Course: Oman • Grade Twelve • Pure Mathematics

Table of Contents

• First Term
  • Unit One • Limits and Continuity
    • Limits by Direct Substitution
    • Limits from Tables and Graphs
    • One-Sided Limits
    • Existence of Limits
    • Evaluating Limits Using Algebraic Techniques
    • Limits at Infinity
    • Continuity at a Point
    • Continuity of Functions
  • Unit Two • Differentiation and Its Applications
    • Slope and Rate of Change
    • Average and Instantaneous Rates of Change
    • Definition of the Derivative
    • Equations of Tangent Lines and Normal Lines
    • The Product Rule
    • The Quotient Rule
    • Implicit Differentiation
    • Second- and Higher-Order Derivatives
    • Increasing and Decreasing Intervals of a Function
    • Increasing and Decreasing Intervals of a Function Using Derivatives
    • Critical Points and Local Extrema of a Function
    • Absolute Extrema
    • Second Derivative Test for Local Extrema
  • Unit Three • Coordinate Geometry of Circles
    • Equation of a Circle
    • Equation of a Circle Passing through Three Noncollinear Points
• Second Term
  • Unit Four • Integration and Its Application
    • Indefinite Integrals: The Power Rule
    • Rectilinear Motion and Integration
    • Integration by Substitution: Indefinite Integrals
    • Integration by Parts
    • Properties of Definite Integrals
    • Area between a Curve and a Line
    • Area between Curves
    • Volumes of Solids of Revolution
  • Unit Five • Probability and Statistics
    • Expected Values of Discrete Random Variables
    • Standard Deviation of Discrete Random Variables
    • Binomial Distribution
    • Continuous Random Variables
  • Unit Six • Conic Sections