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Our Mathematics Subjects

We’ve Got Your Back. All STEM related subjects, we have you covered.

( Engineering, Science, Mathematics, Commerce and Technology )

Subject description:

This subject introduces important mathematical methods required in engineering such as manipulating vector differential operators, computing multiple integrals and using integral theorems.

Topics including:

Vector Calculus, Gauss’ and Stokes’ Theorems; Sequences and Series; Fourier Series, Laplace Transforms, Systems of Homogeneous Ordinary Differential Equations, Phase Plane, Linearisation for Nonlinear Systems, Second Order Partial Differential Equations, Separation of Variables.

Subject description:

This study provides an introduction of fundamental aspects of Discrete Mathematics, which deals with 'things that come in chunks that can be counted'. It focuses on the enumeration of a set of numbers, Viz. Catalan numbers.

Topics including:

Sets and Functions, Counting Principles, Discrete Probability, Boolean Expressions, Mathematical Induction, Linear Recurrence Relations, Graphs and Trees.

Specialist Mathematics

Topics including:

Algebra and Structure
Logic and Algebra, Transformations, Trigonometry, Matrices

Arithmetic and Number
Number Systems, Recursion, Principles of Counting

Discrete Mathematics
Graph Theory

Geometry, Measurement and Trigonometry
Geometry in the Plane and Proof, Vectors in the Plane

Graphs of Linear and Non-linear Relations
Graphs of Linear and Non-linear Relations

Mathematical Methods

Topics including:

Functions and Graphs
Circular Functions, Graphs of Polynomials, Euler's Number, Exponential Functions, Logarithmic Functions

Algebra
Logs, Exponentials, Sine, Cosine, Tangent

Calculus
Differentiation, Integration, Velocity, Acceleration

Probability
Basics Probability, Discrete Random Variables, Continuous Random Variables

Further Mathematics

Topics including:

Functions and Graphs
Circular Functions, Graphs of Polynomials, Euler's Number, Exponential Functions, Logarithmic Functions

Algebra
Logs, Exponentials, Sine, Cosine, Tangent

Calculus
Differentiation, Integration, Velocity, Acceleration

Probability
Basics Probability, Discrete Random Variables, Continuous Random Variables

Mathematics: Analysis and Approaches HL
Mathematics: Analysis and Approaches SL

Topics including:

Number and Algebra
Permutations and Combinations, Partial Fractions, Complex Numbers, Proof by Induction, Contradiction and Counter-Example, Solutions of Systems of Linear Equation

Functions
Factors, Remainder Theorem, Sums of Polynomials, Products of Polynomials, Rational Functions, Odd and Even Functions, Self- Inverse Functions, Solving Function Inequalities, The Modulus Function

Geometry and Trigonometry
Reciprocal Trigonometric Ratios, Inverse Trigonometric Functions, Compound Angle Identity for Tangent, Symmetry Properties of Trigonometric Graphs, Vector Theory, Lines, Planes, Vector Algebra

Statistics and Probability
Bayes Theorem, Probability Distributions, Probability Density Functions, Expectation Algebra

Calculus
Introduction to Continuity and Differentiability, Convergence and Divergence, Derivatives of Inverse, Reciprocal Trigonometric Functions, Integration by Substitution and Parts, Volume of Revolutions, Solution of First Order Differential Equations, Euler's Method, Maclaurin Series

HSC Mathematics Extension 1
HSC Mathematics Extension 2

Topics including:

Functions
Further Work with Functions and Polynomials

Vectors
Further Work with Vectors
Introductions to Vectors

Complex Numbers
Introduction to Complex Numbers, Using Complex Numbers

Mechanics
Applications of Calculus to Mechanics

Calculus
Rates of Change

HSC Mathematics Advanced

Topics including:

Functions
Working with Functions

Trigonometric
Functions Trigonometry, Measure of Angles, Trigonometric Functions and Identities

Calculus
Introduction to Differentiation

Exponential and Logarithmic Functions Logarithms and Exponentials

Statistical Analysis
Probability and Discrete Probability Distributions

Functions
Graphing Techniques

Trigonometric Functions
Trigonometric Functions and Graphs

Calculus
Differential Calculus, The second derivative, Integral Calculus

Financial Mathematics
Modelling Financial Situations

Statistical Analysis
Descriptive Statistics, Bivariate Data Analysis, Random Variables

WACE Mathematical Application 3&4
WACE Mathematical Application 1&2

Topics including:

Mathematical Application 3&4
Bivariate Data Analysis, Growth and Decay in Sequences, Graphs and Networks, Time Series Analysis, Loans, Investments and Annuities, Networks and Decision Mathematics

Mathematical Application 1&2

Algebra, Measurement, Financial Mathematics, Geometry, Probability and Statistics.

IB Mathematics: Applications Interpretation (SL/HL)

Topics including:

Number and Algebra
Laws of Logarithms, Complex Numbers, Matrices, Geometric Transformations, Probability

Functions
Use of Log Graphs, Graphs Transformations, Further Trigonometric, Logarithmic, Rational, Logistic, Piecewise Functions

Geometry and Trigonometry
Vector Concepts, Kinematics, Applications of Adjacency Matrices, Tree Cycle Algorithms

Statistics and Probability
Binomial, Poisson Distributions, Designing Data Collection Methods, Tests for Reliability and Validity, Hypothesis Testing, Confidence Intervals

Calculus
Kinematics, Rates of Change, Volumes of Revolution, Models involving Differential Equations, Numerical and Analytical Methods, Slope Fields, Coupled and Second-Order Differential Equations

Foundation Mathematics

Topics including:

Space, Shape and Design
Geometric Conventions, Properties of Shapes and Objects, Use of Plans, Elevations, Maps, Models and Diagrams, Similarity and Symmetry, Pythagoras’ Theorem

Patterns and Number
Application of Integers, Decimals, Fractions, Ratios, Proportions, Percentages, Rates

Data
Use of Diagrammatic, Graphical and Tabular Forms, Interpretation of Diagrams, Charts, Tables and Graphs , Measures of Central Tendency (Averages), Comparison and Interpretation of Data Sets

Measurement
Metric Units and Measures, Derived Measures, Scales On Digital and Analogue Instruments, Estimation and Approximation Strategies, Time and Date Specifications, Conventions, Schedules, Timetables and Time Zones

Topics including:

Algebra and Structure
Linear Relations and Equations

Arithmetic and Number
Computation and Practical Arithmetic, Financial Arithmetic

Discrete mathematics
Matrices, Graphs and Networks, Number Patterns and Recursion

Geometry Measurement and Trigonometry
Shape and Measurement, Applications of Trigonometry

Graphs of Linear and Non-linear relations
Linear Graphs, Models, Inequalities, Linear Programming, Variation

Statistics
Data Distributions, Relationships between Two Numerical Variables

Mathematics Standard

Topics including:

Number and Place Value
Number and Place Value, Real Numbers, Money and Financial Mathematics, Patterns and Algebra, Linear and Non-Linear Relations

Measurement and Geometry
Using Units of Measurement, Geometric Reasoning

Statistics and Probability
Chance, Data Representation, Data Interpretation

Subject description:

The study of such fundamental ideas as length, area, volume, arc length and surface area. It is the basis for the integration theory used in advanced mathematics since it was developed by Henri Lebesgue in about 1900.

Topics including:

Measure Theory and Integration, Fubini's Theorem, Dominated Convergence Theorem, Fourier Analysis, Inversion Formula, Plancherel's Theorem, Probability Theory, The Law of Large Numbers.

Subject description:

This course provides a more advanced treatment of large sample approximation theory and some of its applications to statistical inference.

Topics including:

Simple Statistical Models, Taylor Series Expansions, Basic Concepts of Robust Estimation, Uses of Randomisation in Statistics, Basic Principles of Statistical Inference

Subject description:

This course introduces the necessary skills to model and solve such problems through the introduction of mathematical techniques of linear algebra, data analysis as well as statistical inference.

Topics including:

Vector Techniques on Lines and Planes, Matrix Manipulations in Engineering Problems, Systems of Linear Algebraic Equations, Calculating Inverses of Matrices, Exploratory Statistics, Inferential Statistics, Logical Mathematical Arguments for Engineering Problems

Complex Numbers, Functions of a Single Variable, Limits and Continuity, Differentiation, Optimisation, Taylor Polynomials, Taylor’s Theorem, Taylor Series, Riemann Sums, Riemann Integrals, Intermediate Value Theorem, Rolle’s Theorem, Mean Value Theorem