Mathematics 12 Part I

1.Relations and Functions
    1.1 Introduction
    1.2 Types of Relations
    1.3 Types of Functions
    1.4 Composition of Functions and Invertible Function
    1.5 Binary Operations

2.Inverse Trigonometric Functions
    2.1 Introduction
    2.2 Basic Concepts
    2.3 Properties of Inverse Trigonometric Functions

3.Matrices
    3.1 Introduction
    3.2 Matrix
    3.3 Types of Matrices
    3.4 Operations on Matrices
    3.5 Transpose of a Matrix
    3.6 Symmetric and Skew Symmetric Matrices
    3.7 Elementary Operation (Transformation) of a Matrix
    3.8 Invertible Matrices

4.Determinants
    4.1 Introduction
    4.2 Determinant
    4.3 Properties of Determinants
    4.4 Area of a Triangle
    4.5 Minors and Cofactors
    4.6 Adjoint and Inverse of a Matrix
    4.7 Applications of Determinants and Matrices

5.Continuity and Differentiability
    5.1 Introduction
    5.2 Continuity
    5.3 Differentiability
    5.4 Exponential and Logarithmic Functions
    5.5 Logarithmic Differentiation
    5.6 Derivatives of Functions in Parametric Forms
    5.7 Second Order Derivative
    5.8 Mean Value Theorem

6.Application of Derivatives
    6.1 Introduction
    6.2 Rate of Change of Quantities
    6.3 Increasing and Decreasing Functions
    6.4 Tangents and Normals
    6.5 Approximations
    6.6 Maxima and Minima

Appendix 1: Proofs in Mathematics
    A.1.1 Introduction
    A.1.2 What is a Proof?

Appendix 2: Mathematical Modelling
    A.2.1 Introduction
    A.2.2 Why Mathematical Modelling?
    A.2.3 Principles of Mathematical Modelling

Answers

Supplementary Material

7. Integrals
    7.1 Introduction
    7.2 Integration as an Inverse Process of Differentiation
    7.3 Methods of Integration
    7.4 Integrals of some Particular Functions
    7.5 Integration by Partial Fractions
    7.6 Integration by Parts
    7.7 Definite Integral
    7.8 Fundamental Theorem of Calculus
    7.9 Evaluation of Definite Integrals by Substitution
    7.10 Some Properties of Definite Integrals

8. Application of Integrals
    8.1 Introduction
    8.2 Area under Simple Curves
    8.3 Area between Two Curves

9. Differential Equations
    9.1 Introduction
    9.2 Basic Concepts
    9.3 General and Particular Solutions of a Differential Equation
    9.4 Formation of a Differential Equation whose General Solution is given
    9.5 Methods of Solving First order, First Degree Differential Equations

10. Vector Algebra
    10.1 Introduction
    10.2 Some Basic Concepts
    10.3 Types of Vectors
    10.4 Addition of Vectors
    10.5 Multiplication of a Vector by a Scalar
    10.6 Product of Two Vectors

11. Three Dimensional Geometry
    11.1 Introduction
    11.2 Direction Cosines and Direction Ratios of a Line
    11.3 Equation of a Line in Space
    11.4 Angle between Two Lines
    11.5 Shortest Distance between Two Lines
    11.6 Plane
    11.7 Coplanarity of Two Lines
    11.8 Angle between Two Planes
    11.9 Distance of a Point from a Plane
    11.10 Angle between a Line and a Plane

12. Linear Programming
    12.1 Introduction
    12.2 Linear Programming Problem and its Mathematical Formulation
    12.3 Different Types of Linear Programming Problems

13. Probability
    13.1 Introduction
    13.2 Conditional Probability
    13.3 Multiplication Theorem on Probability
    13.4 Independent Events
    13.5 Bayes' Theorem
    13.6 Random Variables and its Probability Distributions
    13.7 Bernoulli Trials and Binomial Distribution

Answers

Supplementary Material