In this course, students will develop the mathematical understanding and skills to solve problems relating to:
- Complex Numbers 1
- Trigonometry and Functions
- Matrices
Complex numbers 1 introduces the complex plane, complex arithmetic and complex algebra. Trigonometry and functions build on the nature of proof and models periodic phenomena. Matrices introduce basic operations and extend to transformations in the plane.
These topics further develop the thinking techniques and mathematical rigour introduced in QCE Specialist Mathematics – Combinatorics, Vectors and Proof, and provide opportunities to nurture curiosity about the nature and utility of mathematics.
Source – QCAA General Senior Syllabus 2019
Lessons
Complex Conjugates
- Video - Conjugate Pairs of Complex Numbers (3:54)
- Topic - Writing Conjugate Pairs of Complex Numbers
- Topic - Writing Conjugate Pairs of Complex Numbers using Notation
- Topic - Proof using Conjugate Pairs 1
- Topic - Proof using Conjugate Pairs 2
- Topic - Quadratic Equations with Real Coefficients Having Complex Roots 1
- Topic - Quadratic Equations with Real Coefficients Having Complex Roots 2
Conjugates and Division of Complex Numbers
- Video - Realising the Denominators using Conjugate Pairs (6:28)
- Video - Proof regarding Conjugate Pairs (4:13)
- Video - Proof regarding Conjugate Pairs & Realising Denominators (2:20)
- Topic - Division of Complex Numbers 1
- Topic - Division of Complex Numbers 2
- Topic - Multiplicative Inverse of Complex Numbers 1
- Topic - Multiplicative Inverse of Complex Numbers 2
Square Roots of Complex Numbers
- Video - Square Roots of Complex Numbers in Positive Real Parts (13:45)
- Video - Square Roots of Complex Numbers in Negative Real Parts (4:50)
- Video - Square Roots of Complex Numbers using Factorise Method 1 (7:03)
- Video - Square Roots of Complex Numbers using Factorise Method 2 (5:33)
- Video - Square Roots of Complex Numbers with Irrational Coefficients (2:43)
Modulus
- Topic - Modulus of Complex Numbers
- Topic - Modulus of Purely Imaginary Complex Numbers
- Topic - Modulus of Purely Real Complex Numbers
- Topic - Modulus of Conjugate Pairs
- Topic - Modulus of Polar Form
- Topic - Proof Regarding Modulus
- Topic - Proof Regarding Modulus and Conjugate Pairs
- Topic - Modulus Squared and Multiple of Complex Number and its Conjugate
- Topic - Finding Modulus by Polar Form
General Solutions in Radians
- Video - Graphical Understanding to General Solution of Sine (10:13)
- Video - General Solution of Sine in Radians (1:46)
- Video - General Solution of Negative Sine in Radians (1:42)
- Video - General Solution of sin x involving Transformation (5:12)
- Video - Graphical Understanding to General Solution of Cosine (7:01)
- Video - Graphical Understanding to General Solution of Tangent (4:04)
- Video - General Solutions of Sine Function (5:39)
- Video - General Solutions of Cosine Function (4:35)
- Video - General Solutions of Tangent Function (4:17)
Further Graphs of Absolute Value (Modulus) Functions
- Video - Absolute Value of Sine Graphs (1:26)
- Video - Graphing Absolute Value Functions (4:23)
- Video - Transformation of Absolute Value Graphs (3:29)
- Video - Graphs involving Absolute Value (1:40)
- Video - Understanding Absolute Value Graphs (7:37)
- Video - Absolute Graphs involving Quadratics (3:59)
- Video - Absolute Value Graphs Given Initial Graphs 1 (5:30)
- Video - Absolute Value Graphs Given Initial Graphs 2 (7:11)
- Video - Absolute Value Graphs involving Natural Logarithmic Graphs (1:48)
- Video - Absolute Value Graphs involving Sine Trigonometric Graphs (2:26)
Reciprocal Functions
- Video - Reciprocal Graphs (5:31)
- Video - Reciprocal Graphs of Irrational Functions (1:37)
- Video - Reciprocal Graphs of Modulus Functions (0:48)
- Video - Reciprocal Graphs of Natural Exponential Functions (1:01)
- Video - Reciprocal Graphs of Natural Logarithmic Functions (0:30)
- Video - Reciprocal Graphs of Inverse Tangent Functions (1:45)
- Video - Reciprocal Graphs of Given Initial Graphs (2:52)
- Video - Reciprocal Graphs of Parabola (5:11)
Compound Angle Formula
- Video - Trigonometric Expressions using Sums & Differences of Sine (6:33)
- Video - Evaluating Exact Values using Sums & Differences of Sine (6:29)
- Video - Evaluate sin 3x using Sums & DIfferences of Sine (3:17)
- Video - Sums & Differences of Cosine (6:26)
- Video - Evaluating Exact Values using Sums & Differences of Cosine (5:01)
- Video - Proof involving Sums & Differences of Cosine (3:09)
- Video - Sums & Differences of Tangent (4:48)
- Video - Evaluating Exact Values using Sums & Differences of Tangent (8:28)
- Video - Proof involving Sums & Differences of Tangent (7:04)
- Topic - Compound Angle Formula
Sums and Products of Sine and Cosine
- Topic - Sums of Sine or Cosine Ratios to Products of Cosine or Sine Ratios
- Topic - Sums to Products of Sine and Cosine Ratios 1
- Topic - Sums to Products of Sine and Cosine Ratios 2
- Topic - Products to Sums of Sine and Cosine Ratios 1
- Topic - Products to Sums of Sine and Cosine Ratios 2
- Topic - Application of Products to Sums of Sine and Cosine Ratios
- Topic - Products of Cosine Ratios to Sums of Cosine Ratios
- Topic - Products of Cosine and Sine Ratios to Sums of Sine Ratios
- Topic - Products of Sine Ratios to Sums of Cosine Ratios
- Topic - Differences of Sine Ratios to Products
- Topic - Sums of Cosine Ratios to Products of Cosine Ratios
- Topic - Sums and Differences of Cosine Ratios to Products
- Topic - Sums and Differences of Sine and Cosine Ratios to Products
Complementary Angle Formula
- Topic - Complementary Angle Formula
- Topic - Complementary Angles of Sine and Cosine
- Topic - Complementary Angles of Tangent and Cotangent
- Topic - Complementary Angle Formula for Second Quadrant Angles
- Topic - Complementary Angle Formula for Third Quadrant Angles 1
- Topic - Complementary Angle Formula for Third Quadrant Angles 2
- Topic - Complementary Angle Formula for Third Quadrant Angles 3
Trigonometric Models
- Video - Definition of Simple Harmonic Motion (10:50)
- Video - Features of Simple Harmonic Motion (5:00)
- Video - Motions of Sine Function (6:55)
- Video - Motions of Cosine Function (2:47)
- Video - Finding Equations of Motion of Cosine Function (6:52)
- Video - Finding Equations of Motion of Sine Function (8:24)
- Video - High Tide and Low Tide with Negative Displacement (9:47)
- Video - High Tide and Low Tide with Positive Displacement (7:05)
Simple Harmonic Motion: Velocity
- Video - Simple Harmonic Motion: First Time when Velocity is Zero (1:56)
- Video - Simple Harmonic Motion: First Position when Velocity is Zero (0:56)
- Video - Simple Harmonic Motion: Maximum Velocity (1:25)
- Video - Simple Harmonic Motion: First Time when Velocity is Maximum (1:32)
- Video - Simple Harmonic Motion: First Position when Velocity is maximum (0:53)
Simple Harmonic Motion: Acceleration
- Video - Simple Harmonic Motion: First Time when Acceleration is Zero (1:26)
- Video - Simple Harmonic Motion: First Position when Acceleration is Zero (0:45)
- Video - Simple Harmonic Motion: Maximum Acceleration (1:20)
- Video - Simple Harmonic Motion: First Time when Acceleration is Maximum (0:58)
- Video - Simple Harmonic Motion: First Position when Acceleration is Maximum (0:55)
Properties of Matrix Multiplication
- Topic - Commutative Law of Matrices
- Topic - Commutative Law with Zero Matrix
- Topic - Verifying Distributivity of Matrix Multiplication using 2 by 2 Matrices
- Topic - Associative Law of Matrix Multiplication using 2 by 2 Matrices
- Topic - Identify Matrix of Multiplication using 2 by 2 Matrices
- Topic - Square of 2 by 2 Matrices
- Topic - Cube of 2 by 2 Matrices
- Topic - Square of 3 by 3 Matrices
- Topic - Conditions of Square a Matrix
