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VCE Algorithmics (HESS) Administrative information for School-based Assessment in 2021

School-assessed TaskThe School-assessed Task (SAT) contributes 40 per cent to the study score.

Teachers will provide to the Victorian Curriculum and Assessment Authority (VCAA) a score against each criterion that represents an assessment of the student’s level of performance for Unit 3 Outcomes 1, 2 and 3 and Unit 4 Outcomes 1, 2 and 3. The recorded scores must be based on the teacher’s assessment of the student’s performance according to the criteria on pages 9–22. This assessment is subject to the VCAA’s statistical moderation process.

The 2021 VCE Algorithmics (HESS) assessment sheet on pages 26 and 27 is to be used by teachers to record the Unit 3 and Unit 4 SAT scores. The completed assessment sheet for each student’s SAT must be available on request by the VCAA.

The mandated assessment criteria are published annually on the Algorithmics study page of the VCAA website and notification of their publication is given in the February VCAA Bulletin.

Details of authentication requirements and administrative arrangements for School Assessed Tasks are published annually in the VCE and VCAL Administrative Handbook 2021.

The Authentication record form on pages 24–25 is to be used to record information for each student and must be made available on request by the VCAA.

The SAT for Unit 3 relates to:

Outcome 1 Outcome 2 Outcome 3.

The SAT for Unit 4 relates to:

Outcome 1 Outcome 2 Outcome 3.

Teachers should be aware of the dates for submission of scores into VASS in June and November. These dates are published in the 2021 Important Administrative Dates and Assessment Schedule, published annually on the VCAA website. vcaa.vic.edu.au/pages/schooladmin/admindates/index.aspx

© VCAA

http://www.vcaa.vic.edu.au/pages/schooladmin/admindates/index.aspx

https://www.vcaa.vic.edu.au/administration/vce-vcal-handbook/Pages/index.aspx


Unit 3

Data modelling with abstract data types

Outcome 1On completion of this unit the student should be able to devise formal representations for modelling various kinds of information problems using appropriate abstract data types, and apply these to a real-world problem.

Nature of tasks a folio of two to four tasks using a range of abstract data types (ADTs) to model the salient aspects of

problems a written explanation of the specification and application of ADTs (approximately 45−60 minutes) a data model of a real-world problem, including:

specification of the data model a concrete instance of the data model (worked example).

Scope of tasks

Folio

Teachers must provide students with a range of small tasks that require them to use a variety of ADTs to model aspects of problems. These tasks should not be onerous, but rather form part of the teaching and learning program, while still subject to authentication conditions. The folio will typically comprise incremental pieces of work, reflecting the student’s learning progression through the levels. It is recommended that students submit four pieces of work and the teacher selects the best two or more pieces for assessment. The folio pieces should allow students to provide evidence for statements at all levels of performance through criterion 2.

Written explanation

Teachers must provide students with a task that allows them to explain in writing the specifications and applications of standard ADTs. This would be done under test conditions within a timeframe of 45 to 60 minutes. It is recommended that the task include a mixture of question types that allows the students to provide evidence for statements at all levels of performance. The evidence from this task is assessed through criterion 1.

Data model

Students devise specific-task definitions based on a real-world problem in order to create a data model. Teachers can provide generic real-world problems, but each student must model, using mainly the graph ADT, a specific or concrete instance of that problem. Teachers can better authenticate student work when there are individual instances of a generic problem. Teachers should approve each student’s proposal before they model the problem as a worked example. The performance descriptors at the highest level for criterion 2 should be used to help make this decision. Note: this data model will form the basis of a task in Outcome 2.

The evidence related to the quality of the data model is assessed through criterion 2.

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Algorithm design

Outcome 2On completion of this unit the student should be able to design algorithms to solve information problems using basic algorithm design patterns, and implement the algorithms.

Nature of task a folio of two to four tasks using a range of algorithm design patterns to specify algorithms to solve

problems a written explanation of the specification and application of algorithms for graphs (approximately 45−60

minutes) an algorithm to solve a real-world problem that builds on an existing data model including:

pseudocode to solve the problem implementation of the algorithms in a high-level programming language making appropriate use of

standard ADTs.

Scope of task

Folio

Teachers must provide students with a range of small tasks that require them to use a variety of standard algorithms for graphs to solve problems. These tasks should not be onerous, but rather form part of the teaching and learning program, while still subject to authentication conditions. The folio will typically comprise incremental pieces of work, reflecting the student’s learning progression through the levels. It is recommended that students submit four pieces of work and the teacher select the best two or more pieces for assessment. The folio pieces should allow students to provide evidence for statements at all levels of performance through criterion 4.

Written explanation

Teachers must provide students with a task that allows them to explain in writing the specification and application of algorithms for graphs. This would be done under test conditions within a timeframe of 45 to 60 minutes. It is recommended that the task include a mixture of question types that allows the students to provide evidence for statements at all levels of performance. The evidence from this task is assessed through criterion 3.

Solution to a real-world problem

Students build on the data model they developed in Outcome 1 and create a solution by developing an algorithm and implementing it using a high-level programming language. In some circumstances it may be appropriate for the teacher to provide students with a data model, rather than the student using their own. If the student-generated data model is incomplete or contains significant errors, and this would prevent the demonstration of the highest level of achievement on the relevant criteria, then the student could use a provided model. Teachers could either modify the student-generated model or provide a new one.

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When assessing performance with the programming language, it is important that students are judged on their conceptual use of the language rather than their mastery of the language or its libraries. The programming language requirements are published on the Algorithmics study page 2021 Programming language requirements.

The evidence related to the quality of the algorithm is assessed through criterion 4.

Applied algorithms

Outcome 3On completion of this unit the student should be able to evaluate and document algorithms and data representations, and solve a real-world problem, the solution for which requires the integration of algorithms and data types.

Nature of tasks an evaluation of an existing data model and algorithm in the form of a written report (approximately 300–

500 words) documentation that communicates the:

data model development approach (approximately 300–500 words) algorithm development approach (approximately 300–500 words).

Scope of task

Evaluation

Students must evaluate a variety of algorithms and ADTs when determining a suitable combination to solve their real-world problem. Their evaluation involves measuring the extent to which different combinations of algorithms and data models are best fit for purpose. The basis for evaluation includes selection of salient features of the problem, the modular representation of data using ADTs and the quality of the result generated by the algorithms. The word range for this evaluation is 300 to 500 words. The evidence from this task is assessed through criterion 5.

Documentation

Students must document the development of their data model and algorithm. The documentation should include:

a statement of the problem a systematic description of the methods used to develop the data model and algorithm identification of alternative solutions that were considered presentation of results, including a solution to the problem.

The evidence from this task is assessed through criterion 6. Students should be encouraged to use appropriate metalanguage in their documentation.

© VCAA

https://www.vcaa.vic.edu.au/curriculum/vce/vce-study-designs/algorithmics/Pages/Index.aspx

https://www.vcaa.vic.edu.au/curriculum/vce/vce-study-designs/algorithmics/Pages/Index.aspx


Unit 4

Formal algorithm analysis

Outcome 1On completion of this unit the student should be able to establish the efficiency of simple algorithms and explain soft limits of computability.

Nature of tasks a written explanation of formal analysis techniques and the practical limits of computability (approximately

45–60 minutes) formal analysis of a given naïve algorithm (approximately 400 words).

Scope of tasks

Written explanation

Teachers must provide students with a task that allows them to explain, in writing, analysis techniques and the practical limits of computability. For authentication purposes this task may be completed under test conditions within a timeframe of 45 to 60 minutes in class time. Student performance for this task is assessed through criterion 1. The criterion should be used to develop a task that allows all students to demonstrate their level of performance.

Algorithm design

Students analyse the efficiency of a naïve algorithm using mathematical techniques. The naïve algorithm should have scope for improvement through the application of one of the algorithm design patterns studied in Outcome 2. It should take a straightforward approach to the problem and not be unnecessarily complicated. The word range for this report is approximately 400 words. Student performance for this task is assessed through criterion 2. The naïve algorithm analysed by students in this criterion will form the basis of an improved design in Outcome 2, criterion 4.

Advanced algorithm design

Outcome 2On completion of this unit the student should be able to solve a variety of information problems using algorithm design patterns and explain how heuristics can address the intractability of problems.

Nature of tasks a written explanation of algorithm design patterns and techniques for addressing the limits of computation

(approximately 45–50 minutes)

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a response to a naïve algorithm consisting of:

an improved algorithm design an analysis of the improved design, including its correctness (approximately 600 words).

Scope of tasks

Written explanation

Teachers must provide students with a task that allows them to explain, in writing, algorithm design patterns and techniques. For authentication purposes this task may be completed under test conditions within a timeframe of 45 to 60 minutes in class time. Student performance for this task is assessed through criterion 3. The criterion should be used to develop a task that allows all students to demonstrate their level of performance.

Algorithm design

Students design an improved algorithm in response to the naïve algorithm given in Outcome 1. They analyse the efficiency of the improved algorithm and propose a valid argument for its correctness. The word range for this report is approximately 600 words. Student performance on this task will be assessed through criterion 4.

Universality of computation and algorithms

Outcome 3On completion of this unit the student should be able to explain the scope of algorithmics as an approach to computational problem solving and the universality of computation, and its limits, using core concepts from theoretical computer science.

Nature of task an explanation of the universality of computation and algorithms in one or more of the following forms: a written report (approximately 700–800 words) a visual report (images supported by approximately 400–500 words) an oral report (10–15 minutes).

Scope of task

Explanation

Students develop a report using core concepts from theoretical computer science studied in class. They should be able to give detailed descriptions, explanations and evaluations of these core concepts. The word range for this report is 700 to 800 words. Student performance on this task will be assessed through criteria 5 and 6.

Relationships between tasks and criteria

The following rubric is used to assess student achievement on Unit 3 Outcome 1, Outcome 2 and Outcome 3 and Unit 4 Outcome 1, Outcome 2 and Outcome 3. Teachers assess evidence produced from the tasks against the criteria and performance descriptors to grade achievements.

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The criteria identify specific characteristics that are used to judge levels of performance against the outcomes. Performance descriptors describe typical evidence associated with five different levels of performance for a criterion (five levels; 10 marks).

Note: this rubric is based on the premise that each column includes all evidence of the columns to the left for each criterion, that is, the conditions are cumulative.

The following tables show the relationships between the outcomes, tasks and criteria.

Unit 3

Outcome Task Criteria

Outcome 1 A folio of two to four tasks using a range of ADTs to model the salient aspects of problems.

2

Outcome 1 A written explanation of the specification and application of ADTs. 1

Outcome 1 A data model of a real-world problem including:

the specification of the data model

concrete instance of the data model (worked example).

2

Outcome 2 A folio of two to four tasks using a range of algorithm design patterns to specify algorithms to solve problems.

4

Outcome 2 A written explanation of the specification and application of algorithms for graphs. 3

Outcome 2 An algorithm to solve a real-world problem that builds on an existing data model including:

pseudocode to solve the problem

implementation of the algorithms in a high-level programming language making appropriate use of the standard ADTs.

4

Outcome 3 An evaluation of an existing data model and algorithm in the form of a written report.

5

Outcome 3 Documentation of the data model development approach to solve a real-world problem.

6

Outcome 3 Documentation of the algorithm development approach to solve a real-world problem that builds on an existing data model.

6

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Unit 4

Outcome Task Criteria

Outcome 1 A written explanation of formal analysis techniques and the practical limits of computability.

1

Outcome 1 Formal analysis of a given naïve algorithm. 2

Outcome 2 A written explanation of algorithm design patterns and techniques for addressing the limits of computation.

3

Outcome 2 A response to a naïve algorithm consisting of:

an improved algorithm design

an analysis of the improved design, including its correctness.

4

Outcome 3 An explanation of the universality of computation and algorithms in one or more of the following forms:

a written report

a visual report

an oral report.

5 and 6

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VCE Algorithmics (HESS): Unit 3 School-assessed Task 2021

Assessment criteriaLevels of Performance

Not shown 1–2 (very low) 3–4 (low) 5–6 (medium) 7–8 (high) 9–10 (very high)

1. Understanding of abstract data types

Describes motivations for the abstraction of data.

Describes an appropriate example of an application for a given ADT.

Uses some appropriate metalanguage when discussing the operations of ADTs and the components of an ADT signature specification.

Uses appropriate metalanguage when describing graphs.

Describes an example problem attribute that could be modelled by graph node or edge.

Explains the general concept of an ADT using more than one example.

Describes the function and operations of a given ADT using appropriate metalanguage. Provides appropriate example applications for the ADT.

Executes a sequence of ADT operations to a given ADT instance.

Constructs an example of a specific class of graph.

Confirms or rejects the properties of a graph given as a diagram.

Describes how a graph property could be used to model a given aspect of a problem.

Describes the function and operations of several ADTs using appropriate metalanguage. Also, provides appropriate examples of applications for the ADTs.

Translates a natural language description into a sequence of ADT operations.

Writes signature specifications for some of the specified ADTs. Some minor errors or omissions exist.

Constructs a graph satisfying multiple given conditions.

States the graph properties satisfied by a graph given as a diagram.

Writes complete signature specifications for several ADTs, fully utilising appropriate metalanguage.

Analyses the properties satisfied by a given graph and rigorously explains how these properties are satisfied.

Explains the interconnections between the properties of cyclicity, connectedness and distance and the tree specialisation of graphs.

Describes a new operation for one of the standard ADTs to accommodate requirements that cannot be satisfied by the standard definition.

Derives a graph property using the specified properties of graphs.

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2. Skills in the application of abstract data types

Selects ADT representations for problems that represent minimal features of the problem or model only a limited range of possible problem instances. The data model may include extraneous features. Little discrimination is demonstrated when identifying features of the problem.

Models some aspects of a specific problem instance either in writing, graphically or within a programming environment.

Manually follows a sequence of steps through a data model instance for a planning problem, such as a decision tree.

Selects ADT representations for problems that represent some critical features of the problem. Some discrimination is demonstrated in the identification of relevant problem features. The data model may not appropriately consider its scalability to larger problem instances.

Models some aspects of several specific problem instances either in writing, graphically or within a programming environment.

Applies ADT operations to an existing data model.

Describes some aspects of a problem, including planning problems from a given data model instance.

Selects ADT representations, including use of the graph ADT, for problems that are fit for purpose. The full range of problem instances can be represented.

Selects suitable graph attributes to represent a network problem based on information presented in a different form such as a table or diagram.

Fully represents a specific problem instance as a data model either in writing, graphically or within a programming environment.

Constructs accurately a decision tree, with multiple levels, for a simple hierarchical choice scenario.

Clearly describes how aspects of a problem map to aspects of a data model.

Designs ADT representations, including use of the graph ADT, for problems that have a structure that cannot be modelled fully using a single abstract data type.

Identifies aspects of problems that cannot be fully or adequately represented by ADTs as part of a data model.

Fully represents several specific problem instances as data models either in writing, graphically or within a programming environment.

Designs ADT representations, including the use of the graph ADT, for problems that have a structure that cannot be modelled fully using a single abstract data type. The design is fit for purpose and appropriately prioritises aspects of the problem that are most important to the specific context or the requirements of algorithms utilising the data structure.

Fully represents a complex problem instance as a data model either in writing, graphically or within a programming environment.

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3. Understanding of the principles of algorithm design

Explains the concepts of decisions and iteration in algorithms.

Identifies some algorithm design approaches.

Identifies the elements of sequence, selection and repetition in a given algorithm.

Names and states correctly the computational applications of most of the specified graph algorithms.

States informally the input types of the specified graph algorithms.

Explains the concept of modularisation.

Explains the principles of the brute-force search or greedy algorithm design patterns, utilising appropriate examples.

Explains the principles of a graph traversal technique, utilising appropriate examples.

Interprets pseudocode with minimal errors, as demonstrated by the ability to execute it manually. The pseudocode includes sequence, selection and iteration, but not nested iteration.

Explains informally how some of the specified graph algorithms perform their computation and writes the approximate pseudocode for these.

Describes an argument for the correctness of one of the specified graph algorithms that considers only the correctness of a specific example.

Explains the concept of recursion.

Explains the principles of the decrease-and-conquer algorithm design pattern, utilising appropriate examples.

Compares the relative advantages of the different graph traversal techniques.

Interprets fluently pseudocode containing nested iteration and the use of ADTs, demonstrated by the ability to execute it accurately.

Writes pseudocode for a procedure described in natural language, including nesting and modularisation. The pseudocode may contain minor errors.

States precisely the input types of the specified graph algorithms.

Executes any of the specified graph algorithms using manual techniques for given graphs; the execution is performed with few errors.

Explains the concept of equivalence between recursive and iterative algorithms.

Improves a piece of pseudocode by restructuring and modularisation.

Explains the attributes required of problems for one of the algorithm design patterns to be applied.

Identifies cases where a piece of pseudocode does not perform the desired operation correctly.

Executes, without error, any of the specified graph algorithms using manual techniques for complex graphs.

Describes an argument for the correctness of one of the specified graph algorithms that considers the general case of the problem but not all steps in the chain of argument are explained.

Demonstrates the equivalence between recursive and iterative algorithms.

Improves a piece of pseudocode by restructuring and modularisation using non-trivial user-defined functions.

Evaluates the suitability of an algorithm design pattern for a specific problem.

Explains in precise terms why any of the specified graph algorithms are not valid for some classes of graph or graphs with certain properties.

Describes a valid argument for the correctness of at least one of the specified graph algorithms using either the induction or contradiction method.

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4. Skills in the application of the principles of algorithm design

Designs simple algorithms and writes these in pseudocode. There may be significant task scaffolding required, and the final algorithm is only an effective method for a trivial subset of problem instances.

Identifies an appropriate search algorithm to apply to a given problem.

Identifies the input and output data type required by an algorithm.

Designs simple algorithms and write these in pseudocode, with some task scaffolding. The algorithm is an effective method for a non-trivial subset of problem instances.

Compares the execution of depth-first search (DFS), breadth-first search (BFS) or best-first search on a specific problem instance.

Uses a programming environment to complete a partially translated algorithm, including iteration, from pseudocode to program code.

Describes an argument for the correctness of a brute-force, greedy, or decrease and conquer algorithm that considers only the correctness for a specific input.

Designs algorithms, including the use of iteration, and writes these in pseudocode, with minimal errors.

Applies the general concept of a given algorithm design pattern to design an algorithm to solve a problem, with errors in the final solution.

Uses a programming environment to translate a complete algorithm, including nested iteration, from pseudocode to program code.

Uses some of the structural components of an argument by induction or contradiction.

Designs algorithms using iteration and recursion for problems that have a structure that does not allow for the direct application of one of the studied algorithms.

Applies a given algorithm design pattern to design an algorithm to solve a problem.

Uses a programming environment to translate a recursive algorithm from pseudocode into program code.

Describes an argument for the correctness of one of a brute-force, greedy, or decrease and conquer algorithm that considers the general case of the problem but not all steps in the chain of argument are explained.

Designs algorithms using iteration, recursion and non-trivial functions for problems that have a structure that does not allow for the direct application of one of the studied algorithms.

Selects a suitable algorithm design pattern for solving an information problem and applies the design pattern to design an algorithm to solve the problem.

Uses a programming environment to translate an algorithm, containing non-trivial functions, from pseudocode into program code.

Describes a valid argument for the correctness of a brute-force, greedy, or decrease and conquer algorithm using either the induction or contradiction method.

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5. Skills in the evaluation of algorithms and data representation

Describes reasons for the choice of data model and algorithm based on the consideration of limited aspects of the problem.

Compares a data model and algorithm with another possible choice, as provided, based on a consideration of limited aspects of the problem.

Justifies a choice of data model and algorithm based on a comprehensive consideration of aspects of the problem. The selected data model and algorithm combination suitably addresses all essential aspects of the problem.

Identifies competing aspects of a problem that are unable to be mutually satisfied.

Evaluates a choice of data model and algorithm. The evaluation considers the essential aspects of the problem and the properties of alternative choices of data model and algorithm. The chosen data model and algorithm suitably addresses the problem but may have shortcomings in terms of efficiency, clarity or succinctness.

Justifies how competing aspects of a problem were prioritised when designing the data model and algorithm.

Compares and evaluates the relative advantages of data models and algorithm design patterns and consequently selects suitable data models and algorithms for solving a complex information problem to create a complete, correct and elegant solution.

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6. Skills in the documentation and communication of solutions to information problems

Unfocused and superficial discussion of the methods used in the data model and algorithm design.

Communication of simple ideas and arguments lacks some precision and contains some ambiguities.

Documentation contains little organisation of ideas or use of the structural conventions of a written report.

Limited discussion of the methods used in the data model and algorithm design, possibly with some inconsistencies between the methodology described and the submitted design.

Communication of simple ideas and arguments is mostly clear and coherent, with some use of metalanguage.

Documentation contains some organisation of ideas, including some use of the structural conventions of a written report.

Summarises a computed solution.

Relevant and clear discussion of the methods used in the data model and algorithm design.

Communication of simple ideas and arguments is clear and makes use of appropriate metalanguage. Some imprecision or ambiguity exists when communicating more complex concepts.

Documentation contains an orderly development of ideas and elements, including the use of the structural conventions of a written report.

Describes a computed solution, with some connections made to the original problem context.

Thorough and sound discussion of the methods used in the data model and algorithm design.

Communication of complex ideas and arguments is clear and uses appropriate metalanguage.

Documentation contains a well-structured development of ideas and elements.

Synthesises a computed solution to develop an answer in terms of the original problem context.

Highly detailed and complete discussion of the methods used in the data model and algorithm design.

Communication of complex ideas and arguments is clear and concise, with proficient use of metalanguage.

Documentation contains a well-structured and coherent development of ideas and elements.

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1. Understanding of formal algorithm analysis

Describes the meaning of algorithm complexity using everyday language.Uses the written notation of Big-O notation.Orders two different Big-O expressions by their order of growth.States an example of an algorithm with a given time complexity.Informally describes the meaning of intractability and states an example of an intractable problem.Describes the concept of exponential growth using everyday language.Uses the written notation of recurrence relations.States the solutions to some input cases of the Master Theorem.

Describes the meaning of algorithm complexity and describes a motivation for the study of the asymptotic time complexity of algorithms.Describes the difference between time and space complexity using everyday language.Identifies some relevant distinctions between algorithm complexity and the complexity class of problems.Describes the meaning of a given Big-O expression.Identifies that running time may vary between inputs of equal size.Describes some elements of the algorithmic structures that give rise to O(n2) or O(n3) time complexities.Describes the meaning of intractability and describe its practical relevance.

Explains the concept of order of growth as it relates to the asymptotic complexity of algorithms.Explains the distinction between the time and space complexity of an algorithm.Explains the concept of the P complexity class.Determines the order of growth associated with a range of mathematical expressions.Determines whether the running time of a specific algorithm varies for different inputs of equal size.Explains why some computable problems are intractable, with the use of examples of both tractable and intractable problems.Explains one indicator of exponentially sized search spaces based on examples introduced in the study.

Explains clearly and precisely the concept of the asymptotic complexity of algorithms.Explains clearly and precisely the distinction between the time and space complexity of an algorithm.Defines clearly and precisely the P and NP-Complete complexity classes.Explains the general mathematical meaning of statements made using Big-O, Big-Ω and Big-Θ notation.Discusses some differences between best case and worst case analysis of algorithms.Explains some elements of the algorithmic structures that give rise to O(n2), O(n3), O(log(n)) and O(n log(n)) time complexities

Compares the limits placed on the use of an algorithm by its time complexity with those placed by its space complexity.Compares the P and NP-Complete computational complexity classes through the use of well-chosen example problems.Discusses the practical consequences of a problem belonging to either the P or NP-Complete complexity class.Explains precisely the mathematical meaning of statements made using Big-O, Big-Ω and Big-Θ notation.Discusses the differences between and appropriateness of best and worst case complexity analysis for evaluating algorithms in practice.Explains the algorithmic structures that give rise to O(n2), O(n3), O(log(n)) and O(n log(n)) time complexities.

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2. Skills in Identifies lines of the naïve Applies step-counting Analyses the worst case time Analyses clearly and Analyses precisely and

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establishing the efficiency of a naïve algorithm

algorithm’s pseudocode that execute in constant running time and lines whose running time vary depending on the algorithm’s input.

Applies step-counting concepts with limited accuracy to reason about the running time of parts of the naïve algorithm.

Applies recurrence relation methods with very limited accuracy to a recursive component of the naïve algorithm to analyse its worst case time complexity.

methods with some accuracy to iterative or conditional components of the naïve algorithm whose running time varies depending on the input to analyse their worst case time complexity.

Applies recurrence relation methods with some accuracy to a recursive component of the naïve algorithm to analyse its worst case time complexity.

Identifies reasonable estimations for the performance of ADT operations used within the naïve algorithm.

complexity of the naïve algorithm through the selection and application of appropriate techniques. Some errors or omissions in the application of the techniques lead to an overall inaccurate analysis.

Accurately applies step-counting methods to a nested iterative component of the naïve algorithm to analyse its worst case time complexity.

Accurately applies recurrence relation methods to a recursive component of the naïve algorithm to analyse its worst case time complexity.

Identifies a single input instance for the naïve algorithm that would result in the best-case or worst-case running time, respectively.

thoroughly the time complexity of the naïve algorithm through the selection and application of appropriate techniques.

Describes the class of input instances for the naïve algorithm that would result in the best case or worst case running times, respectively.

elegantly the time complexity of the naïve algorithm through the efficient selection and application of appropriate techniques.

Describes efficiently and precisely the classes of input instances for the naïve algorithm that would result in the best case and the worst case running times.

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3. Understanding of advanced algorithm design

States an example of a backtracking, divide and conquer or dynamic programming algorithm.

Identifies the divide and merge steps within the pseudocode of a given divide and conquer algorithm.

States the problems solved by some of the mergesort, quicksort, knapsack, change making and minimax algorithms.

States the algorithmic design paradigm associated with the mergesort, quicksort, knapsack or change making algorithms.

Describes using everyday language the use of heuristics or randomisation as general approaches to intractable problems.

Identifies the attributes of a given algorithm that indicate the use of a specific algorithmic design pattern.

Determines whether a given algorithm is an example of specific algorithmic design paradigm.

Outlines the mergesort, quicksort, knapsack, change making or minimax algorithm, possibly with some minor errors.

Completes the missing lines of mergesort, quicksort, knapsack, change making and minimax algorithm.

Proposes an argument for the correctness of one of the specified divide and conquer or dynamic programming algorithms that does not consider the general case of the problem, rather only the correctness of a specific problem instance.

Describes the general structure of the backtracking, divide and conquer, or dynamic programming algorithmic design patterns.

Describes in pseudocode any of the mergesort, quicksort, knapsack, change making or minimax algorithms.

Proposes an argument for the correctness of one of the specified divide and conquer or dynamic programming algorithms that considers the general case of the problem but only includes a minority of the required steps in the chain of argument.

Outlines a specific algorithm based on either a heuristic or randomisation design approach.

Explains, using appropriate metalanguage, some of the principles of the backtracking, divide and conquer, or dynamic programming algorithmic design patterns.

Analyses the benefits and costs associated with any of the mergesort, quicksort, knapsack or change making algorithms in comparison with naïve algorithms for the same problem.

Proposes an argument for the correctness of one of the specified divide and conquer or dynamic programming algorithms that considers the general case of the problem but not all steps in the chain of argument are included.

Describes in detail a specific algorithm based on either a heuristic or randomisation design approach.

Explains precisely, using appropriate metalanguage, the principles of the backtracking, divide and conquer, or dynamic programming algorithmic design patterns.

Proposes a valid argument for the correctness of one of the specified divide and conquer or dynamic programming algorithms using either the induction or contradiction method.

Discusses the merits and limitations of the use of heuristic and randomised algorithms in practice.

Compares the decision and optimisation versions of the graph colouring, knapsack or travelling salesman problems with appropriate references to the computational complexity classes of the problems.

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3. Understanding of advanced algorithm design (continued)

Describes using everyday language the graph colouring, knapsack or travelling salesman problem.

Identifies a decision within the graph colouring, knapsack or travelling salesman problem that could be randomised.

Describes the principles of heuristic or randomisation algorithms as general approaches to intractable problems, with the inclusion of some technical detail and use of appropriate metalanguage.

Determines whether a problem given in context is an instance of the graph colouring, knapsack or travelling salesman problem.

Describes how a decision within the graph colouring, knapsack or travelling salesman problem could be randomised.

Defines clearly and precisely the graph colouring, knapsack or travelling salesman problem using appropriate metalanguage.

Partially describes an algorithm for the graph colouring, knapsack or travelling salesman problem that would be appropriate for large input instances.

Describes some of the limitations of heuristic and randomised algorithms.

Explains the decision and optimisation versions of the graph colouring, knapsack or travelling salesman problems.

Describes clearly a specific algorithm for the graph colouring, knapsack or travelling salesman problem that would be appropriate for large input instances.

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4. Skills in developing an improved algorithm in response to a naïve algorithm

Selects an algorithm design pattern and applies limited elements of its structure to design an algorithm that is either incomplete or incorrect.

Compares very limited aspects of the student-designed algorithm and the naïve algorithm for the problem.

Identifies lines of the improved algorithm’s pseudocode that execute in constant running time and lines whose running time vary depending on the algorithm’s input.

Applies step-counting concepts with limited accuracy to reason about the running time of parts of the improved algorithm.

Applies recurrence relation methods with very limited accuracy to a recursive component of the improved algorithm to analyse its worst case time complexity.

Selects an algorithm design pattern and applies significant elements of its structure to develop an algorithm that is not correct.

Compares simply the student-designed algorithm and the naïve algorithm for the problem.

Proposes an argument for the correctness of the algorithm that does not consider the general case, rather only the correctness of a specific problem instance.

Applies step-counting methods with some accuracy to iterative or conditional components of the improved algorithm whose running time varies depending on the input to analyse their worst case time complexity.

Applies recurrence relation methods with some accuracy to a recursive component of the improved algorithm to analyse its worst case time complexity.

Selects an appropriate algorithm design pattern and applies it to develop an algorithm that is correct for most inputs and is an improvement in algorithmic complexity on a naïve algorithm.

Compares in detail the student-designed algorithm and the naïve algorithm for the problem, highlighting the improvements made.

Proposes an argument for the correctness of the algorithm that considers the general case but only includes a minority of the required steps in the chain of argument.

Analyses the worst case time complexity of the improved algorithm through the selection and application of generally appropriate techniques. Some errors or omissions in the application of the techniques lead to an overall inaccurate analysis.

Selects an appropriate algorithm design pattern and applies it to develop a clearly expressed and correct algorithm that is an improvement in algorithmic complexity on the naïve algorithm.

Compares comprehensively and accurately the student-designed algorithm and the naïve algorithm for the problem, highlighting the improvements made and any trade-offs required.

Proposes an argument for the correctness of the algorithm that considers the general case of the problem but not all steps in the chain of argument are explained.

Clearly and thoroughly analyses the time complexity of the improved algorithm through the selection and application of appropriate techniques.

Selects an appropriate algorithm design pattern and applies it to develop an elegantly and precisely expressed, correct and efficient algorithm.

Proposes a valid argument for the correctness of the algorithm, if appropriate using either the induction or contradiction method.

Analyses precisely and elegantly the time complexity of the improved algorithm through the efficient selection and application of appropriate techniques.

If relevant, describes efficiently and precisely the class of input instances for the improved algorithm that would result in the best case or the worst case running times.

4. Skills in developing an improved

Identifies reasonable estimations for the performance of ADT

Accurately applies recurrence relation methods to a recursive component of the

If relevant, describes the class of input instances for the improved algorithm that would

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algorithm in response to a naïve algorithm(continued)

operations used within the improved algorithm.

improved algorithm to analyse its worst case time complexity.

Accurately applies step-counting methods to a nested iterative component of the improved algorithm to analyse its worst case time complexity.

result in the best case or worst case running times.

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5. Understanding of the principles of computation

Outlines the goals of Hilbert’s program, with some minor errors.Outlines some characteristics of a Turing machine, with some errors.Outlines the Halting problem, with some minor errors.Uses the term “decision problem” appropriately.Outlines some details of concepts relevant to how the equivalence of computational formalisms is shown, with some errors.Outlines the thought experiment that underpins the Chinese Room argument.Outlines some features of an alternative method of computation.

Describes briefly aspects of the goals of Hilbert’s program, its outcome and its historical context, possibly with minor errors.Describes the components of a Turing machine.Describes briefly some characteristics of decidable or undecidable problems.Describes briefly some concepts relevant to how the equivalence of computational formalism is shown.Describes the thought experiment that underpins Chinese Room argument and briefly describes aspects of its core position, standard replies or historical context.Describes using everyday language the core features of an alternative model of computation.

Describes, with appropriate use of metalanguage, the goals of Hilbert’s program, its outcome and its historical context and connection to the origin of computer science.Describes, with appropriate use of metalanguage, some aspects of the operation of a Turing machine.Describes, with appropriate use of metalanguage, the concept of undecidability and a specific example of an undecidable problem, possibly with minor errors.Describes accurately and clearly concepts relevant to how the equivalence of computational formalism is shown.Describes the core position of Chinese Room argument, one standard response to the argument, and its historical context.Describes, with appropriate use of metalanguage, an alternative model of computation, including some aspects of its operation.

Describes in detail the goals of Hilbert’s program, its outcome, its historical context and connection to the origin of computer science.Describes in detail the operation of a Turing machine.Describes in detail the concept of undecidability. Describes coherently and in detail the characteristics a specific example of an undecidable problem.Explains in detail conceptually how the equivalence of computational formalisms is shown.Describes in detail and with appropriate use of metalanguage the Chinese Room argument, its historical context, motivation and standard responses.Describes in detail an alternative model of computation, including some technical aspects of the method and its operation.

Explains comprehensively and precisely the goals of Hilbert's program, its outcome, its historical context and connection to the origin of computer science.Explains comprehensively and precisely the operation of a Turing machine.Explains comprehensively and precisely the concept of undecidability. Describes comprehensively and precisely the characteristics of a specific undecidable problem.Explains comprehensively and precisely conceptually how the equivalence of computational formalisms is shown.Describes comprehensively and precisely several standard responses to the Chinese Room argument. The standard responses are clearly distinguished, with no confusion or conflation.Explains comprehensively and precisely an alternative model of computation, including significant technical details of the method and its operation.

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6. Skills in the discussion and evaluation of computation concepts

Outlines the central premise of the Church-Turing thesis.Outlines some aspect of the consequences of undecidability.Outlines the relationship between Turing machines and computational complexity theory.Outlines the central premise of Cobham’s thesis.Discusses in brief the strength of one of the standard responses to the Chinese Room argument.Outlines some aspects of the connections between the Chinese Room argument and artificial intelligence.Outlines the merits of an alternative method of computation.

Discusses in brief the Church-Turing thesis, its historical context, and limited aspects of its merits or limitations.Discusses in brief the implications of undecidability for Hilbert’s Program. Demonstrates the undecidability of the Halting problem through the use of a poorly explained and limited argument.Discusses in brief the relationship between Turing machines and computational complexity theory.Discusses in brief Cobham’s thesis and limited aspects of its merits or limitations.Evaluates the strength of at least two of the standard responses to the Chinese Room argument.Discusses in brief the connections between the Chinese Room argument and artificial intelligence.Discusses in brief how an alternative method of computation might be used to overcome current limits of computation.

Discusses clearly the Church-Turing thesis, its historical context, and some aspects of its merits or limitations.Discusses clearly several implications of undecidability. Demonstrates the undecidability of the Halting problem through the use of a relevant and clear argument.Discusses clearly the relationship between Turing machines and computational complexity theory.Describes clearly Cobham’s thesis and some of its merits and limitations.Compares the strength of two of the standard responses to the Chinese Room argument.Discusses clearly the connections between the Chinese Room argument and artificial intelligence.Discusses clearly how an alternative method of computation might be used to overcome current limits of computation and some aspects of its merits and limitations.

Evaluates the merits or limitations of the Church-Turing thesis and discusses its implications.Demonstrates the undecidability of the Halting problem through the use of an effective and detailed argument.Discusses in detail and coherently the relationship between Turing machines and computational complexity theory.Evaluates the merits or limitations of the Cobham’s thesis and discusses its meaning for computational complexity theory.Formulates a position either for or against the Chinese Room argument through an evaluation of standard responses and connects this position to its implications for artificial intelligence.Explains in detail how an alternative model of computation might be used to overcome current limits of computation and evaluates briefly its merits and limitations.

Comprehensively and precisely evaluates the merits and limitations of Church-Turing thesis and discusses its implications.Demonstrates precisely the undecidability of the Halting problem through the use of a comprehensive and well structured argument.Discusses comprehensively and precisely the relationship between Turing machines and computational complexity theory.Comprehensively and precisely evaluates the merits and limitations of Cobham's thesis and discusses its meaning for computational complexity theory.Formulates a substantiated position either for or against the Chinese Room argument through a sound evaluation of several standard responses and connects this position to its implications for artificial intelligence.Explains comprehensively and precisely how an alternative model of computation might be used to overcome current limits of computation and evaluates its merits and limitations.

0 1 2 3 4 5 6 7 8 9 10

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Authentication of VCE Algorithmics (HESS) School-assessed Task (SAT) Teachers are reminded of the need to comply with the authentication requirements specified in the Assessment: School-based Assessment section of the VCE and VCAL Administrative Handbook 2021. This is important to ensure that ‘undue assistance [is] not … provided to students while undertaking assessment tasks’.

Teachers must be aware of the following requirements for the authentication of VCE Algorithmics (HESS) School-assessed Task.

1. The body of work created for the School-assessed Task (SAT) is based on work developed and completed in Unit 3 Outcomes 1, 2 and 3 and Unit 4 Outcomes 1, 2 and 3.

2. Teachers are required to fill out the Authentication record form and provide the student with feedback on their progress at each observation.

3. Undue assistance should not occur at any time during the development of the body of work and teachers need to be vigilant. Students are required to demonstrate development of their thinking and working practices. Teachers are reminded that it is not appropriate to provide ‘detailed advice on, corrections to, or actual reworking of students’ work’.

4. Teachers must sight and monitor the development and documentation of the student’s thinking and working practices throughout the unit to authenticate the work as the student’s own. Students must acknowledge the source of materials and information used to support the development of their work.

5. Students should be encouraged to complete their work at school. Where students use external service providers, their documentation should demonstrate ongoing progress throughout the SAT.

6. During development of the data model and solutions teachers must plan and use observations of student work in order to monitor and record each student’s progress as part of the authentication process. Teachers must ensure that all source and reference material, all use of non-school (home, outsourced) resources and any external assistance (for example, tutors) are acknowledged on the Authentication record form. If a student acknowledges using external resources or receiving external assistance, the teacher should record complete details as an attachment to the Authentication record form.

7. Teachers are reminded that authentication procedures must be followed for all student work in relation to this SAT. The School-based Assessment Audit includes the inspection of Authentication record forms.

© VCAA

https://www.vcaa.vic.edu.au/administration/vce-vcal-handbook/Pages/index.aspx


Authentication record form VCE Algorithmics (HESS) 2021

Unit 3 School-assessed Task This form must be completed by the class teacher. It provides a record of the monitoring of the student’s work in progress for authentication purposes. This form is to be retained by the school and filed. It may be collected by the VCAA as part of the School-based Assessment Audit.

Student name ………………………………………………….. Student No

School .…………………………………………………………………………………….

Teacher: ……………………………………..…………………………………………….

Component of School-assessed Task Date observed/ submitted

Authentication comments Teacher’s initials

Student’s initials

Observation 1: Development of folio (ADTs) Student has developed tasks for the folio for Outcome 1.

Observation 2: Development of folio (algorithm design patterns) Student has developed tasks for the folio for Outcome 2.

Observation 3: Progressive development of data modelStudent has continued to develop a data model and documentation.

Observation 4: Submission of tasksStudent has submitted the folio, data model and documentation.

Observation 5: Progressive development of solution and documentationStudent has continued to write pseudocode, implement it and prepare documentation.

Observation 6: Submission of tasksStudent has submitted the solution and documentation.

Observation 7: EvaluationStudent has submitted the evaluation of the data model and algorithm.

I declare that all resource materials and assistance used have been acknowledged and that all unacknowledged work is my own.

Student signature ……………………………………………………………..……………………………… Date ……………………………...

© VCAA


Authentication record form VCE Algorithmics (HESS) 2021

Unit 4 School-assessed Task This form must be completed by the class teacher. It provides a record of the monitoring of the student’s work in progress for authentication purposes. This form is to be retained by the school and filed. It may be collected by the VCAA as part of the School-based Assessment Audit.

Student name: .......................................................................... Student No

School: ..........................................................................................................................

Teacher: ........................................................................................................................

Component of School-assessed Task Date observed/ submitted

Authentication comments Teacher’s initials

Student’s initials

Observation 1: Submission of written explanation Student has submitted the written explanation of formal analysis techniques and the practical limits of computability.

Observation 2: Analysis of algorithm Student has analysed a naïve algorithm.

Observation 3: Progressive development of data modelStudent has continued to develop a data model and documentation.

Observation 4: Submission of written explanationStudent has submitted the written explanation of algorithm design patterns and techniques for addressing the limits of computation.

Observation 5: Development of algorithmStudent has submitted an improved algorithm and analysis.

Observation 6: ReportStudent has commenced the process of developing their report.

Observation 7: ReportStudent has submitted an explanation of the universality of computation and algorithms.

I declare that all resource materials and assistance used have been acknowledged and that all unacknowledged work is my own.

Student signature ……………………………………………………………………………..…… Date …………………………

© VCAA


2021Victorian Certificate of Education

Algorithmics (HESS) Assessment SheetSchool-assessed Task: Unit 3

STUDENT NAME

This assessment sheet will assist teachers to determine their score for each student. Teachers need to make judgments on the student’s performance for each criterion. Teachers will be required to choose one number from 0–10 to indicate how the student performed on each criterion with comments, as appropriate. Teachers then add the subtotals to determine the total score.

STUDENT NUMBER

ASSESSING SCHOOL NUMBER

Criteria for the award of grades Not Shown (0)

Very Low (1–2)

Low (3–4)

Med (5–6)

High (7–8)

Very High (9–10)

Performance on Criteria: Teacher’s CommentsYou may wish to comment on aspects of the student’s work that led to your assessment.

The extent to which the student demonstrates:

1 understanding of abstract data types 2 skills in the application of abstract data types 3 understanding of the principles of algorithm design 4 skills in the application of the principles of algorithm design 5 skills in the evaluation of algorithms and data representation 6 skills in the documentation and communication of solutions to information problems. If a student does not submit the School-assessed Task

at all, N/A should be entered in the total score box.SUBTOTALS

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TOTAL SCORE


2021 Victorian Certificate of EducationAlgorithmics (HESS) Assessment Sheet

School-assessed Task: Unit 4

STUDENT NAME

This assessment sheet will assist teachers to determine their score for each student. Teachers need to make judgments on the student’s performance for each criterion. Teachers will be required to choose one number from 0–10 to indicate how the student performed on each criterion with comments, as appropriate. Teachers then add the subtotals to determine the total score.

STUDENT NUMBER

ASSESSING SCHOOL NUMBER

Criteria for the award of grades Not Shown (0)

Very Low (1–2)

Low (3–4)

Med (5–6)

High (7–8)

Very High (9–10)

Performance on Criteria: Teacher’s CommentsYou may wish to comment on aspects of the student’s work that led to your assessment.

The extent to which the student demonstrates:

1 understanding of formal algorithm analysis 2 skills in establishing the efficiency of a naïve algorithm 3 understanding of advanced algorithm design 4 skills in developing an improved algorithm in response to a naïve algorithm 5 understanding of the principles of computation 6 skills in the discussion and evaluation of computation concepts. If a student does not submit the School-assessed Task

at all, N/A should be entered in the total score box.SUBTOTALS

© VCAA

TOTAL SCORE

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