Unit 3
Specialist Mathematics (Queensland)
Topic 1: Further complex numbers
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De Moivre’s Theorem for raising a complex number to a power
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Factorising a cubic over C
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Conjugate root theorem
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Factor Theorem for factorising polynomials
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Remainder Theorem: Worked Examples, why it’s useful and Proof
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Roots of a Complex Number: De Moivre’s Theorem
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Roots of Unity
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Factorising & Solving quadratics over C
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Complex Numbers: Polar Form: Fast Recap including Operations on Polar Form.
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Complex Numbers: A Very Fast Recap of i, Operations, Conjugates, Argand Diagrams & Modulus
Topic 2: Mathematical induction and trigonometric proofs
Topic 3: Vectors in two and three dimensions
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All Year 11 Vectors in 30 minutes
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Intro to Vectors in 3D
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Vectors in 3D sample questions
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Vector Functions introduction
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Vector function basics positions, times and distances
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Convert a vector function to a cartesian equation
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Converting Vector function to cartesian equations using trig identities
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Vector equations and finding collision points
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Vector Equations of Lines
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Converting Vector equations to cartesian form and parametric equations
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Vector Cross Product Introduction
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Vector Product on your Casio
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Cross Product Area of shapes
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Vector Equation of a Plane part 1
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Vector Equations of planes part 2
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Equation of spheres in cartesian and vector form
Topic 4: Vector calculus
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Vector Calculus Differentiation worked examples
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Vector Calculus Anti differentiation worked example
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Vector Calculus Displacement, velocity Acceleration
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Vector Calculus Motion in a straight line
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Projectile motion: The Equations (Acceleration, Velocity, Displacement)
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Projectile Motion: All the kinds of questions and how to solve them
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Uniform Circular Motion: A Graphical Vector Understanding
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Uniform Circular Motion worked example
Topic 5: Further matrices
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Matrix Algebra Part 1
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Matrix Algebra Simultaneous equations
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The geometric interpretation of systems of linear equations in 2 & 3 dimensions
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Gaussian Elimination part 1
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Guassian Elimination Part 2 Systems with lines as solutions
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Gaussian Elimination part 3: systems resulting in No Solution
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Gaussian Elimination part 4 Finding the equation of a plane resulting in an intersection
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Gaussian Elimination on the Casio FX CG50AU
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Leslie Matrices – What’s really going on? (downloadable excel file in description)
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Leslie Matrices for population age distribution modelling
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Dominance Matrices from start to finish
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Dominance Matrices as a mathematical model