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Go Forth & Multiply: A Mathematics Adventure

Introduction

Algebra

History of Algebra

Algebra in Ancient Times

Algebra in the Renaissance

Algebra in Modern Times

Algebraic Manipulation

Algebraic Expressions

Evaluation of Algebraic Expressions

Rules of Algebra

Algebraic Fractions

Quiz 1

Expansion: the FOIL Method

Algebraic Identities

Basic Factorisation

Factorisation of Quadratic Polynomials

Factorisation by Grouping

Quiz 2

Long Division

Polynomial Identities

Quiz 3

Partial Fractions

Partial Fractions

Distinct Linear Factors

Repeated Linear Factors

Quadratic Factors

Improper Fractions

Quiz

Equations

Introduction

Solving Simple Equations

Formulae

Factorising Quadratic Equations

Completing the Square Method

General Solution of Quadratic Equations

Problem Solving

Quiz

Simultaneous Equations

Introduction

Elimination Method

Substitution Method

Solving Linear & Quadratic Equations

Problem Solving

Quiz

Indices, Surds & Logarithms

Indices

Laws of Indices

Surds

Laws of Surds

Exponential Equations

Logarithms

Laws of Logarithms

Logarithmic Equations

Quiz

Inequalities

Inequalities

Properties of Inequalities

Solving Linear Inequalities

Quadratic Inequalities

Cubic Inequalities
Fractional Inequalities
Modulus Inequalities
Problem Solving
Quiz

Functions
Relations
Functions
Composite Function
Inverse Functions
Absolute Valued Functions
Quiz

Remainder & Factor Theorems
Introduction
Remainder Theorem
Factor Theorem
Cubic Equations
Quiz

Binomial Expansion
Binomial Expansions
Factorials
Combination Symbol
Binomial Theorem
Binomial Series

Arithmetic & Geometric Progressions
Sequences & Series
Arithmetic Progressions
Geometric Progressions
Sum to Infinity
Quiz

Calculus

History
Beginnings of Calculus
Newton & Leibniz
Post Newton-Leibniz

Limits & First Principles
Limits
First Principles

Techniques of Differentiation
Differentiation
Sum & Difference Rules
Product Rule
Quotient Rule
Chain Rule
Exponential Function
Logarithmic Function
Trigonometric Function
Reciprocal Trigonometric Function
Inverse Trigonometric Function
Implicit Differentiation
Higher Derivatives
Quiz

The Cartesian Plane
The Cartesian Plane
Equations of Tangents & Normals

Stationary Points
First Derivative Test
Second Derivative Test
Quiz

Changes
Rates of Change
Maximization & Minimization
Small Changes
Quiz

Integration of Standard Functions
Integration
Indefinite Integrals
Algebraic Functions
Exponential Functions
Logarithmic Functions
Trigonometric Functions
Inverse Trigonometric Function
Algebraic Fractions
Quiz

Applications of Integration
Definite Integrals
Area Under a Curve
Area Bounded by 2 Curves
Volumes of Revolution
Quiz

Communications
Sign Guestbook
View Guestbook
Message Board
Feedback

Calculator

Geometry

History

Early Geometry

Greek Mathematics

Euclid & the Elements

Later Developments

Analytic Geometry

Mensuration

Parts of Circles

Area of Circles

Length of Arc & Area of Sector

Area of Triangle

Volume of Cylinder
Surface Area of Cylinder
Volume of Cones & Pyramids
Surface Area of Cones & Pyramids
Volume of Sphere
Surface Area of Sphere
Quiz

Angles & Lines

Lines & Line Segment
Angles
Angle Properties of Straight Lines
Angle Properties of Parallel Lines
Quiz

Circle Geometry

Symmetrical Properties
Angle Properties
Cyclic Quadrilaterals
Problems on Angle Properties
Tangents from External Point
Alternate Angle Segment
Quiz

Radian Measure

Radian & Degree
Arc Length
Area of Sector
Quiz

The Cartesian Plane

The Cartesian Plane

Graphing

Linear Equations

Solutions of Equations

Analytic Geometry

Analytic Geometry

Basic Concepts

Area of Polygon

Equation of Straight Lines

Parallel Lines

Perpendicular Lines

Examples

Quiz

Curve Sketching

Curve Sketching

Techniques

Quadratic Functions

Higher Degree Equations

Rectangular Hyperbolas

Conic Sections

Modulus Functions

Rational Functions

Transformations

Transformations

Reflection

Scaling

Translation

Inverse

Modulus

Trigonometric Functions

Trigonometric Functions

Basic Functions

Reciprocal Functions

Inverse Functions

Scaling

Translation

Reflection

Quiz

Exponential & Logarithmic Functions

Exponential & Logarithmic Functions

Exponential Function

Logarithmic Function

Scaling

Translation

Reflection

Quiz

Trigonometry

History

Early Trigonometry

European Developments

Pythagoras Theorem

Pythagoras Theorem

Proof 1

Proof 2

Pythagorean Triples

Angles & Ratios

Ratio for Acute Angles
Ratio for General Angles
Ratio for Negative Angles
Ratio for Special Angles
Ratio for Complementary Angles
Other Trigonometry Ratios
Inverse Functions
Quiz

Basic Identities

Basic Identities
Second Degree Identities
Simple Equations
Second Degree Equations
Quiz

Formulae

Trigonometric Formulae

Addition Formula (Sine)

Addition Formula (Cosine)

Addition Formula (Tangent)

Double Angle Formulae

Triple Angle Formulae

Half Angle Formulae

Factor Formulae

R-formulae

Examples

Quiz

Sine & Cosine Rules

Sine Rule

Solution of Triangle (Sine)

Cosine Rule

Solution of Triangle (Cosine)

Quiz

General Solution

General Solution

Sine Function

Cosine Function

Tangent Function

Trigonometric Equations

Quiz

Interact
Quizzes

Animation
Message Board

Credits
References
Acknowledgements
Disclaimer
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