## About the course

This Cambridge Mathematics IGCSE Extended course on algebra gives students that are aiming to achieve grades A* – E the opportunity to learn and excel online.

Making learning enjoyable, you can gain one of the world’s most respected qualifications using a laptop, internet connection, calculator, notepad and pen.

Once you have completed this prestigious course, you will have worked towards securing new opportunities in your education and career.

## What to expect

This course aims to teach a comprehensive understanding of the syllabus, covering every relevant aspect of algebra.

Breaking the course down into separate sections and lessons, you can tackle each stage one step at a time. Enter your answers for each question, making corrections as they are marked in real-time, to give you confidence in your answers and knowledge.

The progress bar shows your course completion percentage as you mark each section as complete, keeping you motivated and on track at all times.

## Benefits

- Designed for convenience
- Gives an in-depth understanding of algebra
- Globally respected course
- Enter answers and mark them in real-time
- Requires minimal equipment
- Learn at your own pace

#### Course Materials

#### 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 = 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

#### 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
- Topic - Expand and Simplify Linear Expressions

#### 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
- Topic - Expand and Simplify Binomial Expressions
- Topic - Expand and Simplify Cubic Expressions
- Topic - Expand and Simplify Trinomial Expressions

#### 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
- Topic - Expand and Simplify the Difference of Squares

#### 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

#### 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

#### 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

#### Factorising using Common Factors

- Video - Factorising Expressions (10:07)
- Video - Factorising & Negative Terms (3:41)
- Video - Factorise by Common Factors (5:26)
- Video - Factorise by Common Factors involving Brackets (5:15)
- Video - Solving Quadratics by Common Factors (4:59)
- Video - Understanding Factorise by Common Factors for Various Cases (3:07)
- Video - Factorise by Common Factors for Various Cases (9:35)
- Topic - Factorise using Common Factors
- Topic - Factorise using Common Factors and Indices
- Topic - Factorise Common Factors in Brackets
- Topic - Factorise Common Factors in Brackets and Indices

#### Factorising using Difference of Squares

- Video - Factorising Difference of Two Squares (5:50)
- Video - Factorising Difference of Two Squares & Common Factors (2:17)
- Video - Factorising Difference of Two Quartic (2:06)
- Video - Factorise Quadratics by Difference of Squares (3:08)
- Video - Factorise Quadratics by Difference of Squares & Common Factors (0:58)
- Video - Factorise Quartics by Difference of Squares Twice (2:52)
- Video - Harder Factorise by Difference of Squares (4:22)
- Topic - Introduction to Factorising Difference of Squares
- Topic - Factorising Difference of Squares: Non-Monic Coefficients
- Topic - Factorising Difference of Squares: Polynomial Terms and Common Factors
- Topic - Factorising Difference of Squares: Quartic Factorise

#### Factorising with Four Terms

- Video - Factorise by Common Factors in Two Levels (6:11)
- Topic - Factorising Expressions with Four Terms 1
- Topic - Factorising Expressions with Four Terms 2
- Topic - Factorising Expressions with Four Terms 3
- Topic - Factorising Expressions with Four Terms 4
- Topic - Factorise using Double Common Factors

#### Simplifying Algebraic Fractions using Quadratic Factorise

- Video - Quadratic & Linear by Quadratic Factorise (4:55)
- Video - Quadratic & Linear by Difference of Squares (2:10)
- Video - Quadratic & Linear by Quadratic Factorise & Common Factors (3:45)
- Video - Quadratic & Linear by Non-Monic Quadratic Factorise (3:12)
- Video - Quadratic Fractions by Quadratic Factorise (3:08)
- Video - Non-Monic Quadratic Fractions by Quadratic Factorise (5:16)
- Video - Quadratic Fractions by Factorising Difference of Squares (5:06)
- Video - Quadratic Fractions by Quadratic Factorise & Common Factors (6:30)
- Topic - Fractions involving Quadratic and Linear Terms: Monic Expressions
- Topic - Fractions involving Quadratic and Linear Terms: Common Factors
- Topic - Fractions involving Quadratic and Linear Terms: Difference of Squares
- Topic - Fractions involving Quadratic and Linear Terms: Non-Monic Expressions
- Topic - Fractions involving Quadratic Terms: Monic Expressions
- Topic - Fractions involving Quadratic Terms: Difference of Squares
- Topic - Fractions involving Quadratic Terms: Common Factors
- Topic - Fractions involving Quadratic Terms: Non-Monic Expressions

#### Product of Algebraic Fractions using Quadratic Factorise

- Video - Algebraic Fractions by Quadratic Factorise 1 (2:19)
- Video - Algebraic Fractions by Quadratic Factorise 2 (1:43)
- Video - Algebraic Fractions by Quadratic Factorise 3 (1:28)
- Video - Algebraic Fractions by Quadratic Factorise 4 (1:56)
- Video - Algebraic Fractions by Quadratic Factorise 5 (1:52)
- Video - Algebraic Fractions by Quadratic Factorise 6 (2:05)
- Topic - Simplifying Algebraic Fractions: Monic Expressions
- Topic - Simplifying Algebraic Fractions: Difference of Squares
- Topic - Simplifying Algebraic Fractions: Common Factors
- Topic - Simplifying Algebraic Fractions: Non-Monic Expressions

#### Sum of Algebraic Fractions using Quadratic Factorise

- Video - Fractions using Common Denominators by Quadratic Factorise 1 (2:05)
- Video - Fractions using Common Denominators by Quadratic Factorise 2 (2:03)
- Video - Fractions using Common Denominators by Quadratic Factorise 3 (1:25)
- Video - Fractions using Common Denominators by Quadratic Factorise 4 (1:45)
- Video - Algebraic Fractions in Common Denominators by Common Factors 1 (1:42)
- Video - Algebraic Fractions in Common Denominators by Common Factors 2 (2:03)
- Video - Algebraic Fractions in Common Denominators by Common Factors 3 (1:31)
- Topic - Addition of Algebraic Fractions: Monic Expressions
- Topic - Addition of Algebraic Fractions: Difference of Squares

#### 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)

#### 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 Factorisation with Exponents

- Video - Factorise by Common Factors of Exponents (4:16)
- Video - Quadratic Factorise of Exponents (5:02)
- Video - Simplification of Exponents in Rational Expressions (2:37)
- Topic - Algebraic Factorise with Exponents
- Topic - Algebraic Factorise with Exponents involving Constants
- Topic - Algebraic Factorise with Exponents involving Common Exponents
- Topic - Algebraic Factorise with Exponents involving Difference of Squares
- Topic - Algebraic Factorise with Exponents involving Complete Squares
- Topic - Algebraic Factorise 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 - Indicial Equations by Changing the Base (7:19)
- Video - Exponential Equations involving Surds (7:09)
- Video - Indicial Equations Involving Linear Equations (1:11)
- Video - Reducible Quadratic Equations of Indices in Factored Form (4:18)

#### Basic Linear Equations

- Video - One Step Equations (3:26)
- Check - One Step Equations
- Video - Two Step Equations (2:58)
- Video - Equations with Variables on Both Sides (2:47)
- 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 (3:21)
- 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 (6:36)
- Video - Equations and Formulae (5:10)
- Video - Equations and Geometry (3:35)
- 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 - Understanding Linear Inequalities (5:10)
- 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 - Linear Inequalities (4:36)

#### 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)