# Course: Oman • Pure Mathematics • Stage Twelve • Second Edition

• First Term
• Unit One Limits and Continuity
• Limits
• Limit of a Function at a Point
• Left-Hand and Right-Hand 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
• 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
• 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
• Real-Life Examples
• Tangents of Circles
• 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
• 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
• 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

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