Unit 1
Specialist Mathematics (Western Australia)
Topic 1: Combinatorics
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Addition and Multiplication principles
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Factorials!
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Permutations
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Arrangements in a circle
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Arrangements from like objects
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Addition and multiplication principles revision
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Factorials and permutations revision
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Permutations of like objects
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Permutations with restrictions
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Combinations
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Combinations with restrictions
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Pascals triangle and subsets of a set
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Pigeonhole principle
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Basic Set Theory
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The inclusion exclusion principle for 2 and 3 sets
Topic 2: Vectors in the Plane
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Vectors Introduction
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Adding Vectors Graphically
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Vectors Multiplying by a scalar
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Vectors in 2D and 3D Shapes
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Vectors in component form
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Adding Vectors in component form
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Vectors multiplying by a scalar in component form
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Vectors finding the magnitude
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Vectors finding the unit vector
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Defining a vector between 2 points
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Finding direction of a vector
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Force Vector Diagrams
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Resolving Force Vectors
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Resolving forces into their components
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Resolving Forces into components part 2
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Vector Revision part 1
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Vector midpoints
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Vectors in linear combinations
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Vectors in component form recap
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Vectors in polar form
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The scalar product or dot product of a vector revisited
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What’s a vector projection?
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Calculating vector projections
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Applications of vectors displacement and velocity
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Applications of vectors displacement and velocity collisions
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Applications of vectors relative velocity
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Triangle of forces
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Inclined plane recap part 1
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Solving equilibrium questions using resolution of forces
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Resolving a vector into components parallel and perpendicular to a second vector
Topic 3: Geometry
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The Real Number System
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Expressing a recurring decimal as a fraction
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Mathematical Notation: ∀ “For all” and ∃ “There Exists”
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Direct proof
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Proof by contrapositive
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Proof by contradiction
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Equivalent statements
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Disproving statements
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Geometric proofs from the ground up
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Proving the angle in a semi-circle is a right angle
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Prove the angle at the centre theorem
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The angle on the same arc theorem
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Proving Chord of Circle Theorem
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Proving Tangent to a circle and the radius are perpendicular Using Proof by Contradiction
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Proving the tangents from an external point theorem
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Proving the cyclic quadrilateral theorem
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Alternate Segment Theorem Proof
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Intersecting Chord Theorem Proof
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Proving the tangent secant theorem
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Equidistant chord Theorem Proof
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Intersecting Secants Theorem Proof: Teacher vs Student
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Geometric Proofs using Vectors part 1
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Geometric proofs using vectors Part 2