CONTENTS - 2

This page gives the contents of class 12. For contents of class 11, click here.

1. Chapter 17 - Relations and Functions
• Empty relation
• Universal relation
• Equivalence relation 

Chapter 17.1
• Equivalence classes
• Solved examples

Chapter 17.2
• Types of functions
• Condition for a function to be one-one or onto

Chapter 17.3
• Solved examples demonstrating the conditions for a function to be one-one or onto

Chapter 17.4
• Composition of functions
• Explanation based on graphs
• Explanation based on set theory

Chapter 17.5
• Properties of Composite functions
Chapter 17.6
• Invertible function
• Method for finding the Inverse
Chapter 17.7
• Composite of composite function
Chapter 17.8
• Properties of invertible functions
Chapter 17.9
• Binary operations
Chapter 17.10
• Commutative property
• Associative property
Chapter 17.11
• Identity element
• Inverse element
Chapter 17.12
• Miscellaneous examples
Chapter 17.13
• More Miscellaneous examples

18. Chapter 18 - Inverse Trigonometric Functions
• sine function is one-one and onto in restricted domains
• Details about inverse sine function
• Graph of inverse sine function is the mirror image of sine function, the mirror line being the graph of y = x.
Chapter 18.1
• cosine function is one-one and onto in restricted domains
• Details about inverse cosine function
Chapter 18.2
• cosec function is one-one and onto in restricted domains
• Details about inverse cosec function
Chapter 18.3
• sec function is one-one and onto in restricted domains
• Details about inverse sec function
Chapter 18.4
• tan function is one-one and onto in restricted domains
• Details about inverse tan function
Chapter 18.5
• cot function is one-one and onto in restricted domains
• Details about inverse cot function
Chapter 18.6
• Table showing principal values of inverse trigonometric functions
• Solved examples
Chapter 18.7
• First property of inverse trigonometric functions
Chapter 18.8
• Second and third properties of inverse trigonometric functions
Chapter 18.9
• Fourth and fifth properties of inverse trigonometric functions
Chapter 18.10
• Sixth property of inverse trigonometric functions
• Solved examples
Chapter 18.11
• More solved examples related to the properties of inverse trigonometric functions
Chapter 18.12
• Miscellaneous examples

19. Chapter 19 - Matrices
• Rows and columns in a matrix.
• Order of a matrix.
• General form of matrix.
Chapter 19.1
• Types of matrices
Chapter 19.2
• Equality of matrices 
Chapter 19.3
• Addition of matrices 
Chapter 19.4
• Negative of a matrix
• Difference of two matrices
• Multiplication of a matrix by a scalar
Chapter 19.5
• Solved examples related to Multiplication of a matrix by a scalar
Chapter 19.6
• Multiplication of matrices
Chapter 19.7
• Non-commutativity of Multiplication of matrices
Chapter 19.8
• Properties of Multiplication of matrices
• Associative law
• Distributive law
Chapter 19.9
• Existence of multiplicative identity
Chapter 19.10
• Transpose of a Matrix
• Properties of Transpose of a Matrix
Chapter 19.11
• Symmetric Matrix
• Skew Symmetric Matrix
Chapter 19.12
• Second theorem
Chapter 19.13
• Elementary operations
• Invertible Matrices
Chapter 19.14
• Theorems related to Invertible Matrices
• Finding the inverse by applying elementary operations
Chapter 19.15
• Solved examples
Chapter 19.16
• Miscellaneous examples

20. Chapter 20 - Determinants
• Determinant of order 2.
• Determinant of order 3.
• Expansion along R₁.
Chapter 20.1
• Expansion along R₂.
• Expansion along C₃.
• Six possible Expansions.
Chapter 20.2
• Solved examples.
Chapter 20.3
• Property I.
Chapter 20.4
• Property II.
Chapter 20.5
• Property III.
Chapter 20.6
• Property IV.
Chapter 20.7
• Property V.
Chapter 20.8
• Property VI.
Chapter 20.9
• Solved examples.
Chapter 20.10
• Area of a triangle.
Chapter 20.11
• Minors and Cofactors.
Chapter 20.12
• Adjoint matrix. 
• Method for finding inverse matrix using adjoint matrix. 
Chapter 20.13
• Solved examples.
Chapter 20.14
• Applications of determinants and matrices.
• Solving a system of linear equation by matrix inversion method.
Chapter 20.15
• Solved examples on matrix method.
Chapter 20.16
• Miscellaneous examples.

21. Chapter 21 - Continuity and Differentiability
• Conditions for checking continuity at any given point.
Chapter 21.1
• Continuous functions.
• Concept of infinity.
Chapter 21.2
• Method of checking continuous functions.
Chapter 21.3
• Algebra of continuous functions.
• Continuity of polynomial functions.
Chapter 21.4
• Solved examples on algebra of continuous functions.
Chapter 21.5
• Differentiability.
Chapter 21.6
• Derivatives of composite functions.
• Chain rule.
Chapter 21.7
• Chain rule (Easy method).
Chapter 21.8
• Derivatives of Implicit functions.
Chapter 21.9
• Derivatives of Implicit functions (easy method).
• Solved examples.
Chapter 21.10
• Derivatives of Inverse trigonometric functions.
• Solved examples.
Chapter 21.11
• Exponential functions.
Chapter 21.12
• Logarithmic functions.
Chapter 21.13
• Properties of Logarithm.
Chapter 21.14
• Solution of exponential and logarithmic equations.
Chapter 21.15
• Derivatives of exponential and logarithmic functions.
Chapter 21.16
• Method of logarithmic differentiation.
Chapter 21.17
• Parametric functions.
• Derivatives of Parametric functions.
Chapter 21.18
• Solved examples related to derivatives of Parametric functions.
Chapter 21.19
• Second order derivatives.
Chapter 21.20
• Rolle's Theorem.
• Mean Values Theorem.
Chapter 21.21
• Miscellaneous examples.
Chapter 21.22
• More Miscellaneous examples.

22. Chapter 22 - Applications of Derivatives
• Derivative to find rate of change.
Chapter 22.1
• Increasing and Decreasing functions.
Chapter 22.2
• First derivative test for Increasing and Decreasing functions.
Chapter 22.3
• Solved examples demonstrating the first derivative test.
Chapter 22.4
• Tangents and Normals.
Chapter 22.5
• Solved Examples on Tangents and Normals.
Chapter 22.6
• Linear approximation.
Chapter 22.7
• Solved examples on Linear approximation.
Chapter 22.8
• Differentials.
Chapter 22.9
• Solved examples on Differentials.
Chapter 22.10
• Calculating the amount of error.
Chapter 22.11
• Calculating the change in quantity.
Chapter 22.12
• Maxima and Minima.
• Absolute Maximum and Minimum.
• Local Maxima and Minima.
• Critical points.
Chapter 22.13
• Solved examples on Critical points.
Chapter 22.14
• Analytical method for finding Absolute Maximum and Minimum.
Chapter 22.15
• First derivative test for finding local extrema.
Chapter 22.16
• Concavity test for finding shape of graph.
Chapter 22.17
• Second derivative test for finding local maxima and minima.
Chapter 22.18
• Solved examples on Second derivative test.
Chapter 22.19
• Miscellaneous examples - 1.