Algebra in Mathematics  Revised
Gain a good understanding of the fundamentals and key aspects of Algebra in mathematics
Description
Do you know that the word algebra came from the Arabic word aljabr. This word dates back to the title of a 9thcentury manuscript written by the mathematician AlKhwarizmi, who is known as the Father of Algebra. Now that you know whom to thank Algebra for, it's time to learn it. First, this course will clearly explain how to simplify your algebraic expressions, with expansion of brackets and factorising.
The course starts off with teaching you how to factorise an algebraic equation, and the two different methods for expanding brackets, how to rearrang simple formulae, what a surd is and how binomial expansion works. In the second module you will be learn about solving different types of quadratic equations, along with what simultaneous equations are and how to solve them. The module ends with explain hidden quadratics, the discriminant and how to solve equations with indices.
In the following module you will be taught about how to solve logarithmic and exponential equations, along with the factor and the remainder theorems. The third module finishes with explaining how to find the root of a cubic equation and what modulus is and how to work it out. Next you will learn about inequalities in quadratic equations and linear equations, and how to solve them using either the trial and error method, the algebra method or the graphical method.
In the last module you will learn about complex numbers and what they are, imaginary numbers and the meaning of I, converting numbers to the polar form and multiplying and dividing in the polar form. The module finishes by showing you how to prove De Moivre’s theorem, complex numbers when solving quadratic equations, complex roots and cube roots.
This course would be of great interest to any one looking to further or upskill their mathematical knowledge and capability.
Start Course NowModules
Expressions and Formulae

Expressions and Formulae  Learning Outcomes

Factorising Quadratics

Factorising  Difference of Two Squares

Expanding Brackets (Grid Method)

Expanding Brackets (FOIL method)

Expanding Any Two Brackets

Rearranging Simple Formulae

Rearranging Simple Formulae 2 Steps

Rearranging Formulae with Squares and Square Roots

Rearranging Formulae New Subject Appearing Twice

Simplifying Surds

Further Calculations with Surds

Completing The Square

General Completing The Square

Binomial Expansion

Expressions and Formulae Lesson Summary
Solving Equations  Part 1

Solving Equations  Part 1  Learning Outcomes

Equations with Linear Functions in The Denominator

Quadratic Equations Using The Formula

Quadratic Equations Non Unitary x Squared

Quadratic Equations Both Brackets The Same Sign

Quadratic Equations Brackets With Different Signs

Quadratic Equations That Have to be Rearranged

Solving Simultaneous Equations Graphically

Simultaneous Equations Both Negative Signs

Simultaneous Equations Negative and Positive Signs

Simultaneous Equations Both Positive

Hidden Quadratics

Use of The Discriminant

Equations With Indices

Solving Equations  Part 1  Lesson Summary
Solving Equations  Part 2

Solving Equations  Part 2  Learning Outcomes

Logarithmic Equations

Solving Exponential Equations

From Roots to Functions

Non Linear Simultaneous Equations

Factor Theorem

The Remainder Theorem

General Remainder and Factor Theorem

Finding Roots of Cubic Equation

Modulus Equations

Using Graphs to Solve Modulus Equations

Solving Equations  Part 2  Lesson Summary
Inequalities

Inequalities  Learning Outcomes

Finding Inequalities from Shaded Regions

Solving Linear Inequalities with Fractions

Solving Quadratic Inequalities – Method 1

Solving Quadratic Inequalities – Method 2

Solving Quadratic Inequalities – Method 3

NonUnitary x^2  Trial and Error Method

NonUnitary x^2  Algebra Method

Nonunitary x^2  Graphical Method

Solving Quadratic Inequalities  Special Cases

Rational Inequalities

Modulus Equations

Using Graphs to Solve Modulus Equations

Modulus Inequalities

Modulus Function On a Graph

Graphical Solution of Modulus Inequalities

Inequalities  Lesson Summary
Complex Numbers

Complex Numbers  Learning Outcomes

Manipulating Complex Numbers and The Complex Conjugate

The Argand Diagram and Modulus

The Meaning of i

Patterns with Imaginary Numbers

Writing Complex Numbers in Polar Form

Multiplying and Dividing in Polar Form (Proof)

Multiplying and Dividing in Polar Form (Example)

Proof of De Moivre’s Theorem

Complex Numbers When Solving Quadratic Equations

Cubic Equations With Complex Roots

Finding The Cube Roots of 8

Complex Numbers  Lesson Summary
Course assessment
Learning Outcomes
Having completed this course students will be able to:
 Recognize how to factorise quadratics
 Identify how to expand brackets using both the grid and FOIL methods
 Discuss and define binomial Expansion
 Recognize how to solve linear equations that contain fractions
 Recognize how to solve quadratic equations, using formula and graphics
 Recognize how to solve simultaneous equations
 Identify how to solve logarithmic and exponential equations
 Recognize how to solve Quadratic inequalities using the Graphical Method
 Recognize how to solve Quadratic inequalities using three different methods
 Define Rational Inequalities and recognize how to solve them
 Identify how to work out and calculate modulus inequalities and functions algebraically and graphically
Certification
All Alison courses are free to enrol, study and complete. To successfully complete this Certificate course and become an Alison Graduate, you need to achieve 80% or higher in each course assessment. Once you have completed this Certificate course, you have the option to acquire an official Certificate, which is a great way to share your achievement with the world. Your Alison Certificate is:
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