Table of Contents

First Term

Unit One Limits and Continuity

Limits
 Limit of a Function at a Point
 LeftHand and RightHand Limits
 Theorems on Limits
 Limit of the Function at Infinity

Continuity
 Continuity of a Function at a Point
 Continuity of a Function on an Interval

Limits

Unit Two Differentiation and Its Applications

Differentiation
 Variation
 Derivative (A Rate of Change)
 Geometric Interpretation of Derivatives
 Physical Interpretation of Derivatives
 Relationship between Continuity and Differentiability

Rules of Differentiation
 Derivative of a Product and a Quotient of Two Functions
 Chain Rule
 Implicit Differentiation
 Higher Order Derivatives

Related Rates
 Increasing and Decreasing
 Using the First Derivative to Study Increasing and Decreasing of Functions

Extrema
 Local Extrema
 Absolute Extrema
 Second Derivative Test
 Real Life Application of Local Extrema

Differentiation

Unit Three Coordinate Geometry of Circles
 Coordinate Geometry

Circle
 The General Form of the Equation of a Circle
 Converting the General Form of the Equation of Circle to Standard Form

Special Cases of Circle
 (a) The Equation of a Circle Given the Coordinates of Its Diameter Extremities
 (b) The Equation of a Circle If Tangent to One Axis Given the Center Coordinates
 (c) The Equation of a Circle If Tangent to Both Coordinate Axes Given Radius or the Coordinates of One Tangent Point
 (d) The Equation of a Circle Given the Coordinates of One Tangent Point
 RealLife Examples
 Tangents of Circles

Unit One Limits and Continuity

Second Term

Unit Four Integration and Its Application

Integration
 Integration
 Integration Laws

Simple Differential Equations and Its Applications
 Physical Applications
 Geometric Applications

Integration Techniques
 Integration by Substitution
 Integration by Parts

Definite Integration
 Properties of Definite Integration

Application on Integration
 Areas
 Volumes of Revolutions

Integration

Unit Five Probability and Statistics

Random Variables
 Discrete Random Variable
 The Standard Deviation of Discrete Random Variables
 Binomial Distribution
 Continuous Probability Distribution

Normal Distribution
 Standard Normal Distribution
 Calculating Probability in Domain of Standard Normal Distribution Function

Random Variables

Unit Six Conic Sections
 Conic Sections

Parabola
 The Standard Form for the Equation of Parabola Whose Vertex Is (0 , 0)
 The Standard Form for the Equation of Parabola Whose Vertex Is (d , h)
 The Standard Form for the Equation of Parabola

Ellipse
 The Standard Form for the Equation of Ellipse Whose Vertex Is (0 , 0)
 The Standard Form for the Equation of Ellipse Whose Vertex Is (d , h)
 Eccentricity of Ellipse
 The Standard Form for the Equation of Ellipse

Hyperbola
 The Standard Form for the Equation of Hyperbola Whose Vertex Is (0 , 0)
 The Standard Form for the Equation of Hyperbola Whose Vertex Is (d , h)
 The Standard Form for the Equation of Hyperbola
 The Standard Form for the Equation of Conic Section

Unit Four Integration and Its Application