Mathematical Methods Units 1&2

  • Study Design
  • Unit Materials
  • VCAA Resources
  • Changelog
  • Other
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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)
  • Unit 1
  • Unit 2
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Quick Links:
​Area of Study 1 - Functions, Relations, and Graphs
Area of Study 2 - Algebra, Number, and Structure
Area of Study 3 - Calculus
Area of Study 4 - Data Analysis, Probability, and Statistics

Area of Study 1 - Functions, Relations, and Graphs

Study Design
Functions, Relations, and Graphs Summary ​
  • Notes
  • Videos & Interactives
  • Questions
  • Exam Questions
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Set Notation: Introduction (Joel Speranza Math Video)

Introduction to Functions
Function Notation (Eddie Woo Video)
Function Notation: Better ways of representing functions (Joel Speranza Math Video)
Algebra Basics: What are functions? (Maths Antics Video)
Functions: Input & Output (GeoGebra Interactive)

Domain and Range of functions and relations (Joel Speranza Math Video)
​Domain & Range Illustrator (GeoGebra Interactive)

Domain and Range
​Classifying Functions & Relations
Interval Notation
Even Functions (GeoGebra Interactive)
​Odd Functions (GeoGebra Interactive)

The Circle
Graphing Circles - Completing the Square (Eddie Woo Video)
​Equation of a Semicircle (Eddie Woo Video)
The Hyperbola - Understanding the Graph & its Behaviour (Eddie Woo Video)
Sketching Hyperbolas and why there's an asymptote (Joel Speranza Math Video)
Power Functions for n={1,2,3,4} (Eddie Woo Video)
The square root function (Joel Speranza Math Video)

The Power Curves
Review of Graphing Parabolas (Eddie Woo Video)
​Quadratic Function (GeoGebra Interactive)
3 forms of the quadratic equation (Joel Speranza Math Video)
​Graphing the Quadratic (Crash Course)​
Cubic Curves (Eddie Woo Video)
Fitting Quadratics to Data (James Tanton Video)

​Transforming Functions (Eddie Woo Video)
Function Transformations (GeoGebra Interactive)
Cubics in "Turning Point" Form: (But it's not a turning point) (Joel Speranza Math Video)

Graphing Cubic Functions
Polynomial Division & Graphing ​
Straight Up Curriculum Mathematics for the 21st Century
Relations, Functions and the vertical line test (Joel Speranza Math Video)

Inverse Functions
Reading inverse values from a graph (Khan Academy)
Reading inverse values from a table (Khan Academy)
Using specific values to test for inverses (Khan Academy)
​Verifying inverse functions from tables (Khan Academy)
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Distance between Two Points (Corbettmaths Exam Style)
Midpoint of a Line Segment and Ratios (Corbettmaths Exam Style)
Coordinate Geometry (Mr Sourthern Maths)
Linear Graphs: Parallel and Perpendicular Lines (Corbettmaths Exam Style)
Parallel and Perpendicular Lines (Corbettmaths Exam Style)
Coordinate Geometry Mixed Exercise (Mr Southern Maths)
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Evaluating Functions Algebraically (Interactive Practice)
Evaluating Functions Using Graphs (Interactive Practice)
​Interval Notation (Interactive Practice)
Domain and Range (Interactive Practice)

Circle Equation (Interactive Practice)
Circle Graph - EQ in Standard Form (Interactive Practice)
​Circle Graphing - EQ in General Form (Interactive Practice)
Increasingly Difficult Circle Equations (Starting Poins Maths)
​Sketching Linear Graphs (Interactive Practice)
Graphing Quadratic Equations in Vertex Form (Interactive Practice)
Quadratic Graphs: Fill in the Gaps (Variation Theory)​
Sketching Quadratics (Corbettmaths)
​Quadratic Graphs (Corbettmaths Exam Style)
Cubic Graphs (Corbettmaths Exam Style)
​Graphing a Cubic Function (Interactive Practice)
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FUNCTIONS (Dr Austin 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)

Area of Study 2 - Algebra, Number, and Structure

Study Design
​Algebra, Number, and Structure Summary
  • Notes
  • Videos & Interactives
  • Questions
  • Exam Questions
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Pseudocode and Algorithms
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​Algebraic Expressions
Substitution and Arithmetic
Algebraic Fractions and Algebraic Surds

Polynomials
Polynomial Operations
Polynomial Operations with Algebra Tiles
Manipulating Quadratic Expressions
Expanding and Factorising Polynomials
Equating Coefficients to Convert between Forms
Determining the Equation of a Polynomial
Fitting a Polynomial to Data

Transformations of the Plane and Functions
Transformations of a Single Parameter

​Remainder, Factor, and Rational Root Theorems

Power Equations
Polynomial Equations
Quadratic Formula​
Bisection Method

Polynomial Inequalities

Systems of Simultaneous Linear Equations
Systems of Simultaneous Linear Equations with More Than 2 Variables (Optional)
​Number of Solutions of Systems of Linear Equations
​Equations of the Form f(x)=g(x)

Algebra, Number, and Structure Technology
TI-nSpire
Casio
Python - VCAA Pseudocode (Simon Tyler Notes)

Completing the Square (Eddie Woo Video)
Intuition behind Operations to Solve Systems (Khan Academy Video)
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Simultaneous Equations
Forming Simultaneous Equations
Quadratic Factorisation
A Different Way to Solve Quadratic Equations (Expii Video)
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Problem Solving with Quadratic Equations
Factorising Algebraic Expressions ​
The Discriminant (Corbettmaths Video)
Why We Care About Quadratics? (Eddie Woo Video)
Solving Quadratic Equations Review and Pitfalls (Eddie Woo Video)

Simultaneous Linear/Quadratic Equations
Intersecting Functions (Joel Speranza Math Video)

Polynomial Operations
Intro to Polynomial Division ​
Polynomial Division
Remainder & Factor Theorem
Remainder & Factor Theorem
​Using the Factor Theorem (Eddie Woo Video)
Factor & Remainder Theorems: Proof and Application (Joel Speranza Math Video)

Solving Polynomial Equations
Bisection Method
Solving Inequalities with Graphs
Solving Cubic Inequalities
Graphing Regions on the Cartesian Plane (Eddie Woo Video)

Reflecting Functions
Expanding Brackets (Corbettmaths Exam Style)
​Expanding Three Brackets (Corbettmaths)
Expanding 3 Brackets (Corbettmaths Exam Style)
Expanding Three Brackets (Variation Theory)
Expanding using Pascal's Triangle (Corbettmaths Exam Style)
​Binomial Expansion ​(Variation Theory)
Binomial Expansion (Variation Theory)

Fractional and Negative Indices (Corbettmaths Exam Style)
Power, Roots, and Index Equations (Corbettmaths Exam Style)

Completing the Square (Monic) (Variation Theory)
Completing the Square (Non-Monic) (Variation Theory)
​​Completing the Square (Interactive Practice)
​Completing the Square (Corbettmaths)
Completing the Square (Corbettmaths Exam Style)
Completing the Square (Corbettmaths Exam Style)

Factorising Common Factors (Corbettmaths Exam Style)
Increasingly Difficult Common Factors (Starting Points Maths)
Factorising into Double Brackets (Positive) (Variation Theory)
Factorising into Double Brackets (Positive 2) (Variation Theory)
Factorising into Double Brackets (Negative) (Variation Theory)
Factorising into Double Brackets (Mixed) (Variation Theory)
Increasingly Difficult Factorisation: Quadratics (Starting Points Maths)
Factorising Binomial Products (Interactive Practice)
Finish factorising: double brackets (Variation Theory)
Factorising Quadratics (Corbettmaths Exam Style)
Difference of Two Squares - Pattern Spotting (Variation Theory)
Difference of Two Squares (Variation Theory)
Algebraic Fractions (Corbettmaths)
Dividing Algebraic Fractions (Corbettmaths)
Simplifying Algebraic Fractions (Corbettmaths)​
Simplifying Algebraic Fractions with Quadratics (Variation Theory)
How many brackets? (Variation Theory)
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Using the Quadratic Formula (Minimally Different)
Solving Quadratic Equations Using Quadratic Formula (Interactive Practice)
Solving Quadratics by Factorising (Corbettmaths)
Solve Non-Monic Quadratics by Factorising (Corbettmaths)
Solving Quadratics by Factorising (Corbettmaths Exam Style)
Solving Quadratics by Completing the Square (Corbettmaths)
Solving Quadratics by Completing the Square (Corbettmaths Exam Style)
Quadratic Formula (Corbettmaths)
Solving Quadratics by Quadratic Formula (Corbettmaths Exam Style)
Equations involving Fractions (Advanced) (Corbettmaths Exam Style)
Quadratic Inequalities: Pre-requisite Task (Starting Points Maths)
Introducing Quadratic Inequalities (Mr Southern Maths)
​Solving Quadratic Inequalities (Corbettmaths)
Quadratic Inequalities (Corbettmaths Exam Style)
Linear and Quadratic Inequalities (Corbettmaths Exam Style)
Inequalities (Corbettmaths Exam Style)
Solving Quadratic Inequalities (Variation Theory)
Mixed Linear and Quadratic Equations (Starting Points Maths)

Simplifying Algebraic Fractions (Minimally Different)
Grid Multiplication and Division (Starting Points Maths)
Dividing Polynomial Expressions (Interactive Practice)
Factor Theorem (Corbettmaths Exam Style)
Increasingly Difficult Quadratics and Polynomials (Starting Points Maths)
Cubic Polynomials – Factorise and Sketch (Starting Points Maths)
Polynomials – Finding missing coefficients (Starting Points Maths)
Finish factorising: triple brackets (Variation Theory)
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Equation of a Line and Points of Intersection (Corbettmaths Exam Style)
​Equation of a Circle (Corbettmaths)
Equation of a Circle (Corbettmaths Exam Style)
Equation of a Tangent to a Circle (Corbettmaths Exam Style)
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Transformations of Functions (Starting Points Maths)
Transformations of Graphs – Summary (Starting Points Maths)
Transformations of Graphs (Corbettmaths Exam Style)
Transformation of functions – 2 steps (Starting Points Maths)
Transformations of functions – 3 steps (Starting Points Maths)

Linear Simultaneous Equations (Corbettmaths)
Linear Simultaneous Equations: Graphical (Corbettmaths)
Linear Simultaneous Equations (Corbettmaths Exam Style)
Linear and Quadratic Simultaneous Equations (Corbettmaths Exam Style)
Linear Simultaneous Equations with 3 Unknowns (Corbettmaths)
Linear Simultaneous Equations with 3 Variables (Corbettmaths Exam Style)
​Linear Simultaneous Equations (Corbettmaths Exam Style)
Simultaneous Equations with Linear and Quadratics (Corbettmaths)
Simultaneous Equations: Linear and Non-Linear (Corbettmaths Exam Style)

Area of Study 3 - Calculus

Study Design
​Calculus Summary
  • Notes
  • Videos & Interactives
  • Questions
  • Exam Questions
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Average Rate of Change of a Function (GeoGebra Interactive)
​Average to Instantaneous Rate of Change (GeoGebra Interactive)

Prologue to Calculus
Filling Glasses: Graphing and Comparing (Fuse Interactive - Flash Required)
Filling Glasses: Create the Right Graph (Fuse Interactive - Flash Required)
Filling Vase - Investigating Rate of Change (GeoGebra Interactive)
Real Life Graphs: Filling a Beaker (GeoGebra Interactive)
Intuitive Derivative Graphing Exercise (GeoGebra Interactive)
Average Rate of Change of a Function using a Rule (Interactive Practice)
Average Rate of Change of a Functions using Two Points (Interactive Practice) ​
​Distance-Time Graphs (Corbettmaths)
Travel Graphs (Corbettmaths Exam Style)
​Estimating Rates of Change (Corbettmaths)
Estimate Rates of Change (Corbettmaths Exam Style)
Practise Rough Sketching Derivative Functions (Interactive Practice)
Sketching Graphs of the Derived Function (Starting Points Maths)

Area of Study 4 - Data Analysis, Probability, and Statistics

Study Design
​Data Analysis, Probability, and Statistics Summary
  • Notes
  • Videos & Interactives
  • Questions
  • Exam Questions
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​​Compound Probability: Counting (Seeing Theory Interactive)
Interpreting general multiplication rule (Khan Academy Video)
Probability with general multiplication example: independent events (Khan Academy Video)
​Probability with general multiplication rule example: dependent events (Khan Academy Video)
Probability with combinations example: choosing cards (Khan Academy Video)
Probability with combinations example: choosing groups (Khan Academy Video)

Ordered Selections
Unordered Selections​ ​
Rearranging the Word DECISION​
Navigating a Rectangular Grid
Binomial Expansion up to Quartic (GeoGebra Interactive)
Product Rule for Counting (Corbettmaths)
Product Rule for Counting (Corbettmaths Exam Style)
Quick Links:
​Area of Study 1 - Functions, Relations, and Graphs
Area of Study 2 - Algebra, Number, and Structure
Area of Study 3 - Calculus
Area of Study 4 - Data Analysis, Probability, and Statistics

Area of Study 1 - Functions, Relations, and Graphs

Study Design​
​Functions, Relations, and Graphs Summary ​
  • Notes
  • Videos & Interactives
  • Questions
  • Exam Questions
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The Unit Circle Model (GeoGebra Interactive)
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Trigonometry on the Unit Circle
​Redefining the Trig Functions on the Unit Circle - Understanding Non-Acute Angles (Eddie Woo Video)

​Intro to Trigonometric Functions
One Radian (Twitter Video)
What is a radian? (PatrickJMT Video)

Introduction to Radians
Introduction to Radians
What is a Radian? (GeoGebra Interactive)

Exact Values
Radian Measure
​Degrees and Radians Conversion (GeoGebra Interactive)
Complementary Trigonometric Relationships (Joel Speranza Math Video)

​Trigonometric Ratios of Complementary Angles
Unwrapping the Unit Circle (GeoGebra Interactive)
Introduction to Trigonometric Graphs (Joel Speranza Math Video)

​How to Graph Trigonometric Functions
Graphs of Basic Trigonometric Functions
Sketching f(x) = tan(x) and why it looks like that (Joel Speranza Math Video)
Graphing Trigonometric Functions (Example: y=3cos(x)-2) (Eddie Woo Video)

Behaviour of sin(x) & tan(x) for Small x
Sine & Cosine Period (GeoGebra Interactive)
​Tangent Period (GeoGebra Interactive)
Ferris Wheel: Modelling with Trigonometric Functions (GeoGebra Interactive)
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Straight Up Curriculum Math for the 21st Century: The Story of Trigonometry
Trig Identities
Trigonometry Fundamentals (3Blue1Brown Video) [Optional]

​Graphs of Logarithms
Graphing Exponentials & Logs
Sketching Log Functions & why they look the way they do (Joel Speranza Math Video)
​Logarithmic Functions: Graphs (GeoGebra Interactive)
Radian Measure - Intro (Starting Points Maths)
​Fraction Calculations involving Pi (Starting Points Maths)
DEG to RAD and RAD to DEG (Interactive Practice)
Convert between Degrees and Radians (mathworksheets4kids)
Sketching Angles in Standard Position (Interactive Practice)
Radians (Vic Maths Notes)
Circular Functions Worksheet Radians [Degrees] (Vic Maths Notes)
Exact Values Match Up (Starting Points Maths)
Exact Values of Trigonometric Ratios (MathsBot)
Related Exact Values (Starting Points Maths)
Evaluating Trig Expressions (Starting Points Maths)
​Using Exact Trigonometric Ratios (Variation Theory)
Trigonometry Exact Values - Finding Sides (Variation Theory)
Trigonometry Exact Values - Finding Angles (Variation Theory)
Exact Trig Values (Corbettmaths)
Exact Trig Values in Degrees (Corbettmaths Exam Style)
Trigonometric Ratios from Other Trigonometric Ratios (Corbettmaths Exam Style)

Graphs of Circular Functions Radians [Degrees] (Vic Maths Notes)
​Graphs of Trigonometric Functions (Degrees) (Corbettmaths)
Trigonometric Graphs in Degrees (Corbettmaths Exam Style)
Graphing Trig Functions (Interactive Practice)
Graphing Trig Equations 2 (Interactive Practice)​​
Writing Trigonometric Functions (Interactive Practice)
​Modelling with Trigonometric Functions (Interactive Practice)

Exponential Graphs (Corbettmaths Exam Style)
Domain and Range (Starting Points Maths)
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Area of Study 2 - Algebra, Number, and Structure

Study Design​
​Algebra, Number, and Structure Summary
  • Notes
  • Videos & Interactives
  • Questions
  • Exam Questions
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Solving sinx=1/2 (Eddie Woo Video)
​Solving Simple Trigonometric Equations (Eddie Woo Video)
Solving Trigonometric Equations with Quadrants (Eddie Woo Video)
Solving Trigonometric Equations with the Unit Circle (Eddie Woo Video)
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Logarithms, Explained (TED-Ed Video)

Logarithms
Logarithms and Exponents (Crash Course Video)

Introduction to Logarithms
Logarithm Laws
Understanding Logarithms
Newton's Method​
Newton's Fractal (which Newton knew nothing about) (3Blue1Brown Video)
Approximations. The engineering way. (Zach Star Video)
Trigonometric Equations in Degrees (Corbettmaths Exam Style)
Trig Equation Matching (Starting Points Maths)
Circular Equations Worksheet Radians [Degrees] (Vic Maths Notes)
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​Fractional Indices (Variation Theory)
​Applying the Rules of Indices to Form and Solve Equations (Variation Theory)
Index Laws and Equations (Corbettmaths Exam Style)
Logarithms (Variation Theory)
Log Relationships (Starting Points Maths)
​Solving Logarithmic Equations (Interactive Practice)

Area of Study 3 - Calculus

Study Design​​
​Calculus Summary
  • Notes
  • Videos & Interactives
  • Questions
  • Exam Questions
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The Four Words at the Heart of Calculus (Article)
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What is continuity? (Eddie Woo Video)
Dividing by Zero? (Eddie Woo Video)

Limits
Examples Finding Limits for Piecewise Defined Functions (Khan Academy Video)
Introduction to Limits (GeoGebra Interactive)
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Introduction to Average Rate of Change (Khan Academy Video)

Introduction to Calculus
Derivative Function: Without Words (GeoGebra Interactive)

The Problem of Tangents
The Differential Operator
Basics of Calculus, Continued
Rules for differentiation (MaffsGuru Video)
Graphs of the derivative function (MaffsGuru Video)
​Intuitive Derivative Graphing Exercise (GeoGebra ​Interactive)
​Equations of Tangents & Normals (Eddie Woo Video)
Interpreting the Meaning of Derivatives (Eddie Woo Video)

Examples using the Power Rule for Derivatives (Khan Academy Video)
Angle of Inclination (with Calculus) (Eddie Woo Video)

Understanding Stationary Points
Sign of the Derivative
Classifying Stationary Points
How to Recognise Relative and Absolute Maxima and Minima (Khan Academy Video)

Critical Values
Graphing Stationary Points
Determine Functions from Stationary Points (Eddie Woo Video)

​Maximum/Minimum with Quadratics
​Max/Min - Cutting a Wire
​Introduction to Primitive Functions (Eddie Woo Video)
Continuity (Interactive Practice)
Differentiation using Power Rule (Corbettmaths Exam Style)
Gradient of a Curve using Power Rule (Corbettmaths Exam Style)
Equation of Tangent to a Curve (Starting Points Maths)
Equation of a Tangent (Corbettmaths Exam Style)
Equation of a Normal (Corbettmaths Exam Style)
Scaffolded Stationary Points (Starting Points Maths)
Stationary Points (Corbettmaths Exam Style)
Calculus: Curve Sketching (Starting Points Maths)
Increasing and Decreasing Functions (Corbettmaths Exam Style)
Using Differentiation to Solve Problems (Corbettmaths Exam Style)
Rates of Change (CIMT Chapter)

Area of Study 4 - Data Analysis, Probability, and Statistics

Study Design
​Data Analysis, Probability, and Statistics Summary