Lessons
Multiplication using Exponents
- Video - Index Law of Addition (6:17)
- Video - Index Equations using Index Law of Addition (3:17)
- Video - Evaluation using Index Law of Addition (5:12)
- Video - Simplification using Index Law of Addition (3:32)
- Video - Addition Law of Exponents (4:12)
- Video - Multiplication using Indices (3:32)
- Topic - Equations by Adding Indices
- Topic - Simplifying by Adding Indices
- Topic - Evaluation by Adding Indices
Division using Exponents
- Video - Simplification of Exponent in Fractions (2:24)
- Video - Index Law of Subtraction (5:51)
- Video - Simplification using Index Law of Subtraction (1:54)
- Video - Mixed Simplification using Index Law of Subtraction (4:58)
- Video - Evaluation using Index Law of Subtraction (4:14)
- Video - Subtraction Law of Exponents (3:26)
- Video - Division using Indices (5:20)
- Topic - Simplifying by Subtracting Indices
- Topic - Simplifying by Adding and Subtracting Indices
- Topic - Evaluation by Subtracting Indices
Raising a Power to Another Power
- Video - Index Law of Powers (4:35)
- Video - Simplification using Index Law of Powers (6:53)
- Video - Evaluation using Index Law of Powers (6:37)
- Video - Index Law of Raising a Power to Another Power (4:19)
- Video - Raising a Power to Another Base (5:27)
- Video - Raising a Power to Another Indices (5:56)
- Topic - Equations involving Power of Power
- Topic - Simplifying by Power of Power
- Topic - Evaluation by Power of Power
Negative Exponents
- Video - Writing in Negative Exponents (7:40)
- Video - Equations involving Negative Exponents (2:03)
- Video - Writing in Positive Exponents (2:28)
- Video - Expressing in Positive Exponents (4:08)
- Video - Fractions to Index Form in Positive Exponents (2:27)
- Video - Simplifying Positive Exponents (4:05)
- Video - Mixed Simplification involving Negative Exponents (2:26)
- Video - Evaluating Negative Exponents (3:39)
- Video - Quadratic Equations involving Negative Indices (1:05)
- Topic - Rational Fractions and Negative Indices
- Topic - Handling Negative Indices
- Topic - Expressing with Negative Indices
Rational Exponents
- Video - Rational Exponents using Index Law of Addition (4:50)
- Video - Rational Exponents using Index Law of Subtraction (2:38)
- Video - Rational Exponents using Index Law of Powers (3:10)
- Video - Rational Exponents using Surds (4:00)
- Video - Index Form in Rational Indices (5:42)
- Video - Index Form in Negative Indices (4:46)
- Video - Evaluating Rational Indices using Calculators (2:34)
- Video - Equations involving Rational Indices (2:03)
Simplifying Surds
- Video - Simplifying Square Roots (5:22)
- Video - Simplifying Cube Roots (4:39)
- Video - Simplifying Quad Roots (2:11)
- Video - Simplifying Cube Roots and Quad Roots (4:19)
- Video - Simplifying Square Roots using Tree Diagrams (6:01)
- Video - Simple Equations involving Surds (1:32)
- Video - Completing the Surds (1:36)
- Video - Simple Equations involving Higher Order Surds (3:13)
- Video - Completing the Higher Order Surds (5:27)
Distributive Law of Surds
- Video - Expansion of Surds 1 (3:20)
- Video - Expansion of Surds 2 (3:57)
- Video - Binomial Products of Two Surds (3:13)
- Video - Binomial Products of Three Surds (1:11)
- Video - Binomial Products of Four Surds 1 (1:59)
- Video - Binomial Products of Four Surds 2 (2:16)
- Video - Binomial Products of Four Surds 3 (1:21)
- Video - Binomial Products of Four Surds 4 (2:37)
- Video - Expansion & Simplify of Surds 2 by 3 (6:26)
- Video - Expansion & Further Simplify of Surds 2 by 3 (5:30)
- Video - Difference of Squares with Surds (4:45)
- Video - Difference of Squares with Surds of Surds (2:13)
- Video - Basic Rules of Surds: Expanding Binomial Terms (3:53)
Rationalising Denominators
- Video - Rationalise Denominators in Single Term Denominators (5:37)
- Video - Rationalise Denominators in Single Term Denominators & Simplifying (2:49)
- Topic - Rationalising Denominators: Basic 1
- Topic - Rationalising Denominators: Basic 2
- Topic - Rationalising Denominators: Simplifying Surds
- Topic - Rationalising Denominators: Simplifying Fractions
Rationalising Denominators using Conjugate Pairs
- Video - Rationalise Denominators using Conjugate Pairs (5:31)
- Video - Rationalise Denominators using Conjugate Pairs & Simplifying (4:01)
- Video - Rationalise Denominators using Conjugate Pairs & Binomial Numerators (6:38)
- Video - Pronumerals using Rationalise Denominators (7:49)
- Video - Simplify Fractions using Rationalise Denominators & Multiplications (5:17)
- Video - Simplify Fractions using Rationalise Denominators & Additions 1 (6:09)
- Video - Simplify Fractions using Rationalise Denominators & Additions 2 (4:45)
- Video - Simplify Fractions using Rationalise Denominators & Additions 3 (3:57)
- Video - Simplify Fractions using Rationalise Denominators & Additions 4 (3:00)
- Video - Simplify Fractions using Rationalise Denominators & Additions 5 (3:10)
Equality of Surds
- Topic - Equality of Surds: Basic Comparison
- Topic - Equality of Surds: Single Term Comparison
- Topic - Equality of Surds by Simplification
- Topic - Equality of surds involving Simultaneous Equations 1
- Topic - Equality of surds involving Simultaneous Equations 2
- Topic - Equality of surds involving Simultaneous Equations 3
- Topic - Equality of surds involving Simultaneous Equations 4
- Topic - Equality of surds involving Simultaneous Equations 5
Equations involving Surds
- Video - Equations involving Square Roots (6:19)
- Video - Equations involving Cube Roots (1:05)
- Video - Quadratic Equations using Substitutions involving Surds (1:30)
- Video - Quadratic Equations involving Surds Solving by Quadratic Equations (4:58)
- Video - Quadratic Equations from Surds (6:59)
- Video - Quadratic Equations from Surds & Fractions (2:49)
- Video - Equations involving Nested Surds (2:23)
- Video - Equations involving Surds (7:18)
- Video - Linear Equations involving Surds (1:41)
Quadratic Equations in Square Form
- 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)
Adding and Subtracting Algebraic Fractions
- Video - Simplifying Fractions with Same Denominators (4:10)
- Video - Simplifying Fractions with Different Denominators (5:18)
- Video - Adding Algebraic Fractions (0:48)
- Video - Subtracting Algebraic Fractions (3:22)
- Video - Adding Algebraic Fractions involving Expansions (4:35)
- Video - Subtracting Algebraic Fractions involving Expansions (3:23)
- Topic - Algebraic Fractions: Addition and Subtraction
- Topic - Algebraic Fractions: Simplify by Denominators
- Topic - Algebraic Fractions: Simplify by More Denominators
Multiplying and Dividing Algebraic Fractions
- Video - Multiplying Algebraic Fractions (2:16)
- Video - Dividing Algebraic Fractions (5:35)
- Topic - Multiplying Algebraic Fractions 1
- Topic - Multiplying Algebraic Fractions 2
- Topic - Multiplying Algebraic Fractions 3
- Topic - Multiplying Algebraic Fractions 4
- Topic - Multiplying Algebraic Fractions 5
- Topic - Dividing Algebraic Fractions 1
- Topic - Dividing Algebraic Fractions 2
- Topic - Algebraic Fractions: Multiplication
- Topic - Algebraic Fractions: Division
- Topic - Algebraic Fractions: Multiplication and Division
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 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 - Range of Reciprocal of Quadratic Expressions (5:37)
Ranges of Linear Inequalities
- Video - Regions Bounded by Horizontal & Vertical Lines (3:49)
- Video - Regions Bounded by Horizontal, Vertical & Straight Lines (4:27)
- Video - Regions Bounded between Straight Lines (4:00)
- Video - Regions Bounded between Straight Lines in General Form (6:01)
- Video - Regions involving Linear Inequalities: Greater Than (5:11)
- Video - Regions involving Linear Inequalities: Less Than (0:55)
- Video - Regions involving Linear Inequalities including Borders (1:44)
- Video - Regions involving Linear Inequalities in General Form (2:55)
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
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)
