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