Unit 2
Specialist Mathematics (Queensland)
Topic 1: Complex Numbers
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Intro to complex numbers
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Working with imaginary and complex numbers
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Powers of i
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Simplifying with powers of i
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Adding and subtracting complex numbers
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Multiplying complex numbers by a constant
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Multiplying complex numbers by each other
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Equality of complex numbers
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Complex Numbers The Recap
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Complex number conjugates
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The multiplicative inverse of a complex number
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Argand Diagrams What complex numbers and Vectors have in common
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Solving equations with complex numbers
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Completing the square with complex numbers
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Polar Form of a complex number
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Polar form Multiplication and division of complex numbers
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De Moivres theorem raising complex numbers to a power
Topic 2: Trigonometry & Functions
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The modulus or absolute value function introduction
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The modulus or absolute value solving equations
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The Absolute value solving inequalities
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Absolute Value Functions
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Sketch Absolute Value Functions with a vertical shift
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Sketching an absolute value function worked example
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Reflecting Functions in the y axis using absolute value functions
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Reciprocals of functions
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Sketching Reciprocal Functions Worked Example
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Sketching Functions using Addition of Ordinates
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Rational Functions as Hyperbolas
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Rational Functions with slant asymptotes
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Rational Functions Part 3
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Trigonometry: Unit circle revision done fast
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Solving trig equations of the form sin(ax+b) = c
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Pythagorean identity
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Pythagorean identity rearrangement
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Using Pythagorean Identities Part 1
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The general solution of trigonometric equations
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Sketching Tan Functions
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Reciprocals of Trigonometric Functions
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Transformations of the reciprocal Trigonometric functions
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Complementary Trigonometric Relationships
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Exact values of reciprocal trigonometric functions
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Solving reciprocal trig functions
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The pythagorean Identity and reciprocal trigonometric functions
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Proving Trigonometric identities
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2 more pythagorean identities
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Angle sum and difference indentities
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Angle sum and difference identities part 2
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Double angle identity proofs and an example
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More proofs of trig identities
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Express the sum of trigonometric functions as a single function
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Express the sum of trigonometric functions as a single function part 2
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Product Sum Trigonometric Identities
Topic 3: Matrices
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Introduction to Matrices: Order, Elements, Addition and Multiplication by a scalar
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What is a matrix
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Matrix Equality
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Storing Information in Matrices
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Adding and subtracting matrices
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Multiplying matrices by a scalar
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Multiplying Matrices the better way
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An Application of Matrix Multiplication
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Powers of Matrices
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The Identity Matrix
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Matrices Recap
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Solving Matrix equations using the multiplicative inverse
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Simultaneous equations using matrices
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Matrix Calculations on the Casio FX-CG50AU
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Transformations in one dimensional space A different to think about mathematical operations
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Linear Transformations Introduction
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Transforming a figure using Matrix Transformations
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What is actually happening in a linear transformation
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Dilation transformations Using Matrices
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Shear Transformations Using Matrices
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Reflections in the x and y axis using Matrix Transformations
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Projections of an image onto the x axis or y axis using Matrix Transformations
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Rotations about the Origin Using Matrices
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Reflect an object in y= x and y = -x using Matrix Transformations
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Reflecting in the line y = mx with Matrix Transformations
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Composition of Matrix Transformations
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Inverse Matrix Transformation
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Transforming multiple points using a single matrix transformation
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Transforming relations using matrices part 1
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Transforming relations using matrices part 2
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Transforming relations no shortcuts
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Transforming relations using matrices part 3
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Finding an unknown matrix of transformation
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Equation of ellipses crash course
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Finding area of a transformation using the determinant
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General Transformations part 1
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General Transformations part 2