VCE Mathematics

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Foundation Mathematics 

Course Description 

Foundation Mathematics provides for the continuing mathematical development of students entering VCE. There is a strong emphasis on the use of mathematics in practical contexts encountered in everyday life in the community, at work and at study.  

Unit 1 

In this unit students will apply the use of integers, decimals, fractions, ratios, proportions, percentages and rates to solve practical problems. They will use and interpret formulas and algebraic expressions to describe relationships between variables and to model patterns that exist in everyday contexts. Students will apply and use metric units and measures, including derived measures. They will apply procedures for the solution of personal, societal and workplace problems involving metric measurement with consideration of error, required accuracy and tolerances. They will interpret and use time and duration including time and date specifications, conventions, schedules, timetables and time zones. 

Unit 2 

In this unit students will investigate how to interpret and use plans, elevations, maps, models and diagrams. They will investigate geometric conventions and properties of shapes and objects, the application and the processes involved in the enlargement and reduction of diagrams and models. The interpretation and use of location, distance, direction and scale on diagrams, maps and plans will be discussed in regards to their use in practical situations. They will cover the processes involved in the collection, presentation and analysis of gathered and provided data from community, work, recreation and media contexts. Students will interpret diagrams, charts, tables and graphs and use measures of averages and spread to summarise, interpret and compare data sets. 

Unit 3 

 In this unit students will use estimation, calculations and computational thinking to solve practical problems in community, business and industry contexts. Students will also undertake the study of ‘Data analysis’ including collection and modelling of data, the construction of tables or spreadsheets and graphs to represent data. Students will use data and statistics to make predictions, inferences and draw conclusions. Students will also study financial and consumer math including money management, investments and loans, credit and debit, comparing mortgages versus rental costs, debt consolidation, taxation, financial risk and insurance. 

Unit 4 

In this unit students study 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. Students investigate how to interpret and use plans and elevation diagrams and to convert a range of metric units. Performing a range of measurements and calculations students research and model the process of renovating a house.  

Additional Information: 

Students are expected to have a calculator as prescribed on the booklist. 

To access further information please click here: https://www.vcaa.vic.edu.au/curriculum/vce/vce-study-designs/foundationmathematics/Pages/Index.aspx  

General Mathematics

Course Description 

Further Mathematics is intended to provide for students with diverse needs and aspirations and is intended to be widely accessible. It is intended to provide general preparation for employment and further study in a variety of different fields. 

Unit 1 

In this unit students will investigate and compare data distributions and discuss how to display and interpret categorical and numerical data distributions using summary statistics. They will cover continuous models involving linear relations and their graphs and construct linear model to represent practical situations. The representation and manipulation of linear relations and equations will be investigating including simultaneous linear equations, and their applications in a range of contexts. Students will cover mental, by-hand and technology assisted computation with rational numbers and practical arithmetic. Number patterns and recursion is investigated and their use to model practical situations and solve a range of related problems is discussed. 

Unit 2 

In this unit students will cover representing, analysing and investigating relationships between two numerical variables, including an introduction to correlation. This will involve students investigating the relationships between two numerical variables and the use of models to make predictions and identify limitations of extrapolation. In this unit students will cover financial arithmetic including investigating percentage increase and decrease applied to various financial contexts and applications of simple and compound interest. Students will investigate matrices as well as graphs and networks, discuss their use in modelling practical situations, and solve a range of related problems. 

Unit 3  

In this unit students will undertake the study of ‘Data analysis’ including investigating data distributions, associations between two variables as well as investigating and modelling linear associations and time series data. They will also cover the topic of ‘Recursion and financial modelling’ which will see them investigate the use of first-order linear recurrence relations and technology to model and analyse a range of financial situations, and solve related problems involving interest, appreciation and depreciation, loans, annuities and perpetuities. 

Unit 4 

In this unit students will undertake the study of the ‘Matrices’ module which will 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. Students will also cover the ‘Networks and decision mathematics’ module which will cover the definition and representation of different kinds of undirected and directed graphs, Eulerian trails and circuits, bridges, Hamiltonian paths and cycles, and the use of networks 

Additional Information: 

Students must have a Ti-Nspire CAS calculator as prescribed on the booklist. 

To access further information about Unit 1 & 2, please click here: https://www.vcaa.vic.edu.au/curriculum/vce/vce-study-designs/generalmathematics/Pages/Index.aspx 

To access further information about Unit 3 & 4, please click here:  https://www.vcaa.vic.edu.au/curriculum/vce/vce-study-designs/furthermathematics/Pages/Index.aspx  

Mathematical Methods  

This subject requires higher-order mathematical skills and necessitates intense focus on homework completion and continuous practice. 

Course Description 

Mathematical Methods Units 1 and 2 provide an introductory study of simple elementary functions of a single real variable, algebra, calculus, probability and statistics and their applications in a variety of practical and theoretical contexts.  

Mathematical Methods Units 3 and 4 extends the introductory study of simple elementary functions of a single real variable studied in Mathematical Methods Units 1 and 2 to include combinations of these functions, algebra, calculus, probability and statistics, and their applications in a variety of practical and theoretical contexts. The appropriate use of technology, including but not limited to computer algebra system (CAS) technology, will be incorporated throughout these units to assist in the development of mathematical ideas and concepts. Mathematical Methods is intended to provide students with an appropriate foundation for further study in, but not limited to, areas such as Science, Engineering, Economics or Medicine.  

This subject is a prerequisite (may be studied concurrently) for any student considering undertaking Specialist Mathematics. 

Unit 1 

In this unit students will cover the graphical representation of polynomial and power functions of a single real variable and the key features of functions and their graphs such as axis intercepts, domain, co-domain and range, stationary points, asymptotic behavior and symmetry. The behavior of functions and their graphs will be explored in a variety of modelling contexts and theoretical investigations. There is a focus on the algebra of polynomial functions of low degree and transformations of the plane including numerical approximation of roots. The concepts of event, frequency, probability and representation of finite sample spaces and events using various forms will be covered. This will include the consideration of impossible, certain, complementary, mutually exclusive, conditional and independent events involving one, two or three events, including the rules for computation of probabilities for compound events. Students will cover constant and average rates of change and an introduction to instantaneous rate of change of a function in familiar contexts. 

Unit 2 

In this unit students will cover the graphical representation of functions and the key features of graphs of sine, cosine, tangent, exponential and logarithmic functions such as axis intercepts, domain, co-domain and range, asymptotic behavior, periodicity and symmetry. There is a focus on the algebra of some simple transcendental functions and transformations of the plane. Students will cover first principles approach to differentiation, differentiation and anti-differentiation of polynomial functions and power functions by rule, and related applications including the analysis of graphs. Introductory counting principles and techniques and their application to probability and the law of total probability in the case of two events will be discussed and investigated. 

Unit 3 

In this unit students cover transformations of the plane and key features of elementary functions and their graphs. The behavior of these functions and their graphs will also be linked to applications in practical situations. Students will cover the algebra of functions and study the identification of appropriate solution processes for solving equations, and systems of simultaneous equations, presented in various forms. Graphical and numerical approaches for problems involving equations where exact value solutions are not required or which are not solvable by other methods will be investigated. Students will be introduced to the graphical treatment of limits, continuity and differentiability of functions and differentiation of these functions whilst linking these processes to application in practical situations.  

Unit 4  

In this unit students will continue with the study of calculus, in particular with the anti-differentiation and integration of functions of a single real variable and be introduced to their application of practical situations. They will cover discrete and continuous random variables, their representation using tables, probability functions; 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 give probability distribution. 

Prerequisites: A minimum Victorian Curriculum standard of ‘excellent’ for either Year 10 Mathematics Methods Core or VCE General Mathematics (Advanced) Units 1 and 2 to move into Unit 1 & 2. 

Additional Information: 

Students must have a Ti-Nspire CAS calculator as prescribed on the booklist and bring it to every class. 

To access further information, please click here: https://www.vcaa.vic.edu.au/curriculum/vce/vce-study-designs/mathematicalmethods/Pages/Index.aspx  

Specialist Mathematics 

This subject requires higher-order maths skills and necessitates intense focus on homework completion and continuous practice. 

Course Description 

Specialist Mathematics Units 1 and 2 is highly recommended for those students who wish to study Specialist Mathematics Units 3 and 4. Students must also be studying Mathematical Methods Units 1 and 2 concurrently with this course. 

Enrolment in Specialist Mathematics Units 3 and 4 assumes a concurrent enrolment in, or previous completion, of Mathematical Methods Units 3 and 4. A large proportion of the material studied in Mathematical Methods 3 and 4 will be assumed knowledge for Specialist Mathematics Units 3 and 4.  The course is intended to provide an appropriate foundation for students wishing to undertake further study in, but not limited to, areas such as Science and Engineering. 

Unit 1 

In this unit students will investigate geometry in the plane and proof which includes proofs of circle theorems as well as the similarity and congruence of triangles. Students will undertake an investigation of the definitions and properties of natural, rational and complex numbers and employ proofs using various strategies such as the method of direct proof, proof by contrapositive and by mathematical induction. Students will review trigonometry and investigate the use and application of the sine and cosine rules in non-right angled triangles and solve problems involving direction and the angles of elevation and depression. The definition and properties of the natural and rational numbers will be discussed as well as the applications of set notation and sets when solving worded problems. Students will discuss arithmetic and geometric sequences and series, including the use of technology to assist in the solution of worded problems arising from these. The definition and properties of the complex numbers will be investigated including their representation on an argand diagram and their involvement in the general solution of quadratic equations. The topic of kinematics will be discussed and will include modelling and analysis of rectilinear motion under constant acceleration, including the use of the constant acceleration formulas. 

Unit 2 

In this unit students will cover vectors in the plane which will include the representation of vectors as directed line segments, with specific examples involving position, displacement and velocity. They will also be introduced to vector algebra and the application of vectors to geometric proofs, orienteering, navigation and statics. Cartesian, polar and parametric forms and graphs of lines, parabolas, circles, ellipses and hyperbola will be discussed and explored. Students will be introduced to and apply trigonometric identities including the Pythagorean identity; the angle sum, difference and double angle identities. Matrices will also be used to model situations and solve a range of problems including solving a system of simultaneous linear equations. Linear transformations of the plane will be explored and the effect of these linear transformations and their inverse transformations and compositions of these transformations on subsets of the plane such as points, lines, shapes and graphs will be discussed. Students will also undertake the study of statistics which includes simulations, sampling and sampling distributions including the introduction to random variables for discrete distributions. 

Unit 3 

In this unit students will cover proofs using various strategies such as the method of direct proof, proof by contrapositive and by mathematical induction. Students will solve and graph inverse circular functions, reciprocal functions, rational functions and other simple quotient functions and the absolute value function. They will investigate the expression of simple rational functions as a sum of partial fractions; the arithmetic and algebra of complex numbers, including polar form; points and curves in the complex plane; introduction to factorisation of polynomial functions over the complex field; and an informal treatment of the fundamental theorem of algebra. Students will cover the arithmetic and algebra of vectors, linear dependence and independence of a set of vectors and proof of geometric results using vectors. 

Unit 4 

In this unit students will cover advanced calculus techniques for analytic and numeric integration of a range of functions and their application in a variety of theoretical and practical situations including area and volume and kinematics. They will investigate vector representation of curves in the plane and vector kinematics in one and two dimensions. They will cover advanced calculus techniques for analytic and numeric differentiation of a range of functions and their application in a variety of theoretical and practical situations including curve sketching and differential equations. They will cover statistical inference related to the definition and distribution of sample means, simulations and confidence intervals for means and will include the investigation of hypothesis testing for a population mean.  

Prerequisites: A minimum Victorian Curriculum standard of ‘excellent’ for either Year 10 Mathematics Methods Core or Advanced Mathematics enter Unit 1 & 2. 

Additional Information: Students must have a Ti-Nspire CAS calculator as prescribed on the booklist and bring to every class. 

To access further information please click here: https://www.vcaa.vic.edu.au/curriculum/vce/vce-study-designs/specialistmathematics/Pages/Index.aspx  

Maths Pathways