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# Mathematics - Textbook for Class XII (Part I & II)

by Shveta Uppal### Price

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#### Product ID:24907

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Author: Shveta Uppal

Foreword/Introduction: Director,National Council of Educational Research

Publisher: NCERT

Year: 2007

Language: English

Pages: 612

ISBN/UPC (if available): 8174506292 8174506535

** Description**

From Foreword:

The first draft of the present book (Class XII) was prepared by the team consisting of NCERT faculty, experts and practicing teachers. The draft was refined by the development team in different meetings. This draft of the book was exposed to a group of practicing teachers teaching mathematics at higher secondary stage in different parts of the country, in a review workshop organized by the NCERT at Delhi. The teachers made useful comments and suggestions which were incorporated in the draft textbook. The draft textbook was finalized by an editorial board constituted out of the development team. Finally, the Advisory Group in Science and Mathematics and the Monitoring Committee constituted by the HRD Ministry, Government of India have approved the draft of the textbook.

From Foreword:

The National Curriculum Framework, 2005, recommends that children’s life at school must be linked to their life outside the school. This principle marks a departure from the legacy of bookish learning which continues to shape our system and causes a gap between the school, home and community. The syllabi and textbooks developed on the basis of NCF signify an attempt to implement this basic idea. They also attempt to discourage rote learning and the maintenance of sharp boundaries between different subject areas. We hope these measures will take us significantly further in the direction of a child-centered system of education outlined in the National Policy on Education (1986).

The success of this effort depends on the steps that school principals and teachers will take to encourage children to reflect on their own learning and to pursue imaginative activities and questions. We must recognize that, given space, time and freedom, children generate new knowledge by engaging with the information passes on to them by adults. Treating the prescribed textbook as the sole basis of examination is one of the key reasons why other resources and sites of learning are ignored. Inculcating creativity and initiative is possible if we perceive and treat children as participants in learning, not as receivers of a fixed body of knowledge.

These aims imply considerable change in school routines and mode functioning. Flexibility in the daily time-table is as necessary as rigor in implementing the annual calendar so that the required number of teaching days is actually devoted to teaching. The methods used for teaching and evaluation will also determine how effective this textbook proves for making children’s life at school a happy experience, rather than a source of stress or boredom. Syllabus designers have tried to address the problem of curricular burden by restructuring and reorienting knowledge at different stages with greater consideration for child psychology and the time available for teaching. The textbook attempts to enhance this endeavor by giving higher priority and space to opportunities for contemplation and wondering, discussion in small groups, and activities requiring hands-on experience.

Contents

PART - I

Foreword

Preface

RELATIONS AND FUNCTIONS

Introduction

Types of Relations

Types of Functions

Composition of Functions and Invertible Function

Binary Operations

INVERSE TRIGONOMETRIC FUNCTIONS

Introduction

Basic Concepts

Properties of Inverse Trigonometric Functions

MATRICES

Introduction

Matrix

Types of Matrices

Operations on Matrices

Transpose of a Matrix

Symmetric and Skew Symmetric Matrices

Elementary operation (Transformation) of a Matrix

Invertible Matrices

DETERMINANTA

Introduction

Determinant

Properties of Determinants

Area of a Triangle

Minors and cofactors

Adjoint and Inverse of a Matrix

Applications of Determinants and Matrices

DETERMINANTS

Introduction

Determinant

Properties of Determinants

Area of a Triangle

Minors and Cofactors

Adjoint and Inverse of a Matrix

Applications of Determinants and Matrices

CONTINUITY AND DIFFERENTIABILITY

Introduction

Continuity

Differentiability

Exponential and Logarithmic Functions

Logarithmic Differentiation

Derivatives of Functions in Parametric Forms

Second order Derivative

Mean Value Theorem

APPLICATION OF DERIVATIVES

Introduction

Rate of Change of Quantities

Increasing and Decreasing Functions

Tangents and Normals

Approximations

Maxima and Minima

APPENDIX I: PROOFS IN MATHEMATICS

Introduction

What is a Proof?

APPENDIX 2: MATHEMATICAL MODELLING

Introduction

Why Mathematical Modelling?

Principles of Mathematical Modelling

ANSWERS

PART-II

Foreword

Preface

INTEGRALS

Introduction

Integration as an Inverse Process of Differentiation

Methods of Integration

Integrals of Some Particular Functions

Integration by Partial Fractions

Integration by Parts

Definite Integral

Fundamental Theorem of Calculus

Evaluation of Definite Integrals by Substitution

Some properties of Definite Integrals

APPLICATION OF INTEGRALS

Introduction

Area under Simple Curves

Area between two Curves

DIFFERENTIAL EQUATIONS

Introduction

Area under Simple Curves

Area between Two Curves

DIFFERENTIAL EQUATIONS

Introduction

Basic Concepts

General and Particular Solutions of a Differential Equation

Formation of a Differential Equation whose General Solution is given

Methods of Solving First order, First Degree Differential Equations

VECTOR ALGEBRA

Introduction

Some Basic Concepts

Types of Vectors

Addition of Vectors

Multiplication of a Vector by a Scalar

Product of Two Vectors

THREE DIMENSIONAL GEOMETRY

Introduction

Direction Cosines and Direction Ratios of a Line

Equation of a Line in Space

Angle between two Lines

Shortest Distance between Two Lines

Plane

Coplanarity of Two Lines

Angle between Two Planes

Distance of a Point from a Plane

Angle between a Line and a Plane

LINEAR PROGRAMMING

Introduction

Linear programming Problem and its Mathematical Formulation

Different Types of Linear Programming Problems

PROBABILITY

Introduction

Conditional Probability

Multiplication Theorem on Probability

Independent Events

Bayes’ Theorem

Random Variables and its Probability Distributions

Bernoulli Trials and Binomial Distribution

ANSWERS