Unit 2
Specialist Mathematics (Queensland)
Topic 1 & 2: Complex Numbers
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Introduction to imaginary and complex numbers
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Working with imaginary and complex numbers
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Raising i to a power
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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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Multiply complex numbers
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Equality of complex numbers
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Conjugates definition and the argand diagram
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Multiplying conjugates of complex numbers
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Dividing complex numbers using conjugates
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Solving equations over C
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Completing the square with complex numbers
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Argand Diagrams What complex numbers and Vectors have in common
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Complex Numbers in Polar form
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Multiplying and dividing complex numbers
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De Moivre’s Theorem for raising a complex number to a power
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Sketching Subsets of the complex Plane
Topic 3: Circle and Geometric Proofs
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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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Alternate Segment Theorem Proof
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Proving Tangent to a circle and the radius are perpendicular Using Proof by Contradiction
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Geometric Proofs using Vectors part 1
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Geometric proofs using vectors Part 2
Topic 4: Trigonometry and 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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Solving Absolute value: quadratic equations
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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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Reciprocals of Trigonometric Functions
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Transformations of the reciprocal Trigonometric functions
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Sketching Tan Functions
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Exact values of reciprocal trigonometric functions
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Solving reciprocal trig functions
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Pythagorean identity
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Pythagorean identity rearrangement
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Using the Pythagorean Identity Part 1
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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 5: Matrices and transformations
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Linear Transformations Translations
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Linear Transformations Dilations
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Linear Transformations Dilations Part 2
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Linear Transformations Rotations
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Linear Transformations Reflections in the line y =mx
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Linear Transformations Reflections with double angle identities
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Composition of Matrices
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Linear Transformations Inverses
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Linear Transformations Determinants and Area