Course Materials
Lessons
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)
- 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 - Applications involving Perpendicular Lines (6:36)
- 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 Unknowns in Perpendicular Line Equations (2:55)
- Video - Finding Equations of Perpendicular Lines (2:36)
- 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)
- 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
Finding Equations of Lines
- Video - Introduction of Gradients & y-Intercepts (4:39)
- Video - Equations of Straight Lines using Gradients & y-Intercepts (2:16)
- Video - Equations of Straight Lines using Gradients & Passing Points (7:57)
- Video - Linear Equations using Two Point Formula (2:55)
- Video - Equation of Straight Lines involving Gradient & y-intercept (1:09)
- Video - Equation of Straight Lines involving Gradient & Origin (0:43)
- Video - Equation of Straight Lines involving Gradient & Points (1:57)
- Video - Equation of Straight Lines involving Angles & y-intercept (3:19)
- Video - Intercept Form of Straight Lines (2:41)
- Video - Equation of Horizontal Straight Lines (1:13)
- Video - Equation of Vertical Straight Lines (3:14)
- Video - Point-Gradient Formula (3:09)
- Video - Two-Point Formula (6:17)
- Video - Equations of Straight Lines using Gradients & Points (2:05)
- Video - Equations of Straight Lines using Positive Angles & Points (1:22)
- Video - Equations of Straight Lines using Gradients & Midpoints (1:30)
General Form of a Line
- Video - General Form & Gradient-Intercept Form of Straight Lines (6:35)
- Video - General Form of Straight Lines (3:28)
- Video - Equations of Straight Lines using Gradients & Points in General Form (3:05)
- Video - Gradient-Intercept Form (1:42)
- Video - Sketching Straight Lines using Intercepts in General Form (3:22)
Relations and Functions
- Video - Vertical Line Test (9:37)
- Video - One-to-One Relations (2:02)
- Video - One-to-Many Relations (1:56)
- Video - Many-to-One Relations (1:50)
- Video - Many-to-Many Relations (2:21)
- Video - Functions and Vertical Line Test (3:13)
- Video - Checking Functions using Ordered Pairs (3:31)
- Video - Checking Functions using Graphs (9:43)
Domain and Range
- Video - Definition of Domain and Range (4:11)
- Video - Finding Domain and Range (9:02)
- Video - Range of Squares (7:21)
- Video - Domain and Range by Graphs (7:16)
- Video - Domain and Range of Functions (6:53)
- Video - Domain and Range of Functions involving Asymptotes (5:12)
- Video - Domain and Range of Surds (7:03)
- Video - Domain and Range of Logarithmic Graphs (1:16)
- Video - Domain of Sum of Two Functions (3:41)
- Video - Restricting the Domain of Cubic Polynomials (4:22)
- Video - Quadratic Graphs: Ranges (9:20)
- Video - Range of x^2 (4:50)
- Video - Range of Reciprocal of Quadratic Expressions (5:37)
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)
Composite Functions
- Video - Combining Functions (5:25)
- Video - Composite of Functions (4:39)
- Topic - Composite of Linear Functions 1
- Topic - Composite of Linear Functions 2
- Topic - Nested Composite of Linear Functions 1
- Topic - Nested Composite of Linear Functions 2
- Topic - Composite of Quadratic Functions and Linear Functions 1
- Topic - Composite of Quadratic Functions and Linear Functions 2
- Topic - Nested Composite of Quadratic Functions 1
- Topic - Nested Composite of Quadratic Functions 2
- Topic - Composite Functions of Ordered Pairs 1
- Topic - Composite Functions of Ordered Pairs 2
- Topic - Composite Functions of Ordered Pairs 3
- Topic - Composite Function Equations
- Topic - Composite of Linear and Square Root Functions
X-intercept Y-intercept
- Video - Graphs of Parabola x-intercepts and y-intercepts (5:58)
- Video - Graphs of Parabola using Quadratic Formula (4:30)
- Video - Sketching Parabola (3:29)
- Video - Graphs of Parabola Concave Downwards with No x-intercepts (6:27)
- Video - Transformation of Parabola Up Down (6:59)
- Video - Quadratic Graphs: Axes Intercepts (11:25)
Quadratic Graphs by Completing the Square
- Video - Finding Vertex using Completing Square (3:12)
- Video - Sketching Parabola in Left Side by Completing Square (6:13)
- Video - Sketching Parabola in Right Side by Completing Square (2:28)
- Video - Sketching Parabola Concave Down by Completing Square (3:39)
- Video - Sketching Non-Monic Parabola Concave Up by Completing Square (3:15)
- Video - Sketching Non-Monic Parabola Concave Down by Completing Square (2:26)
- Video - Graphs of Parabola Concave Upwards with No x-intercepts (5:16)
- Video - Translating Graphs of Quadratic Functions (2:15)
Finding Quadratics from Graphs
- Video - Finding Equation of Parabola using Vertex & y-Intercept 1 (2:55)
- Video - Finding Equation of Parabola using Vertex & y-Intercept 2 (2:39)
- Video - Finding Equation of Parabola using Vertex & y-Intercept 3 (1:35)
- Video - Finding Equation of Parabola using Vertex & y-Intercept 4 (2:33)
- Video - Finding Quadratics using Intercepts (7:53)
- Video - Finding Quadratics for Touching x-axis (4:13)
- Video - Finding Quadratics using Axes of Symmetry (6:26)
- Video - Finding Quadratics using Coefficients (4:00)
- Video - Finding Quadratics using Vertices (4:10)
Discriminant
- Video - Calculating the Discriminant (5:38)
- Video - Types of Roots of Quadratic Equations (3:40)
- Video - Discriminant of Real Equal Roots (5:43)
- Video - Tangents and Discriminant of Real Equal Roots (4:32)
- Video - Discriminant of Real Unequal Rational Roots (5:13)
- Video - Discriminant of Real Unequal Irrational Roots (3:55)
- Video - Discriminant of Imaginary Roots (2:39)
- Video - Discriminant of Real Roots (5:09)
- Video - Discriminant of Real Unequal Roots (4:25)
Positive Definite and Negative Definitive Quadratics
- Video - Positive Definite or Negative Definite of Quadratics (3:36)
- Video - Identifying Negative Definite using Discriminant 1 (7:19)
- Video - Identifying Negative Definite using Discriminant 2 (3:28)
- Video - Identifying Positive Definite using Discriminant (7:18)
- Topic - Concave Up & Cuts x-axis Once
- Topic - Concave Up & Cuts x-axis Twice
- Topic - Concave Down & Cuts x-axis Twice
- Topic - Concave Down & Cuts x-axis Once
- Topic - Positive Definite
- Topic - Negative Definite
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 involving Fractions 1 (6:34)
- Video - Quadratic Equations involving Fractions 2 (3:31)
- Video - Quadratic Equations using Substitutions (9:04)
- Video - Quadratic Equations using Indices (4:21)
- Video - Quadratic Equations using Indices with Undefined Solutions (2:21)
- 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 - Right-Angled Triangle by Quadratic Equations (2:39)
- Video - Sum of Squares of Numbers by Quadratic Equations (4:20)
- Video - Area of Composite Shapes by Quadratic Equations (5:28)
- Video - Similar Triangles by Quadratic Equations (3:43)
- Video - Sum of Number and Its Reciprocal by Quadratic Equations (3:49)
- Video - Intersections of Quadratic Parabola and Straight Line (3:29)
- Video - Checking the Solutions of Quadratic Equations (8:51)
- Video - Application of Quadratic Equations: Finding Numbers (2:10)
- Video - Application of Quadratic Equations: Area of Rectangular Shapes (2:34)
- Video - Application of Quadratic Equations: Border of Rectangular Fields (7:44)
- Video - Application of Quadratic Equations: Sum of N Positive Integers (3:08)
- Video - Applications of Quadratic Functions (3:16)
- 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)
