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VCE Mathematics: Mathematical Methods


Mathematical Methods Units 1-4 cover functions, algebra, calculus, probability, and statistics. Students learn to represent and analyse polynomial, exponential, logarithmic, and circular functions, perform algebraic manipulations, and solve equations. The course includes differentiation and integration with applications to real-world problems, as well as data analysis and probability distributions. These units prepare students for STEM fields and provide a solid foundation for applying mathematics in various practical and theoretical contexts.

Prior Learning:

Prerequisites for Units 1 & 2: Successful completion of the Pre-Methods elective and/or Strong performance in High level mathematics class (Algebra and Graphing expecially). 

Prerequisites for Units 3 & 4: Successful completion of Units 1 and 2 Mathematical Methods.

Study design 2023-2027 (word doc)


Satisfactory completion 

Demonstrated achievement of the set of outcomes.

Outcome 1

Define and Explain Key Concepts

  • Define and explain key concepts from the areas of study.

  • Apply a range of related mathematical routines and procedures to solve practical problems from everyday and real-life contexts.

Outcome 2

Apply Mathematical Processes

  • Apply mathematical processes in practical, non-routine contexts.

  • Analyse and discuss the applications of mathematics in various situations, using investigative modelling or problem-solving approaches.

Outcome 3

Use Technology and Computational Thinking

  • Use computational thinking and the functionalities of technology (numerical, graphical, symbolic, and statistical).

  • Develop mathematical ideas, produce results, and perform analysis in practical situations requiring investigative modelling or problem-solving techniques.

Units 1 and 2: 

Individual school decision on the levels of achievement.

Unit 3:  

School assessed coursework (20%)

Unit 4: 

School assessed coursework (20%)

Units 3 and 4:

End-of-year examination 1 (20%)

End-of-year examination 2 (40%)



  • Functions and Graphs

    • Understanding different types of functions: linear, quadratic, polynomial, and rational.

    • Graphing functions and analysing their key features: intercepts, asymptotes, domain, and range.

    • Transformations of functions: translations, reflections, dilations, and rotations.

    • Inverse functions and their properties.

  • Algebra

    • Simplifying algebraic expressions.

    • Solving linear, quadratic, and simultaneous equations.

    • Factorising polynomials and using algebraic fractions.

    • Understanding and applying the binomial theorem.

  • Calculus (Introduction)

    • Concept of limits and continuity.

    • Differentiation of simple functions.

    • Basic rules of differentiation.

    • Applications of differentiation: finding slopes, tangents, and rates of change.

  • Exponential and Logarithmic Functions

    • Properties and graphs of exponential functions.

    • Properties and graphs of logarithmic functions.

    • Solving exponential and logarithmic equations.

    • Applications in real-world contexts, such as compound interest and population growth.

  • Trigonometry

    • Trigonometric functions and their graphs.

    • Solving trigonometric equations.

    • Trigonometric identities and simplification.

    • Applications of trigonometry in various contexts, including wave motion and circular motion.

  • Probability and Statistics

    • Basics of probability theory.

    • Calculating probabilities for single and multiple events.

    • Introduction to statistical data analysis.

    • Descriptive statistics: mean, median, mode, variance, and standard deviation.



  • Functions and Graphs

    • Graphing and analysing polynomial, exponential, logarithmic, and circular functions.

    • Key features of graphs: intercepts, asymptotes, domain, range, and behaviour at infinity.

    • Transformations of functions and their effects on graphs.

  • Algebra

    • Solving polynomial, exponential, logarithmic, and trigonometric equations.

    • Understanding and applying properties of algebraic structures.

    • Techniques for manipulating and solving complex algebraic expressions.

  • Calculus

    • Differentiation and its applications: finding tangents, rates of change, and optimisation problems.

    • Introduction to integration and its applications.

    • Understanding the relationship between differentiation and integration.

  • Calculus (Advanced)

    • Techniques of integration, including substitution and integration by parts.

    • Applications of integration: calculating areas, volumes, and solving differential equations.

    • Understanding and applying the Fundamental Theorem of Calculus.

  • Probability and Statistics

    • Probability theory: conditional probability, independence, and combinatorics.

    • Discrete and continuous probability distributions.

    • Statistical inference, hypothesis testing, and confidence intervals.

  • Functions and Algebra (Advanced)

    • In-depth study of functions, including inverse functions and composite functions.

    • Solving systems of equations.

    • Applications of advanced algebraic techniques to real-world problems.

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