Unit 1
Specialist Mathematics (Queensland)
Topic 1: Combinatorics
-
Addition and Multiplication principles
-
Factorials!
-
Introduction to Permutations
-
Permutations
-
Combinatorics on the Casio FX CG50 Calculator (Factorials, Permutations, Combinations)
-
Arrangements in a circle
-
Arrangements from like objects
-
Addition and multiplication principles revision
-
Factorials and permutations revision
-
Permutations of like objects
-
Permutations with restrictions
-
Combinations
-
Combinations with restrictions
-
Pascals triangle and subsets of a set
-
Pigeonhole principle
-
Basic Set Theory
-
The inclusion exclusion principle for 2 and 3 sets
Topic 2: Vectors in the Plane
-
Vectors Introduction
-
Adding Vectors Graphically
-
Vectors Multiplying by a scalar
-
Vectors in 2D and 3D Shapes
-
Vectors in component form
-
Adding Vectors in component form
-
Vectors multiplying by a scalar in component form
-
Vectors finding the magnitude
-
Vectors finding the unit vector
-
Finding direction of a vector
-
Defining a vector between 2 points
-
Vectors: Polar form (converting from component to polar and polar to component)
-
Vector Revision part 1
-
The dot product part 1
-
The dot product part 2
-
The dot product part 3
-
The scalar product or dot product of a vector revisited
-
Force Vector Diagrams
-
Resolving Force Vectors
-
Resolving forces into their components
-
Resolving Forces into components part 2
-
Vector midpoints
-
Vectors in linear combinations
-
Vectors in component form recap
-
Vectors in polar form
-
What’s a vector projection?
-
Calculating vector projections
-
Resolving a vector into components parallel and perpendicular to a second vector
-
Applications of vectors displacement and velocity
-
Applications of vectors displacement and velocity collisions
-
Applications of vectors relative velocity
-
Relative Velocity: EVERY QUESTION: fully worked solutions
-
Triangle of Forces: Constructing the triangle from a force diagram
-
Triangle of forces: Worked Example
-
Triangle of Forces: Inclined Plane
-
Triangle of forces
-
Inclined plane recap part 1
-
Solving equilibrium questions using resolution of forces
-
Vectors in component form and operations
-
Determining a vector between two points
-
Vectors in 2D shapes
Topic 3: Introduction to Proof
-
The Real Number System
-
Expressing a recurring decimal as a fraction
-
Mathematical Notation: ∀ “For all” and ∃ “There Exists”
-
Direct proof
-
Proof by contrapositive
-
Proof by contradiction
-
Equivalent statements
-
Disproving statements
-
Geometric proofs from the ground up
-
Proving the angle in a semi-circle is a right angle
-
Prove the angle at the centre theorem
-
The angle on the same arc theorem
-
Proving Chord of Circle Theorem
-
Proving Tangent to a circle and the radius are perpendicular Using Proof by Contradiction
-
Proving the tangents from an external point theorem
-
Proving the cyclic quadrilateral theorem
-
Alternate Segment Theorem Proof
-
Intersecting Chord Theorem Proof
-
Proving the tangent secant theorem
-
Equidistant chord Theorem Proof
-
Intersecting Secants Theorem Proof: Teacher vs Student
-
Geometric Proofs using Vectors part 1
-
Geometric proofs using vectors Part 2