Strand 4 Leaving Certificate Higher Level Algebra  Revised
Enhance your mathematical knowledge from Algebra to Numbers
Description
Algebra is the natural language and the lifeblood of Mathematics and perfectly links between number, trigonometry, geometry and functions. It would be impossible to solve or even formulate realworld problems without algebraic notation.
Firstly, students are introduced to representing numbers with letters and then they move on to look at how to convert problems into equations which can be solved by various wellknown techniques in algebra.
Students are taught how to solve quadratic, cubic and simultaneous equations and then they expand their knowledge to the solutions of inequalities. Using trial and error to search for roots and using synthetic division is covered in this strand.
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
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