Course Materials
Lessons
Linear Inequalities involving Absolute Values
- Video - Introduction to Inequalities involving Absolute Values (3:46)
- Video - Linear Absolute Value Inequalities: Less Than (4:54)
- Video - Linear Absolute Value Inequalities: Greater Than 1 (3:42)
- Video - Linear Absolute Value Inequalities: Greater Than 2 (7:44)
- Video - Linear Absolute Value Inequalities Unknowns Both Sides: Less Than (4:04)
- Video - Linear Absolute Value Inequalities Unknowns Both Sides: Greater Than (4:52)
Inequalities involving Absolute Values by Graphs
- Video - Linear Absolute Value Inequalities by Graphs (4:08)
- Video - Linear Inequalities involving Multiple Absolute Values (8:54)
- Video - Linear Inequalities involving Absolute Values and Surds (7:32)
- Video - Intersections of Absolute Value Graphs & Straight Lines (2:46)
- Video - Quadratic Absolute Value Inequalities (1:50)
Absolute Value (Modulus) Graphs
- Video - Basic Theory of Absolute Value Graphs (3:30)
- Video - Sketching Absolute Value Graphs (4:41)
- Video - Transformation of Absolute Value Graphs: Up Down (3:09)
- Video - Transformation of Absolute Value Graphs: Left Right (5:01)
- Video - Absolute Value Graphs Regarding Steepness (3:47)
- Video - Absolute Value Graphs involving Quadratics (5:28)
- Topic - Translating Absolute Value (Modulus) Graphs 1
- Topic - Translating Absolute Value (Modulus) Graphs 2
- Topic - Translating Absolute Value (Modulus) Graphs 3
- Topic - Translating Absolute Value (Modulus) Graphs 4
- Topic - Translating Absolute Value (Modulus) Graphs 5
- Topic - Translating Absolute Value (Modulus) Graphs 6
- Topic - Vertices of Absolute Value (Modulus) Graphs
- Topic - x-intercepts of Absolute Value (Modulus) Graphs
- Topic - y-intercepts of Absolute Value (Modulus) Graphs
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)
Division of Polynomials
- Video - Long Division: Linear Polynomial by Linear Polynomial (4:34)
- Video - Long Division: Quadratic Polynomial by Linear Polynomial (4:43)
- Video - Long Division: Cubic Polynomial by Linear Polynomial (2:16)
- Video - Long Division: Non-Monic Cubic by Linear Polynomials (4:04)
- Video - Long Division: Non-Monic Linear by Non-Monic Linear Polynomials (3:35)
- Video - Long Division: Non-Monic Quadratic by Linear Polynomials (1:50)
- Video - Long Division: Non-Monic Quadratic by Non-Monic Linear Polynomials (1:39)
- Video - Basic Long Division (6:40)
- Video - Long Division of Quadratic Polynomials by Rational Divisors (8:51)
- Video - Long Division of Cubic Polynomials by Rational Divisors (5:30)
- Video - Long Division with Unknowns in Dividends (3:31)
- Video - Long Division with Unknowns in Divisors (1:25)
Remainder Theorem
- Video - Understanding Remainder Theorem (6:40)
- Video - Remainder Theorem involving Unknowns (3:09)
- Video - Applications of Remainder Theorem (3:33)
- Video - Applications of Remainder Theorem by Simultaneous Equations (6:14)
- Video - Applications of Remainder Theorem by Quadratic Equations (1:45)
- Video - Remainders using Remainder Theorem (5:54)
- Video - Pronumerals using Remainder Theorem (2:17)
- Video - Remainders using Remainder Theorem Given Two Divisions (6:38)
Factor Theorem
- Video - Finding Factors using Remainder Theorem (5:38)
- Video - Listing Possible Roots of Polynomial Equations (3:11)
- Video - Understanding Factor Theorem (6:13)
- Video - Factorising by Factor Theorem using Positive Roots (6:47)
- Video - Factorising by Factor Theorem using Negative Roots (4:36)
- Video - Finding Polynomials Given Factors (5:39)
- Video - Factorising Polynomials Given Roots (3:30)
- Video - Finding Polynomials Factors and Remainders (3:15)
- Video - Factorise Polynomials by Factor Theorem by Possible Roots (4:56)
- Video - Factorise Non-Monic Polynomials by Factor Theorem on Possible Roots (4:21)
- Video - Factorise Quartic Polynomials Given Two Roots (5:56)
- Video - Finding Unknowns Given Two Factors from Quartic Polynomials (4:50)
- Video - Theory of Factor Theorem (1:56)
- Video - Factorise Cubic Expressions by Factor Theorem (3:16)
- Video - Factorise Non-Monic Cubic Expressions by Factor Theorem (6:19)
- Video - Proof of Quartic Expression Having No Integer Roots (1:38)
- Topic - Factorise cubic polynomials using factor theorem 1
- Topic - Factorise cubic polynomials using factor theorem 2
- Topic - Factorise cubic polynomials using factor theorem 3
- Topic - Factorise quartic polynomials using factor theorem
Exponential Equations using Logarithms
- Video - Equations involving Natural Logarithms (3:22)
- Video - Index Equations involving Logarithms (5:05)
- Video - Equations involving Logarithms (2:37)
- Topic - Indicial Equations by Logarithms: Bases > 1
- Topic - Indicial Equations by Logarithms: Bases > 1 and Non-Monic Indices
- Topic - Indicial Equations by Logarithms: Bases < 1 and Non-Monic Indices
- Topic - Indicial Equations by Logarithms: Two Indicial Expressions
Equations with Natural Logarithms
- Topic - Equations with Single Natural Logarithm 1
- Topic - Equations with Single Natural Logarithm 2
- Topic - Equations with Single Natural Logarithm 3
- Topic - Equations with Single Natural Logarithm 4
- Topic - Equations with Single Natural Logarithm 5
- Topic - Equations with Two Natural Logarithms
- Topic - Equations with Three Natural Logarithms 1
- Topic - Equations with Three Natural Logarithms 2
- Topic - Equations with Four Natural Logarithms 1
- Topic - Equations with Four Natural Logarithms 2
- Topic - Natural Logarithm Equations involving Quadratic Equations 1
- Topic - Natural Logarithm Equations involving Quadratic Equations 2
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)
Negative Angle Formulae
- Topic - Sine Ratios of Negative Angles in Degree 1
- Topic - Sine Ratios of Negative Angles in Degree 2
- Topic - Cosine Ratios of Negative Angles in Degree 1
- Topic - Cosine Ratios of Negative Angles in Degree 2
- Topic - Tangent Ratios of Negative Angles in Degree 1
- Topic - Tangent Ratios of Negative Angles in Degree 2
- Topic - Sine Ratios of Negative Angles in Radian
- Topic - Cosine Ratios of Negative Angles in Radian
- Topic - Tangent Ratios of Negative Angles in Radian
Simplifying Trigonometric Expressions
- Video - Trigonometric Relationships (5:37)
- Video - Pythagorean Identities (4:59)
- Video - Proofs using sin^2 x + cos^2 x = 1 (4:55)
- Video - Simplifications using sin^2 x + cos^2 x = 1 (3:27)
- Video - Geometrical Applications using sin^2 x + cos^2 x = 1 (7:03)
- Video - Proofs using tan^2 x + 1 = sec^2 x (1:23)
- Video - Eliminating Sine and Cosine Trigonometric Parameters (9:20)
- Video - Eliminating Tangent and Secant Trigonometric Parameters (1:57)
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)
Sums and Products of Sine and Cosine
- Topic - Compound Angle Formula
- 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
Derivatives of Exponential Functions
- Video - Derivative of Exponential Functions (1:30)
- Video - Derivative of Exponential Functions using Chain Rule (6:29)
- Video - Derivative of Exponential Functions using Quotient Rule (7:20)
- Video - Derivative of Exponential Functions using Product Rule (6:12)
- Video - Second Derivative of Exponential Functions (6:10)
- Video - Equations of Tangent of Exponential Functions (4:46)
- Video - Stationary Point using Derivative of Exponential Functions (9:56)
- Video - Maximum Turning Point of Exponential Functions (7:18)
Definite Integral of Exponential Functions
- Video - Definite Integration of Exponential Functions (6:47)
- Video - Volume of Region bounded by Exponential Graphs (1:57)
- Topic - Definite Integral of Exponential Functions
- Topic - Definite Integral of Exponential Functions involving Reciprocals
- Topic - Definite Integral of Exponential Functions involving Expansions
- Topic - Definite Integral of Exponential Functions involving Surds
Derivatives of Logarithmic Functions
- Video - Fundamental of Derivative of Logarithmic Functions (2:41)
- Video - Derivative of Logarithmic Functions using Logarithm Law of Addition (4:06)
- Video - Derivative of Logarithmic Functions using Logarithm Law of Subtraction (1:47)
- Video - Derivative of Logarithmic Functions involving Indices (3:36)
- Video - Derivative of Mixed Logarithmic Functions (5:24)
- Video - Derivative of Non-Natural Logarithmic Functions (3:09)
- Video - Stationary Points using Derivative of Logarithmic Functions (5:32)
- Video - Derivative of Logarithmic Functions using Quotient Rule (4:40)
- Video - Tangents and Normals of Logarithmic Functions (2:15)
Integrations Resulting Natural Logarithmic Functions
- Video - Integrations involving Natural Logarithmic functions (3:17)
- Video - Integrating Linear by Linear Resulting Natural Log Functions (3:11)
- Video - Integrating Quadratics by Linear Resulting Natural Log Functions (2:18)
- Video - Integrations of Cubic by Quadratic Resulting Natural Log Functions (2:31)
- Video - Prove Integration Formula Resulting Natural Log Functions (6:53)
Definite Integral of Rational Functions
- Video - Finding Area by Differentiating Logarithmic Functions (3:12)
- Video - Integration Rule of Rational Functions involving Natural Exponents (1:20)
- Video - Definite Integration of Rational Functions (2:10)
- Topic - Integral of Rational Functions: Basic Form
- Topic - Integral of Rational Functions: Monic Linear Denominator
- Topic - Integral of Rational Functions: Non-Monic Linear Fractions
- Topic - Integral of Rational Functions: Multi-Term Denominators
- Topic - Integral of Rational Functions: Multi-Term by Non-Monic
- Topic - Integral of Rational Functions: Non-Monic Factor by Multi-Term
- Topic - Integral of Rational Functions: Non-Monic Factor Fractions
- Topic - Integral of Rational Functions: Non-Monic Multi-Term
- Topic - Integral of Rational Functions: Non-Monic Multi-Term Fractions
- Topic - Integral of Rational Functions: Monic Quadratic Denominators
- Topic - Integral of Rational Functions: Non-Monic Quadratic Denominators
- Topic - Integral of Rational Functions: Non-Monic Cubic Denominators
- Topic - Integral of Rational Functions: Rational Expressions
- Topic - Integral of Rational Functions: Non-Monic Rational Expressions
Derivative of Sine Functions
- Video - Differentiation of Sine Function: Chain Rule 1 (3:21)
- Video - Differentiation of Sine Function: Chain Rule 2 (2:01)
- Video - Differentiation of Sine Function: Chain Rule 3 (2:33)
- Video - Differentiation of Sine Function: Chain Rule 4 (5:02)
- Video - Differentiation of Sine Function: Product Rule 1 (4:54)
- Video - Differentiation of Sine Function: Product Rule 2 (4:16)
- Video - Differentiation of Sine Function: Product Rule 3 (3:06)
- Video - Differentiation of Sine Function: Quotient Rule 1 (3:17)
- Video - Differentiation of Sine Function: Quotient Rule 2 (2:39)
- Video - Differentiation of Sine in Degrees (7:16)
- Video - Derivative Value of Sine Functions (1:33)
Derivatives of Cosine Functions
- Video - Differentiation of Cosine Function: Chain Rule 1 (3:17)
- Video - Differentiation of Cosine Function: Chain Rule 2 (5:10)
- Video - Differentiation of Cosine Function: Chain Rule 3 (4:10)
- Video - Differentiation of Cosine Function: Chain Rule 4 (3:02)
- Video - Differentiation of Cosine Function: Product Rule 1 (2:25)
- Video - Differentiation of Cosine Function: Product Rule 2 (2:58)
- Video - Differentiation of Cosine Function: Product Rule 3 (3:16)
- Video - Differentiation of Cosine Function: Quotient Rule (6:30)
- Video - Differentiation of Cosine in Degrees (2:55)
- Video - Stationary Points involving Cosine Functions (4:05)
