Leaving Certificate Maths: Calculus Series

4^th September - Limits, The Derivative and First Principles

• Review of Slope
• Concept of Limits
• The Derivative (an intuitive explanation with the aid of Geogebra simulations)
• Differentiation from first principles
• Section A Exam Questions

11^th September - Differentiation by Rule / Applications of Differentiation

Differentiation by Rule

• Polynomials, Trigonometric Functions, Rational Functions, Exponential Functions
• Log Functions, Inverse Trigonometric Functions
• Chain Rule, Product Rule, Chain Rule

Applications of Differentiation

• Second Derivative
• Increasing/Decreasing Functions
• Max/Min/Points of Inflection

18^th September - Applications of Differentiation / Integration

Applications of Differentiation

• Rates of Change
• Section B Exam Questions - Applications of Differentiation

Integration

• Inverse Functions
• The Antiderivative as an Inverse Function of the Derivative
• Indefinite Integrals
• Rules for Polynomials, Trigonometric Functions, Exponential Functions

25^th September - Definite Integrals and Applications of Integration

• Definite Integrals and Limits
• Approximation of Area using Trapezoidal Rule
• Area using Integration
• Average Value of a Function using Integration
• Integration Exam Questions