Course: Maths - Khan Academy, Educomp & Vimbue

Section outline

Select section General

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General

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Select section 1. Relations and Functions

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1. Relations and Functions
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  Introduction
  
  Select activity What are Relations?
  
  
  
  What are Relations? Lesson
  
  Students must
  
  Mark as done
  
  Select activity Domain and Range of a Relation
  
  
  
  Domain and Range of a Relation Lesson
  
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  Select activity What is a Function?
  
  
  
  What is a Function? Lesson
  
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  Select activity What is the Domain of a Function?
  
  
  
  What is the Domain of a Function? Lesson
  
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  Select activity What is the Range of a Function?
  
  
  
  What is the Range of a Function? Lesson
  
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  Types of Relations
  
  Select activity Types of Relation
  
  
  
  Types of Relation Lesson
  
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  Select activity Relations and Function
  
  
  
  Relations and Function Lesson
  
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  Select activity Empty and Universal Relations
  
  
  
  Empty and Universal Relations Lesson
  
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  Select activity Equivalence Relations and their Properties
  
  
  
  Equivalence Relations and their Properties Lesson
  
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  Select activity Equivalence Relations in Geometry
  
  
  
  Equivalence Relations in Geometry Lesson
  
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  Select activity Equivalence Relations - Non math example
  
  
  
  Equivalence Relations - Non math example Lesson
  
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  Select activity Example: Prove Equivalence Relation
  
  
  
  Example: Prove Equivalence Relation Lesson
  
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  Select activity Example 1
  
  
  
  Example 1 Lesson
  
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  Select activity Example 2
  
  
  
  Example 2 Lesson
  
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  Select activity Example 3
  
  
  
  Example 3 Lesson
  
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  Select activity Example 4
  
  
  
  Example 4 Lesson
  
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  Types of Functions
  
  Select activity Surjective (onto) and Injective (one-to-one) Functions
  
  Surjective (onto) and Injective (one-to-one) Functions Lesson
  
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  Select activity Functions Part 1
  
  Functions Part 1 Lesson
  
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  Example: Find Domain and Range
  
  Select activity Example: Find Domain and Range
  
  Example: Find Domain and Range Lesson
  
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  Composition of Functions and Invertible Function
  
  Select activity Functions Part 2
  
  
  
  Functions Part 2 Lesson
  
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  Select activity Evaluating Composite Functions
  
  
  
  Evaluating Composite Functions Lesson
  
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  Select activity Finding Composite Functions
  
  
  
  Finding Composite Functions Lesson
  
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  Select activity Determining if a Function is Invertible
  
  
  
  Determining if a Function is Invertible Lesson
  
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Select section 2. Inverse Trigonometric Functions

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2. Inverse Trigonometric Functions
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  Basic Concepts
  
  Select activity Domain and Range of Inverse Functions
  
  
  
  Domain and Range of Inverse Functions Lesson
  
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  Select activity Graph of Sine Inverse Function
  
  
  
  Graph of Sine Inverse Function Lesson
  
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  Select activity Inverse Trigonometric Functions Part 1
  
  
  
  Inverse Trigonometric Functions Part 1 Lesson
  
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  Select activity Inverse Trigonometric Functions Part 2
  
  
  
  Inverse Trigonometric Functions Part 2 Lesson
  
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  Select activity Using Trigonometric Identities on ITFs
  
  
  
  Using Trigonometric Identities on ITFs Lesson
  
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  Select activity Principal Value of Inverse Functions
  
  
  
  Principal Value of Inverse Functions Lesson
  
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  Select activity Example: Find Principle Value of Function
  
  
  
  Example: Find Principle Value of Function Lesson
  
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  Select activity Example: Evaluate Inverse Trigonometric Functions
  
  
  
  Example: Evaluate Inverse Trigonometric Functions Lesson
  
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  Properties of Inverse Trigonometric Functions
  
  Select activity Properties of Inverse Trigonometric Functions I
  
  
  
  Properties of Inverse Trigonometric Functions I Lesson
  
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  Select activity Properties of Inverse Trigonometric Functions II
  
  
  
  Properties of Inverse Trigonometric Functions II Lesson
  
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  Select activity Evaluating Expressions
  
  
  
  Evaluating Expressions Lesson
  
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  Select activity Evaluating Inverse
  
  
  
  Evaluating Inverse Lesson
  
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  Select activity Expressing Inverse in Simplest Form
  
  
  
  Expressing Inverse in Simplest Form Lesson
  
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  Select activity Evaluating Compound Inverse Trigonometric Functions
  
  
  
  Evaluating Compound Inverse Trigonometric Functions Lesson
  
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  Select activity Solving Equations Involving Inverse Trigonometric Functions
  
  
  
  Solving Equations Involving Inverse Trigonometric Functions Lesson
  
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  Select activity Proving Identities involving Inverse Trigonometric Functions
  
  
  
  Proving Identities involving Inverse Trigonometric Functions Lesson
  
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  Select activity Example: Solve Inverse Trigonometric Function
  
  
  
  Example: Solve Inverse Trigonometric Function Lesson
  
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Select section 3. Matrices

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3. Matrices
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  Matrix
  
  Select activity Introduction to the Matrix
  
  
  
  Introduction to the Matrix Lesson
  
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  Select activity Finding Possible Orders and Matrices
  
  
  
  Finding Possible Orders and Matrices Lesson
  
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  Select activity Constructing a Matrix from its Elements
  
  
  
  Constructing a Matrix from its Elements Lesson
  
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  Types of Matrices
  
  Select activity Key Concepts: Order and Types of Matrices
  
  
  
  Key Concepts: Order and Types of Matrices Lesson
  
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  Select activity Types of Matrices
  
  
  
  Types of Matrices Lesson
  
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  Select activity Understanding Row and Column Matrix with Examples
  
  
  
  Understanding Row and Column Matrix with Examples Lesson
  
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  Select activity Introduction to the Identity Matrix
  
  
  
  Introduction to the Identity Matrix Lesson
  
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  Select activity Equality of Matrices
  
  
  
  Equality of Matrices Lesson
  
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  Operations on Matrices
  
  Select activity Properties of Matrix Addition
  
  
  
  Properties of Matrix Addition Lesson
  
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  Select activity Solving for Elements using Addition Properties
  
  
  
  Solving for Elements using Addition Properties Lesson
  
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  Select activity Solving for Matrices using Addition Properties
  
  
  
  Solving for Matrices using Addition Properties Lesson
  
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  Select activity Example: Adding & Subtracting Matrices
  
  
  
  Example: Adding & Subtracting Matrices Lesson
  
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  Select activity Introduction to Matrix Multiplication
  
  
  
  Introduction to Matrix Multiplication Lesson
  
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  Select activity Is a Matrix Multiplication Commutative?
  
  
  
  Is a Matrix Multiplication Commutative? Lesson
  
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  Select activity Associative Property of a Matrix Multiplication
  
  
  
  Associative Property of a Matrix Multiplication Lesson
  
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  Select activity Distributive Property of a Matrix Multiplication
  
  
  
  Distributive Property of a Matrix Multiplication Lesson
  
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  Select activity Properties of Scalar Multiplication
  
  
  
  Properties of Scalar Multiplication Lesson
  
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  Select activity Multiplying Matrices by Scalars
  
  
  
  Multiplying Matrices by Scalars Lesson
  
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  Select activity Evaluating Expressions using a Matrix Multiplication
  
  
  
  Evaluating Expressions using a Matrix Multiplication Lesson
  
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  Select activity Applying Trigonometric Identities to Evaluate Matrices
  
  
  
  Applying Trigonometric Identities to Evaluate Matrices Lesson
  
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  Select activity Solving for Matrix given Product
  
  
  
  Solving for Matrix given Product Lesson
  
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  Select activity Conceptual Problems on Multiplication of Matrices
  
  
  
  Conceptual Problems on Multiplication of Matrices Lesson
  
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  Transpose of a Matrix
  
  Select activity Transpose of a Matrix
  
  
  
  Transpose of a Matrix Lesson
  
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  Select activity Properties of Transpose of the Matrices
  
  
  
  Properties of Transpose of the Matrices Lesson
  
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  Select activity Transpose of a Matrix Product
  
  
  
  Transpose of a Matrix Product Lesson
  
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  Select activity Example: Verify Property of Transpose
  
  
  
  Example: Verify Property of Transpose Lesson
  
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  Symmetric and Skew Symmetric Matrices
  
  Select activity Symmetric and Skew Symmetric Matrices
  
  Symmetric and Skew Symmetric Matrices Lesson
  
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  Select activity Expressing as a Sum of Symmetric and Skew Symmetric Matrix
  
  Expressing as a Sum of Symmetric and Skew Symmetric Matrix Lesson
  
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  Invertible Matrices
  
  Select activity Introduction to the Matrix Inverses
  
  
  
  Introduction to the Matrix Inverses Lesson
  
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  Select activity Determining Invertible Matrices
  
  
  
  Determining Invertible Matrices Lesson
  
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  Select activity Matrix Inverse using Equations
  
  
  
  Matrix Inverse using Equations Lesson
  
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  Select activity Transposes of Sums and Inverses
  
  
  
  Transposes of Sums and Inverses Lesson
  
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  Select activity Example: Finding Inverse of a Matrix (Elementary Transformation)
  
  
  
  Example: Finding Inverse of a Matrix (Elementary Transformation) Lesson
  
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Select section 4. Determinants

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4. Determinants
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  Determinant
  
  Select activity Determinant Part 1
  
  
  
  Determinant Part 1 Lesson
  
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  Select activity Finding the Determinant of a 2x2 Matrix
  
  
  
  Finding the Determinant of a 2x2 Matrix Lesson
  
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  Select activity Finding the Determinant of a 3x3 Matrix Method 1
  
  
  
  Finding the Determinant of a 3x3 Matrix Method 1 Lesson
  
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  Select activity Finding the Determinant of a 3x3 Matrix Method 2
  
  
  
  Finding the Determinant of a 3x3 Matrix Method 2 Lesson
  
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  Select activity Evaluating Determinants involving Trigonometric Functions
  
  
  
  Evaluating Determinants involving Trigonometric Functions Lesson
  
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  Area of a Triangle
  
  Select activity Finding Area of a Triangle using Determinants
  
  Finding Area of a Triangle using Determinants Lesson
  
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  Select activity Finding Equation of a Line using Determinants
  
  Finding Equation of a Line using Determinants Lesson
  
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  Minors and Cofactors
  
  Select activity Minors and Cofactors
  
  Minors and Cofactors Lesson
  
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  Select activity Finding Determinants using Cofactors
  
  Finding Determinants using Cofactors Lesson
  
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  Adjoint and Inverse of a Matrix
  
  Select activity Adjoint of a Matrix
  
  Adjoint of a Matrix Lesson
  
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  Select activity Intuition behind Product with Adjoint
  
  Intuition behind Product with Adjoint Lesson
  
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  Applications of Determinants and Matrices
  
  Select activity Example: Solve System of Equations using the Matrix Method
  
  
  
  Example: Solve System of Equations using the Matrix Method Lesson
  
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  Select activity Solving System of 3 Equations using Determinants
  
  
  
  Solving System of 3 Equations using Determinants Lesson
  
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  Select activity Word Problems using Matrices and Determinants
  
  
  
  Word Problems using Matrices and Determinants Lesson
  
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Select section 5. Continuity and Differentiability

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5. Continuity and Differentiability
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  Continuity
  
  Select activity Continuity Introduction
  
  
  
  Continuity Introduction Lesson
  
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  Select activity Continuity of Greatest Integer Function
  
  
  
  Continuity of Greatest Integer Function Lesson
  
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  Select activity Continuity of Polynomial f(x)
  
  
  
  Continuity of Polynomial f(x) Lesson
  
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  Select activity Continuity Over an Interval
  
  
  
  Continuity Over an Interval Lesson
  
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  Select activity Algebra of Continuous Functions
  
  
  
  Algebra of Continuous Functions Lesson
  
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  Select activity Continuity of Rational Functions
  
  
  
  Continuity of Rational Functions Lesson
  
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  Select activity Continuity of Trigonometric Functions
  
  
  
  Continuity of Trigonometric Functions Lesson
  
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  Select activity Making a Piecewise Defined Function Continuous
  
  
  
  Making a Piecewise Defined Function Continuous Lesson
  
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  Select activity Continuity of Composite Functions
  
  
  
  Continuity of Composite Functions Lesson
  
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  Select activity Continuity of Piecewise Defined Functions
  
  
  
  Continuity of Piecewise Defined Functions Lesson
  
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  Select activity Example: Points of Discontinuity
  
  
  
  Example: Points of Discontinuity Lesson
  
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  Differentiability
  
  Select activity Introduction
  
  
  
  Introduction Lesson
  
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  Select activity Derivatives using the First Principle
  
  
  
  Derivatives using the First Principle Lesson
  
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  Select activity Find the Derivation of the given Equation by the First Principle
  
  
  
  Find the Derivation of the given Equation by the First Principle Lesson
  
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  Select activity Derivatives of Trigonometric Functions
  
  
  
  Derivatives of Trigonometric Functions Lesson
  
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  Select activity Example 1
  
  
  
  Example 1 Lesson
  
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  Exponential and Logarithmic Functions
  
  Select activity Example: Chain Rule
  
  Example: Chain Rule Lesson
  
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  Logarithmic Differentiation
  
  Select activity Log Differentiation of Implicit Functions
  
  Log Differentiation of Implicit Functions Lesson
  
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  Derivatives of Functions in Parametric Forms
  
  Select activity Parametric Form
  
  
  
  Parametric Form Lesson
  
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  Select activity Applying Parametric Substitutions for Differentiation
  
  
  
  Applying Parametric Substitutions for Differentiation Lesson
  
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  Select activity Example: Parametric Function Derivative
  
  
  
  Example: Parametric Function Derivative Lesson
  
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  Second Order Derivative
  
  Select activity Second Order Derivatives of Composite Functions
  
  Second Order Derivatives of Composite Functions Lesson
  
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Select section 6. Applications of Derivatives

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6. Applications of Derivatives
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  Rate of Change of Quantities
  
  Select activity Application of Derivatives Part 1
  
  Application of Derivatives Part 1 Lesson
  
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  Select activity Example : Find the Rate of Change
  
  Example : Find the Rate of Change Lesson
  
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  Increasing and Decreasing Functions
  
  Select activity Application of Derivatives Part 2
  
  Application of Derivatives Part 2 Lesson
  
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  Select activity Example : Increasing & Decreasing Function
  
  Example : Increasing & Decreasing Function Lesson
  
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  Maxima and Minima
  
  Select activity Application of Derivatives Part 3
  
  
  
  Application of Derivatives Part 3 Lesson
  
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  Select activity Example 1 : Finding Maxima or Minima
  
  
  
  Example 1 : Finding Maxima or Minima Lesson
  
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  Select activity Application of Derivatives Part 4
  
  
  
  Application of Derivatives Part 4 Lesson
  
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Select section 7. Integrals

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7. Integrals
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  Integration as an Inverse Process of Differentiation
  
  Select activity Antiderivatives and Indefinite Integrals
  
  
  
  Antiderivatives and Indefinite Integrals Lesson
  
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  Select activity Indefinite Integrals of sin(x), cos(x), and eˣ
  
  
  
  Indefinite Integrals of sin(x), cos(x), and eˣ Lesson
  
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  Select activity Example: Finding Integral
  
  
  
  Example: Finding Integral Lesson
  
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  Select activity Indefinite Integral of 1/x
  
  
  
  Indefinite Integral of 1/x Lesson
  
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  Methods of Integration
  
  Select activity Integration by Substitution- Introduction I
  
  
  
  Integration by Substitution- Introduction I Lesson
  
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  Select activity Integration by Substitution- Introduction II
  
  
  
  Integration by Substitution- Introduction II Lesson
  
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  Select activity Example 1 : Integration by Substitution
  
  
  
  Example 1 : Integration by Substitution Lesson
  
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  Select activity Example 2 : Integration by Substitution
  
  
  
  Example 2 : Integration by Substitution Lesson
  
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  Select activity Example 3 : Integration by Substitution
  
  
  
  Example 3 : Integration by Substitution Lesson
  
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  Select activity Example 4 : Integration by Substitution
  
  
  
  Example 4 : Integration by Substitution Lesson
  
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  Select activity Example 5 : Integration by Substitution
  
  
  
  Example 5 : Integration by Substitution Lesson
  
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  Integrals of Some Particular Functions
  
  Select activity Part 1
  
  Part 1 Lesson
  
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  Select activity Part 2
  
  Part 2 Lesson
  
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  Integration by Partial Fractions
  
  Select activity Example : Integration by Partial Fractions
  
  Example : Integration by Partial Fractions Lesson
  
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  Integration by Parts
  
  Select activity Introduction
  
  
  
  Introduction Lesson
  
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  Select activity Part 1
  
  
  
  Part 1 Lesson
  
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  Select activity Part 2
  
  
  
  Part 2 Lesson
  
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  Select activity Part 3
  
  
  
  Part 3 Lesson
  
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  Select activity Example 1 : Integration by Parts
  
  
  
  Example 1 : Integration by Parts Lesson
  
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  Select activity Example 2 : Integration by Parts
  
  
  
  Example 2 : Integration by Parts Lesson
  
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  Select activity Example 3 : Integration by Parts
  
  
  
  Example 3 : Integration by Parts Lesson
  
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  Select activity Example 4 : Integration by Parts
  
  
  
  Example 4 : Integration by Parts Lesson
  
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  Fundamental Theorem of Calculus
  
  Select activity Introduction
  
  
  
  Introduction Lesson
  
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  Select activity Fundamental Theorem of Calculus (Part 1)
  
  
  
  Fundamental Theorem of Calculus (Part 1) Lesson
  
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  Select activity Fundamental Theorem of Calculus (Part 2)
  
  
  
  Fundamental Theorem of Calculus (Part 2) Lesson
  
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  Select activity Intuition for Second Part of Fundamental Theorem of Calculus
  
  
  
  Intuition for Second Part of Fundamental Theorem of Calculus Lesson
  
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  Select activity Worked Example: Finding Derivative with Fundamental Theorem of Calculus
  
  
  
  Worked Example: Finding Derivative with Fundamental Theorem of Calculus Lesson
  
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  Select activity Finding Derivative with Fundamental Theorem of Calculus: x is on Lower Bound
  
  
  
  Finding Derivative with Fundamental Theorem of Calculus: x is on Lower Bound Lesson
  
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  Select activity Finding Derivative with Fundamental Theorem of Calculus: x is on Both Bounds
  
  
  
  Finding Derivative with Fundamental Theorem of Calculus: x is on Both Bounds Lesson
  
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  Evaluation of Definite Integrals by Substitution
  
  Select activity Substitution: Definite Integrals
  
  Substitution: Definite Integrals Lesson
  
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  Select activity Substitution: Definite Integral of Exponential Function
  
  Substitution: Definite Integral of Exponential Function Lesson
  
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  Some Properties of Definite Integrals
  
  Select activity Part 1
  
  
  
  Part 1 Lesson
  
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  Select activity Part 2
  
  
  
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8. Applications of Integrals
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  Area under Simple Curves
  
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9. Differential Equations
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  General and Particular Solutions of a Differential Equation
  
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  Methods of Solving First Order, First Degree Differential Equations
  
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10. Vector Algebra
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  Product of Two Vectors
  
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  Learn More…
  
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11. Three Dimensional Geometry
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  Shortest Distance between Two Lines
  
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12. Linear Programming
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  Linear Programming Problem and its Mathematical Formulation
  
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13. Probability
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  Probability
  
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  Solved Examples
  
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