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## Algebra

Simplifying Algebraic Fractions using Factorising

Expanding expressions using Pascals triangles

The Binomial Theorem

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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

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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