Course Materials
Lessons
Quadratic Equations in Square Form (ax^2 + c = 0)
- Video - Basic Quadratic Equations in Approximated Solutions (2:30)
- Video - Quadratic Equations in Completing Square Form (4:38)
- Video - Quadratic Equations with Square Roots (4:53)
- Video - Quadratic Equations in Completing Square Form with Surds (6:45)
- Topic - Quadratic Equations in Square Form: Basic
- Topic - Quadratic Equations in Square Form: Non-Monic
- Topic - Quadratic Equations in Square Form: Non-Monic & Moving Terms
- Topic - Quadratic Equations in Square Form: No Solutions
- Topic - Quadratic Equations in Square Form: Zeroes
- Topic - Quadratic Equations in Square Form: Simplifying
- Topic - Quadratic Equations in Square Form: Non-Monic Simplifying
- Topic - Quadratic Equations in Square Form: Variables on Both Sides
- Topic - Quadratic Equations in Square Form: Completed Square Form
- Topic - Quadratic Equations in Square Form: Non-Monic Completed Square Form
- Topic - Quadratic Equations in Square Form: Zeroes in Completed Square Form
Quadratic Identities
- Video - Theory of Quadratic Identities (3:15)
- Video - Quadratic Identities: Expanding & Comparing 1 (6:13)
- Video - Quadratic Identities: Expanding & Comparing 2 (6:08)
- Video - Quadratic Identities: Expanding & Comparing 3 (3:31)
- Video - Quadratic Identities: Expressing in Quadratic Form (7:52)
- Topic - Quadratic Identities: Simple Comparison
- Topic - Quadratic Identities: Expand and Comparison
- Topic - Quadratic Identities: Substitution 1
- Topic - Quadratic Identities: Substitution 2
Substitutions into Quadratics
- Video - Finding y-values Given x-values from Quadratics (2:42)
- Video - Quadratics: Substituting Points (1:51)
- Video - Quadratics: Finding x given y (5:41)
- Topic - Substitutions into Quadratics
- Topic - Checking Quadratics
- Topic - Substitution into Quadratic Function Values: Single Values
- Topic - Substitution into Quadratic Function Values: Two Values 1
- Topic - Substitution into Quadratic Function Values: Two Values 2
- Topic - Substitution into Quadratic Function Values: Quadratic Formula
- Topic - Substitution into Quadratic Function Values: No Values
Solving by Factorisation
- Video - Solving Quadratic Equations by Factorise (6:04)
- Video - Solving Quadratic Equations by Factorise involving Rearrangements (9:34)
- Video - Quadratic Equations using Substitutions (9:04)
- Video - Quadratic Equations using Indices (4:21)
- Video - Equations Involving Higher Orders (5:38)
- Video - Equations Involving Higher Orders with Undefined Solutions (1:35)
- Video - Solving Quadratic Equations by Factorising Monic Quadratic Trinomials (2:22)
- Video - Solving Non-Monic Quadratic Equations by Factorising (4:09)
- Video - Solving Quadratic Equations by Rearranging and Factorising (1:26)
- Video - Quadratic Equations by Factorise Difference of Squares (1:30)
Solving by Completing the Square
- Video - Quadratic Equations given Perfect Square (4:01)
- Video - Quadratic Equations given Perfect Square involving Irrationals (2:09)
- Video - Evaluation of the Solutions to Decimal Numbers (2:55)
- Video - Theory of Completing Square for Solving Quadratic Equations (6:44)
- Video - Non-Monic Completing the Square by Filling Blanks (6:36)
- Video - Non-Monic Completing the Square (5:33)
- Video - Solving Monic Quadratic Equations by Completing the Square (8:06)
- Video - Solving Non-Monic Quadratic Equations by Completing the Square (9:01)
- Video - Basics of Completing the Square (6:14)
- Video - Completing the Square with Rational Numbers (4:48)
- Video - Solving by Completing the Square (3:12)
- Video - Solving by Completing the Square of Non-Monic Quadratic Equations (3:41)
- Video - Solving Quadratic Equations by Completing the Square (2:49)
Quadratic Formula
- Video - Deriving Quadratic Formula (4:50)
- Video - Solving Quadratic Equations using Quadratic Formula 1 (9:00)
- Video - Solving Quadratic Equations using Quadratic Formula 2 (6:50)
- Video - Forming Quadratic Equations using Quadratic Formula (2:45)
- Video - Quadratic Equations using Quadratic Formula Approximated Roots (6:18)
- Video - Quadratic Equations using Quadratic Formula Undefined Solutions (2:23)
- Video - Quadratic Equations using Substitutions involving Quadratic Formula (4:50)
- Topic - Quadratic Formula: Monic Quadratic Equations
- Topic - Quadratic Formula: Non-Monic Quadratic Equations
- Topic - Quadratic Formula: Monic Equations
- Topic - Quadratic Formula: Non-Monic Equations
- Topic - Quadratic Formula: Undefined
Problem Solving with Quadratics
- Video - Product of Two Consecutive Numbers by Quadratic Equations (5:31)
- Video - Product of Two Consecutive Odd Numbers by Quadratic Equations (2:44)
- Video - Sum of Squares of Numbers by Quadratic Equations (4:20)
- Video - Sum of Number and Its Reciprocal by Quadratic Equations (3:49)
- Video - Checking the Solutions of Quadratic Equations (8:51)
- Video - Application of Quadratic Equations: Finding Numbers (2:10)
- Video - Application of Quadratic Equations: Sum of N Positive Integers (3:08)
- Video - Applications of Quadratic Functions (3:16)
Problem Solving with Quadratics involving Geometry
- Video - Right-Angled Triangle by Quadratic Equations (2:39)
- Video - Area of Composite Shapes by Quadratic Equations (5:28)
- Video - Similar Triangles by Quadratic Equations (3:43)
- Video - Intersections of Quadratic Parabola and Straight Line (3:29)
- Video - Application of Quadratic Equations: Area of Rectangular Shapes (2:34)
- Video - Application of Quadratic Equations: Border of Rectangular Fields (7:44)
- Video - Quadratic Equations using Pythagoras Theorem (3:04)
Forming Quadratic Equations
- Video - Forming Quadratic Equations (4:17)
- Video - Form Quadratics involving Fractional Roots (3:09)
- Video - Finding Quadratic Equations from Solutions (4:56)
- Video - Theory of Forming Quadratic Equations (5:35)
- Video - Forming Quadratic Equations: Integral Roots (2:35)
- Video - Forming Quadratic Equations: Rational Roots (4:46)
- Video - Forming Quadratic Equations: Irrational Roots (4:15)
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)
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)
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)
Finding Cubic Polynomials with Zeros
- Video - Finding the Rules of Cubic Graphs (6:19)
- Topic - Positive Equations of Cubic Polynomials Passing Origin
- Topic - Negative Equations of Cubic Polynomials Passing Origin
- Topic - Positive Equations of Cubic Polynomials in Factor Form
- Topic - Negative Equations of Cubic Polynomials in Factor Form
- Topic - Positive Equations of Cubic Polynomials of Repeated Factors 1
- Topic - Positive Equations of Cubic Polynomials of Repeated Factors 2
- Topic - Negative Equations of Cubic Polynomials of Repeated Factors 1
- Topic - Negative Equations of Cubic Polynomials of Repeated Factors 2
- Topic - Negative Equations of Cubic Polynomials in Basic Form
Cubic Equations
- Video - Solving Cubic Equations by Factorise (3:45)
- Topic - Solving Cubic Equations in Factorised Form 1
- Topic - Solving Cubic Equations in Factorised Form 2
- Topic - Solving Cubic Equations in Square Form 1
- Topic - Solving Cubic Equations in Square Form 2
- Topic - Solving Cubic Equations in Cubic Form
- Topic - Solving Cubic Equations by Quadratic Formula
- Topic - Solving Cubic Equations by Factorising 1
- Topic - Solving Cubic Equations by Factorising 2
Cubic Inequalities
- Video - Inequalities of Cubic Polynomials (8:32)
- Topic - Cubic Inequalities with 3 x-intercepts Positive Above
- Topic - Cubic Inequalities with 3 x-intercepts Positive Below
- Topic - Cubic Inequalities with 3 x-intercepts Negative Above
- Topic - Cubic Inequalities with 3 x-intercepts Negative Below
- Topic - Cubic Inequalities with 3 x-intercepts Positive Above Equal
- Topic - Cubic Inequalities with 3 x-intercepts Positive Below Equal
- Topic - Cubic Inequalities with 3 x-intercepts Negative Above Equal
- Topic - Cubic Inequalities with 3 x-intercepts Negative Below Equal
- Topic - Cubic Inequalities with 2 x-intercepts Positive 1
- Topic - Cubic Inequalities with 2 x-intercepts Positive 2
- Topic - Cubic Inequalities with 2 x-intercepts Positive 3
- Topic - Cubic Inequalities with 2 x-intercepts Positive 4
- Topic - Cubic Inequalities with 2 x-intercepts Negative 1
- Topic - Cubic Inequalities with 2 x-intercepts Negative 2
- Topic - Cubic Inequalities with 2 x-intercepts Negative 3
- Topic - Cubic Inequalities with 1 x-intercept Shift Up Down 1
- Topic - Cubic Inequalities with 1 x-intercept Shift Up Down 2
- Topic - Cubic Inequalities with 1 x-intercept Shift Left Right 1
- Topic - Cubic Inequalities with 1 x-intercept Shift Left Right 2
- Topic - Cubic Inequalities with 1 x-intercept Translation 1
- Topic - Cubic Inequalities with 1 x-intercept Translation 2
Linear Simultaneous Equations - Elimination Method
- Video - Elimination Method for Simultaneous Equations (3:32)
- Video - Elimination Method for Simultaneous Equations by Subtraction (4:29)
- Video - Elimination Method for Simultaneous Equations by Addition (3:25)
- Video - Elimination Method by Manipulating One Pronumeral (6:40)
- Video - Elimination Method by Manipulating Two Pronumerals 1 (3:31)
- Video - Elimination Method by Manipulating Two Pronumerals 2 (1:49)
- Video - Elimination Method by Manipulating Two Pronumerals 3 (2:15)
- Video - Simultaneous Equations by Elimination Method (7:42)
- Video - Simultaneous Equations: Elimination Method (5:53)
- Topic - Elimination Method by Subtracting Equations
- Topic - Elimination Method by Adding Equations
- Topic - Elimination Method by Considering One Coefficient
- Topic - Elimination Method by Considering Two Coefficients
Linear Simultaneous Equations - Substitution Method
- Video - Equation Method for Simultaneous Equations (2:16)
- Video - Basic Substitution Method for Simultaneous Equations (6:43)
- Video - Substitution Method for Simultaneous Equations (7:48)
- Video - Simultaneous Equations by Substitution Method (5:26)
- Video - Simultaneous Equations: Substitution Method (3:00)
- Topic - Basic Substitution Method
- Topic - Substitution Method by Non-Monic Equations
- Topic - Substitution Method by Equating Equations
- Topic - Substitution Method by Rearranging Equations
- Topic - Substitution Method by Rearranging Non-Monic Equations
Numerical Application of Linear Simultaneous Equations
- Video - Number Applications of Simultaneous Equations 1 (2:58)
- Video - Number Applications of Simultaneous Equations 2 (2:54)
- Video - Number Applications of Simultaneous Equations 3 (2:11)
- Video - Number Applications of Simultaneous Equations 4 (1:42)
- Video - Digit Applications of Simultaneous Equations (8:33)
- Video - Coin Value Applications of Simultaneous Equations 1 (3:12)
- Video - Coin Value Applications of Simultaneous Equations 2 (2:52)
- Video - Age Applications of Simultaneous Equations 1 (2:04)
- Video - Age Applications of Simultaneous Equations 2 (3:51)
- Video - Geometry Applications of Simultaneous Equations 1 (3:14)
- Video - Geometry Applications of Simultaneous Equations 2 (3:13)
- Video - Cost Applications of Simultaneous Equations 1 (2:59)
- Video - Cost Applications of Simultaneous Equations 2 (2:01)
- Video - Measurement Applications of Simultaneous Equations (2:23)
- Video - Review Problem Solving of Simultaneous Equations (6:09)
Undefined or All Real Values of Simultaneous Equations
- Video - No Points of Intersection of Two Straight Lines (2:16)
- Video - Simultaneous Equations by Substitution Method & Graphs (4:55)
- Video - Simultaneous Equations in No Solutions & Graphs (3:40)
- Video - Theory of Undefined Solutions in Simultaneous Equations (2:56)
- Video - Simultaneous Equations in Undefined Solutions (2:49)
- Video - Simultaneous Equations in All Real Value Solutions (2:20)
- Video - Simultaneous Equations: No Solutions (1:39)
- Video - Simultaneous Equations: All Real values (2:23)
- Video - Intersections of Hyperbola and Linear Equations: Undefined (2:23)
Distance Between Two Points using Coordinates
- Video - Understanding Distance between Two Points Formula (2:24)
- Video - Distance between Two Points (9:10)
- Video - Distance between Two Vertical and Horizontal Points (1:45)
- Video - Find Unknown Values using Distance between Two Points Formula (8:02)
- Video - Understanding Distance Between Two Points (6:26)
- Video - Finding Unknown from Distance between Two Points (5:12)
- Topic - Distance between Two Points 1
- Topic - Distance between Two Points 2
- Topic - Distance between Two Points 3
- Topic - Distance between Two Vertical Points
- Topic - Distance between Two Horizontal Points
- Topic - Distance between Two Points in Surds
- Topic - Finding Unknowns using Distance between Two Points 1
- Topic - Finding Unknowns using Distance between Two Points 2
Midpoint Formula
- Video - Understanding Midpoint Formula (4:27)
- Video - Application of Midpoint Formula (6:42)
- Video - Divide a Line Segment Equally Using Midpoint Formula (3:20)
- Video - Understanding Midpoints (4:40)
- Video - Midpoints and Circles (3:45)
- Topic - Midpoint of Two Points
- Topic - Finding Unknowns in Midpoint of Two Points 1
- Topic - Finding Unknowns in Midpoint of Two Points 2
- Topic - Finding Unknowns in Midpoint of Two Points 3
- Topic - Finding Unknowns in Midpoint of Two Points 4
- Topic - Division of Line Segments in Four Equal Pieces
Gradient of Lines
- Video - Understanding Gradient Formula (3:56)
- Video - Finding Gradients of Straight Lines (2:56)
- Video - Applications of Gradients (6:38)
- Video - Gradient from Two Points (4:10)
- Video - Gradient from an Angle (4:03)
- Video - Finding the Positive Angle of x-axis (4:10)
- Video - Finding Gradients (4:55)
- Video - Gradient Undefined (1:21)
- Video - Gradient Zero (1:32)
- Video - Gradient from Rise and Run (4:48)
Intercepts
- Video - Straight Line Equations with Intercepts & Points (5:47)
- Video - Graphing Linear Equations using Intercepts (3:25)
- Video - Sketching Straight Lines using Intercepts (6:03)
- Topic - x-intercepts of Straight Lines in Standard Form
- Topic - y-intercepts of Straight Lines in Standard Form
- Topic - x-intercepts of Straight Lines in General Form
- Topic - y-intercepts of Straight Lines in General Form
- Topic - Gradients using x- and y-intercepts
Parallel Lines
- Video - Parallel Lines (4:16)
- Video - Identifying Parallel Lines (4:49)
- Video - Application of Parallel Lines (4:50)
- Video - Parallel Lines involving Similar Figures (9:46)
- Video - Equations of Parallel Lines Passing Through Points (4:27)
- Video - Equations of Parallel Lines in General Form Passing Through Points (4:25)
- Video - Equations of Parallel Lines in General form Passing through Midpoints (4:06)
- Video - Equations of Parallel Lines with Angles Passing Through Points (2:51)
- Video - Proof of Parallel Lines (2:58)
- Topic - Matching Parallel Lines
Perpendicular Lines
- Video - Finding the Gradients of Perpendicular Straight Lines (5:59)
- Video - Matching Perpendicular Lines (2:28)
- Video - Perpendicular Lines (4:44)
- Video - Perpendicular Lines in General Form (8:36)
- Video - Perpendicular Lines involving x-intercepts & y-intercepts (3:16)
- Video - Perpendicular Lines involving Angles (1:40)
- Video - Finding Equations of Perpendicular Lines (2:36)
- Topic - Gradient of a Straight Line which is Perpendicular to
- Topic - Choose the Straight Lines which is Perpendicular to
- Topic - Unknown Values Determining Two Straight Lines are Perpendicular
- Topic - Perpendicular Gradient from General Form
- Topic - Perpendicular Gradient involving x & y-intercepts
- Topic - Perpendicular Gradient involving Angles
Application of Perpendicular Lines
- Video - Applications involving Perpendicular Lines (6:36)
- Video - Finding Unknowns in Perpendicular Line Equations (2:55)
- Video - Equation of Lines Perpendicular to Line Joining Two Points (3:38)
- Video - Perpendicular Lines involving Triangles (8:47)
- Video - Perpendicular Lines involving Right-Angled Triangles (13:09)
- Video - Perpendicular Lines involving Locus (3:43)
- Video - Perpendicular Lines involving Angles Between Lines (9:10)
Vertical Lines and Horizontal Lines
- Video - Horizontal Lines and Vertical Lines (2:25)
- Video - Equations of Vertical Lines & Horizontal Lines (2:57)
- Topic - Graphs of Vertical Lines Horizontal Lines
- Topic - Equations of Vertical Lines Horizontal Lines
- Topic - Coordinates of Vertical Lines Horizontal Lines
- Topic - Gradients of Vertical Lines Horizontal Lines
- Topic - Intersections of Vertical Lines Horizontal Lines
- Topic - Status of Vertical Lines Horizontal Lines
