Topic 1: Complex Numbers
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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
Conjugate root theorem: What it is and Proof
Factor & Remainder Theorems: Proof and Application
Factorising Polynomials over C worked examples
Calculating Roots of a complex number using De Moivre's Theorem
Roots of Unity
Sketching Subsets of the complex Plane
Topic 2: Functions & Sketching Graphs (coming soon)
coming soon.
Topic 3: Real and Complex Numbers
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 and converting vector functions to cartesian functions
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
Guassian Elimination Part 2 Systems with lines as solutions
Gaussian Elimination on the Casio FX CG50AU
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
Vector Calculus Projectile Motion Calculating Launch Angle
Uniform Circular Motion Introduction
Uniform Circular Motion worked example
