General Mathematics Units 3&4

Quick Links:
​Area of Study 1 - Data Analysis
Area of Study 2 - Recursion and Financial Modelling
Area of Study 2 - Matrices
Area of Study 2 - Networks and Decision Mathematics
  • Study Design
  • Unit Materials
  • VCAA Resources
  • Exam Report Summaries
  • Changelog
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​VCAA General Mathematics

​General Mathematics Examination Information
Bound Reference Specifications
VCAA Formula Sheet

​​General Mathematics Implementation Videos
Advice for Teachers (2016-2022)
Planning: Sample Course, Employability Skills, Resources ​
Sample Learning Activities

​Assessment: Scope of Tasks, Sample SACs, Performance Descriptors
Unit 3 SAC - How to develop an application task
Unit 3 SAC - How to develop a modelling or problem-solving task for Recursion and financial modelling
Unit 4 SAC - How to develop a modelling or problem-solving task for Matrices
Unit 4 SAC - How to develop a modelling or problem-solving task for Networks and decision mathematics​
​
Past Exams and Examination Reports
​Northern Hemisphere Past Exams and Examination Reports
​Multiple Choice Answer Sheet (Last Page of the PDF)

Previous Years Grade Distributions (Click Year, Click Section 3, Click Subject)

Area of Study 1 - Data Analysis, Probability, and Statistics

Data Analysis
​Study Design
​Data Analysis Summary
  • Notes
  • Videos & Interactives
  • Exam Questions
  • Questions
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Investigating Data Distributions
Types of Data
Categorical Distributions
Numerical Distributions
​The Log (Base 10) Scale
​Summary of the Distribution of Numerical Variables
​The Normal Distribution (The 68-95-99.7% Rule)
Standardised Values (z-Scores)

Investigating Data Distributions
TI-nSpire
​Casio

​Investigating Associations Between Two Variables
Response and Explanatory Variables
​Associations between Categorical Variables
Associations between Numerical and Categorical Variables
Associations between Numerical Variable: Scatterplots
​Pearson's Product Moment Correlation Coefficient
Calculating the Correlation Coefficient Manually (Optional)
Cause and Effect

​Investigating Associations Between Two Variables
TI-nSpire
Casio

Investigating and Modelling Linear Associations
Determining the Least Squares Regression Line
​Sketching a Least Squares Regression Line
​Interpreting a Least Squares Regression Line
​Predicting with a Least Squares Regression Line
​Coefficient of Determination
​​Residual Analysis ​
Data Transformations
​Determining the Best Transformation
​Predicting with a Transformed Least Squares Regression Line

Investigating and Modelling Linear Associations
TI-nSpire
​Casio 

​Investigating and Modelling Time Series Data
​Time Series
​Numerical Smoothing - Moving Mean
Graphical Smoothing - Moving Median
​Seasonal Adjustment ​
Modelling Trends and Forecasting
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​Investigating and Modelling Time Series Data
TI-nSpire
​Casio
Investigating Data Distributions
Classifying Data (Maffs Guru Video)
Displaying and Describing the Distributions of Categorical Variables (Maffs Guru Video)
Dot Plots and Stem Plots (Maffs Guru Video)
​Displaying and Describing the Distributions of Numerical Variables (Maffs Guru Video)
Boxplots (GeoGebra Interactive)
The Five Number Summary and the Box Plot (Maffs Guru Video)
Using Box Plots to Describe and Compare Distributions (Maffs Guru Video)
Logarithms, Explained (TED-Ed Video)
Using a Log Scale to Display Data (Maffs Guru Video)
The Median, Range, and Interquartile Range IQR (Maffs Guru Video)
Mean, Median, and Mode: Measures of Central Tendency (Crash Course Video)
Measures of Spread (Crash Course Video)
​Resistance of Mean and Median (GeoGebra Interactive)
Charts Area Like Pasta - Data Visualisation Part 1 (Crash Course Video)
Plots, Outliers, and Justin Timberlake: Data Visualisation Part 2 (Crash Course Video)
The Shape of Data: Distributions (Crash Course Video)
Describing the Centre and Spread of Symmetric Distributions (Maffs Guru Video)
Relating a Box Plot to Shape (Maffs Guru Video)
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The Normal Distribution and the 68-95-99.7% Rule (Maffs Guru Video)
Standard Scores (Maffs Guru Video)
Z-Score and Percentiles (Crash Course Video)​

Investigating Associations Between Two Variables
Response and Explanatory Variables (Maffs Guru Video)
Investigating Associations between Categorical Variables (Maffs Guru Video)
Using Two Way Tables to Investigate Associations between Categorical Variables (Joel Speranza Math Video)
Composite Bar Charts (Corbettmaths Video)
Investigating the Association between a Numerical and a Categorical Variable (Maffs Guru Video)
How to Interpret a Scatterplot (Maffs Guru Video)

​Correlation
​Pearson's Correlation Coefficient
Calculating the Correlation Coefficient (Maffs Guru Video)
Scatterplot from Correlation (GeoGebra Interactive)
Which Graph? (Maffs Guru Video)
Correlation and Causality (Maffs Guru Video)
The Question of Causation: Smoking and Cancer (Annenberg Learner Video) [Broken?]
​Correlation and Causation (Khan Academy Video)
Correlation Doesn't Equal Causation (Crash Course Video)
​Spurious Correlations (Tyler Vigen Article)
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Investigating and Modelling Linear Associations
Determining the Equation of the Least Squares Line (Maffs Guru Video)
Least-Squares Regression (PhET Interactive)
Performing a Regression Analysis (Maffs Guru Video)
Conducting a Regression Analysis using Raw Data (Maffs Guru Video)
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​Fitting Equations to Data (Crash Course Video)
Regression Analysis: Ordinary Least Squares (Seeing Theory Interactive)
Regression Line and Residual Introduction (Khan Acadmey Video)
The Coefficient of Determination (Maffs Guru Video)
View of Challenging misconceptions about the coefficient of determination (R^2) with a dynamic Geogebra applet (Meagher, Edwards, Ozg ̈un-Koca Article and Interactive)

Data Transform Introduction (Maffs Guru Video)
Using Data Transformation to Linearise a Scatter Plot (Maffs Guru Video)
The Log Transformation (Maffs Guru Video)
The Reciprocal Transformation (Maffs Guru Video)
Least Squares Regression Line (Maffs Guru Video)

Investigating and Modelling Time Series Data
Time Series Analysis: The Basics (ABS Article)​
Time Series Data (Maffs Guru Video)
Smoothing a Time Series Plot using Moving Means (Maffs Guru Video)
Smoothing a Time Series Plot using Moving Medians (Maffs Guru Video)
Seasonal Indices (Maffs Guru Video)
Fitting a Trend Line and Forecasting (Maffs Guru Video)
Solutions to past VCAA exam questions can be looked up in the appropriate examiner's report on the Further Mathematics Past Examinations and Examination Reports page or the Northern Hemisphere Timetable (NHT) Past Examinations and Examination Reports page. Exam 1 is multiple choice. Exam 2 is short answer. 

Investigating Data Distributions
Types of Data (2016-2022 Study Design Questions)
Types of Data (2000-2015 Study Design Questions)
Categorical Data (2016-2022 Study Design Questions)
Categorical Data (2000-2015 Study Design Questions)
Numerical Data: Dot Plots, Stem Plots, and Histograms (2016-2022 Study Design Questions)
Numerical Data: Dot Plots, Stem Plots, and Histograms (2000-2015 Study Design Questions)
​Histograms using a Log (Base 10) Scale (2016-2022 Study Design Questions)
Numerical Data: Boxplots, Fences, and Outliers (2016-2022 Study Design Questions)
Numerical Data: Boxplots, Fences, and Outliers (2000-2015 Study Design Questions)
Numerical Data: Mean and Standard Deviation (2016-2022 Study Design Questions)
Numerical Data: Mean and Standard Deviation (2000-2015 Study Design Questions)
Normal Distribution (2016-2022 Study Design Questions)
Normal Distribution (2000-2015 Study Design Questions)

Investigating Associations Between Two Variables
Response and Explanatory Variables (2016-2022 Study Design Questions)
​Response and Explanatory Variables (2000-2015 Study Design Questions)
Association between Categorical Variables (2016-2022 Study Design Questions)
Associations between Categorical Variables (2000-2015 Study Design Questions)
​Association between Numerical and Categorical Variables ​(2016-2022 Study Design Questions)
​Association between Numerical and Categorical Variables (2000-2015 Design Questions)
Scatterplots: Association between Numerical Variables (2016-2022 Study Design Questions)
Scatterplots: Association between Numerical Variables (2000-2015 Study Design Questions)
​Correlation Coefficient (2016-2022 Study Design Questions)
Correlation Coefficient (2000-2015 Study Design Questions)
Correlation vs. Causation (2016-2022 Study Design Questions)
​Correlation vs. Causation (2000-2015 Study Design Questions)
Which Display? (2016-2022 Study Design Questions)
Which Display? (2000-2015 Study Design Questions)

​Investigating and Modelling Linear Associations
​Determine and Draw Least-Squares Lines (2016-2022 Study Design Questions)
Determine and Draw Least-Squares Lines (2000-2015 Study Design Questions)
​Using and Analysing the Least-Squares Line (2016-2022 Study Design Questions)
Using and Analysing the Least-Squares Line (2000-2015 Study Design Questions)
​Coefficient of Determination (2016-2022 Study Design Questions)
Coefficient of Determination (2000-2015 Study Design Questions)
​Residual Analysis (2016-2022 Study Design Questions)
Residual Analysis (2000-2015 Study Design Questions)
Transformations (2016-2022 Study Design Questions)
​Transformations (2000-2015 Study Design Questions)

Investigating and Modelling Time Series Data
​Features of a Time Series (2016-2022 Study Design Questions)
Features of a Time Series (2000-2015 Study Design Questions)
Smoothing (2016-2022 Study Design Questions)
Smoothing (2000-2015 Study Design Questions)
Seasonal Adjustment (2016-2022 Study Design Questions)
Seasonal Adjustment (2000-2015 Study Design Questions)
​Linear Trends and Forecasting (2016-2022 Study Design Questions)
​​Linear Trends and Forecasting (2000-2015 ​Study Design Questions)
Investigating Data Distributions
What's the difference between numerical and categorical data? (Worksheet)
​Quartiles (mathworksheets4kids)
Five-Number Summary (mathworksheets4kids)
Box-and-Whisker Plot (mathworksheets4kids)
Box-and-Whisker Plot Worded (mathworksheets4kids)
Read and Interpret the Boxplot 1 (mathworksheets4kids)
Read and Interpret the Boxplot 2 (mathworksheets4kids)
Make and Interpret the Boxplot (mathworksheets4kids)
Outliers (mathworksheets4kids)
68-95-99.7 Rule (Worksheet)
68-95-99.7% Rule - Determine Percentage (Interactive Practice)
z-Score (Worksheet)
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Investigating Associations Between Two Variables
Scatterplots (Corbettmaths)
​Scatterplots (Corbettmaths Exam Style)
Scatter Diagrams (MathsHKO)
Scatter Plots: Correlation Strength (Variation Theory)
Guess the Correlation (Interactive Practice)
​Direction, Strength, and Form of Scatterplots (Worksheet)
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Investigating and Modelling Linear Associations

Investigating and Modelling Time Series Data
​

Area of Study 2 - Discrete Mathematics

Recursion and Financial Modelling
Study Design
​Recursion & Financial Modelling Summary
​​Relationships Between Financial Models
  • Notes
  • Videos & Interactives
  • Exam Questions
  • Questions
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Recurrence Relations (Maffs Guru Video)
Modelling Linear Growth and Decay (Maffs Guru Video)
Rules for Linear Growth and Decay (Maffs Guru Video)
Modelling Geometric Growth and Decay (Maffs Guru Video)
A Rule for the nth Term in a Sequence Representing Geometric Growth or Decay (Maffs Guru Video)
Nominal and Effective Interest Rates (Maffs Guru Video)
Combining Geometric Growth and Linear Decay (Maffs Guru Video)
Analysing Reducing Balance Loans with Recurrence Relations (Maffs Guru Video)
Amortisation tables (Maffs Guru Video)
Annuities (Maffs Guru Video)
Perpetuities (Maffs Guru Video)
Compound Interest Investments with Regular Additions to the Principal (Maffs Guru Video)
Using a finance solver to find the balance and final payment (Maffs Guru Video)
Using a finance solver to find interest rates time takes and regular payments (Maffs Guru Video)

Simple Interest and Flat Rate Depreciation Calculator ​(GeoGebra Interactive)
Compound Interest and Reducing Balance Depreciation Calculator ​​(GeoGebra Interactive)
​TVM Finance Solver Calculator ​​(GeoGebra Interactive)
Solutions to past VCAA exam questions can be looked up in the appropriate examiner's report on the Further Mathematics Past Examinations and Examination Reports page or the Northern Hemisphere Timetable (NHT) Past Examinations and Examination Reports page. Exam 1 is multiple choice. Exam 2 is short answer. 
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​Generating Terms of a Recurrence Relation (2016-2022 Study Design Questions)
​Generating Terms of a Recurrence Relation (2000-2015 Study Design Questions)
​Writing and Interpreting Linear Recurrence Relations (2016-2022 Study Design Questions)
Writing and Interpreting Linear Recurrence Relations (2000-2015 Study Design Questions)
Using Recurrence Relations (2016-2022 Study Design Questions)
​Using Recurrence Relations (2000-2015 Study Design Questions)
Using Rules (2016-2022 Study Design Questions)
Using Rules (Depreciation) (2000-2015 Study Design Questions)
​Using Rules (Interest) (2000-2015 Study Design Questions)
Effective Interest Rates (2016-2022 Study Design Questions)
Using Tables (2016-2022 Study Design Questions)
​Using Finance Solver (2016-2022 Study Design Questions)
Using Finance Solver (2000-2015 ​Study Design Questions)
Depreciation of Assets
Recurrence Relations (Starting Points Maths)
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​Compound Interest Investments and Loans
Compound Interest (Mathsbot Completion Table)
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​Reducing Balance Loans

​Annuities and Perpetuities

​Annuity Investments

Matrices
​Study Design
​​Matrices Summary
  • Notes
  • Videos & Interactives
  • Exam Questions
  • Questions
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What is a Matrix? (Maffs Guru Video)
Using Matrices to Represent Information (Maffs Guru Video)
Matrix Arithmetic: Addition, Subtraction, and Scalar Multiplication (Maffs Guru Video)
Matrix Arithmetic: The Product of Two Matrices (Maffs Guru Video)
Multiplying Matrices by Each Other (Joel Speranza Math Video)
Matrix Powers (Maffs Guru Video)
How to organise, add and multiply matrices (TED-Ed Video)
Matrix Equality (Joel Speranza Math Video)
​Matrix Calculations on the TI Nspire (Joel Speranza Math Video)
Storing Information in Matrices (Joel Speranza Math Video)
Using matrices to manipulate data: Game show (Khan Academy Video)
Using matrices to manipulate data: Pet store (Khan Academy Video
An Application of Matrix Multiplication (Joel Speranza Math Video)
Transpose of a Matrix and an Application of a Matrix Transpose (Joel Speranza Math Video)
Communication Matrices (Joel Speranza Math Video)

The Identity Matrix (Joel Speranza Math Video)
​Intro to determinant notation and computation (Khan Academy Video)
The Inverse Matrix (Maffs Guru Video)
The Multiplicative Inverse of a Matrix (Joel Speranza Math Video)
Solving Matrix Equations using the Multiplicative Inverse (Joel Speranza Math Video)
Simultaneous Equations using Matrices (Joel Speranza Math Video)
Applications of the Inverse Matrix Solving Simultaneous Linear Equations (Maffs Guru Video)​
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Transition Matrices and their Applications (Maffs Guru Video)
Leslie Matrices for Population Age Distribution Modelling (Joel Speranza Math Video)
Leslie Matrices - What's really going on? (Joel Speranza Math Video)
Leslie Matrices (Maffs Guru Video)
Solutions to past VCAA exam questions can be looked up in the appropriate examiner's report on the Further Mathematics Past Examinations and Examination Reports page or the Northern Hemisphere Timetable (NHT) Past Examinations and Examination Reports page. Exam 1 is multiple choice. Exam 2 is short answer. 
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Order and Elements of Matrices (2016-2022 Study Design Questions)
​Order and Elements of Matrices (2000-2015 Study Design Questions)
​Matrix Arithmetic (2016-2022 Study Design Questions)
​​Matrix Arithmetic (2000-2015 Study Design Questions)
​Numerical Information in Matrices (2016-2022 Study Design Questions)
​Numerical Information in Matrices (2000-2015 Study Design Questions)
​Inverse Matrix (2016-2022 Study Design Questions)
​Inverse Matrix (2000-2015 Study Design Questions)
​Communication and Dominance (2016-2022 Study Design Questions)
​Communication and Dominance (2000-2015 Study Design Questions)
Systems of Linear Equations (2016-2022 Study Design Questions)
​Systems of Linear Equations (2000-2015 Study Design Questions)
​Transition Matrices and Diagrams (2016-2022 Study Design Questions)
​​Transition Matrices and Diagrams (2000-2015 Study Design Questions)
​Matrix Recursion S_(n+1)=TS_n (2016-2022 Study Design Questions)
​Matrix Recursion S_(n+1)=TS_n (2000-2015 Study Design Questions)
Steady State / Equilibrium State / Long Term (2016-2022 Study Design Questions)
​Steady State / Equilibrium State / Long Term (2000-2015 Study Design Questions)
​Matrix Recursion S_(n+1)=TS_n+B (2016-2022 Study Design Questions)
​​Matrix Recursion S_(n+1)=TS_n+B (2000-2015 ​Study Design Questions)
​Elements of a Matrix (mathworksheets4kids)
Addition of Square Matrices (mathworksheets4kids)
Addition of Matrices (mathworksheets4kids)
Subtraction of Square Matrices (mathworksheets4kids)
Subtraction of Matrices (mathworksheets4kids)
Scalar Multiplication of Matrices (mathworksheets4kids)
Multiplication of Square Matrices (mathworksheets4kids)
Multiplication of Matrices 1 (mathworksheets4kids)
Multiplication of Matrices 2 (mathworksheets4kids)
Order of Matrix Products 1 (mathworksheets4kids)
Order of Matrix Products 2 (mathworksheets4kids)
Matrix Arithmetic (Corbettmaths Exam Style)
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Determinant of 2×2 Matrices 1 (mathworksheets4kids)
Determinant of 2×2 Matrices 2 (mathworksheets4kids)
​2×2 Determinant Practice (Interactive Practice)
Determinant of 3×3 Matrices (mathworksheets4kids)
Check if Inverse Exists (mathworksheets4kids)
Inverse of 2×2 Matrices (mathworksheets4kids)
Inverse of 3×3 Matrices (mathworksheets4kids)
Networks and Decision Mathematics
Study Design
​Networks and Decision Mathematics Summary
  • Notes
  • Videos & Interactives
  • Exam Questions
  • Questions
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Rediscovering Euler's Formula with a Mug (not that Euler's Formula) (3Brown1Blue Video)
​Euler's Formula and Graph Duality (3Brown1Blue Video)

The Bridges of Konigsberg
Vertices and Edges (D3 Graph Theory Interactive)
Degree of a Vertex (D3 Graph Theory Interactive)
Complete Graph (D3 Graph Theory Interactive)
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Graphs and Networks (Maffs Guru Video)
Adjacency Matrices (Maffs Guru Video)
Planar Graphs Introduction - Equivalent (Isomorphic Graphs) and Drawing Graphs in Planar Form (Joel Speranza Math Video)
Planar Graphs - Euler's Formula (Joel Speranza Math Video)
Walk (D3 Graph Theory Interactive)
Open vs Closed Walks (D3 Graph Theory Interactive)
Networks: Open and Closed Walks (Joel Speranza Math Video)
Connectivity (D3 Graph Theory Interactive)
Networks Trails and Paths (Joel Speranza Math Video)
Networks Weighted Graphs Shortest Paths and the Travelling Salesperson Problem (Joel Speranza Math Video)
Networks: Eulerian Graphs and Semi-Eulerian Graphs (Joel Speranza Math Video)
Eulerian Circuit (D3 Graph Theory Interactive)
Eulerian Trail (D3 Graph Theory Interactive)
Hamiltonian and Semi Hamiltonian Graphs (Joel Speranza Math Video)
Exploring and travelling (Maffs Guru Video)

​Networks: Intro to Trees (Joel Speranza Math Video)
Networks: Prim's Algorithm for Finding Minimum Spanning Trees (Joel Speranza Math Video)
Trees (D3 Graph Theory Interactive)
Spanning Tree of a Graph (D3 Graph Theory ​Interactive)
Prim's Algorithm Solver (Jake Baker Maths Interactive)
Trees and minimum connector problems (Maffs Guru Video)

Flow problems (Maffs Guru Video)
Maximum Flow Minimum Cut Algorithm (Joel Speranza Math Video)
​Ford-Fulkerson Algorithm (Michael Sambol Video) [Optional]
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​Dijkstra's Algorithms: A Quick Intro on How it Works (PatrickJMT Video)
Weighted graphs and networks (Dijkstra's algorithm) (Maffs Guru Video)
Shortest Path Solver​ (Julian Browne Interactive)

Bipartite Graph (D3 Graph Theory Interactive)
Bipartite Graphs and Assignment Problems (Joel Speranza Math Video)
Complete Bipartite Graph (D3 Graph Theory ​Interactive)
​Hungarian Algorithm Solver ​(HungarianAlgorithm.com Interactive)
The Hungarian Algorithm for Weighted Assignments (Joel Speranza Math Video)
​​Graph Creator (yED Live Interactive)
Matching and allocation problems (Maffs Guru Video)
Maximum allocation problem - Hungarian Algorithm (RouTube Video)

Activity Networks and Precedence Tables (Joel Speranza Math Video)
Activity Networks and Dummy Activities (Joel Speranza Math Video)​
Weighted Precedence Tables and Float Times (Joel Speranza Math Video)
Critical Path Analysis Earliest Starting Time and Latest Finishing Time (Joel Speranza Math Video)
Critical Path Analysis Latest Starting Time (Joel Speranza Math Video)
​Scheduling problems (Maffs Guru Video)
Precedence tables and activity networks (Maffs Guru Video)

How to draw a PDM network diagram (Engineer4Free Video)
Construct a PDM network diagram when given a table of dependencies (Engineer4Free Video)
Construct a table of dependencies when given a PDM network diagram (Engineer4Free Video)
Use forward and backward pass to determine project duration and critical path (Engineer4Free Video)
Determine the Early Start (ES) and Early Finish (EF) of activities in a PDM network diagram (Engineer4Free Video)
Determine Late Start (LS) and Late Finish (LF) of acitivies in PDM network diagram (Engineer4Free Video)
What is Total Float (Total Slack) and how to calculate it in a network diagram (Engineer4Free Video)

Crashing (Maffs Guru Video)
Solutions to past VCAA exam questions can be looked up in the appropriate examiner's report on the Further Mathematics Past Examinations and Examination Reports page or the Northern Hemisphere Timetable (NHT) Past Examinations and Examination Reports page. Exam 1 is multiple choice. Exam 2 is short answer. 

​Constructing Graphs and Networks ​(2016-2022 Study Design Questions)
​Constructing Graphs and Networks (2000-2015 Study Design Questions)
Features of Graphs and the Degree of a Vertex (2016-2022 Study Design Questions)
Features of Graphs and the Degree of a Vertex (2000-2015 Study Design Questions)
​Euler's Formula and Planar Graphs (2016-2022 Study Design Questions)
Euler's Formula and Planar Graphs (2000-2015 Study Design Questions)
​Matrix Representation (2016-2022 Study Design Questions)
​Matrix Representation (2000-2015 Study Design Questions)
​Types of Graphs and Walks (2016-2022 Study Design Questions)
​Types of Graphs and Walks (2000-2015 Study Design Questions)
​Exploring and Travelling Problems (2016-2022 Study Design Questions)
Exploring and Travelling Problems (2000-2015 Study Design Questions)
​Minimum Connector Problems (2016-2022 Study Design Questions)
​Minimum Connector Problems (2000-2015 Study Design Questions)
​Flow Problems (2016-2022 Study Design Questions)
Flow Problems (2000-2015 Study Design Questions)
​Shortest Path Problems (2016-2022 Study Design Questions)
Shortest Path Problems (2000-2015 Study Design Questions)
​Matching Problems (2016-2022 Study Design Questions)
Matching Problems (2000-2015 Study Design Questions)
​Scheduling Problems (2016-2022 Study Design Questions)
​Scheduling Problems (2000-2015 ​Study Design Questions)