NCERT Exemplar Problems Math Textbook for Class IX

NCERT Exemplar Problems Math Textbook for Class IX

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PREFACE The Department of Education in Science and Mathematics DESM , National Council of Educational Research and Training NCERT , initiated the development of Exemplar Problems in science and mathematics for secondary and higher secondary stages after completing the preparation of textbooks based on National Curriculum Framework 2005. The main objective of the book on Exemplar Problems in Mathematics is to provide the teachers and students a large number of quality problems with varying cognitive levels to facilitate teaching learning of concepts in mathematics that are presented through the textbook for Class IX. It is envisaged that the problems included in this volume would help the teachers to design tasks to assess effectiveness of their teaching and to know about the achievement of their students besides facilitating preparation of balanced question papers for unit and terminal tests. The feedback based on the analysis of students responses may help the teachers in further improving the quality of classroom instructions. In addition, the problems given in this book are also expected to help the teachers to perceive the basic characteristics of good quality questions and motivate them to frame similar questions on their own. Students can benefit themselves by attempting the exercises given in the book for self assessment and also in mastering the basic techniques of problem solving. Some of the questions given in the book are expected to challenge the understanding of the concepts of mathematics of the students and their ability to applying them in novel situations. The problems included in this book were prepared through a series of workshops organised by the DESM for their development and refinement involving practicing teachers, subject experts from universities and institutes of higher learning, and the members of the mathematics group of the DESM whose names appear separately. We gratefully acknowledge their efforts and thank them for their valuable contribution in our endeavour to provide good quality instructional material for the school system. I express my gratitude to Professor Krishna Kumar, Director and Professor G.Ravindra, Joint Director, NCERT for their valuable motivation and guidiance from time to time. Special thanks are also due to Dr. R.P.Maurya, Reader in Mathematics, DESM for coordinating the programme, taking pains in editing and refinement of problems and for making the manuscript pressworthy. We look forward to feedback from students, teachers and parents for further improvement of the contents of this book. Hukum Singh Professor and Head
29052014
D EVELOPMENT TEAM EXEMPLAR PROBLEMS MATHEMATICS MEMBERS G. P. Dikshit, Professor Retd. , Lucknow University, Lucknow Hukum Singh, Professor and Head, DESM, NCERT, New Delhi J.C. Nijhawan, Principal Retd. , Directorate of Education, Delhi Jharna De, T.G.T., Dev Samaj Hr. Secondary School, Nehru Nagar Mahendra Shankar, Lecturer S.G. Retd. , DESM, NCERT, New Delhi P. Sinclair, Professor and Pro Vice Chancellor, IGNOU, New Delhi Ram Avtar, Professor Retd. , DESM, NCERT, New Delhi Sanjay Mudgal, Lecturer, DESM, NCERT, New Delhi Vandita Kalra, Lecturer, Sarvodaya Kanya Vidyalaya, Vikaspuri District Centre,