VCE General Mathematics - Syllabus & Notes
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Study VCE General Mathematics Topics
What is a Graph?
Setting Up and Interpreting Transition Matrices
The Basics of a Matrix
Trigonometry Basics
Approximations, Decimal Places, and Significant Figures
Time Series Data
The Squared Transformation
Fitting a Least Squares Regression Line to Numerical Data
Scatterplots
Classifying and Displaying Categorical Data
Direct Variation
Substitution of Values Into a Formula and Constructing a Table of Values
Modelling Compound Interest Investments With Additions to the Principal
Sequences and Recurrence Relations
Number Patterns
Percentages
Isomorphic (Equivalent) Connected Graphs and Adjacency Matrices
Transition Matrices – Using Recursion
Adding and Subtracting Matrices
Finding an Unknown Side in a Right-Angled Triangle
Pythagoras’ Theorem
Smoothing a Time Series Using Moving Means
The Log Transformation
Using the Least Squares Regression Line to Model a Relationship Between Variables
How to Interpret a Scatterplot
Interpreting and Describing Frequency Tables and Bar Charts
Inverse Variation
Solving Linear Equations and Developing Formulas
Analysing and Modelling Reducing Balance Loans and Annuities
Modelling Linear Growth and Decay
Writing Recurrence Relations in Symbolic Form
Percentage Increase and Decrease
Planar Graphs and Euler’s Formula
Transition Matrices – Using a Certain Rule
Scalar Multiplication
Finding an Angle in a Right-Angled Triangle
Perimeter and Area
Smoothing a Time Series Plot Using Moving Medians
The Reciprocal Transformation
Conducting a Regression Analysis Using Data
Pearson’s Correlation Coefficient (r)
Displaying and Describing Numerical Data
Data Transformations
Developing a Formula: Setting Up and Solving an Equation in Two Unknowns
Amortisation Tables
Using an Explicit Rule for Linear Growth or Decay
An Introduction to Arithmetic Sequences
Goods and Services Tax (GST)
Walks, Trails, Paths, Circuits, and Cycles
Leslie Matrices
Matrix Multiplication
Applications of Right-Angled Triangles
Length of an Arc and Area of a Sector
Seasonal Indices
Choosing and Applying the Appropriate Transformation
Fitting a Linear Model to the Data
Characteristics of Distributions, Dot Plots, and Stem Plots
Logarithms
Drawing Straight-Line Graphs and Finding Their Slope
Analysing Financial Situations Using Amortisation Tables
Modelling Geometric Growth and Decay
Arithmetic Sequences Using Recursion
Ratio and Proportion
Eulerian Trails and Circuits (Extension)
Inverse Matrices and Solving Simultaneous Equations Using Matrices
Angles of Elevation and Depression
Volume
Fitting a Trend Line and Forecasting
Interpreting and Predicting From a Linear Model
Measures of Centre
Further Modelling of Non-Linear Data
Equations of Straight Lines
Using a Finance Solver to Find the Balance and Final Payment
Using an Explicit Rule for Geometric Growth or Decay
Finance Applications Using Arithmetic Sequences and Recurrence Relations
Dividing Quantities in Given Ratios
Hamiltonian Paths and Cycles (Extension)
Using Matrices to Model Road and Communication Networks
Bearings and Navigation
Volume of a Pyramid
Bivariate Data – Classifying the Variables
Measures of Spread
Finding the Equation of a Straight-Line Graph
Using a Finance Solver to Find Interest Rates, Time Taken, and Regular Payments
Interest Rates Over Different Time Periods and Effective Interest Rates
An Introduction to Geometric Sequences
Unitary Method
Weighted Graphs, Networks, and the Shortest Path Problem
Introduction to Transition Matrices
The Sine Rule
Surface Area
Investigating Associations Between Categorical Variables
Percentages of Data Lying Within Multiple Standard Deviations of the Mean
Linear Modelling
Solving Harder Financial Problems
Recursion With Geometric Sequences
Minimum Spanning Trees and Greedy Algorithms
Answering Questions That Require Multiple Applications of a Transition Matrix
The Cosine Rule
Similar Figures
Investigating the Association Between a Numerical and a Categorical Variable
Boxplots
Solving Simultaneous Equations
Interest-Only Loans
Finance Applications Using Geometric Sequences and Recurrence Relations
Graphs and Networks
Applications of Matrices
The Area of a Triangle
Similar Triangles
Investigating Associations Between Two Numerical Variables
Comparing the Distribution of a Numerical Variable Across Groups
Practical Applications of Simultaneous Equations
Perpetuities
Finding Term n in a Sequence Modelling Geometric Growth and Decay
Adjacency Matrices
What is a Matrix?
Similar Solids
How to Interpret a Scatterplot - Further Exploration
Types of Data
Piecewise Linear Graphs
Exploring and Travelling
Using Matrices to Represent Information
Strength of a Linear Relationship: The Correlation Coefficient
Displaying and Describing the Distributions of Categorical Variables
Weighted Graphs and Networks
Matrix Arithmetic: Addition, Subtraction, and Scalar Multiplication
The Coefficient of Determination
Displaying and Describing Numerical Data - Further Exploration
Dijkstra’s Algorithm
Matrix Arithmetic: The Product of Two Matrices
Correlation and Causality
Dot Plots and Stem Plots
Trees and Minimum Connector Problems
Matrix Inverse, the Determinant, and Matrix Equations
Using a Logarithmic (Base 10) Scale to Display Data
Flow Problems
Binary, Permutation, and Communication Matrices
Measures of Centre and Spread
Matching and Allocation Problems
Dominance Matrices
The Five-Number Summary and the Boxplot
Precedence Tables and Activity Networks
The Normal Distribution and the 68–95–99.7% Rule
Scheduling Problems
Crashing
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