Unit 3
Specialist Mathematics (Western Australia)
Topic 1: Complex Numbers
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Complex Numbers: A Very Fast Recap of i, Operations, Conjugates, Argand Diagrams & Modulus
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Complex Numbers: Polar Form: Fast Recap including Operations on Polar Form.
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Factorising & Solving quadratics over C
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Conjugate root theorem: What it is and Proof
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Factor & Remainder Theorems: Proof and Application
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Factorising Polynomials over C worked examples
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Calculating Roots of a complex number using De Moivre’s Theorem
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Roots of Unity
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Sketching Subsets of the complex Plane
Topic 2: Functions & Sketching Graphs (Coming Soon)
Coming Soon
Topic 3: Real and Complex Numbers
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15 Vector Questions you should know how to do by the end of year 11
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An Introduction to vectors in 3 dimensions
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Converting 3D Vectors between Cartesian and Polar forms
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Scalar or Dot Product in 3 Dimensions
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Vector Functions Introduction and converting vector functions to cartesian functions
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Converting Vector Equations to Cartesian Equations using trigonometric 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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Parallel and perpendicular vector equations
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Calculating distance from a point to a vector equation of a line
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Vectors: Line of intersection & the angle between two planes
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The Vector Product (Cross Product)
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Vector Equation of a plane fully explained and shown graphically
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Finding equations of planes: Three worked examples
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Vectors: Calculating the distance from a point to a plane or a plane to a plane
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Vectors Intersection points between lines and planes and the angle between a line and a plane
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Vector Calculations & 3D Graphing on the Casio FX CG50AU
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Intersections of 3D Lines, Skew Lines and angles between lines
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Equation of spheres in cartesian and vector form
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The geometric interpretation of systems of linear equations in 2 & 3 dimensions
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Using Matrix Algebra to find an intersection point of 3 planes
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Solving Simultaneous Equations on the Casio FX CG50AU
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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 on the Casio FX CG50AU
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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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Vector Calculus Displacement, velocity Acceleration
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Vector Calculus Anti differentiation worked example
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Vector Calculus Differentiation worked examples
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Vector Calculus Motion in a straight line
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Vector Calculus Projectile Motion Calculating Launch Angle
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Uniform Circular Motion Introduction
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Uniform Circular Motion worked example