempted communication of
emerging mathematical ideas and
reasoning.
Limited attempt to use appropriate
notation, representations, or
terminology, and with limited
accuracy.
Limited awareness of the reasonableness and
possible limitations of the results.
Stage 2 Mathematics Pathways Optimisation task
Ref: A203779 (revised February 2016)
© SACE Board of South Australia 2010
STAGE 2 MATHEMATICS PATHWAYS
FOLIO TASK
Critical path analysis
Introduction
Select a task with which you are familiar. The task must be one in which several activities can be
done simultaneously and it must be reasonably complex.
Mathematical Investigations
1. Identify all the individual activities involved. Give a brief description of each.
2. Indicate a time for each of the activities. Explain how you arrived at the times listed.
3. State the precedences for each activity. Explain how you arrived at the times listed.
4. Construct a network diagram to represent the above information.
5. Find the minimum completion time for the task.
6. Find the critical path for the task and list those activities that make up the path.
7. Calculate the earliest and latest starting times for each activity.
8. Decide on some reasonable changes to the model used that would reduce the completion time,
and investigate the effect of these changes on the completion time and/or the critical path.
Redo any of the above steps that are relevant to your changes.
Analysis/ Conclusion
Critically analyse your results, considering:





a comparison of the different scenarios investigated
what is the optimal solution
the reasonableness of the optimal solution
the best scenario for the efficient completion of the task
the limitations of the model used.
Notes to teacher:
1. The selection of activities that students choose to investigate in this task should be discussed
with the teacher to enable achievement to the highest level of the performance standards.
2. Students may select an activity that is part of the context being studied, e.g. if an arts or leisure
context has been studied, they may consider tasks such as setting up the stage for a rock
band, planning a camping weekend away, or the preparations necessary for a ballet dress
rehearsal. If they are studying a trade theme they may consider the construction of an
appropriate object. If studying a tourism/hospitality context, they may consider the organisation
of a year 12 formal or a pizza-making situation with more than one person involved in the
process.
3. Teachers may consider adding visual aids to the task to assist students who need support in
accessing the requirements of the task.
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Stage 2 Mathematics Pathways Optimisation task
Ref: A203779 (revised February 2016)
© SACE Board of South Australia 2010