Mathematics: Textbook for Class XII

✍ Scribed by NCERT

• Publisher: NCERT
• Year: 2021
• Tongue: English
• Leaves: 649
• Category: Library

✦ Synopsis

Mathematics for Class XII from NCERT.

This Book contains both Part-I and Part-II

✦ Table of Contents

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

1. 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

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

3. 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

4. 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

5. 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

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

7. 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