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 TI-84 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