NCERT Mathematics - II Textbook for Class XII
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Preface The National Council of Educational Research and Training NCERT had constituted 21 Focus Groups on Teaching of various subjects related to School Education, to review the National Curriculum Framework for School Education - 2000 NCFSE - 2000 in face of new emerging challenges and transformations occurring in the fields of content and pedagogy under the contexts of National and International spectrum of school education. These Focus Groups made general and specific comments in their respective areas. Consequently, based on these reports of Focus Groups, National Curriculum Framework NCF -2005 was developed. NCERT designed the new syllabi and constituted Textbook Development Teams for Classes XI and XII to prepare textbooks in Mathematics under the new guidelines and new syllabi. The textbook for Class XI is already in use, which was brought in 2005. 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 organised by the NCERT at Delhi. The teachers made useful comments and suggestions which were incorporated in the draft textbook. The draft textbook was finalised 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. In the fitness of things, let us cite some of the essential features dominating the textbook. These characteristics have reflections in almost all the chapters. The existing textbook contains thirteen main chapters and two appendices. Each chapter contains the followings Introduction Highlighting the importance of the topic connection with earlier studied topics brief mention about the new concepts to be discussed in the chapter. Organisation of chapter into sections comprising one or more concepts subconcepts. Motivating and introducing the concepts subconcepts. Illustrations have been provided wherever possible.
Proofs problem solving involving deductive or inductive reasoning, multiplicity of approaches wherever possible have been inducted. Geometric viewing visualisation of concepts have been emphasized whenever needed. Applications of mathematical concepts have also been integrated with allied subjects like Science and Social Sciences. Adequate and variety of examples exercises have been given in each section. For refocusing and strengthening the understanding and skill of problem solving and applicabilities, miscellaneous types of examples exercises have been provided involving two or more subconcepts at a time at the end of the chapter. The scope of challenging problems to talented minority have been reflected conducive to the recommendation as reflected in NCF-2005. For more motivational purpose, brief historical background of topics have been provided at the end of the chapter and at the beginning of each chapter, relevant