Specialist Mathematics Units 3&4

Quick Links:
​Area of Study 1 - Discrete Mathematics
Area of Study 2 - Functions, Relations, and Graphs
Area of Study 3 - Algebra, Number, and Structure
Area of Study 4 - Calculus
Area of Study 5 - Space and Measurement
Area of Study 6 - Data Analysis, Probability, and Statistics
  • Study Design
  • Unit Materials
  • VCAA Resources
  • Exam Report Summaries
  • Changelog
  • Other
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VCAA Specialist Mathematics
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​​Specialist Mathematics Examination Information
Bound Reference Specifications
Formula Sheet 

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

Assessment: Scope of Tasks, Sample SACs, Performance Descriptiors
Unit 3 SAC - How to develop an application task
Unit 4 SAC - How to develop a modelling or problem-solving task for calculus and vectors
​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 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 - Discrete Mathematics

Logic and Proof
Study Design
​Logic and Proof Summary
  • Notes
  • Videos & Interactives
  • Exam Questions
  • Questions
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Summation notation or Sigma Notation (Joel Speranza Math Video)
Python - VCAA Pseudocode (Simon Tyler Notes)
Products of terms in sequences: Can We Do That?!? (Maths Like A Legend Video)

Inequality Proof - Fraction Sum
Solutions to past VCAA exam questions can be looked up in the appropriate examiner's report on the Specialist Mathematics Past Examinations and Examination Reports page or the Northern Hemisphere Timetable (NHT) Past Examinations and Examination Reports page. 
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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
Logic
Proof by Induction

Area of Study 2 - Functions, Relations, and Graphs

Study Design
​Functions and Graphs Summary
  • Notes
  • Videos & Interactives
  • Exam Questions
  • Questions
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Graphing Reciprocal Functions
Reciprocals of Functions (Joel Speranza Math Video)
Sketching Reciprocal Functions Worked Example (Joel Speranza Math Video)
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Rational Functions as Hyperbolas (Joel Speranza Math Video)
Rational Functions with Slant Asymptotes (Joel Speranza Math Video)
Rational Functions Part 3 (Joel Speranza Math Video)
​Graphing a Rational Function Step-By-Step (Eddie Woo Video)

Multiplying rational expressions (Khan Academy Video)
Dividing rational expressions (Khan Academy Video)

Partial Fractions
​Quadratic Factors
Partial Fractions: Repeated Linear Factors - ​Technique for Breaking Down into Partial Fractions (Eddie Woo Video)

Straight Up Curriculum Mathematics for the 21st Century
Graphing Rational Functions
Oblique Asymptotes
The Modulus or Absolute Value Function Introduction (Joel Speranza Math Video)
The Modulus or Absolute Value: Solving Equations (Joel Speranza Math Video)
The Absolute Value: Solving Inequalities (Joel Speranza Math Video)

​Solving Absolute Value Equations Example (Eddie Woo Video)

Absolute Value Equations & Inequalities
Absolute Value Functions (Joel Speranza Math Video)
Sketch Absolute Value Functions with a Vertical Shift (Joel Speranza Math Video)
Sketching an Absolute Value Function Worked Example (Joel Speranza Math Video)
Reflecting Functions in the y Axis using Absolute Value Functions (Joel Speranza Math Video)

Graphing Absolute Value Functions
​​Absolute Value Equations (GeoGebra Interactive)
Absolute Value Inequalities (GeoGebra Interactive)
​Absolute Value Function (GeoGebra Interactive)
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Introduction to Trigonometric Expansions
Combining Trigonometric & Inverse Trigonometric Functions (Eddie Woo Video)

Graphs of Inverse Trigonometric Functions
​Reciprocals of Trigonometric Functions​​ (Joel Speranza Math Video)
Transformations of the Reciprocal Trigonometric Functions (Joel Speranza Math Video)
Exact Values of Reciprocal Trigonometric Functions (Joel Speranza Math Video)
Solving Reciprocal Trig Functions (Joel Speranza Math Video)
The Pythagorean Identity and Reciprocal Trigonometric Functions (Joel Speranza Math Video)
2 More Pythagorean Identities (Joel Speranza Math Video)
Angle Sum and Difference Identities (Joel Speranza Math Video)
Angle Sum and Difference Identities Part 2 (Joel Speranza Math Video)
Proving Trigonometric Identities (Joel Speranza Math Video)
Double Angle Identities and Proofs and an Example (Joel Speranza Math Video)
More Proofs of Trig Identities (Joel Speranza Math Video)
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Using Multi-Angle Formula to Solve Polynomials (Eddie Woo Video)
Sine & Cosine of a Sum: Discovery (GeoGebra Interactive)
​Tangent of a Sum: Discovery (GeoGebra Interactive)
​Tangent of a Difference: Discovery (GeoGebra Interactive)

​Trigonometry Fundamentals (3Blue1Brown Video)

Straight Up Curriculum Math for the 21st Century: The Story of Trigonometry
Solutions to past VCAA exam questions can be looked up in the appropriate examiner's report on the Specialist Mathematics Past Examinations and Examination Reports page or the Northern Hemisphere Timetable (NHT) Past Examinations and Examination Reports page. 

Sketching Graphs (2016-2022 Study Design Questions)
Sketching Graphs (2000-2015 Study Design Questions)
​Partial Fractions (2016-2022 Study Design Questions)
Partial Fractions (2000-2015 Study Design Questions)
Rational Functions (2016-2022 Study Design Questions)
Rational Functions (2000-2015 Study Design Questions)
Inverse and Reciprocal Trigonometric Functions (2016-2022 Study Design Questions)
Inverse and Reciprocal Trigonometric Functions (2000-2015 Study Design Questions)
​Absolute Values (2016-2022 Study Design Questions)
Absolute Values (2000-2015 MM Study Design Questions)
​Trigonometric Formulas and Identities (2016-2022 Study Design Questions)
​Trigonometric Formulas and Identities (2000-2015 ​Study Design Questions)
Rational Functions: Asymptotes and Graphs (Starting Points Maths)

Absolute Value Equations ​
Absolute Value Inequalities
​​Graphing Absolute Value Equations (Interactive Practice)
​Trigonometric Functions of Special Angles (Interactive Practice)
Trigonometric Identities (Corbettmaths Exam Style)
​Addition and Double Angle Formulae (Starting Points Maths)

Area of Study 3 - Algebra, Number, and Structure

Study Design
​Algebra, Number, and Structure Summary
  • Notes
  • Videos & Interactives
  • Exam Questions
  • Questions
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​Complex Numbers
​Complex Numbers
Arithmetic of Complex Numbers
Arithmetic of Complex Numbers with Dienes Blocks
Arguments and Polar Form of Complex Numbers
​Multiplication and Division in Polar Form
​Proof of Basic Identities involving Modulus and Argument

​​Relations of the Complex Plane​
Loci Definitions using Arguments on the Complex Plane
More Loci Definitions using Arguments on the Complex Plane (Optional)
Conjugates and Relations on the Complex Plane (Optional)
Distance Definitions of Lines, Circles, and Ellipses 
Distance Definitions of Hyperbolas and Conic Sections (Optional)
Regions of the Complex Plane

Powers of Complex Numbers
​Roots of Complex Numbers
Exponential Form of Complex Numbers (Optional)

​Factorising Polynomials over C
​Solving Polynomial Equations over C
The Conjugate Root Theorem​
Intersections on the Complex Plane Algebraically (Optional)
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​Complex Numbers Technology [TI-nSpire]
​Complex Numbers Technology [Casio]
Complex Numbers
A Visual, Intuitive Guide to Imaginary Numbers (Better Explained Article)
​This Problem Broke Math (and led to quantum physics) (Veritasium Video)
Dienes Blocks (Maths Bot Interactive)​

​Introduction to Complex Numbers
​Complex Arithmetic
Complex Arithmetic
​Complex Numbers as Points
Complex Locus Plotter (GeoGebra Interactive)

Graphs in the Complex Plane
Further Graphs of the Complex Plane
Graphs in the Complex Plane
Semi Circles on Argand Diagrams
Algebraic Proof for Opposing Rays  ​
Arcs on the Complex Plane
​Graphing in the Complex Plane: Worked examples (Eddie Woo Video)
Sketching Subsets of the complex Plane (Joel Speranza Math Video)
Sketching Sets Defined on the Complex Plane (Maths Stats UNSW Video) [7:39 - 13:48] ​

​Square Roots of Complex Numbers
Introducing Polar Form
Complex Numbers - Mod-Arg Form
Multiplying Complex Numbers in Mod-Arg Form
Using Inverse Tan to Find Arguments?
Working in Polar Form 
Exact value of cos(π÷12) (Eddie Woo Video)
Complex Numbers: A Very Fast Recap of i, Operations, Conjugates, Argand Diagrams & Modulus (Joel Speranza Math Video)
Complex Numbers: Polar Form: Fast Recap including Operations on Polar Form (Joel Speranza Math Video)
​Relationships Between Moduli & Arguments in Products of Complex Numbers (Eddie Woo Video)
​Understanding Complex Quotients & Conjugates in Mod-Arg Form (Eddie Woo Video)

Quotient of Complex Numbers
Argument of the Complex Conjugate (Eddie Woo Video)
Working with Moduli and Arguments (Proof Question) (Eddie Woo Video)

​The Triangle Inequalities ​
​De Moivre's Theorem (Eddie Woo Video)
​Using De Moivre's Theorem and Binomial Expansions (Eddie Woo Video)

Proving de Moivre's Theorem
Using de Moivre's Theorem - Example Question
An Interactive Approach to Finding nth Roots (Sine of the Times Interactive)
Factorising & Solving quadratics over C (Joel Speranza Math Video)

Equations with Complex Solutions
Relation to square roots (Eddie Woo Video)
Solving & factorising (Eddie Woo Video)

​Linear Factorisation of Polynomials
Complex Conjugate Root Theorem
Complex Conjugate Root Theorem / Roots of Unity
​Complex Conjugate Root Theorem
Conjugate root theorem: What it is and Proof (Joel Speranza Math Video)
Factorising Polynomials over C worked examples (Joel Speranza Math Video)
Complex Polynomial Roots (Leo C. Stein Interactive)
Roots of Unity (Joel Speranza Math Video)

Roots of Unity
Nth Roots of a ℂ Number 
Calculating Roots of a complex number using De Moivre's Theorem (Joel Speranza Math Video)

​Who cares about complex numbers? (Eddie Woo Video)
Complex Number Fundamentals (3Blue1Brown Video)
Discovering Euler's Trigonometric Formula (James Tanton Video)

The Most Beautiful Identity (Optional)
What does an imaginary power mean? (Eddie Woo Video) [Optional]

Informal Proof of Euler's Formula (Optional)
Proving Euler's Formula (Optional) ​
Trigonometric Expansions from Complex Numbers (Optional)
​Imaginary Numbers are Real
PHANTOM GRAPHS (Philip Lloyd Notes)
Solutions to past VCAA exam questions can be looked up in the appropriate examiner's report on the Specialist Mathematics Past Examinations and Examination Reports page or the Northern Hemisphere Timetable (NHT) Past Examinations and Examination Reports page. 

Complex Numbers (2016-2022 Study Design Questions)
Complex Numbers (2000-2015 Study Design Questions)
Relations of the Complex Plane (2016-2022 Study Design Questions)
Relations of the Complex Plane (2000-2015 Study Design Questions)
​Regions on the Complex Plane (2000-2015 Study Design)
​Polynomials over C (2016-2022 Study Design Questions)
​Polynomials over C (2000-2015 ​Study Design Questions)
Real Part and Imaginary Part (mathworksheets4kids)
Plotting Complex Numbers (mathworksheets4kids)
Complex Numbers: Complex Conjugate (Variation Theory)
​Complex Numbers: Adding and Subtracting (Variation Theory)
Adding and Subtracting Complex Numbers (mathworksheets4kids)
Complex Numbers: Multiplication (Variation Theory)
Multiplying Complex Numbers (mathworksheets4kids)
Complex Numbers: Division (Variation Theory)
Rationalise the Denominator (mathworksheets4kids)
Simplifying Complex Numbers (mathworksheets4kids)
Powers of i (mathworksheets4kids)
Absolute Value of Complex Numbers (mathworksheets4kids)
Absolute Value and Argument of Complex Numbers (mathworksheets4kids)​
Complex Numbers Polar Form (Starting Points Maths)
Using De Moivre's Theorem to Evaluate Powers of Complex Numbers (Variation Theory)
Finding the nth Root of Complex Numbers (Variation Theory)
​Complex Numbers: Polynomials from Roots (Variation Theory)

Area of Study 4 - Calculus

Study Design
​Calculus Summary
  • Notes
  • Videos & Interactive
  • Exam Questions
  • Questions
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​Differential and Integral Calculus
​Graphs of Anti-Derivative Functions

Differentiation Rules
​Derivatives of Inverse Circular Functions
​Second Derivatives
​Related Rates of Change
Implicit Differentiation
Logarithmic Derivative (Optional)
Implicit Second Derivative

Anti-Differentiation and Integration
Integration that Results in Logarithms
Integration that Results in Inverse Circular Functions
​Anti-Differentiation and Integration using Substitutions
Integration using Trigonometric Identities 
Integration using Partial Fractions of Rational Functions
​Integration by Parts
Numeric and Symbolic Integration

Areas of Regions Bounded by Curves
Area of a Circle using Integration
​Arc Length of a Parametric Path
Surface Areas of Surfaces of Revolution
Volumes of Solids of Revolution
​Volumes of Cones and Spheres
​Volumes of Solids of Revolution - Method of Shells (Optional)
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Differential Equations
Formulation of Differential Equations 
Example Applications of Differential Equations
​Verifying Solutions to Differential Equations
Direction (Slope) Field
Solution to Differential Equations 
​Euler's Method of Approximation
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Kinematics: Rectilinear Motion
Kinematics - Straight Line Motion
​Constant Acceleration (Optional)
​Velocity-Time Graphs

Calculus Technology [TI-nSpire]
​Calculus Technology [Casio]
Differential and Integral Calculus
​Derivative of Arcsine Function (GeoGebra Interactive)
​Derivative of Arccosine Function (GeoGebra Interactive)
​Derivative of Arctangent Function (GeoGebra Interactive)
Proofs of derivatives of Inverse Trigonometric Functions (Joel Speranza Math Video)​
Calculating derivatives of inverse trigonometric Functions (Joel Speranza Math Video)
How to Learn Trig Derivatives (Better Explained Video and Article)

Graphing Stationary Points
Related Rates: Introduction and Worked Examples (Joel Speranza Math Video)

Related Rates of a Balloon
Related Rates of a Shrinking Cube (Eddie Woo Video)
Related Rates of Change: Overall Strategy (Eddie Woo Video)

Related Rates of Change - Slipping Ladder
Related Rates of Change - Shifting Shadow
Essence of Calculus
Implicit differentiation (Joel Speranza Math Video)
Derivatives of x=f(y) (Maffs Guru Video)
Differentiation of inverse circular functions (Maffs Guru Video)

The Second Derivative
Using Second Derivative
Geometry of the Derivatives
Identifying Important Points with Calculus (Worked Example) (Eddie Woo VIdeo)
Flowchart for Testing Stationary Points (Eddie Woo Video)
Finding the Second Derivative Implicitly (Eddie Woo Video)

​Points of Inflection
Graphing with Calculus
Integrals & Logarithmic Functions
Logarithms as Primitive Functions (Why are there absolute value signs?) (Eddie Woo Video)
Integration resulting in ln|ax+b| (Joel Speranza Math Video)
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Integration by Unspecified Substitution
Integration by Substitution (Eddie Woo Video)
Identifying a u in u Substitution (Khan Academy Video)
Integration by substitution worked examples part 1 (Joel Speranza Math Video)
Integration by substitution worked examples part 2 (Joel Speranza Math Video)
Definite Integral & U substitution: One Weird Trick (Joel Speranza Math Video)
Integration by linear substitution (Joel Speranza Math Video)
Integration Resulting in Inverse trigonometric functions (Joel Speranza Math Video)
Using trig identities for integration (Joel Speranza Math Video)
Integration by Substitution Introduction (Joel Speranza Math Video)
Integrals of products of sine and cosine (Joel Speranza Math Video)
Integration with partial fractions (Joel Speranza Math Video)
​u Substitution with Definite Integral (Khan Academy Video)
​Definite Integrals by Substitution - Dealing with the Boundaries (Eddie Woo Video)
Integration with Partial Fraction Decomposition (Khan Academy Video)
Integration by Completing the Square and the Derivative of artctan(x) (Khan Academy Video)

​Solids of Revolution (GeoGebra Interactive)
Volumes of solids of revolution introduction (Joel Speranza Math Video)
Volumes of solids of revolution: Around the y axis (Joel Speranza Math Video)
Volume of solids of revolution: between 2 curves (Joel Speranza Math Video)

Solids of Revolution
Volume of a Sphere: Three Different Derivations (Eddie Woo Video)
Find the Volume of Any Shape Using Calculus (Domain of Science Video)

Applications of Integrating Exponential Functions
​Integration by parts (Joel Speranza Math Video)
Integration by parts: choosing u and v' (Joel Speranza Math Video)
Integration by parts e^xcosx (Joel Speranza Math Video)
Integration by parts: Definite Integrals (Joel Speranza Math Video)
Differential Equations: The Logistic Equation (Joel Speranza Math Video)

Integration by Parts 

Differential Equations
Overview of Differential Equations (3Brown1Blue Video)
Verifying Solutions to Differential Equations (Khan Academy Video)
Verifying solutions to differential equations (Joel Speranza Math Video)
Slope Fields (GeoGebra Interactive)
Introduction to Slope Fields for Differential Equations (Joel Speranza Math Video)
Slope Fields Using the TI NSPIRE (Joel Speranza Math Video)

Solving differential equations (Joel Speranza Math Video)
Solving differential equations given in terms of f(y) (Joel Speranza Math Video)
Separable differential equations (Joel Speranza Math Video)
Setting up differential equations (Joel Speranza Math Video)
Differential Equations with Related Rates (Joel Speranza Math Video)

Differential Equations in Terms of Dependent Variable
Growth/Decay with Environmental Factors
Newton's Law of Cooling (GeoGebra Interactive)
Isaac Newton & My Cup of Coffee: Differential Equations Applications (Joel Speranza Math Video)
Differential equations: Mixing Problems (Joel Speranza Math Video)
How I wish logistic growth was taught to me in Calc 2 (Zach Star)
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Growth & Decay - Saltwater/Freshwater Problem
Growth & Decay - Trout/Carp Problem
Kinematics: Rectilinear Motion
​Motion in a Straight Line (Crash Course Video)
Derivatives and Motion (Crash Course Video)
​Integrals and Motion (Crash Course Video)

Derivatives of Motion
Intro to Straight Line Motion
Velocity in terms of displacement Acceleration in terms of velocity (Joel Speranza Math Video)
Other Expressions for acceleration part 1 (Joel Speranza Math Video)
Other Expressions for acceleration part 2 (Joel Speranza Math Video)

Acceleration in terms of Displacement
Motion Graphs
Integrating with Respect to Time ​(Eddie Woo Video)
Position, Velocity, and Acceleration vs Time Graphs (GeoGebra Interactive)
Kinematics Graphs: Adjust the Acceleration (GeoGebra Interactive)
GeoGebra Apps for Mechanics (GeoGebra Interactives)
Solutions to past VCAA exam questions can be looked up in the appropriate examiner's report on the Specialist Mathematics Past Examinations and Examination Reports page or the Northern Hemisphere Timetable (NHT) Past Examinations and Examination Reports page. 

​First and Second Derivatives (2016-2022 Study Design Questions)
First and Second Derivatives (2000-2015 Study Design Questions)
​Turning Points and Points of Inflection (2016-2022 Study Design Questions)
Turning Points and Points of Inflection (2000-2015 Study Design Questions)
Implicit Differentiation (2016-2022 Study Design Questions)
Implicit Differentiation (2000-2015 Study Design Questions)
Related Rates (2016-2022 Study Design Questions)
Related Rates (2000-2015 Study Design Questions)
Related Rates (2000-2015 MM Study Design Questions)
Integration Techniques (2016-2022 Study Design Questions)
Integration Techniques (2000-2015 Study Design Questions)
Arc Lengths (2016-2022 Study Design Questions)
Arc Lengths of Parametric Functions (2016-2022 Study Design Questions)
Areas (2016-2022 Study Design Questions)
Areas (2000-2015 Study Design Questions)
Volumes of Solids of Revolution (2016-2022 Study Design Questions)
Volumes of Solids of Revolution (2000-2015 Study Design Questions)
​Differential Equations (2016-2022 Study Design Questions)
Differential Equations (2000-2015 Study Design Questions)
Verification of Solutions to Differential Equations (2016-2022 Study Design Questions)
Verification of Solutions to Differential Equations (2000-2015 Study Design Questions)
Direction (Slope) Fields (2016-2022 Study Design Questions)
Direction (Slope) Fields (2000-2015 Study Design Questions)
​Applications of Differential Equations (2016-2022 Study Design Questions)
Applications of Differential Equations (2000-2015 Study Design Questions)
Euler's Method of Approximation (2016-2022 Study Design Questions)
Euler's Method of Approximation (2000-2015 Study Design Questions)
​Kinematics in One Dimension (2016-2022 Study Design Questions)
​Kinematics in One Dimension (2000-2015 Study Design Questions)
Constant Acceleration (2000-2015 Study Design Questions)
Velocity-Time Graphs (2016-2022 Study Design Questions)
Velocity-Time Graphs (2000-2015 ​Study Design Questions)
Second Derivative (Corbettmaths Exam Style)
​Implicit Differentiation with Product Rule (Variation Theory)
Integrations Looky-Likeys (Fortunate Sums)
Integration: Reverse Chain Rule (Variation Theory)
Integration by Substitution a-Day (mathematicsandcoding)
Differential Equations: Separation of Variables (Variation Theory)

Area of Study 5 - Space and Measurement

Vectors
Study Design​
​Vectors Summary
  • Notes
  • Videos & Interactives
  • Exam Questions
  • Questions
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Vectors
Vectors
Linear Dependence of Vectors
Orthogonal Unit Vectors
​Resolution of a Vector into Rectangular Components
​Scalar Product / Dot Product
​​Scalar and Vector Resolutes
​The Vector (Cross) Product
Triple Products (Optional?)

Vector Proofs and Lines and Ratios
Vector Proofs and Triangles
Vector Proofs and Quadrilaterals
Vector Proofs and Circles

​Vectors Technology [TI-nSpire]
​Vectors Technology [Casio]

Vector and Cartesian Equations
Vector Equation of a Line
Vector Equations of Curves 
Converting Vector Equations to Cartesian Equations
Vector Equations using Perpendicular Distances from Lines (Optional)
Equations of and the Normal to a Plane
Intersections between Lines and Planes (Optional?)
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Vector Calculus
​Position Vectors as a Function of Time
Collisions and Crossing Paths
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Calculus of Vector Functions
Velocity and Acceleration Vectors as Functions of Time
​Projectile Motion

Vector Calculus Technology [TI-nSpire]
​Vector Calculus Technology [Casio]
Vectors
Vectors Introduction (Joel Speranza Math Video)
Adding Vectors Graphically (Joel Speranza Math Video)
Vectors Multiplying by a Scalar (Joel Speranza Math Video)
Introduction to vectors (Maffs Guru Video)
Vectors Make Sense (Looking Glass Universe Video)
What is a Vector? (TED-Ed Video)
Adding Vectors in Component Form (Joel Speranza Math Video)
Adding Vectors Geometrically (GeoGebra Interactive)
Vectors Multiplying by a Scalar in Component Form (Joel Speranza Math Video)
Scaling Vectors (GeoGebra Interactive)
​Defining a Vector between 2 Points (Joel Speranza Math Video)
Vectors Finding the Magnitude (Joel Speranza Math Video)
Vectors Finding the Unit Vector (Joel Speranza Math Video)
​​Dot Product Insight (GeoGebra Interactive)
The Dot Product (Part 1) (Joel Speranza Math Video)
The Dot Product (Part 2) (Joel Speranza Math Video)
The Dot Product (Part 3) (Joel Speranza Math Video)
​Dot Product Basics (Eddie Woo Video)

Dot Product, Continued
Projections
What's a Vector Projection? (Joel Speranza Math Video)
Calculating Vector Projections (Joel Speranza Math Video)
​Resolving a Vector into Components Parallel and Perpendicular to a Second Vector (Joel Speranza Math Video)
Vector Projections (GeoGebra Interactive)
​2D Projection of Vectors (GeoGebra Interactive)
Finding Direction of a Vector (Joel Speranza Math Video)
​Introduction to Vectors in 3 Dimensions (Joel Speranza Math Video)
Scalar or Dot Product in 3 Dimensions (Joel Speranza Math Video)
​Coordinate Direction Angles (GeoGebra Interactive)
Concurrence of Medians: Proof via Similar Triangles (Eddie Woo Video)

3D Coordinate System 
​Extending 2D Vectors 
​3D Dot Product 
Applications of Dot Products
Vectors in 2D and 3D Shapes (Joel Speranza Math Video)
Vector Midpoints (Joel Speranza Math Video)
Vectors in 2D shapes (Joel Speranza Math Video)
Vectors in Linear Combinations (Joel Speranza Math Video)
Geometric Proofs using Vectors (Part 1) (Joel Speranza Math Video)
Geometric Proofs using Vectors (Part 2) (Joel Speranza Math Video)
​15 Vector Questions You Should Know How to do by the End of the Year (Joel Speranza Math Video)
Vectors Proof: A fun parallelogram proof style question (Joel Speranza Math Video)
Ratio Division with Vectors: Internal (Eddie Woo Video)
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Vector Calculus
​Vectors and 2D Motion (Crash Course Video)
Equation of Ellipses Crash Course (Joel Speranza Math Video)

Introduction to Parametrics
Parametric Equations → Cartesian Equation
What does the Parameter Mean?
Equation of Path
​Vector Functions Introduction and Converting Vector Functions to Cartesian Functions (Joel Speranza Math Video)
Converting Vector Equations to Cartesian Equations using Trigonometric Identities (Joel Speranza Math Video)
Vector Equations and Finding Collision Points (Joel Speranza Math Video)

Vector Calculus: Differentiation Worked Examples (Joel Speranza Math Video)
Vector Calculus: Anti-Differentiation Worked Examples (Joel Speranza Math Video)
Related Rates Parametric equations (Joel Speranza Math Video)
​
Vector Calculus: Displacement, Velocity, Acceleration (Joel Speranza Math Video)
Vector Calculus: Motion in a Straight Line (Joel Speranza Math Video)
Vector Calculus: Projectile Motion Calculating Launch Angle (Joel Speranza Math Video)
Projectile Motion (GeoGebra Interactive)
Projectile Motion (PhET Interactive)

​Uniform Circular Motion (Crash Course Video)
Uniform Circular Motion Introduction (Joel Speranza Math Video)
Uniform Circular Motion worked example (Joel Speranza Math Video)
​Angular Motion Variables​ (Khan Academy Video)
​Distance or Arc Length from Angular Displacement (Khan Academy Video)
​Angular Velocity and Speed ​(Khan Academy Video)

The Beauty of Bézier Curves (Freya Holmér Video)


​Cross Products (3Brown1Blue Video)
Cross Product (GeoGebra Interactive)
​Normal Vector (GeoGebra Interactive)​

Angle Between Two Vectors (Starting Points Maths)

Vector and cartesian equations
​Vector Equations of Lines (Joel Speranza Math Video)

Vector Equation of a Line
Lines in Three Dimensions
3D Line Problems
Applying Vector Equations of Lines 
Vector Equations of Curves
Vector Equations of Spheres
Converting Vector Equations to Cartesian Form and Parametric Equations (Joel Speranza Math Video)
Parallel and Perpendicular Vector Equations (Joel Speranza Math Video)
Calculating Distance from a Point to a Vector Equation of a Line (Joel Speranza Math Video)
The Vector Product (Cross Product) (Joel Speranza Math Video)
Vector Calculus: Understanding the Cross Product (Better Explained Article)
Vector Equation of a Plane Fully Explain and Shown Graphically (Joel Speranza Math Video)
Finding Equations of Planes: Three Worked Examples (Joel Speranza Math Video)
Vectors: Calculating the Distance from a Point to a Plane or a Plane to a Plane (Joel Speranza Math Video)
Intersections of 3D Lines, Skew Lines, and Angles between Lines (Joel Speranza Math Video)
Vectors Intersection Points between Lines and Planes and the Angle between a Line and a Plane (Joel Speranza Math Video)
Vectors: Line of Intersection & the Angle between Two Planes (Joel Speranza Math Video)
Equation of a plane: 2 points on a plane, find the 3rd to make an equilateral triangle (Joel Speranza Math Video)
Equation of Spheres in Cartesian and Vector Form (Joel Speranza Math Video)
Solutions to past VCAA exam questions can be looked up in the appropriate examiner's report on the Specialist Mathematics Past Examinations and Examination Reports page or the Northern Hemisphere Timetable (NHT) Past Examinations and Examination Reports page. 

​Vector Operations (2016-2022 Study Design Questions)
Vector Operations (2000-2015 Study Design Questions)
​Linear Dependence of Vectors (2016-2022 Study Design Questions)
Linear Dependence of Vectors (2000-2015 Study Design Questions)
Scalar and Vector Resolutes (2016-2022 Study Design Questions)
Scalar and Vector Resolutes (2000-2015 Study Design Questions)
Vector Proofs (2016-2022 Study Design Questions)
Vector Proofs (2000-2015 Study Design Questions)
​Curves Defined Parametrically (2016-2022 Study Design Questions)
Curves Defined Parametrically (2000-2015 Study Design Questions)
Circles, Ellipses, and Hyperbolas in Cartesian Form (2016-2022 Study Design Questions)
Circles, Ellipses, and Hyperbolas in Cartesian Form (2000-2015 Study Design Questions)
​Position, Distance, and Collisions (2016-2022 Study Design Questions)
Position, Distance, and Collisions (2000-2015 Study Design Questions)
​Velocity, Speed, and Direction of Motion (2016-2022 Study Design Questions)
Velocity, Speed, and Direction of Motion (2000-2015 Study Design Questions)
​Derivatives of Parametric Functions (2016-2022 Study Design Questions)
Derivatives of Parametric Functions (2000-2015 Study Design Questions)
Projectile Motion (2016-2022 Study Design Questions)
​Projectile Motion (2000-2015 Study Design Questions)
Motion in Three Dimensions (2000-2015 Study Design)
Vectors: Adding and Subtracting (Variation Theory)
Adding Vector Geometrically (Interactive Practice)
Vectors: Multiplying by a Scalar (Variation Theory)
Vectors (Corbettmaths Exam Style)
Writing Ordered Triplets (Interactive Practice)
Determining if Vectors are Parallel (Minimally Different)
Dot Product: Basic Synthesis Questions (Interactive Practice)
Properties of Scalar Product (Starting Points Maths)
Angle Between Two Vectors (Starting Points Maths)
Dividing a Line in a Given Ratio (Starting Points Maths)

Graphing Ellipses (EQ in Standard Form) (Interactive Practice)

Area of Study 6 - Probability and Statistics

Study Design
​​Probability and Statistics Summary
  • Notes
  • Videos & Interactives
  • Exam Questions
  • Questions
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>
Statistical Analysis Spreadsheet
Modifying Statistical Scale & Origin​
Variance on a Modified Distribution
So why is the "central limit" a normal distribution? (3Brown1Blue Video)​

Variance of sum and difference of random variable (Khan Academy Video)
Intuition for why independence matters for variance of sum (Khan Academy Video)
​
Exploring Sample Means (Joel Speranza Math Video)
The distribution of a sample mean for a normal random variable (Joel Speranza Math Video)
The distribution of the sample mean for other random variables (Joel Speranza Math Video)
​​Sample Means Simulation (Online Stat Book Interactive)
Sampling Distribution of Means (GeoGebra Interactive)
​Confidence Intervals Simulation (Rossman/Chance Interactive)
Confidence Intervals (Crash Course Video)
​Frequentist Inference: Confidence Interval (Seeing Theory Interactive)
Probability Distributions: Central Limit Theorem (Seeing Theory Interactive)
The Normal Distribution (Crash Course Video)

Idea behind Hypothesis Testing (Khan Academy Video)
​Examples of Null and Alternative Hypotheses (Khan Academy Video)
​p Values and Significance Tests (Khan Academy Video)
​Comparing p Values to Significance Levels (Khan Academy Video)
How p-values Help us Test Hypotheses (Crash Course Video)
​P-Value Problems (Crash Course Video)
Playing with Power: P-Values Pt 3 (Crash Course Video)
Test Statistics (Crash Course Video)

​Examples Identifying Type I and Type II Errors (Khan Academy Video)
Solutions to past VCAA exam questions can be looked up in the appropriate examiner's report on the Specialist Mathematics Past Examinations and Examination Reports page or the Northern Hemisphere Timetable (NHT) Past Examinations and Examination Reports page. 

​Linear Combinations of Random Variables (2016-2022 Study Design Questions)
Sample Distribution of Means (2016-2022 Study Design Questions)
​Confidence Intervals (2016-2022 Study Design Questions)
Hypothesis Testing (2016-2022 Study Design Questions)