Course Materials
Lessons
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)
Square Root Functions
- Video - Square Root Graphs: Basics (2:56)
- Video - Square Root Graphs: Shift to the Left (4:01)
- Video - Square Root Graphs: Shift to the Right (0:48)
- Video - Square Root Graphs: Move Upwards (1:05)
- Video - Square Root Graphs: Transform involving Steepness (1:24)
- Video - Square Root Graphs: Shift to the Right & Upwards (1:14)
- Video - Square Root Graphs: Transform Symmetrically (6:28)
- Video - Dilation of Square Root Functions (4:39)
- Video - Transformation of Square Root Functions (3:40)
- Video - Domain Range of Square Root Functions (6:38)
- Video - Sketching Graphs involving Square Root Functions (6:39)
- Video - Equations of Square Root Function in Power Form (8:04)
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)
Product of Functions
- Video - Understanding Multiplication of Graphs (3:55)
- Video - Multiplication of Graphs involving Straight Lines (6:09)
- Video - Multiplication of Graphs involving Absolute Value Curves (2:47)
- Video - Multiplication of Graphs involving Exponential Curves (2:35)
- Video - Multiplication of Graphs involving Trigonometric Curves (4:10)
- Video - Division of Graphs (2:57)
Quadratic Inequalities by Given Graphs
- Video - Understanding Quadratic Inequalities (7:08)
- Video - Quadratic Inequalities: Concave Up & Less Than (6:47)
- Video - Quadratic Inequalities: Concave Up & Greater Than by Given Graphs (9:39)
- Video - Quadratic Inequalities: Concave Down & Greater Than (5:49)
- Video - Quadratic Inequalities: Undefined or No Solutions (7:12)
- Video - Quadratic Inequalities: All Real Values by Given Graphs (3:26)
- Video - Quadratic Inequalities: Single Solutions (8:26)
Quadratic Inequalities by Sketching Graphs
- Video - Quadratic Inequalities: Concave Up & Greater Than by Graphs (8:30)
- Video - Quadratic Inequalities: Concave Down & Less Than (2:07)
- Video - Quadratic Inequalities: All Real Values by Sketching Graphs (6:23)
- Video - Quadratic Inequalities: All Real Values by Algebra (2:43)
- Video - Quadratic Inequalities involving Quadratic Formula (5:18)
- Video - Quadratic Inequalities involving Quadratic Formula by Rearrangement (6:00)
- Video - Quadratic Inequalities involving Expanding & Simplifying (1:38)
Inequalities with Pronumerals in Denominators
- Video - Inequality: Pronumerals in Denominators (7:37)
- Video - Inequality: Pronumerals in Denominators & Numerators (4:44)
- Video - Inequality: Pronumerals in Denominators & the Other Side (6:19)
- Video - Inequality: Pronumerals in Denominators in Multiple Fractions (4:17)
- Video – Pronumerals in Denominators in Multiple Fractions (4:32)
Inequalities with Pronumerals in Denominators involving Quadratics
- Video - Inequality: Linear Denominators & Quadratic Numerators (7:56)
- Video - Inequality: Linear by Quadratic Fractions in Factorised Form (3:29)
- Video - Inequality: Quadratic Denominators & Linear Numerators (1:52)
- Video - Inequality: Linear by Quadratic Fractions by Graphs (3:52)
- Video - Inequalities in Fraction: Linear by Quadratic Expressions (6:19)
- Video - Inequalities in Fraction: Quadratic by Linear Expressions (6:47)
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)
Relations and Their Inverses
- Video - Introduction to Inverse Relations (5:36)
- Video - Inverse of Ordered Pairs (0:39)
- Video - Inverse of Linear Expressions (1:51)
- Video - Inverse of Hyperbolic Expressions (2:28)
- Video - Inverse of Even Expressions (2:19)
- Video - Inverse of Odd Expressions (0:45)
- Video - Inverse of Surd Expressions (2:32)
- Video - Inverse of Quadratic Expressions using Completing the Square (2:45)
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 - Finding Polynomials Given Factors (5:39)
- Video - Finding Polynomials Factors and Remainders (3:15)
- Video - Finding Unknowns Given Two Factors from Quartic Polynomials (4:50)
Factorise Polynomials by Factor Theorem
- Video - Factorising by Factor Theorem using Positive Roots (6:47)
- Video - Factorising by Factor Theorem using Negative Roots (4:36)
- Video - Factorising Polynomials Given Roots (3:30)
- 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 - 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
Sum and Product of Roots
- Video - Sums and Products of Roots of Quadratics 1 (3:15)
- Video - Sums and Products of Roots of Quadratics 2 (6:13)
- Video - Sums and Products of Roots of Quadratics 3 (6:08)
- Video - Sums and Products of Roots of Quadratics: Applications 1 (3:31)
- Video - Sums and Products of Roots of Quadratics: Applications 2 (8:04)
- Video - Sums and Products of Roots of Quadratics: Applications 3 (6:39)
- Video - Sums and Products of Roots of Quadratics: Applications 4 (6:30)
- Video - Sums and Products of Roots involving Graphs (6:46)
- Video - Sums and Products of Roots involving Circles (6:06)
