Unit 3
Specialist Mathematics (Queensland)
Topic 1: Proof by Mathematical Induction
Topic 2: Vectors and Matrices

Dominance Matrices from start to finish

Dominance Matrices as a mathematical model

Matrix Multiplication and Addition in Excel for Dominance Matrices

Markov Chains & Matrices: Part 1

Markov Chains Worked examples

Matrix Multiplication and Matrix Powers in Excel

Matrix Calculations on the TI84 plus

Leslie Matrices for population age distribution modelling

Leslie Matrices – What’s really going on? (downloadable excel file in description)

15 Vector Questions you should know how to do by the end of year 11

An Introduction to vectors in 3 dimensions

Converting 3D Vectors between Cartesian and Polar forms

Scalar or Dot Product in 3 Dimensions

Vector Functions Introduction

Converting Vector Equations to Cartesian Equations using trigonometric Identities

Vector equations and finding collision points

Vector Equations of Lines

Converting Vector equations to cartesian form and parametric equations

Parallel and perpendicular vector equations

Calculating distance from a point to a vector equation of a line

Vectors: Line of intersection & the angle between two planes

The Vector Product (Cross Product)

Vector Equation of a plane fully explained and shown graphically

Finding equations of planes: Three worked examples

Vectors: Calculating the distance from a point to a plane or a plane to a plane

Vectors Intersection points between lines and planes and the angle between a line and a plane

Vector Calculations & 3D Graphing on the Casio FX CG50AU

Intersections of 3D Lines, Skew Lines and angles between lines

Equation of spheres in cartesian and vector form

The geometric interpretation of systems of linear equations in 2 & 3 dimensions

Using Matrix Algebra to find an intersection point of 3 planes

Solving Simultaneous Equations on the Casio FX CG50AU

Gaussian Elimination part 1

Gaussian Elimination on the Casio FX CG50AU

Guassian Elimination Part 2 Systems with lines as solutions

Gaussian Elimination part 3: systems resulting in No Solution

Gaussian Elimination part 4 Finding the equation of a plane resulting in an intersection

Vector Calculus Displacement, velocity Acceleration

Vector Calculus Anti differentiation worked example

Vector Calculus Differentiation worked examples

Vector Calculus Motion in a straight line

Projectile Motion: A Graphical Understanding using Vectors

Projectile motion: The Equations (Acceleration, Velocity, Displacement)

Vector Calculus Projectile Motion Calculating Launch Angle

Projectile Motion: All the kinds of questions and how to solve them

Uniform Circular Motion: A Graphical Vector Understanding

Uniform Circular Motion worked example

Vector calculus & the dot product: Finding where the velocity & the acceleration are at right angles

Challenging vector calculus dot product question
Topic 3: Complex Numbers 2

Complex Numbers: A Very Fast Recap of i, Operations, Conjugates, Argand Diagrams & Modulus

Complex Numbers: Polar Form: Fast Recap including Operations on Polar Form.

Factorising & Solving quadratics over C

Remainder Theorem: Worked Examples, why it’s useful and Proof

Factor Theorem for factorising polynomials

Conjugate root theorem

Conjugate root theorem: What it is and Proof

Factorising a cubic over C

Roots of a Complex Number: De Moivre’s Theorem

Roots of Unity

Sketching Subsets of the complex Plane