#### Course Materials

Lessons

#### Directed Numbers: Fractions

- Topic - Additions of Directed Fractions: Same Denominators
- Topic - Additions of Directed Fractions: Different Denominators 1
- Topic - Additions of Directed Fractions: Different Denominators 2
- Topic - Additions of Directed Mixed Numbers
- Topic - Multiplications of Directed Fractions
- Topic - Multiplications of Directed Mixed Numbers
- Topic - Divisions of Directed Fractions
- Topic - Divisions of Directed Mixed Numbers

#### Doing the Same to Both Sides

- Topic - Doing the Same to Both Sides
- Topic - Solving Monic Equations
- Topic - Solving Plus Plus Equations
- Topic - Solving Plus Minus Equations
- Topic - Solving Minus Plus Equations
- Topic - Solving Minus Minus Equations
- Topic - Solving Equations involving Brackets
- Topic - Solving Equations involving Like Terms

#### Solving Equations using Backtracking

- Topic - Solving Equations using Backtracking
- Topic - Solving Equations using Backtracking: Fractions 1
- Topic - Solving Equations using Backtracking: Fractions 2
- Topic - Solving Equations using Backtracking: Fractions 3
- Topic - Solving Equations using Backtracking: Fractions 4
- Topic - Solving Equations using Backtracking: Fractions 5
- Topic - Solving Equations using Backtracking: Fractions 6
- Topic - Solving Equations using Backtracking: Fractions 7
- Topic - Solving Equations using Backtracking: Fractions 8

#### Equations with the Pronumerals on Both Sides

- Topic - Monic Equations 1
- Topic - Monic Equations 2
- Topic - Positive Positive Equations 1
- Topic - Positive Positive Equations 2
- Topic - Positive Negative Equations 1
- Topic - Positive Negative Equations 2
- Topic - Negative Positive Equations 1
- Topic - Negative Positive Equations 2
- Topic - Negative Negative Equations 1
- Topic - Negative Negative Equations 2
- Topic - Monic Equations involving Brackets 1
- Topic - Monic Equations involving Brackets 2
- Topic - Non-Monic Equations involving Brackets 1
- Topic - Non-Monic Equations involving Brackets 2
- Topic - Equations involving Brackets in Both Sides 1
- Topic - Equations involving Brackets in Both Sides 2

#### Basic Linear Equations

- Video - One Step Equations (4:16)
- Video - Two Step Equations (3:40)
- Video - Equations with Variables on Both Sides (3:29)
- Video - Basic Linear Equations 1 (2:52)
- Video - Basic Linear Equations 2 (3:46)
- Video - Basic Linear Equations 3 (2:46)
- Video - Linear Equations (4:25)
- Topic - Linear Equations involving Subtractions
- Topic - Linear Equations involving Additions
- Topic - Linear Equations involving Multiplications
- Topic - Linear Equations involving Divisions
- Topic - Linear Equations involving Multiplications & Divisions
- Topic - Non-Monic Linear Equations
- Topic - Linear Equations involving Brackets

#### Linear Equations Involving Expansions

- Video - Equations with Brackets (4:23)
- Video - Equations with Pronumerals on Both Sides 1 (3:19)
- Video - Equations with Pronumerals on Both Sides 2 (4:29)
- Video - Equations with Grouping Symbols 1 (5:51)
- Video - Equations with Grouping Symbols 2 (4:37)
- Topic - Linear Equations involving Single Brackets
- Topic - Linear Equations involving Single Non-Monic Brackets
- Topic - Linear Equations involving Single Brackets & Extra Variables
- Topic - Linear Equations involving Multiple Brackets
- Topic - Linear Equations involving Multiple Non-Monic Brackets
- Topic - Linear Equations involving Squares

#### Linear Equations Involving Fractions

- Video - Solving Equations involving Fractions (4:47)
- Video - Equations with One Fraction 1 (5:18)
- Video - Equations with One Fraction 2 (5:01)
- Video - Equations with Multiple Fractions 1 (6:31)
- Video - Equations with Multiple Fractions 2 (6:59)
- Video - Equations With Single Pronumerals In The Denominator (2:28)
- Video - Equations With Multiple Pronumerals In The Denominator (7:40)
- Video - Equations With Compound Pronumerals In The Denominator (3:01)
- Video - Equations With Compound Pronumerals In Both Denominators and Numerators (2:39)
- Video - Linear Equations with Fractions 1 (5:45)
- Video - Linear Equations with Fractions 2 (4:01)
- Video - Linear Equations with Fractions: Variables in Denominators (3:37)
- Video - Linear Equations with Fractions: Variables in Numerators & Denominators (2:20)
- Video - Linear Inequalities involving Fractions (4:35)
- Topic - Linear Equations involving Single Fractions
- Topic - Linear Equations involving Single Non-Monic Fractions
- Topic - Linear Equations involving Two Fractions
- Topic - Linear Equations involving Variables in Both Numerators & Denominators

#### Problem Solving with Linear Equations

- Video - Applications of Equations (7:06)
- Video - Equations and Formulae (5:28)
- Video - Equations and Geometry (3:50)
- Video - Problem Solving with Linear Equations: Numbers (8:44)
- Video - Problem Solving with Linear Equations: Ages (3:17)
- Video - Problem Solving with Linear Equations: Coins (2:47)
- Topic - Problem Solving involving Averages
- Topic - Problem Solving involving Arithmetic
- Topic - Problem Solving involving Sum
- Topic - Problem Solving involving Costs
- Topic - Problem Solving involving Geometry
- Topic - Problem Solving involving Age
- Topic - Problem Solving involving Speed

#### Linear Inequalities

- Video - Inequalities in Number Lines (5:22)
- Video - Writing Inequalities from Number Lines (2:29)
- Video - Simple Inequalities (2:04)
- Video - Linear Inequalities Pronumerals on Both Sides (2:48)
- Video - Reversing Inequality Sign (4:46)
- Video - Two Inequality Signs in Inequalities (5:20)
- Video - Inequalities in Fractions 1 (4:32)
- Video - Inequalities in Fractions 2 (4:08)
- Video - Understanding Linear Inequalities (5:10)
- Video - Linear Inequalities involving Multiple Pronumerals (1:30)
- Video - Linear Inequalities involving Reciprocals (1:47)
- Video - Linear Inequalities (4:36)

#### Regions of Linear Inequalities

- Video - Understanding Sketching Regions (2:43)
- Video - Regions Bounded by Horizontal Lines (1:41)
- Video - Regions Bounded by Vertical Lines (1:28)
- Video - Regions Bounded by Straight Lines (5:24)
- Video - Regions Bounded by Straight Lines in General Form (6:16)
- Video - Writing Inequalities (5:20)
- Video - Vertical & Horizontal Regions (4:20)
- Video - Regions involving Linear Lines (3:53)
- 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)

#### Algebraic Expansion with Exponents

- Video - Algebraic Expansions of Exponents (5:17)
- Video - Expanding Binomial Terms of Exponents (8:16)
- Topic - Algebraic Expansions with Exponents
- Topic - Algebraic Expansions with Exponents involving Binomial Terms
- Topic - Algebraic Expansions with Exponents involving Squaring Terms
- Topic - Algebraic Expansions with Exponents involving Difference of Squares

#### Algebraic Factorization with Exponents

- Video - Factorize by Common Factors of Exponents (4:16)
- Video - Quadratic Factorize of Exponents (5:02)
- Video - Simplification of Exponents in Rational Expressions (2:37)
- Topic - Algebraic Factorize with Exponents
- Topic - Algebraic Factorize with Exponents involving Constants
- Topic - Algebraic Factorize with Exponents involving Common Exponents
- Topic - Algebraic Factorize with Exponents involving Difference of Squares
- Topic - Algebraic Factorize with Exponents involving Complete Squares
- Topic - Algebraic Factorize with Exponents involving Quadratic Trinomials
- Topic - Simplifying Algebraic Expressions involving Exponents

#### Exponential Equations

- Video - Basic Exponential Equations (2:03)
- Video - Exponential Equations involving Negative Exponents (1:40)
- Video - Exponential Equations involving Rational Exponents (3:35)
- Video - Exponential Equations by Changing Bases (2:25)
- Video - Exponential Equations involving Surds (7:09)
- Video - Indicial Equations by Changing the Base (7:19)
- Video - Solving Natural Exponential Equations from Definition (2:43)
- Video - Solving Natural Exponential Equations by Factorize (5:15)
- Video - Exponential Literal Equations (3:54)
- Video - Indicial Equations Involving Linear Equations (1:11)
- Video - Reducible Quadratic Equations of Indices in Factored Form (4:18)

#### Using Rules

- Topic - Using Rules: Subtraction
- Topic - Using Rules: Addition
- Topic - Using Rules: Multiplication
- Topic - Using Rules: Division
- Topic - Using Rules: Multiply and Add
- Topic - Using Rules: Multiply and Subtract
- Topic - Using Rules: Add and Multiply
- Topic - Using Rules: Multiply Itself
- Topic - Using Rules: Missing Numbers involving Multiply and Add
- Topic - Using Rules: Missing Numbers involving Multiply and Subtract
- Topic - Using Rules: Missing Numbers involving Subtract and Divide

#### Writing and Finding Formulas

- Topic - Rewriting Formula Leaving Out Multiplication Signs
- Topic - Writing Formulas: Addition
- Topic - Writing Formulas: Subtraction
- Topic - Writing Formulas: Mixed Addition
- Topic - Writing Formulas: Mixed Subtraction
- Topic - Writing Formulas: Positive Coefficients and Addition
- Topic - Writing Formulas: Positive Coefficients and Subtraction
- Topic - Writing Formulas: Negative Coefficients and Addition
- Topic - Writing Formulas: Negative Coefficients and Subtraction
- Topic - Writing Formulas: Positive Coefficients
- Topic - Writing Formulas: Negative Coefficients

#### Substitution

- Topic - Substitution to y = x + a Form
- Topic - Substitution to y = a - x Form
- Topic - Substitution to y = ax + b Form
- Topic - Substitution to y = -ax + b Form
- Topic - Substitution to y = a (x + b) Form
- Topic - Substitution to y = -a (x + b) Form
- Topic - Substitution to y = a (x + b) + c Form
- Topic - Substitution to y = a (b - x) + c Form
- Topic - Substitution to ax + by Form
- Topic - Substitution to Square Expressions

#### 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)

#### 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

#### Algebraic Substitution

- Video - Basic Substitution (11:17)
- Video - Algebraic Substitution (4:20)
- Video - Algebraic Substitution involving Indices (4:20)
- Video - Substitutions into Surds (4:24)
- Topic - Substitution to Additions & Subtractions
- Topic - Substitution to Additions & Subtractions involving Multiplications
- Topic - Substitution to Additions & Subtractions involving Divisions
- Topic - Substitution to Additions & Subtractions involving Squares
- Topic - Substitution to Additions & Subtractions involving Squares & Brackets
- Topic - Substitution to Additions & Subtractions involving Squares & Binomial Terms
- Topic - Substitution to Additions & Subtractions involving Cubes
- Topic - Substitution to Mixed Expressions
- Topic - Substitution to Square Roots

#### Formula Substitution

- Video - Substitution into a Basic Formula (5:00)
- Video - Substitution into Exponents Involving Formulae (2:20)
- Video - Substitution into Rational Formulae (3:20)
- Video - Substitution into Irrational Formulae (2:55)
- Video - Equations Arising from Substitution 1 (4:19)
- Video - Equations Arising from Substitution 2 (3:39)
- Video - Evaluating Formula using Substitutions (4:49)
- Topic - Formula Substitution of Linear Expressions
- Topic - Formula Substitution of Approximation Values
- Topic - Formula Substitution of Quadratic Expressions
- Topic - Evaluating Values using Formula Substitution of Linear Expressions
- Topic - Evaluating Values using Formula Substitution of Approximation Values
- Topic - Evaluating Values using Formula Substitution of Quadratic Expressions

#### Formula Rearrangement

- Video - Changing the Subject of a Formula (5:49)
- Video - Changing the Subject on Both Sides (4:28)
- Video - Changing the Subject involving Square Roots (2:53)
- Video - Changing the Subject Involving Squares (2:04)
- Video - Changing the Subject on Denominators (4:45)
- Video - Changing the Subject on Both Numerators & Denominators (6:02)
- Video - Rearrangement (6:55)
- Topic - Rearranging Linear Formulas Subject to x
- Topic - Rearranging Linear Formulas Subject to y
- Topic - Rearranging Formulas involving Squares Subject to x
- Topic - Rearranging Formulas involving Squares Subject to y
- Topic - Rearranging Formulas involving Square Roots
- Topic - Rearranging Formulas involving Multiple Variables

#### Expanding Single Brackets

- Video - Expanding Expressions (6:15)
- Video - Expanding Single Brackets (4:27)
- Video - Expansion of Single Brackets (4:58)
- Video - Expansion of Single Brackets and Simplify (2:58)
- Video - Expansion of two Single Brackets and Simplify (4:10)
- Topic - Expand & Simplify: Coefficients Times Linear Binomial Terms
- Topic - Expand & Simplify: Variables Times Linear Binomial Terms
- Topic - Expand & Simplify: Coefficient Times Trinomials
- Topic - Expand & Simplify: Variables Times Trinomials
- Topic - Expand & Simplify: Quadratic Times Linear Binomial Terms
- Topic - Expand & Simplify: Multiple Single Brackets
- Topic - Expand & Simplify: Multiple Single Brackets with Variables

#### Expanding Pairs of Brackets

- Video - Expanding and Simplifying Expressions (9:40)
- Video - Expanding Formula of Binomial Algebraic Expressions (6:05)
- Video - Expanding Pair of Brackets (4:19)
- Video - Expanding Pair of Brackets and Additional Terms (9:52)
- Video - Expanding with Trinomials (4:28)
- Video - 2 by 3 Expansions (4:48)
- Video - The Product of Two Linear Expressions (2:58)
- Video - Expanding Pairs of Brackets (7:27)
- Topic - Linear Times Linear
- Topic - Linear Times Linear with Coefficients
- Topic - Non-Monic Linear Times Non-Monic Linear
- Topic - Non-Monic Linear Times Non-Monic Linear with Coefficients
- Topic - Square of Linear Expressions
- Topic - Square of Linear Expressions with Coefficients
- Topic - Linear Times Quadratics
- Topic - Linear Times Trinomials

#### Expanding Difference of Squares

- Video - Expanding Difference of Squares (7:02)
- Video - Expanding Difference of Two Squares (4:51)
- Topic - Expand Difference of Squares: Variables & Constants
- Topic - Expand Difference of Squares: Mixed Variables & Constants
- Topic - Expand Difference of Squares: Constants & Variables
- Topic - Expand Difference of Squares: Non-Monic Variables
- Topic - Expand Difference of Squares: Multiplier
- Topic - Expand Difference of Squares: Multiplier to Non-Monic Variables

#### Perfect Square Expansions

- Video - Basic Square Expansions (5:19)
- Video - Further Square Expansions (6:37)
- Video - Expanding with Squares (7:40)
- Video - Expanding with Completed Squares (9:46)
- Video - Expanding Perfect Squares (6:56)
- Video - Basic Rules of Completing the Square (7:19)
- Video - Completing the Square of Quadratic Expressions (3:52)
- Topic - Expand Squares of Additions of Monic Expressions
- Topic - Expand Squares of Subtractions of Monic Expressions
- Topic - Expand Squares of Additions of Non-Monic Expressions
- Topic - Expand Squares of Subtractions of Non-Monic Expressions
- Topic - Expand Squares of Additions of Non-Monic Expressions with Coefficients
- Topic - Expand Squares of Subtractions of Non-Monic Expressions with Coefficients
- Topic - Expand & Simplify Squares

#### Further Expansions Cubes

- Video - Cube Expansions (3:23)
- Video - Monic Cubic Expansions (5:31)
- Video - Non-Monic Cubic Expansions (9:42)
- Video - Cubic Expansions (2:55)
- Video - Expanding Cubics and more Terms (7:32)
- Video - Evaluating by Expanding Squares & Cubic Expressions (5:09)
- Topic - Expansion of Cubes: Linear Times Quadratic Expressions
- Topic - Expansion of Cubes: Cubes of Monic Linear Expressions involving Additions
- Topic - Expansion of Cubes: Cubes of Monic Linear Expressions involving Subtractions
- Topic - Expansion of Cubes: Cubes of Non-Monic Linear Expressions involving Additions
- Topic - Expansion of Cubes: Cubes of Non-Monic Linear Expressions involving Subtraction
- Topic - Expansion of Cubes: Cubes of Non-Monic Linear Expressions involving Additions & Coefficients
- Topic - Expansion of Cubes: Cubes of Non-Monic Linear Expressions involving Subtraction & Coefficients

#### 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

#### Problem Solving with 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)

#### Simultaneous Linear Inequations

- 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 - Common Regions between Horizontal and Straight Lines (3:49)
- Video - Common Regions between Vertical and Horizontal Lines (3:42)
- Video - Common Regions between Straight Lines (1:43)
- Video - Common Regions between Two Straight Lines (4:26)
- Video - Common Regions between Two Straight Lines in General Form (2:15)
- Video - Common Regions between Three Straight Lines (2:54)
- Video - Common Regions involving Vertical and Horizontal Lines (2:21)
- Video - Intersecting Regions involving Linear Inequalities (5:16)