Mathematical Methods​ ​Units 3&4 

Quick Links:
​Area of Study 1 - Functions and Graphs
Area of Study 2 - Algebra
Area of Study 3 - Calculus
Area of Study 4 - Probability and Statistics
  • Study Design
  • Unit Materials
  • VCAA Resources
  • Exam Report Summaries
  • Changelog
  • Other
<
>
VCAA Mathematical Methods

​​Mathematical Methods Examination Information
Bound Reference Specifications
Formula Sheet
​
​​Mathematical Methods Implementation Videos
Advice for Teachers (2016-2022)
Planning: Sample Course, Employability Skills, Resources
Sample Learning Activities
Pseudocode: Examples and Sample Questions

​Assessment: Scope of Tasks, Sample SACs, Performance Descriptors
Unit 3 SAC - How to develop an application task
Unit 4 SAC - How to develop a modelling or problem-solving task for functions, algebra and calculus
​Unit 4 SAC - How to develop a modelling or problem-solving task for probability and statistics

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)
Australian Mathematics Competition (Australian Maths Trust AMT)
Past Maths Competition and Olympiad Papers Archives (Australian Maths Trust AMT)
AMC Past papers: PDF (Australian Maths Trust AMT)

Area of Study 1 - Functions and Graphs

Study Design
​Functions and Graphs Summary
  • Notes
  • Video & Interactives
  • Exam Questions
  • Questions
<
>
Domain & Range (GeoGebra Interactive)

The Hyperbola ​
Square Root Function (GeoGebra Interactive)
​Cube Root Function (GeoGebra Interactive)

​​Graphing Quadratics Equations
Graphing Parabolas via Transformation
The Power Curves ​​
Polynomials of a Higher Degree (Maffs Guru Video)
Identifying and Describing Relations and Functions (Maffs Guru Video)
Types of Functions and Implied Domains (Maffs Guru Video)

An Intuitive Guide To Exponential Functions & e​ (Better Explained Article)
​What is e? (Eddie Woo Video)
e (Euler's Number) is Seriously Everywhere | The strange times it shows up and why it's so important (Zach Star Video)
Exponential Functions (Maffs Guru Video)
The Exponential Function y=e^x (Maffs Guru Video)
Demystifying the Natural Logarithm (ln) (Better Explained Article)
Graphing Logarithmic Functions (Maffs Guru Video)

Graphing Exponentials & Logs
Graphs of Sine and Cosine (Maffs Guru Video)
Transforming Sine and Cosine Curves 1 (Maffs Guru Video)
Transforming Sine and Cosine Curves 2 (Maffs Guru Video)
The Tangent Function (Maffs Guru Video)
Sketching Tan Functions (Joel Speranza Math Video)

Transformation of Functions (GeoGebra Interactive)
Transforming Functions (Eddie Woo Video)
Matrices (Maffs Guru Video)
Using Matrices for Transformations (Maffs Guru Video)
Translations (Maffs Guru Video)
​Reflections (Maffs Guru Video)
Combinations of Transformations (Maffs Guru Video)
Using Transformations to Sketch Graphs (Maffs Guru Video)
Determining the Rule for a Functions from its Graph (Maffs Guru Video)
Determining Transformations (Maffs Guru Video)
Transformations of Power Functions with Positive Integer Index (Maffs Guru Video)

​Reflecting Functions
Function Symmetry
​Adding Functions
Sketching Functions using Addition of Ordinates (Joel Speranza Math Video)
Adding Functions Graphically (GeoGebra Interactive)

Subtracting Functions
​Multiplying Functions Visually
Sum and Products of Functions (Maffs Guru Video)
​Function Composition (GeoGebra ​Interactive)
Piecewise Functions (Joel Speranza Math Video)

​Piecemeal Functions
​Fitting Quadratics to Data ​(James Tanton Video)
Solutions to past VCAA exam questions can be looked up in the appropriate examiner's report on the Mathematical Methods Past Examinations and Examination Reports page or the Northern Hemisphere Timetable (NHT) Past Examinations and Examination Reports page. 
​
Graphs, Functions, and Relations (2016-2022 Study Design Questions)
​Graphs, Functions, and Relations (2000-2015 Study Design Questions)
​Domain and Range, Period and Amplitude (2016-2022 Study Design Questions)
​Domain and Range, Period and Amplitude (2000-2015 Study Design Questions)
​Coordinate Geometry (2016-2022 Study Design Questions)
Coordinate Geometry (2000-2015 Study Design Questions)
​Graphs of Combined and Hybrid Functions (2016-2022 Study Design Questions)
​Graphs of Combined and Hybrid Functions (2000-2015 Study Design Questions)
​Transformations (2016-2022 Study Design Questions) 
Transformations (2000-2015 Study Design Questions) 
Modelling with Data (2000-2015 ​Study Design Questions)
Domains and Ranges, and Sketching Functions (Corbettmaths Exam Style)
Odd, Even, Neither Functions (Starting Points Maths)
Transformations of Graphs (Minimally Different)
​Transformations of Graphs (Corbettmaths Exam Style)
Non-linear Graphs Transformations (MathsHKO)
Graphing Trig Functions (Interactive Practice) 
Graphing Trig Equations 2 (Interactive Practice)​​​
Graphing Quadratic Equations in Vertex Form (Interactive Practice)
​Graphing a Cubic Function (Interactive Practice)
Function Operations (Interactive Practice)
Adding Functions Graphically (Interactive Practice)
​Composition of Functions: Algebraic (Interactive Practice)
Composition of Functions: Graphical (Interactive Practice)
Functions, Composite Functions, and Inverse Functions (Corbettmaths Exam Style)
​Sketch a Piecewise Function involving Linear Segments (Dr Frost Maths)

Area of Study 2 - Algebra

Study Design
​Algebra Summary
  • Notes
  • Videos & Interactives
  • Exam Questions
  • Questions
<
>
Linear Coordinate Geometry (Maffs Guru Video)
Linear Equations (Maffs Guru Video)
Language of Polynomials (Maffs Guru Video)
Determining the Rule for a Parabola (Maffs Guru Video)
A Different Way to Solve Quadratic Equations (Expii Video)
The General Cubic Function (Maffs Guru Video)
Using the Factor Theorem (Eddie Woo Video)
Division and Factorisation of Polynomials with Rational Root Theorem (Maffs Guru Video)
Determining the Rule for a Graph of a Polynomial (Maffs Guru Video)

Inverse Functions
Inverse Functions (Maffs Guru Video)

Exponential Equations (Maffs Guru Video)
​Logarithms (Maffs Guru Video)
Determining Rules for Graphs of Exponential and Logarithmic Functions (Maffs Guru Video)
Logarithms and Exponents (Crash Course Video)
e to the power of ln(x) (Joel Speranza Math Video)
​
Defining Circular Functions (Maffs Guru Video)
Pythagorean Identity (Maffs Guru Video)
Solutions of Trigonometric Equations (Maffs Guru Video)
Determining Rules for Graphs of Circular Functions (Maffs Guru Video)
General Solution of Trig Functions (Maffs Guru Video)
The General Solution of Trigonometric Equations (Joel Speranza Math Video)

Solving Trigonometric Equations
Solution of Literal Equations and Systems of Equations (Maffs Guru Video)
Linear Literal Equations and Simultaneous Linear Literal Equations (Maffs Guru Video)
The Geometry of Simultaneous Linear Equations (Maffs Guru Video)
Simultaneous Linear Equations with More than Two Variables (Maffs Guru Video)
Solutions to past VCAA exam questions can be looked up in the appropriate examiner's report on the Mathematical Methods Past Examinations and Examination Reports page or the Northern Hemisphere Timetable (NHT) Past Examinations and Examination Reports page. 
​
​Functional Relations (2016-2022 Study Design Questions)
Functional Relations (2000-2015 Study Design Questions)
Inverse Functions and Relations (2016-2022 Study Design Questions)
​Inverse Functions and Relations (2000-2015 Study Design Questions)
Composite Functions (2016-2022 Study Design Questions)
​Composite Functions (2000-2015 Study Design Questions)
​Manipulating Expressions (2016-2022 Study Design Questions)
​Manipulating Expressions (2000-2015 Study Design Questions)
Expressions for Modelling (2016-2022 Study Design Questions)
Expressions for Modelling (2000-2015 Study Design Questions)
​Solving Equations (2016-2022 Study Design Questions)
Solving Equations (2000-2015 Study Design Questions)
Simultaneous Equations and Points of Intersection (2016-2022 Study Design Questions)
​Simultaneous Equations and Points of Intersection (2000-2015 ​Study Design Questions)

Solutions to past VCAA Algorithmics exam questions can be looked up in the appropriate examiner's report on the Algorithmics Past Examinations and Examination Reports page. 
Pseudocode (Algorithmics)
Increasingly Difficult Common Factors (Starting Points Maths)
​Find the Missing Expressions (Worksheet)
Solving Quadratics Equations from Functions (Minimally Different)
Quadratics in Disguise (Maths Helper)
Hidden Quadratics (Swinton Maths)
Cubic Polynomials – Factorise and Sketch (Starting Points Maths)
Polynomials – Finding missing coefficients (Starting Points Maths)
​Applying the Rules of Indices to Form and Solve Equations (Variation Theory)
Solving Logarithmic Equations (Interactive Practice)
Finding Exact Trig Ratios (Interactive Practice)
Trigonometry Exact Values - Finding Sides (Variation Theory)
Trigonometry Exact Values - Finding Angles (Variation Theory)
Trigonometric Ratios from Other Trigonometric Ratios (Corbettmaths Exam Style)
Trigonometric Equations in Degrees (Corbettmaths Exam Style)
Solving Trig Equations with Factor Theorem (Interwoven Maths)
Writing Inverse Functions using a Rule (Interactive Practice)
Writing Inverse Functions using a Graph (Interactive Practice)
Graphing Inverse Functions (Interactive Practice)
​Graphing Inverse Functions (Starting Points Maths)
​Changing the Subject (Advanced) (Corbettmaths)
Changing the Subject (Corbettmaths Exam Style)
Changing the Subject Advanced (Corbettmaths Exam Style)
Substituting expressions into expression (Mr Coward Maths)
Composite Functions (Starting Points Maths)
Composite and Inverse Functions (Maths Bot)
FUNCTIONS (Dr Austin Maths)

Area of Study 3 - Calculus

Study Design
​Calculus Summary
  • Notes
  • Videos & Interactives
  • Exam Questions
  • Questions
<
>
Average and Instantaneous Rates of Change
Differentiation and the Derivative Function
​Graphs of Derivative and Anti-Derivative Functions
Derivatives of Functions
Derivatives of Combinations of Functions​
Tangents and Normals using Derivatives 
​Intervals that are Stationary or Strictly Changing
​Points of Inflection
Maxima and Minima Problems

​Anti-Differentiation
Deriving the Anti-Derivatives of Functions
Area Approximation
Approximation Applications
​The Definite Integral
Anti-Differentiation by Recognition
​Integration and the Fundamental Theorem of Calculus
Proof of the Fundamental Theorem of Calculus
Properties of Anti-Derivatives and Integration
Finding a Function from a Rate of Change
Area Bound by a Curve
Average Value
​
​Calculus Technology [TI-nSpire] ​
​​Calculus Technology [Casio]
The Four Words at the Heart of Calculus (Article)
​
Differential Calculus
Limits and Continuity (Maffs Guru Video)
Differentiation from First Principles (Maffs Guru Video)
When is a Function Differentiable (Maffs Guru Video)
Graphs of Derivative Functions (Maffs Guru Video)

Differentiating Negative Powers (Maffs Guru Video)
Differentiating Rational Powers (Maffs Guru Video)
​Examples using the Power Rule for Derivatives (Khan Academy Video)
Rules for Differentiation (Maffs Guru Video)
Calculus - Rules for Differentiation (Maffs Guru Video)
Differentiating Circular Functions (Maffs Guru Video)
Derivative of Sine & Cosine Functions (GeoGebra Interactive)
​Derivative of Tangent Function (GeoGebra Interactive)
​Derivative of Exponential Function (GeoGebra Interactive)
Derivative of Natural Log Function (GeoGebra Interactive)

Chain Rule
Chain Rule (Khan Academy Video)
Using the Chain (Function of a Function) Rule (Eddie Woo Video)

​Calculus of Exponential Functions
Differentiating Exponentials with Non-e Bases (Eddie Woo Video)

Calculus of Logarithmic Functions
Differentiating the Logarithmic Function
Calculus of Trigonometric Functions
Visual Calculus: Derivative of sin(θ) is cos(θ) (Think Twice Video)

Differentiating Trigonometric Functions
Using Derivatives of Trigonometric Functions
Product Rule
Quotient Rule
The Product Rule (Maffs Guru Video)
The Quotient Rule (Maffs Guru Video)
The Product Rule with Circular Functions (Maffs Guru Video)
The Quotient Rule with Circular Functions (Maffs Guru Video)

​Common Mistakes with Notation (Eddie Woo Video)

Tangents and Normals (Maffs Guru Video)
Joining two functions so that their gradients match (Joel Speranza Math Video)
Joining two functions so that their gradients match: Part 2 (Joel Speranza Math Video)
Stationary Points (Maffs Guru Video)
Types of Stationary Points (Maffs Guru Video)

Max/Min in Geometry
Absolute maximums and minimums (Joel Speranza Math Video)
Absolute Maximum/Minimum: Domain Restricted Polynomial (Eddie Woo Video)

Calculus, what is it good for? (Domain of Science Video)

Essence of Calculus​
Integral Calculus
Introducing Integration
Understanding Integration
What is Integration? 3 Ways to Interpret Integrals (Math The World Video)

​​Trapezoidal Rule
Areas by Integration
Basic Compound Regions
​ Properties of Definite Integrals
Using Definite Integral Properties (Eddie Woo Video)

Indefinite Integrals
Evaluating Constant of Integration 
Integrating Exponential Functions (Basics) (Eddie Woo Video)
Integral Basics and Indefinite Integrals (Maffs Guru Video)
Integral of Complex Functions (Maffs Guru Video)
Antiderivative of e to the Power of kx (e^kx) (Maffs Guru Video)

Integrals & Logarithms - Why does the solution look different? (Eddie Woo Video)
Applications of Integration & Logarithms (Eddie Woo Video)
Integration of Harder Exponential Functions (Eddie Woo Video)

Identifying a Function from its Derivative (Eddie Woo Video)

Indefinite Integrals: Compared to Definite Integrals (Eddie Woo Video)
Evaluating Compound Areas (Eddie Woo Video)

Fundamental Theorem of Calculus
​Definite Integral Illustrator (GeoGebra Interactive)
Definite Integral (Maffs Guru Video)
Area Under Graph (Maffs Guru Video)
​Area Between 2 Curves (GeoGebra Interactive)

Area Between Curves
Area Between Two Curves - Example
Curves with Multiple Crossings
Integration and Area (GeoGebra Interactive)

Antidifferentiation by Recognition
Applications of Trigonometric Integrals
​Derivatives and Motion (Crash Course Video)
​Integrals and Motion (Crash Course Video)
Solutions to past VCAA exam questions can be looked up in the appropriate examiner's report on the Mathematical Methods Past Examinations and Examination Reports page or the Northern Hemisphere Timetable (NHT) Past Examinations and Examination Reports page. 
​
​Average Rate of Change (2016-2022 Study Design Questions)
Average Rate of Change (2000-2015 Study Design Questions)
​Derivatives and Gradients of Functions (2016-2022 Study Design Questions)
​Derivatives and Gradients of Functions (2000-2015 Study Design Questions)
Tangents (2016-2022 Study Design Questions)
​Tangents (2000-2015 Study Design Questions)
​Intervals that are Stationary or Strictly Changing (2016-2022 Study Design Questions)
​Intervals that are Stationary or Strictly Changing (2000-2015 Study Design Questions)
Optimisation Problems (2016-2022 Study Design Questions)
​Optimisation Problems (2000-2015 Study Design Questions)
Optimisation Problems (CAS) (2016-2022 Study Design Questions) **
Optimisation Problems (CAS) (2000-2015 Study Design Questions)
Anti-Derivatives (2016-2022 Study Design Questions)
​Anti-Derivatives (2000-2015 Study Design Questions)
Graphs of Derivative and Anti-Derivative Functions (2016-2022 Study Design Questions)
Graphs of Derivative and Anti-Derivative Functions (2000-2015 Study Design Questions)
Integration (2016-2022 Study Design Questions)
Integration (2000-2015 Study Design Questions)
​Integration by Recognition (2016-2022 Study Design Questions)
​Integration by Recognition (2000-2015 Study Design Questions)
​Area Approximations (2016-2022 Study Design Questions)
Area Approximations (2000-2015 Study Design Questions)
Integrals and Area (2016-2022 Study Design Questions)
​Integrals and Area (2000-2015 Study Design Questions)
Average Value (2016-2022 Study Design Questions)
​Average Value (2000-2015 ​Study Design Questions)

**Note: Maximum and minimum rates have been removed for the 2023 study design. 
Intuitive Derivative Graphing Exercise (Interactive Practice)
​Practise Rough Sketching Derivative Functions (Interactive Practice)
Practise Rough Sketching Antiderivatives (Interactive Practice)
Differentiation using Power Rule (Corbettmaths Exam Style)
Developing Indices Skills for Calculus (Starting Points Maths)
Preparing for Calculus – Quotients (Starting Points Maths)
Multiplication of Terms (Starting Points Maths)
Scaffolded Differentiation (Starting Points Maths)
Harder Differentiation: Scaffolded (Starting Points Maths)
Gradient of a Curve using Power Rule (Corbettmaths Exam Style)
Equation of a Tangent (Corbettmaths Exam Style)
Equation of a Normal (Corbettmaths Exam Style)
Tangents and Normals (Mr Southern Maths)

​Scaffolded Stationary Points (Starting Points Maths)
Stationary Points (Corbettmaths Exam Style)
Increasing and Decreasing Functions (Corbettmaths Exam Style)
Differentiation of the Exponential Function ​(Variation Theory)
Chain Rule (Variation Theory)
Chain Rule (Variation Theory)
Chain Rule – Scaffolded (Starting Points Maths)
Product Rule: Polynomials (Variation Theory)
Product Rule: Non-Polynomial (Variation Theory)
Quotient Rule: Polynomials (Variation Theory)
Optimisation (Interactive Practice)
Optimisation – Scaffolded (Starting Points Maths)
Using Differentiation to Solve Problems (Corbettmaths Exam Style)

Integrals – Isolating the key ideas (Starting Points Maths)
Increasingly Difficult Integration (Starting Points Maths)
Estimating the Area under a Graph (Corbettmaths)
Estimate Area Under a Graph (Corbettmaths Exam Style)
Area between two curves – Scaffolded (Starting Points Maths)
Lines, Parabolas, and Areas (Mr Southern Maths)

Area of Study 4 - Probability and Statistics

Study Design​
Probability and Statistics Summary ​
  • Notes
  • Videos & Interactives
  • Exam Questions
  • Questions
<
>
Random Variables

Discrete Random Variables
Discrete Random Variables
Events from a Sample Space
​Sampling without Replacement
Statistics of Discrete Random Variables
​Proof of Linear Combinations of Discrete Random Variables
Bernoulli Distribution
​Binomial Distribution
Statistics of Binomial Random Variables
Parameters of Binomial Distributions
​Discrete Random Variables Technology [TI-nSpire] 
Discrete Random Variables Technology ​[Casio]

Continuous Random Variables
​Continuous Random Variables
Statistics of Continuous Random Variables
​Proof of Linear Combinations of Continuous Random Variables
​Conditional Probability - Continuous Random Variables
Cumulative Density Functions (Optional)
Normal Distribution
Density Functions for the Normal Distribution (Optional)
Parameters of Normal Distributions
​Inverse Normal Distribution [TI-nSpire]
Inverse Normal Distribution ​[Casio]
Continuous Random Variable Technology [TI-nSpire]
Continuous Random Variable Technology ​[Casio]

Statistical Inference, including Definition and Distribution of Sample Proportions, Simulations, and Confidence Intervals
Statistical Inference
​Sample Distribution of Proportions
Statistics of Sample Distribution of Proportions
Normal Approximation for Sample Proportions
​Simulation of Random Sampling [TI-nSpire]
Simulation of Random Sampling [Casio]
​​​​Confidence Intervals for Proportions
Simulation of Variations in Confidence Intervals [TI-nSpire]
Simulation of Variations in Confidence Intervals [Casio]
​​Sample Proportion Technology [TI-nSpire]
Sample Proportion Technology ​[Casio]​​
Discrete Random Variables
Basic Probability: Chance Events (Seeing Theory Interactive)
Probability Distributions: Random Variable (Seeing Theory Interactive)
Probability Distributions: Discrete and Continuous (Seeing Theory Interactive)
Compound Probability: Conditional Probability (Seeing Theory Interactive)
Sample Spaces and Probability (Maffs Guru Video)
Conditional Probability and Independence (Maffs Guru Video)
Simulators (MathsWhiteboard Interactives)

Discrete Random Variables​
"A Random Variable is NOT Random and NOT a Variable" (Dr Mihai Nica Video)

Discrete Random Variables: Introduction and Examples (Joel Speranza Math Video)
Discrete Random Variables Uniform Distribution (Joel Speranza Math Video)
Discrete Random Variable Worked Example (Joel Speranza Math Video)
Discrete Random Variables (Maffs Guru Video)
Measures of Centre (Mean/Expected Value) and Spread (Maffs Guru Video)
Expected Value of discrete random distributions (Joel Speranza Math Video)
Properties of Expected Value: aE(X)+b = E(aX + b) (Joel Speranza Math Video)
Variance and Standard Deviation: Discrete Random Variables (Joel Speranza Math Video)
What's the Connection between Arithmetic Mean & Expected Value? (Eddie Woo Video)
Basic Probability: Expectation (Seeing Theory Interactive)
​Basic Probability: Variation (Seeing Theory Interactive) 
The alternative Variance formula Proof (Joel Speranza Math Video)
Creating probability distributions from empirical data (Khan Academy Video)
Creating theoretical probability distribution example: multiplication (Khan Academy Video)
Creating theoretical probability distribution example: tables (Khan Academy Video)
​
Statistical Analysis Spreadsheet
Modifying Statistical Scale & Origin
Bernoulli Sequence (Joel Speranza Math Video)
Binomial Distribution Introduction (Joel Speranza Math Video)
Binomial Distribution (Maffs Guru Video)
Binomial Distributions (3Blue1Brown Video)
Binomial Variables (Khan Academy Video)
​Recognising Binomial Variables (Khan Academy Video)
The Binomial Probability Formula (Joel Speranza Math Video)
Binomial Probability Formula Worked Example (Joel Speranza Math Video)
Binomial Probability Formula: At Most and At Least (Joel Speranza Math Video)
Developing Binomial Distribution Intuition  (Joel Speranza Math Video)
Binomial Probability: Conditional Probability (Joel Speranza Math Video)
Construct a Binomial Distribution Graph (Joel Speranza Math Video)
The Graph, Expectation, and Variance of a Binomial Distribution (Maffs Guru Video)
Two Distributions Statistics (GeoGebra Interactive)
Binomial Distribution Finding a Sample Size (Joel Speranza Math Video)
Finding the Sample Size of a Binominal Distribution (Maffs Guru Video)
Expected Value of Binomial Variable (Khan Academy Video)
​Variance of Binomial Variable (Khan Academy Video)
​Finding the Mean and Standard Deviation of a Binomial Random Variable (Example) (Khan Academy Video)

Continuous Random Variables
Why "Probability of 0" Does Not Mean "Impossible" (3Blue1Brown Video)

What are Continuous Random Variables?
Probability Density Functions
Continuous Random Variables (Maffs Guru Video)
Estimating Probability of a Continuous Random Variable using Data (Joel Speranza Math Video)
The Probability Density Function (Joel Speranza Math Video)
​Calculating Probability using a Probability Density Function (Joel Speranza Math Video)
Proving a Function is a Probability Density Function (Joel Speranza Math Video)
Unknowns in Probability Density Functions (Joel Speranza Math Video)
Unbounded Probability Density Functions (Joel Speranza Math Video)
Calculating Percentiles from a Probability Density Function (Joel Speranza Math Video)
The Cumulative Probability Distribution Function (Joel Speranza Math Video)

The Mean of a Continuous Random Variable (Joel Speranza Math Video)
Mean and Median of a Continuous Random Variable (Maffs Guru Video)
Mode & Median of a Continuous Probability Distribution (Eddie Woo Video)
Worked Example: Finding Median of a Continuous Probability Distribution (Eddie Woo Video)
Finding Median with Technology (Eddie Woo Video)
Locating Boundaries of a Distribution from its Median (Eddie Woo Video)
Finding Percentiles of a Continuous Probability Distribution (Eddie Woo Video)

Expected Value of a Continuous Distribution
Variance
​Calculating Variance and Standard Deviation of a Continuous Random Variable (Joel Speranza Math Video)
Alternative Variance Formula Worked Example (Joel Speranza Math Video)
Measures of Spread for a Continuous Random Variable (Maffs Guru Video)

Cumulative Distribution Function [Optional]
What is the Normal Distribution? (Eddie Woo Video) 

Normally Distributed Empirical Data
Probability Density Function of the Normal Distribution (Eddie Woo Video) 

The Normal Distribution Introduction (Joel Speranza Math Video)
Standard Normal Distribution (Maffs Guru Video)
Standardisation and the 68-95-99.7% Rule (Maffs Guru Video)
Solving Problems with the Normal Distribution (Maffs Guru Video)
Normal Approximation to the Binomial Distribution (Maffs Guru Video)
Normal Distribution Calculator (Online Stat Book Interactive)
The Normal Distribution Parameters (GeoGebra Interactive)
A Tricky Normal Distribution Question (Joel Speranza Math Video)
The inverse normal distribution on the TI Nspire (Joel Speranza Math Video)
But what is the Central Limit Theorem? (3Blue1Brown Video)
Why π is in the normal distribution (beyond integral tricks) (3Blue1Brown Video)

Statistical Inference
Why is Sample Proportion Interesting and Important (Joel Speranza Math Video)
Populations and Samples (Maffs Guru Video)
The Exact Distribution of the Sample Proportion (Maffs Guru Video)
Sampling from a Small Population (Joel Speranza Math Video)
Sampling from a Large Population (Joel Speranza Math Video)​
Sample Proportion Mean and Standard Deviation (Joel Speranza Math Video)​​
Approximating the Distribution of a Sample Proportion (Joel Speranza Math Video)​
Binomial Approximation to the Normal and Sample Proportion, One Question Two Ways (Joel Speranza Math Video)
Approximating the Sample Proportion Distribution (Maffs Guru Video)
Sampling Distribution of a Proportion (GeoGebra Interactive)
​Sample Proportion Simulation (Rossman/Chance Interactive)
​Binomial vs Normal Probability Comparison (GeoGebra Interactive)
Confidence Intervals and Margin of Error (Khan Academy Video)
Confidence Interval Simulation (Khan Academy Video)
Confidence Interval for a Proportion (GeoGebra ​Interactive)
Confidence Intervals for Population Proportion (Joel Speranza Math Video)​
Confidence Intervals Simulation (Rossman/Chance Interactive)
Interpreting Confidence Intervals Example (Khan Academy Video) 
​Critical Value for a Given Confidence Level (Khan Academy Video)
Example Calculating Confidence Interval (Khan Academy Video)
Determining Sample Size Based on Confidence and Margin of Error ​(Khan Academy Video)
Determining Required Sample Size for a Given Margin of Error (Joel Speranza Math Video)​
Solutions to past VCAA exam questions can be looked up in the appropriate examiner's report on the Mathematical Methods Past Examinations and Examination Reports page or the Northern Hemisphere Timetable (NHT) Past Examinations and Examination Reports page. 
​
Discrete Random Variables
​Discrete Random Variables (2016-2022 Study Design Questions)
​Discrete Random Variables (2000-2015 Study Design Questions)
Events from a Sample Space (2016-2022 Study Design Questions)
Events from a Sample Space (2000-2015 Study Design Questions)
Sampling without Replacement (2016-2022 Study Design Questions)
Sampling without Replacement (2000-2015 Study Design Questions)
​Discrete Random Variables: Statistics (2016-2022 Study Design Questions)
​Discrete Random Variables: Statistics (2000-2015 Study Design Questions)

​Binomial Random Variables (2016-2022 Study Design Questions)
​Binomial Random Variables (2000-2015 Study Design Questions)
​Binomial Random Variables: Statistics (2016-2022 Study Design Questions)
​Binomial Random Variables: Statistics (2000-2015 Study Design Questions)

Continuous Random Variables
Continuous Random Variables (2016-2022 Study Design Questions)
​Continuous Random Variables (2000-2015 Study Design Questions)
​Continuous Random Variables: Statistics (2016-2022 Study Design Questions)
​Continuous Random Variables: Statistics (2000-2015 Study Design Questions)

Normally Distributed Random Variables (2016-2022 Study Design Questions)
​Normally Distributed Random Variables (2000-2015 Study Design Questions)
​Normally Distributed Random Variables: Statistics (2016-2022 Study Design Questions)
​Normally Distributed Random Variables: Statistics (2000-2015 ​Study Design Questions)

​Statistical Inference, including Definition and Distribution of Sample Proportions, Simulations, and Confidence Intervals
​Sample Distribution of Proportions (2016-2022 Study Design Questions)
​Sample Distribution of Proportions: Statistics (2016-2022 Study Design Questions)
​Confidence Intervals for Sample Proportions (2016-2022 Study Design Questions)
Missing Probabilities with Ratios (MontaigneMaths)
​Binomial Distribution: Cumulative Probabilities (Variation Theory)
Binomial Distribution Completion Table (Catriona Agg via Mr Southern Maths)
Worded Binomial Table (Catriona Agg via Mr Southern Maths)
Normal Distribution: Finding Probabilities (Variation Theory)
Normal Distribution Completion Table (Catriona Agg via Mr Southern Maths)
Inverse Normal Distribution (Catriona Agg via Mr Southern Maths)