Algebra
Simplifying Algebraic Fractions using Factorising
Expanding expressions using Pascals triangles
The Binomial Theorem
For Factorials click here
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Factorising Algebraic Expressions
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The Factor Theorem (An example)
Determining Unknown Coefficients
Rules for sketching Polynomials
Sketching Polynomials (3 examples)
Deriving the Cubic Equation (Cardano's Formula)
Not Required For The Leaving Certificate
The Cubic Formula -
An Example
Not Required For The Leaving Certificate
Completing the Square
Deriving the Quadratic Formula (Not required for LC)
Using the completed square form to sketch graphs
Simultaneous Equations with 3 Variables
Absolute Values (Modulus)
Vieta's Formula
Note: Only Quadratic formula required for LC
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Inequalities
Examples of Linear Inequalities
Quadratic and Rational Inequalities
Absolute (Modulus) Inequalities
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Matrices and Linear Algebra
Not required for Leaving Cert
Matrices - The Basics
The Determinant and Inverse Matrices
Solving Linear Equations using Matrices
Finding the Determinant of a 3 x 3 Matrix
Using Matrix of Minors, Cofactor and Adjugate to find the Inverse of a 3 x 3 Matrix
Transformations using Matrices
Using Gauss Jordan Elimination to find the Inverse of a 3 x 3 Matrix
Linear Combinations
Spanning Sets, Bases and Linear Dependence
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Partial Fractions
Not required for Leaving Cert
Partial Fraction Expansion 1
Partial Fraction Expansion 3
Partial Fraction Expansion 2
Partial Fraction Expansion 4
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The Lambert W Function