Mathematics
Mathematics
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Mathematics is not compulsory in VCE but you must be aware that many tertiary courses have some form of mathematics as a prerequisite study.
Students undertaking Mathematical Methods
Units 1 & 2 in Year 10 (Advanced Mathematics - Accelerated Classes)
If recommended by your mathematics teacher, you may proceed into Mathematical Methods Units 3 & 4 next year. You may also choose Specialist Mathematics Units 1 & 2 if you receive a teacher recommendation.
Mathematics Calculator
The use of calculators is integral to the study of all VCE Mathematics units. The Victorian Curriculum and Assessment Authority, when setting the Unit 3 & 4 exams, assumes that all students have a CAS calculator. It is essential for all VCE Mathematics students to purchase a CAS calculator.
The school has a preferred calculator (Casio ClassPad FX-CP400 Colour Graphing Calculator) which will be available through the College via stationery orders.
VCAA regulations specify that CAS calculators may only be used in Mathematics exams.
Mathematics
Foundation Mathematics is suitable for students who wish to develop skills in using Mathematics in real-world contexts. Students are advised to check prerequisites for entry into courses as some university courses do not accept Foundation Mathematics
General Mathematics Units 1 & 2 prepares students to go on to General Mathematics Units 3 & 4. It is also suitable for students who want to complete Units 1 & 2 Mathematics but do not intend to continue with mathematics at Units 3 & 4 level
Mathematical Methods Units 1 & 2 prepares students to go on to Mathematical Methods Units 3 & 4
Specialist Mathematics Units 1 & 2 prepares students for Units 3 & 4 of Specialist Mathematics. Students undertaking Specialist Mathematics Units 1 & 2 must also be studying Mathematical Methods 1 & 2 or, with teacher recommendation, may be completing Mathematical Methods Units 3 & 4
Possible Mathematics Pathways at Senior School
NOTE:
Progression along a pathway is dependent upon demonstration of a thorough understanding of the previous course
Mathematical Methods 3 & 4 is required to study Specialist Mathematics Units 3 & 4
To undertake Units 1 & 2 Mathematical Methods students must have achieved a 60% average in Year 10 Mathematics (Methods Stream)
To undertake Units 1 & 2 Specialist Mathematics students must have achieved a 70% or above in Year 10 Mathematics (Methods Stream) or a 60% average in Maths Methods Units 1 & 2
For further explanation of the above graphics, please pause on the next section to view the live Mathematics selection process and pathways (as highlighted)
Foundation Mathematics
Unit 1
Areas of Study:
Interpersonal communication
Interpretive communication
Presentational communication
Topics Studied:
Develop an understanding of the language and culture/s of Chinese-speaking communities through the study of three or more topics from a list of prescribed themes
Access and share useful information on the topics and subtopics through Chinese and consolidate and extend vocabulary and grammar knowledge and language skills
Analyse cultural products or practices including visual, spoken or written texts. Cultural products or practices can be drawn from a diverse range of texts, activities and creations
These may include the following: stories, poems, plays, novels, songs, films, photographs, artworks, architecture, technology, food, clothing, sports and festivals
Apply acquired knowledge of Chinese culture and language to new contexts
Reflect on the interplay between language and culture, and its impact on the individual’s language use in specific contexts and for specific audiences
Unit 2
Areas of Study:
Interpersonal communication
Interpretive communication
Presentational communication
Topics Studied:
Aspects of language and culture through the study of three or more topics from the prescribed themes. Each area of study must focus on a different subtopic
Analyse visual, spoken and written texts
Access and share useful information on the topics and subtopics through Chinese and consolidate and extend vocabulary, grammar knowledge and language skills
Cultural products or practices can be used to demonstrate how culture and perspectives may vary between communities
Reflect on the interplay between language and culture, and its impact on meaning, understanding and the individual’s language use in specific contexts and for specific audiences
Assessment (Covers Units 1 & 2):
Assessment for Chinese Second Language includes the following:
Exchange meaning in a spoken interaction in Chinese
Interpret information from two texts on the same subtopic presented in Chinese, and respond in writing in Chinese and in English
Present information, concepts and ideas in writing in Chinese on the selected subtopic and for a specific audience and purpose
Respond in writing in Chinese to spoken, written or visual texts presented in Chinese
Analyse and use information from written, spoken or visual texts to produce an extended written response in Chinese
Explain information, ideas and concepts orally in Chinese to a specific audience about an aspect of culture within communities where Chinese is spoken
Cost: $ (resources and materials)
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Unit 3
Areas of Study:
Interpersonal communication
Interpretive communication
Presentational communication
Topics Studied:
The way Chinese speakers interpret and express ideas, and negotiate and persuade in Chinese through the study of three or more subtopics from the prescribed themes and topics: The Individual, The Chinese-Speaking Communities and The World Around Us
Interpret information, inform others, and reflect upon and develop persuasive arguments.
Access and share useful information on the subtopics through Chinese, and consolidate and extend vocabulary and grammar knowledge and language skills
Consider the influence of language and culture in shaping meaning and reflect on the practices, products and perspectives of the cultures of Chinese-speaking communities
Reflect on how knowledge of Chinese and Chinese-speaking communities can be applied in a range of contexts and endeavours, such as further study, travel, business or community involvement
Unit 4
Areas of Study:
Interpersonal communication
Interpretive communication
Presentational communication
Topics Studied:
Investigate aspects of culture through the study of two or more subtopics from the prescribed themes and topics
Build on knowledge of Chinese-speaking communities, considering cultural perspectives and language and explaining personal observations
Consolidate and extend vocabulary, grammar knowledge and language skills to investigate the topics through Chinese
Identify and reflect on cultural products or practices that provide insights into Chinese- speaking communities
Cultural products or practices can be drawn from a diverse range of texts, activities and creations. Reflect on the ways culture, place and time influence values, attitudes and behaviours
Consider how knowledge of more than one culture can influence the ways individuals relate to each other and function in the world
Assessment (Covers Units 3 & 4):
Assessment for Chinese Second Language includes the following:
Participate in a spoken exchange in Chinese to resolve a personal issue
Interpret information from texts and write responses in Chinese
Express ideas in a personal, informative or imaginative piece of writing in Chinese
Share information, ideas and opinions in a spoken exchange in Chinese
Analyse information from written, spoken and viewed texts for use in a written response in Chinese
Present information, concepts and ideas in evaluative or persuasive writing on an issue in Chinese
Eligibility for Chinese Second Language
A student is NOT eligible for Chinese Second Language if they have had either:
12 months or more education in a school where Chinese is the medium of instruction, or
3 years (36 months) or more residence in any of the VCAA nominated countries or regions
The nominated countries and regions are China, Taiwan, Hong Kong or Macau
The student's level of achievement for Units 3 and 4 will be determined by school-assessed coursework (Unit 3 - 40% and Unit 4 - 20%) and one end-of-year examination (40%).
Cost: $ (resources and materials)
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Contact Teacher: Mr Elbert Salim
General Mathematics
Units 1 & 2
In undertaking these units, students are expected to be able to apply techniques, routines and processes involving rational and real arithmetic, sets, lists, tables and matrices, diagrams and geometric constructions, algorithms, algebraic manipulation, recurrence relations, equations and graphs, with and without the use of technology. A CAS calculator is required for this course.
Areas of Study:
Data analysis, probability and statistics - investigate and compare data distributions and relationships between two numerical variables
Algebra, number and structure - arithmetic and geometric sequences, recurrence relations and financial mathematics
Functions, relations and graphs – linear functions, graphs and equations, transformations and modelling of non-linear data
Discrete mathematics - matrices, graphs and networks
Outcomes
On completion of this unit students should be able to:
Define and explain key concepts, and apply a range of related mathematical routines and procedures.
Select and apply mathematical facts, concepts, models and techniques to investigate and analyse extended application problems in a range of contexts.
Select and use numerical, graphical, symbolic and statistical functionalities of technology to develop mathematical ideas, produce results and carry out analysis in situations requiring problem‐solving, modelling or investigative techniques or approaches.
Assessment (Covers Units 1 & 2):
Assessment for Units 1 & 2 General Mathematics is selected from the following:
Textbook Questions
Summary notes/ review notes
Topic tests
Application Tasks
Examinations
Cost: $ (resources and materials)
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Units 3 & 4
General Mathematics consists of two areas of study. These areas of study enable students to develop mathematical knowledge and skills through the study of relationship and analysis between two variables, financial arithmetic, number patterns and recursion, networks and matrices. Students are required to apply their knowledge and skills to analyse, investigate and solve problems, and to communicate mathematical ideas and to make effective use of technology as required.
Areas of Study:
Data analysis, probability and statistics
Data analysis - data distributions, associations between two variables, and modelling linear associations and time series
Discrete mathematics
Recursion and financial modelling - recursion and financial modelling, including depreciation of assets, compound interest investments and loans
• Matrices – matrix applications and transition matrices
Networks and decision mathematics - graphs and networks
Outcomes
On completion of this unit students should be able to:
Define and explain key concepts, and apply a range of related mathematical routines and procedures.
Select and apply mathematical facts, concepts, models and techniques to investigate and analyse extended application problems in a range of contexts.
Select and use numerical, graphical, symbolic and statistical functionalities of technology to develop mathematical ideas, produce results and carry out analysis in situations requiring problem‐solving, modelling or investigative techniques or approaches.
Assessment (Covers Units 3 & 4):
Assessment for Units 3 & 4 General Mathematics is selected from the following:
Textbook Questions
Topic tests
Application Tasks
The student's level of achievement for Units 3 and 4 will be determined by school-assessed coursework (Unit 3 – 24% and Unit 4 – 16%) and two end-of-year examinations 30% & 30%.
Cost: $ (resources and materials)
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Contact Teacher: Mr Elbert Salim
Mathematical Methods
Units 1 & 2
These units are designed to enable students to develop mathematical knowledge and skills through the study of rational and real numbers, polynomial functions, Karnaugh maps, tree diagrams, rates of change, introduction to calculus, combinations, permutations, circular and exponential functions. Students are required to apply their knowledge and skills to analyse, investigate and solve problems, and to communicate mathematical ideas and to make effective use of technology as required.
Areas of Study:
Functions, relations and graphs - functions and their graphs (e.g., polynomials, power, circular, exponential) in a variety of modelling contexts and theoretical investigations
Algebra, number and structure - support students’ work in the other areas of study
Calculus - rates of change, differentiation and integration
Data analysis, probability and statistics - basic probabilities, counting principles, and the use of lists, tables and diagrams to calculate probabilities
Outcomes
On completion of this unit students should be able to:
Define and explain key concepts as specified in the content of the area of study, specified above.
Apply mathematical processes in non-routine context, and to analyse and critically discuss these applications of mathematics
Use technology to produce results and carry out analysis in situations requiring problem -solving, modelling or investigative techniques of approaches.
Assessment (Covers Units 1 & 2):
Assessment for Units 1 & 2 Mathematical Methods is selected from the following:
Textbook questions
Topic test
application tasks
Examination
Cost: $ (resources and materials)
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Units 3 & 4
These units are designed to enable students to develop mathematical knowledge and skills through the study of rational and real numbers, polynomial functions, exponential functions, trigonometric functions, differentiation, anti-differentiation, integration and statistical inference. Students are required to apply their knowledge and skills to analyse, investigate and solve problems, and to communicate mathematical ideas and to make effective use of technology as required.
Areas of Study:
Functions, relations and graphs – the applications of functions, their graphs and transformations (e.g., polynomials, power, circular, exponential, logarithm, hybrid functions)
Algebra, number and structure – the algebra of functions, including composition of functions, inverse functions and the solution of equations
Calculus – graphical treatment of limits, continuity and differentiability of functions of a single real variable, and differentiation, anti-differentiation and integration of these functions
Data analysis, probability and statistics - discrete and continuous random variables, probability functions, and statistical inference for sample proportions
Outcomes
On completion of this unit students should be able to:
Define and explain key concepts as specified in the content of the area of study, specified above.
Apply mathematical processes in non-routine context, and to analyse and critically discuss these applications of mathematics
Use technology to produce results and carry out analysis in situations requiring problem-solving, modelling or investigative techniques of approaches.
Assessment (Covers Units 3&4):
Assessment for Units 3 & 4 Mathematical Methods is selected from the following:
Textbook Questions
application tasks
topic tests
The student's level of achievement for Units 3 and 4 will be determined by school-assessed coursework (Unit 3 – 20% and Unit 4 – 20%) and two end-of-year examinations 20% & 40%.
Cost: $ (resources and materials)
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Contact Teacher: Mr Elbert Salim
Specialist Mathematics
Units 1 & 2
Specialist Mathematics Units 1 and 2 provide a course of study for students who wish to undertake an in-depth study of mathematics, with an emphasis on concepts, skills and processes related to mathematical structure, modelling, problem-solving and reasoning. This study has a focus on interest in the discipline of mathematics and investigation of a broad range of applications, as well as development of a sound background for further studies in mathematics and mathematics related fields.
Specialist Mathematics Units 1 and 2 can only be taken in conjunction with Mathematical Methods Units 1 and 2.
Areas of Study:
Algebra, number and structure – complex numbers, graph theory and the development of formal mathematical notation, definition, reasoning and proof to solve problems
Discrete mathematics - the study of sequences, series and first-order linear difference equations, combinatorics, and matrices
Data analysis, probability and statistics - the study of simulation, sampling and sampling distributions
Space and measurement - trigonometry, transformations, and vectors in the plane
Functions, relations and graphs - partial fractions; reciprocal and inverse circular functions and their graphs and simple transformations of these graphs; locus definitions of lines, parabolas, circles, ellipses and hyperbolas and the cartesian, parametric and polar forms of these relations
Outcomes
On completion of this unit students should be able to:
Define and explain key concepts, in relation to the topics from the selected areas of study, and apply a range of related mathematical routines and procedures
Apply mathematical processes in non-routine contexts and analyse and discuss these applications of mathematics in at least three of the areas of study
Use technology to produce results and carry out analysis in situations requiring problem-solving, modelling or investigative techniques or approaches in at least three areas of study.
Assessment (Covers Units 1 & 2):
Assessment for Units 1 & 2 Specialist Mathematics is selected from the following:
Textbook Questions
application tasks
topic tests
examination
Cost: $ (resources and materials)
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Units 3 & 4
Specialist Mathematics consists of four areas of study, which develop and extend students skills in many of the areas covered in Mathematical Methods and Specialist Mathematics Units 1 and 2. Therefore it can only be undertaken by students who are also enrolled in Mathematical Methods Units 3 and 4.
These units are designed to enable students to develop mathematical knowledge and skills through the study of rational, real and complex arithmetic, polynomial functions, exponential functions, extended trigonometric functions, differentiation, anti-differentiation, integration and statistical inference. Students are required to apply their knowledge and skills to analyse, investigate and solve problems, and to communicate mathematical ideas and to make effective use of technology as required.
Areas of Study:
Discrete mathematics - the development of mathematical argument and proof (e.g., conjectures, connectives, and proof techniques including mathematical induction)
Functions, relations and graphs - rational functions and other simple quotient functions, curve sketching of these functions and relations, and the analysis of key features of their graphs
Algebra, number and structure - the algebra of complex numbers, including polar form, factorisation of polynomial functions over the complex field
Calculus - the advanced calculus techniques for analytical and numerical differentiation and integration of a broad range of functions, and combinations of functions, kinematics, differential calculus
Space and measurement - the arithmetic and algebra of vectors, vector and cartesian equations, and vector calculus
Data analysis, probability and statistics – the study of linear combinations of random variables and introductory statistical inference, the determination of confidence intervals, and hypothesis testing
Outcomes
On completion of this unit students should be able to:
Define and explain key terms and concepts as specified in the content from the areas of study, and apply a range of related mathematical routines and procedures
Apply mathematical processes, with an emphasis on general cases, in non-routine contexts, and to analyse and discuss these applications of mathematics.
Select and appropriately use Numerical, graphical, symbolic & statistical functions of technology to develop mathematical ideas, produce results and carry out analysis in situations requiring problem-solving, modelling or investigative techniques or approaches
The student's level of achievement for Units 3 and 4 will be determined by school-assessed coursework (Unit 3 – 20% and Unit 4 – 20%) and two end-of-year examinations 20% & 40%.
Cost: $ (resources and materials)
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Contact Teacher: Mr Elbert Salim
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