Mathematics Group
Course Outlines
Mathematics Courses at St Mary's College
Scroll down for descriptions of:
- Foundation Mathematics
- General Mathematics
- Mathematical Methods
- Specialist Mathematics
Foundation Mathematics
Course Description
Foundation Mathematics focuses on providing students with the mathematical knowledge, skills, understanding and dispositions to solve problems in real contexts for a range of workplace, personal, further learning, and community settings relevant to contemporary society. In undertaking these units, students are expected to be able to apply techniques, routines and processes involving integer, rational and real arithmetic, sets, lists and tables, contemporary data displays, diagrams, plans, geometric objects and constructions, algorithms, measures, equations and graphs, with and without the use of technology. They should have facility with relevant mental and by-hand approaches to estimation and computation.
Course structure
Unit 1 and 2
Area of Study 1 – Algebra, number and structure
In this area of study students cover estimation, and the use and application of different forms of number and related calculations, including formulas and other symbolic expressions, in practical, everyday and routine work contexts.
Area of Study 2 – Data analysis, probability and statistics
In this area of study students cover collection, presentation and analysis of gathered and provided data from community, work, recreation and media contexts, including consideration of suitable forms of representation and data summaries.
Area of Study 3 – Discrete mathematics: Financial and consumer mathematics
In this area of study students cover the use and interpretation of different forms of numbers and calculations, and their application in relation to the understanding and management of personal, local and national financial matters.
Area of Study 4 – Space and measurement
In this area of study students cover cover time, shape and location concepts, and the use and application of the metric system and related measurements in a variety of domestic, societal, industrial and commercial contexts.
Unit 3 and 4
Area of Study 1 – Algebra, number and structure
In this area of study students cover estimation, the use and application of different forms of numbers and calculations, algorithmic and computational thinking, and the representation of formal mathematical expressions and processes including formulas and other algebraic expressions to solve practical problems in community, business and industry contexts.
Area of Study 2 – Data analysis, probability and statistics
In this area of study students cover collection, presentation and analysis of gathered and provided data from community, work, recreation and media contexts, including consideration of suitable forms of representation and summaries. This area of study incorporates the ability to critically reflect on statistical data and results, and to be able to communicate and report on the outcomes and any implications.
Area of Study 3 – Discrete mathematics: Financial and consumer mathematics
In this area of study students cover the use and interpretation of different forms of numbers and calculations, relationships and formulae, and their application in relation to the analysis of, and critical reflection on, personal, local, national and global financial, consumer and global matters.
Area of Study 4 – Space and measurement
In this area of study students cover the use and application of the metric system and related measurement in a variety of domestic, societal, industrial and commercial contexts, including consideration of accuracy, precision and error.
Entry and Recommendations
There are no prerequisites for entry to Unit 3; however, students must undertake Unit 3 prior to undertaking Unit 4.
Assessment
Satisfactory Completion
Demonstration of achievement of outcomes and satisfactory completion of a unit are determined by evidence gained through the assessment of a range of learning activities and tasks.
Level of Achievement
Unit 1 and 2
- Coursework
- Assignments
- Tests
- Summary or review notes
- Modelling tasks
- Problem-solving tasks
- Mathematical investigations
- Examination
Unit 3 & 4
- Unit 3 School-assessed Coursework (40 %)
- Mathematical Investigation 1
- Mathematical Investigation 2
- Unit 4 School-assessed Coursework (20%)
- Mathematical Investigation 3
- Examination (40%)
General Mathematics
Course Description
General Mathematics Units 1 and 2 cater for a range of student interests, provide preparation for the study of General Mathematics at the Units 3 and 4 level and contain assumed knowledge and skills for these units.
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. They should have facility with relevant mental and by-hand approaches to estimation and computation. The use of numerical, graphical, geometric, symbolic, financial and statistical functionality of technology for teaching and learning mathematics, for working mathematically, and in related assessment, is to be incorporated throughout each unit as applicable.
Course structure
Unit 1 and 2
Area of Study 1 – Data analysis, probability and statistics
In this area of study students cover types of data, display and description of the distribution of data, summary statistics for centre and spread, and the comparison of sets of data.
Area of Study 2 – Algebra, number and structure
In this area of study students cover the concept of a sequence and its representation by rule, table and graph, arithmetic or geometric sequences as examples of sequences generated by first-order linear recurrence relations, and simple financial and other applications of these sequences.
Area of Study 3 – Functions, relations and graphs
In this area of study students cover linear function and relations, their graphs, modelling with linear functions, solving linear equations and simultaneous linear equations, line segment and step graphs and their applications.
Area of Study 4 – Discrete Mathematics
In this area of study students cover the concept of matrices and matrix operations to model and solve a range of practical problems, including population growth and decay.
Unit 2
Area of Study 1 – Data analysis, probability and statistics
In this area of study students cover association between two numerical variables, scatterplots, and lines of good fit by eye and their interpretation.
Area of Study 2 – Discrete Mathematics
In this area of study students cover the use of graphs and networks to model and solve a range of practical problems, including connectedness, shortest path and minimum spanning trees.
Area of Study 3 – Functions, relations and graphs
In this area of study students cover direct and inverse variation, transformations to linearity and modelling of some non-linear data.
Area of Study 4 – Shape and measurement
In this area of study students cover units of measurement, accuracy, computations with formulas for different measures, similarity and scale in two and three dimensions, and their practical applications involving simple and composite shapes and objects, trigonometry, problems involving navigation and Pythagoras’ theorem and their applications in the plane.
Unit 3
Area of Study 1 – Data analysis, probability and statistics
Students cover data types, representation and distribution of data, location, spread, association, correlation and causation, response and explanatory variables, linear regression, data transformation and goodness of fit, times series, seasonality, smoothing and prediction.
Area of Study 2 – Discrete Mathematics
Students cover the use of first-order linear recurrence relations and the time value of money (TVM) to model and analyse a range of financial situations, and using technology to solve related problems involving interest, appreciation and depreciation, loans, annuities and perpetuities.
Unit 4
Area of study 1 – Data analysis, probability and statistics
Students cover the definition of matrices, different types of matrices, matrix operations, transition matrices and the use of first-order linear matrix recurrence relations to model a range of situations and solve related problems.
Area of study 2 – Discrete Mathematics
Students cover the definition and representation of different kinds of undirected and directed graphs, Eulerian trails, Eulerian circuits, bridges, Hamiltonian paths and cycles, and the use of networks to model and solve problems involving travel, connection, flow, matching, allocation and scheduling.
Entry and Recommendations
There are no prerequisites for entry to Unit 3; however, students must undertake Unit 3 prior to undertaking Unit 4.
Assessment
Satisfactory Completion
Demonstration of achievement of outcomes and satisfactory completion of a unit are determined by evidence gained through the assessment of a range of learning activities and tasks.
Level of Achievement
Unit 1 and 2
- Coursework
- Assignments
- Tests
- Summary or review notes
- Modelling tasks
- Problem-solving tasks
- Mathematical investigations
- Examination
Unit 3 & 4
- Unit 3 School-assessed Coursework: (24 %)
- Data analysis, probability and statistics task
- Recursion and financial modelling task
- Unit 4 School-assessed Coursework: (16 %)
- Matrices task
- Networks and decision task
- Examination 1: (30 %)
- Examination 2: (30 %)
Mathematical Methods
Course Description
Mathematical Methods provide for the study of simple elementary functions, transformations and combinations of these functions, algebra, calculus, probability and statistics, and their applications in a variety of practical and theoretical contexts. They also provide background for further study in, for example, science, technology, engineering and mathematics (STEM), humanities, economics and medicine. In undertaking this unit, students are expected to be able to apply techniques, routines and processes involving rational and real arithmetic, sets, lists and tables, diagrams and geometric constructions, algorithms, algebraic manipulation, equations, graphs and differentiation, with and without the use of technology. They should have facility with relevant mental and by-hand approaches to estimation and computation. The use of numerical, graphical, geometric, symbolic and statistical functionality of technology for teaching and learning mathematics, for working mathematically, and in related assessment, is to be incorporated throughout the unit as applicable.
Course structure
Unit 1
Area of Study 1 – Functions, relations and graphs
In this area of study students cover the graphical representation of simple algebraic functions (polynomial and power functions) of a single real variable and the key features of functions and their graphs such as axis intercepts, domain (including the concept of maximal, natural or implied domain), co-domain and range, stationary points, asymptotic behaviour and symmetry. The behaviour of functions and their graphs is to be explored in a variety of modelling contexts and theoretical investigations.
Area of Study 2 – Algebra, number and structure
This area of study supports students’ work in the ‘Functions, relations and graphs’, ‘Calculus’ and ‘Data analysis, probability and statistics’ areas of study, and content is to be distributed between Units 1 and 2. In Unit 1 the focus is on the algebra of polynomial functions of low degree and transformations of the plane.
Area of Study 3 – Calculus
In this area of study students cover constant and average rates of change and an introduction to instantaneous rate of change of a function in familiar contexts, including graphical and numerical approaches to estimating and approximating these rates of change.
Area of Study 4 – Probability and statistics
In this area of study students cover the concepts of experiment (trial), outcome, event, frequency, probability and representation of finite sample spaces and events using various forms such as lists, grids, Venn diagrams and tables. They also cover introductory counting principles and techniques and their application to probability.
Unit 2
Area of Study 1 – Functions, relations and graphs
In this area of study students cover graphical representation of circular, exponential and logarithmic functions of a single real variable and the key features of graphs of functions such as axis intercepts, domain (including maximal, natural or implied domain), co-domain and range, asymptotic behaviour, periodicity and symmetry. The behaviour of functions and their graphs is to be explored in a variety of modelling contexts and theoretical investigations.
Area of Study 2 – Algebra, number and structure
This area of study supports students’ work in the ‘Functions, relations and graphs’, ‘Calculus’ and ‘Data analysis, probability and statistics’ areas of study. In Unit 2 the focus is on the algebra of some simple transcendental functions and transformations of the plane.
Area of Study 3 – Calculus
In this area of study students cover differentiation and anti-differentiation of polynomial functions by rule, different notations, and related applications including the analysis of graphs.
Area of Study 4 – Probability and statistics
In this area of study students cover the use of lists, tables and diagrams to calculate probabilities, including consideration of complementary, mutually exclusive, conditional and independent events involving one, two or three events (as applicable), including rules for computation of probabilities for compound events.
Units 3 and 4
Area of Study 1 – Functions, relations and graphs
In this area of study students cover transformations of the plane and the behaviour of some elementary functions of a single real variable, including key features of their graphs such as axis intercepts, stationary points, points of inflection, domain (including maximal, implied or natural domain), co-domain and range, asymptotic behaviour and symmetry. The behaviour of functions and their graphs is to be explored in a variety of modelling contexts and theoretical investigations.
Area of Study 2 – Algebra, number and structure
In this area of study students cover the algebra of functions, including composition of functions, inverse functions and the solution of equations. They also study the identification of appropriate solution processes for solving equations, and systems of simultaneous equations, presented in various forms. Students also cover recognition of equations and systems of equations that are solvable using inverse operations or factorisation, and the use of graphical and numerical approaches for problems involving equations where exact value solutions are not required, or which are not solvable by other methods. This content is to be incorporated as applicable to the other areas of study.
Area of Study 3 – Calculus
In this area of study students cover graphical treatment of limits, continuity and differentiability of functions of a single real variable, and differentiation, anti-differentiation and integration of these functions. This material is to be linked to applications in practical situations.
Area of Study 4 – Data, probability and statistics
In this area of study students cover discrete and continuous random variables, their representation using tables, probability functions (specified by rule and defining parameters as appropriate); the calculation and interpretation of central measures and measures of spread; and statistical inference for sample proportions. The focus is on understanding the notion of a random variable, related parameters, properties and application and interpretation in context for a given probability distribution.
Entry and Recommendations
There are no prerequisites for entry to Units 1, 2 and 3; however, students undertaking Mathematical Methods are assumed to have a sound background in number, algebra, function, geometry, probability and statistics. Students must undertake Unit 3 prior to undertaking Unit 4.
Assessment
Satisfactory Completion
Demonstration of achievement of outcomes and satisfactory completion of a unit are determined by evidence gained through the assessment of a range of learning activities and tasks.
Level of Achievement
Unit 1 and 2
- Coursework
- Assignments
- Tests
- Summary or review notes
- Modelling tasks
- Problem-solving tasks
- Mathematical investigations
- Examination
Unit 3 and 4
- Unit 3 School-assessed Coursework (20 %)
- Application Task
- Unit 4 School-assessed Coursework (20 %)
- Modelling Task
- Problem-solving Task
- Examination 1 (20 %)
- Examination 2 (40 %)
Specialist Mathematics
Course Description
Specialist Mathematics provides 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, reasoning and proof. 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.
In undertaking this unit, students are expected to be able to apply techniques, routines and processes involving rational, real and complex arithmetic, sets, lists, tables and matrices, diagrams, graphs, logic gates and geometric constructions, algorithms, algebraic manipulation, recurrence relations, equations and graphs, with and without the use of technology. They are expected to be able to construct proofs and develop and interpret algorithms to solve problems. They should have facility with relevant mental and by-hand approaches to estimation and computation. The use of numerical, graphical, geometric, symbolic and statistical functionality of technology for teaching and learning mathematics, for working mathematically, and in related assessment, is to be incorporated throughout each unit as applicable.
Course structure
Unit 1
Area of Study 1 – Algebra, number and structure
In this area of study students cover the development of formal mathematical notation, definition, reasoning and proof applied to number systems, graph theory, sets, logic, and Boolean algebra, and the development of algorithms to solve problems.
Area of Study 2 – Discrete mathematics
In this area of study students cover the study of sequences, series, and first-order linear difference equations, combinatorics, including the pigeon-hole principle, the inclusion-exclusion principle, permutations and combinations, combinatorial identities, and matrices.
Unit 2
Area of Study 1 – Data analysis, probability and statistics
In this area of study students cover the study of linear combinations of random variables and the distribution of sample means of a population, with the use of technology to explore variability of sample means.
Area of Study 2 – Space and measurement
In this area of study students cover trigonometry and identities, rotation and reflection transformations of the plane and vectors for working with position, shape, direction and movement in the plane and related applications.
Area of Study 3 – Algebra, number and structure
In this area of study students cover the arithmetic and algebra of complex numbers, including polar form, regions and curves in the complex plane and introduction to factorisation of quadratic functions over the complex field.
Area of Study 4 – Functions, relations and graphs
In this area of study students cover an introduction to 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.
Unit 3 and 4
Area of Study 1 – Discrete mathematics: Logic and proof
In this area of study students cover the development of mathematical argument and proof. This includes conjectures, connectives, quantifiers, examples and counter-examples, and proof techniques including mathematical induction. Proofs will involve concepts from topics such as: divisibility, inequalities, graph theory, combinatorics, sequences and series including partial sums and partial products and related notations, complex numbers, matrices, vectors and calculus.
Area of Study 2 – Functions, relations and graphs
In this area of study students cover rational functions and other simple quotient functions, curve sketching of these functions and relations, and the analysis of key features of their graphs including intercepts, asymptotic behaviour and the nature and location of stationary points and points of inflection and symmetry.
Area of Study 3 – Algebra, number and structure
In this area of study students cover the algebra of complex numbers, including polar form, factorisation of polynomial functions over the complex field and an informal treatment of the fundamental theorem of algebra.
Area of Study 4 – Calculus
In this area of study students cover the advanced calculus techniques for analytical and numerical differentiation and integration of a broad range of functions, and combinations of functions; and their application in a variety of theoretical and practical situations, including curve sketching, evaluation of arc length, area and volume, differential equations and kinematics, and modelling with differential equations drawing from a variety of fields such as biology, economics and science.
Area of Study 5 – Shape and measurement
In this area of study students cover the arithmetic and algebra of vectors; linear dependence and independence of a set of vectors; proof of geometric results using vectors; vector representation of curves in the plane and their parametric and cartesian equations; vector kinematics in one, two and three dimensions; vector, parametric and cartesian equations of lines and planes.
Area of Study 6 – Data analysis, probability and statistics
In this area of study students cover the study of linear combinations of random variables and introductory statistical inference with respect to the mean of a single population, the determination of confidence intervals, and hypothesis testing for the mean using the distribution of sample means.
Entry and Recommendations
Students are required to be enrolled in Mathematical Methods to enrol in Specialist Mathematics.
Assessment
Satisfactory Completion
Demonstration of achievement of outcomes and satisfactory completion of a unit are determined by evidence gained through the assessment of a range of learning activities and tasks.
Level of Achievement
Units 1 and 2
- Coursework
- Assignments
- Tests
- Summary or review notes
- Modelling tasks
- Problem-solving tasks
- Mathematical investigations
- Examination
Units 3 and 4
- Unit 3 School-assessed Coursework: (20%)
- Unit 4 School-assessed Coursework: (20 %)
- Examination 1: (20 %)
- Examination 2: (40 %).