IX maths EM Covers - Telangana

1 SC. ER. T. TE. LA. NG. AN. A. CHILDREN! THESE DIINSTRUCTIONS FOR For each and every conceptual understanding, a real life context with appropriate illustrations are given in the textbook. Try to understand the concept through keen A. reading of context along with observation of illustration. While understanding the concepts through activities , some doubts may arise. Clarify those doubts by through discussion with your friends and teachers, AN. understand the mathematical concepts without any doubts. ''Do this/Do these" exercises are given to test yourself, how far the concept has been understood. If you are facing any difficulty in solving problems in these exercises, you can clarify them by discussing with your teacher. NG. The problems given in "Try this/try these", can be solved by reasoning, thinking creatively and extensively. When you face difficulty in solving these problems, you can take the help of your friends and teachers.

2 The activities or discussion points given "Think and disicuss" have been given for extensive understanding of the concept by thinking critically. These activities LA. should be solved by discussions with your fellow students and teachers. Different typs of problems with different concepts discussed in the chapter are given in an "Exercise" given at the end of the concept/chapter. Try to solve these problems by yourself at home or leisure time in school. TE. The purpose of "Do this"/do these", and "Try this/try these" exercises is to solve problems in the presence of teacher only in the class itself. Wherever the "project works" are given in the textbook, you should complete them in groups. But the reports of project works should be submitted individually. Try to solve the problems given as homework on the day itself. Clarify your T. doubts and make corrections also on the day itself by discussions with your teachers. ER. Try to collect more problems or make new problems on the concepts learnt and show them to your teachers and fellow students.

3 Try to collect more puzzles, games and interesting things related to mathematical concepts and share with your friends and teachers. SC. Do not confine mathematical conceptual understanding to only classroom. But, try to relate them with your suroundings outside the classroom. Student must solve problems, give reasons and make proofs, be able to communicate mathematically, connect concepts to understand more concepts &. solve problems and able to represent in mathematics learning. Whenever you face difficulty in achieving above competencies/skills/standards, you may take the help of your teachers. mathematics . A. CLASS - IX. AN. TEXTBOOK DEVELOPMENT & PUBLISHING COMMITTEE. Chief Production Officer : Sri. A. Satyanarayana Reddy, NG. Director, SCERT, Hyderabad. Executive Chief Organiser : Sudhakar, LADirector, Govt. Text Book Press, Hyderabad. Organising Incharge : Dr. Nannuru Upender Reddy, Prof. & Head, Curriculum & Text Book Department, SCERT, Hyderabad.

4 TE. Chairperson for Position Paper and mathematics Curriculum and Textbook Development Prof. , Department of mathematics and Statistics, Hyderabad Central University, Hyderabad Chief Advisors Sri Chukka Ramaiah Dr. Eminent Scholar in mathematics Educational Advisor, Vidya Bhawan Society T. Telangana , Hyderabad. Udaipur, Rajasthan ER. Published by SC. The Government of Telangana , Hyderabad Respect the Law Grow by Education Get the Rights Behave Humbly FREE DISTRIBUTION BY GOVERNMENT 2019-20. A. AN. Government of Telangana , Hyderabad. First Published 2013. New Impressions 2014, 2015, 2017,2018, 2019. NG. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means without the prior permission in LA. writing of the publisher, nor be otherwise circulated in any form of binding or cover other than that in which it is published and without a similar condition including this condition being imposed on the sub- sequent purchaser.

5 TE. The copy right holder of this book is the Director of School Education, Hyderabad, Telangana . This Book has been printed on 70 Maplitho Title Page 200 White Art Card T. ER. Free distribution by Telangana Government 2019-20. SC. Printed in India at Telangana Govt. Text Book Press, Mint Compound, Hyderabad, Telangana . o . (ii). FREE DISTRIBUTION BY GOVERNMENT 2019-20. Text Book Development Committee A. Writers Sri. Tata Venkata Rama Kumar Sri. Gottumukkala Raju AN. , ZPPHS, Mulumudi, Nellore Dt. SA, Mpl. High School, Kaspa, Vizianagaram. Sri. Soma Prasad Babu Sri. Sunder Reddy PGT. APTWRS, Chandrashekarapuram, Nellore SA, ZPHS,Thakkasila, Alampur Mandal Mahabubnagar Dt. Sri. Komanduri Murali Srinivas Sri. Abbaraju Kishore School of Excellence, Srisailam. SGT, MPUPS,Chamallamudi, Guntur Dt. NG. Sri. Padala Suresh Kumar Sri. G. Anantha Reddy SA,GHS, Vijayanagar Colony, Hyderabad. Retd. Headmaster, Ranga Reddy Dt. Sri. Ganapati Sharma Sri.

6 M. Ramanjaneyulu SA,GHS, Zamisthanpur, Manikeshwar Nagar, Hyd. Lecturer, Govt , Vikarabad, Dt. Sri. Duggaraju Venu Sri. M. Rama Chary SA,UPS, Allawada, Chevella Mandal, Dt. LA Lecturer,Govt , Vikarabad, Dt. Sri. P. Anthony Reddy Dr. A. Rambabu ,St. Peter's High School, , Nellore. Lecturer, Government CTE, Warangal Sri D. Manohar Dr. Poondla Ramesh TE. SA, ZPHS, Brahmanpally, Tadwai (Mandal) Nizamabad Dt. Lecturer, Government lASE, Nellore Editors Dr. S Suresh Babu Prof. Ramacharyulu (Retd.) Sri. K Brahmaiah Professor, Dept. of Statistics, National Institute of Technology, (Retd.). SCERT, Hyderabad Warangal. Prof., SCERT, Hyderabad Prof. V. Shiva Ramaprasad Sri A. Padmanabham Dr. Murthy (Retd.). (Retd.) (Retd.) Reader in mathematics T. Dept. of mathematics , of mathematics Rajah College, Bobbili Osmania University, Hyderabad Maharani College, Paddapuram Co-ordinators ER. Sri Kakulavaram Rajender Reddy Sri Rayalu Resource Person, SCERT, Hyderabad Lecturer, IASE, Masab Tank, Hyderabad Academic Support Group Members Sri Inder Mohan Sri Yashwanth Kumar Dave Sri Hanif Paliwal Sri Asish Chordia Vidyabhawan Society Resource Centre, Udaipur SC.

7 Sri Sharan Gopal Kum M. Archana Sri P. Chiranjeevi Department of mathematics and Statistics, University of Hyderabad Illustrations and Design Team Sri Prasanth Soni Sri Sk. Shakeer Ahmad Sri S. M. Ikram Vidyabhawan Society Resource Centre, Udaipur Cover Page Designing Sri. K. Sudhakara Chary, HM, UPS Neelikurthy, , Dist. Warangal (iii). FREE DISTRIBUTION BY GOVERNMENT 2019-20. Foreword A. Education is a process of human enlightenment and empowerment. Recognizing the enormous potential of education, all progressive societies have committed themselves to the AN. Universalization of Elementary Education with an explicit aim of providing quality education to all. As the next step, universalization of Secondary Education has gained momentum. The secondary stage marks the beginning of the transition from functional mathematics studied upto the upper primary stage to the study of mathematics as a discipline. The logical proofs of propositions, theorems etc.

8 Are introduced at this stage. Apart from being a specific NG. subject, it is to be treated as a concommitant to any subject involving analysis as reasoning. I am confident that the children in our state of Telangana learn to enjoy mathematics , make mathematics a part of their life experience, pose and solve meaningful problems, understand the basic structure of mathematics by reading this text book. For teachers, to understand and absorb critical issues on curricular and pedagogic LA. perspectives duly focusing on learning in place of marks, is the need of the hour. Also coping with a mixed class room environment is essentially required for effective transaction of curriculum in teaching learning process. Nurturing class room culture to inculcate positive interest among children with difference in opinions and presumptions of life style, to infuse life into knowledge is a thrust in the teaching job. TE. The afore said vision of mathematics teaching presented in State Curriculum Frame work (SCF -2011) has been elaborated in its mathematics position paper which also clearly lays down the academic standards of mathematics teaching in the state.

9 The text books make an attempt to concretize all the sentiments. The State Council for Education Research and Training Telangana appreciates the hard T. work of the text book development committee and several teachers from all over the state who have contributed to the development of this text book. I am thankful to the District ER. Educational Officers, Mandal Educational Officers and head teachers for making this possible. I also thank the institutions and organizations which have given their time in the development of this text book. I am grateful to the office of the Commissioner and Director of School Education ( ) and Vidya Bhawan Society, Udaipur, Rajastan for extending co-operation in developing this text book. In the endeavor to continuously improve the quality of our work, we welcome your comments and suggestions in this regard. SC. Place : Hyderabad Director Date : 03 December 2012 SCERT, Hyderabad (iv) FREE DISTRIBUTION BY GOVERNMENT 2019-20.

10 Preface A. The Government of Telangana has decided to revise the curriculum of all the subjects based on State Curriculum Frame work (SCF - 2011) which recommends that children's life at schools must be linked to their life outside the school. Right to Education (RTE - 2009). AN. perceives that every child who enters the school should acquire the necessary skills prescribed at each level upto the age of 14 years. The introduction of syllabus based on National Curriculum Frame Work - 2005 is every much necessary especially in mathematics and Sciences at secondary level with a national perspective to prepare our students with a strong base of mathematics and Science. NG. The strength of a nation lies in its commitment and capacity to prepare its people to meet the needs, aspirations and requirements of a progressive technological society. The syllabus in mathematics for three stages primary, upper primary and secondary is based on structural and spiral approaches.