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VCE Mathematics: General Mathematics

Aim

General Mathematics Units 1-4 aim to equip students with practical mathematical skills for real-world applications. The course focuses on data analysis, probability, statistics, financial mathematics, and discrete mathematics. Students develop computational thinking, problem-solving abilities, and effective use of technology. The curriculum prepares students for further study, general employment, or business by fostering critical thinking and the ability to model, analyse, and communicate mathematical information. This sequence provides a solid foundation for advanced mathematical studies and practical problem-solving in everyday contexts.


All assessments in General mathematics utilise the CAS calcultor.


Prior Learning:

Prerequisites for Units 1 & 2: Successful completion of Year 10 Mathematics.

Prerequisites for Units 3 & 4: Successful completion of Units 1 and 2 General Mathematics.


Study design 2023-2027 (word doc)

Assessments

Satisfactory completion

Demonstrated achievement of the set of outcomes.


Outcome 1

Application of Mathematical Concepts and Procedures 

  • Use and apply a range of mathematical concepts, skills, and procedures to solve practical problems from real-life contexts.

Outcome 2

Mathematical Processes in Practical Contexts 

  • Apply mathematical processes in practical, non-routine contexts.
    Analyse and discuss the applications of mathematics in various situations, employing investigative modelling or problem-solving approaches.

Outcome 3

Computational Thinking and Technology

  • Use computational thinking and technology.

  • Apply numerical, graphical, symbolic, and statistical functionalities of technology to develop mathematical ideas, produce results, and perform analysis in practical situations requiring investigative modelling or problem-solving.

Assessment Tasks

Units 1 and 2:

Individual school decision on the levels of achievement.


Unit 3:  

School assessed coursework (24%)


Unit 4:

School assessed coursework (16%)


Units 3 and 4:  

End-of-year examination 1 (30%)

End-of-year examination 2 (30%)


Study Design (word doc)



UNIT 1

UNIT 2

  • Investigating and Comparing Data Distributions

    • Types of data: categorical (nominal, ordinal) and numerical (discrete, continuous).

    • Displaying data distributions using frequency tables, bar charts, histograms, stem plots, and dot plots.

    • Summary statistics: median, range, interquartile range (IQR), mean, and standard deviation.

    • Comparing distributions with back-to-back stem plots or parallel boxplots.

  • Number atterns and Financial Mathematics

    • Generating sequences using first-order linear recurrence relations.

    • Modelling linear growth or decay (e.g., simple interest, depreciation).

    • Geometric sequences for growth and decay (e.g., compound interest).

    • Financial applications: percentage increase/decrease, GST, and inflation.

  • Linear Functions, Graphs, Equations, and Models

    • Graphing linear functions and interpreting parameters.

    • Formulating and analysing linear models from descriptions or data.

    • Solving linear and simultaneous linear equations.

    • Piecewise linear graphs for practical situations (e.g., tax scales).

  • Matrices

    • Using matrices to store and display information.

    • Types of matrices and basic operations (addition, subtraction, scalar multiplication, matrix multiplication).

    • Modelling practical problems using matrices (e.g., costing).

    • Introduction to transition matrices for population growth or decay.

  • Investigating Relationships Between Two Numerical Variables

    • Identifying response and explanatory variables.

    • Using scatterplots to describe associations between variables.

    • Making predictions using lines of best fit.

    • Understanding interpolation and extrapolation.

  • Graphs and Networks

    • Basic graph notation: edge, vertex, degree, adjacency matrix.

    • Types of graphs: isomorphic, connected, planar.

    • Euler’s formula for planar graphs.

    • Practical applications of connected graphs and shortest path problems.

    • Trees and minimum spanning trees using greedy algorithms.

  • Variation

    • Direct and inverse variation: numerical, graphical, and algebraic approaches.

    • Transforming data to linearity for modelling relationships.

  • Space, Measurement, and Applications of Trigonometry

    • Units of measurement for length, angle, area, volume, and capacity.

    • Calculating perimeter and areas of shapes and volumes of solids.

    • Pythagoras’ theorem and trigonometric ratios for right-angled triangles.

    • Sine and cosine rules for non-right-angled triangles.



UNIT 3

UNIT 4

  • Data Analysis, Probability, and Statistics

    • Types of data: categorical (nominal, ordinal) and numerical (discrete, continuous).

    • Displaying data distributions using various charts and graphs.

    • Summary statistics: median, mean, range, and standard deviation.Investigating associations between variables using scatterplots, correlation coefficients, and regression analysis.

    • Understanding causation versus correlation.

  • Recursion and Financial Modelling

    • Introduction to recursion and recurrence relations.

    • Modelling financial scenarios: loans, investments, and annuities.

    • Using recursion to solve real-world problems.

    • Understanding and applying financial mathematics concepts like compound interest and amortisation.

  • Matrices

    • Basic operations: addition, subtraction, scalar multiplication, and matrix multiplication.

    • Using matrices to represent and solve systems of linear equations.

    • Applications of matrices in real-world contexts such as transformations and network analysis.

    • Understanding the inverse of a matrix and its applications.

  • Networks and Decision Mathematics

    • Graph theory: vertices, edges, paths, and circuits.

    • Types of graphs: connected, planar, and weighted.

    • Algorithms for finding shortest paths and minimal spanning trees.

    • Practical applications of networks in various fields such as transportation and communication.


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