Xth Cover EM - Telangana

[Pages:406]SCERT TELANGANA

INSTRUCTIONS TO STUDENTS

F Pictures/figures are provided for many items/situations for better understanding of the concepts in the text book.You have to read them carefully in relation with the concepts.

F Clarify your doubts with the help of your teachers while you are doing the activites related to the concepts time to time.

F ''Do this"Problems are meant to test your progress immediately after learning a concept.So you have to do these problems on your own.Check these with your teacher.

F "Try these"items in every chapter are provided to sharpen your ideas and thoughts.some logic will be there behind these questions.You have to try all these questions with out fail.

F Do this and Try these problems are meant to solve in the class room under the guidance of your teacher.Do not leave them at all.

F The questions under "Think discuss and write" are given to test your analytical ability.You can answer these questions by discussing in groups.

F The exercises given at the end of some sub topics arerelated to the concepts learned to a particular level.You try to solve these problems on your own.Do not copy them from guides and from other sources.

F Some projects given in in the textbook are meant to be done with proper plan and guidance with the teacher.you can do this in a group.A report is to be submitted at the end of the project.

F Some blank spaces are provided in tables,try these exercises to facilitate you to answer quickely.You can fill it in the text book it self.

F Every student is required to finish the day's work on the same day it self.Donot post pone it.You may feel burden later.

F Try to collect some more information to create some similar problems based on the concepts you have learned.Ask your friends to solve your questions.

F Games,Puzzles provided in the textbooks shall encourage you to feel joy in doing maths.For recreation collect some more .

F You should always connect the concepts learned in the class with other subject areas and situations out side the class room.

F You have to develop abilities with regard to academic standards prescribed at the end of the text book based on the syllabus .The academic standards at the secondary level are based on a) Problem solving 2)Reasoning and Proof 3)Mathematical communication 4)Connections 5)Representation.

F You have to go through various reference books,Internet,Forums for finding different ways of solutions for a problem and for better understanding of the concepts.

F Optional exercises are provided to think critically to solve certain problems.These exercises will help you to face Talent tests conducted at national level on par with other students.

F The appendix chapter "Mathematical modelling" will help you to know modelling of mathematical concepts in the fields of business,Agriculture,Stock markets etc,You can see the connection of mathematics with different areas.

F Syllabus is also provided at the end of the textbook for your reference that how you are making your progress.You can also compare with others.

We wish you all the best

SCERT TELANGANA

SIGNS AND SYMBOLS OF SCHOOL MATHEMATICS

Sign/symbol

Read as

Mathematical meaning

?

plus or minus

not equal to

Add or Substract unequal

therefore

infinite

is similar to

logical flow of a statement not finite same in geometrical shape

is congruent to

same shape and same size

is identically equal to

equivalent statements

for all

universal quantifier

square root of

3

cube root of

cup of

cap of

phi

%

percent of

square root of a number cube root of a number union of sets intersection of sets

symbol for golden ratio per hundred

o

, ,

sin , cos , tan

degree

angle measure

delta / triangle belongs to

symmetric difference in sets/symbol of triangle an element belong to a particular set

equivilent to

one to one correspondence

alfa,beta,gamma

greek lettetrs to represent zeroes of polynomial

mu

universal set symbol

pi

circumference of a circle / diameter

sigma

sum of scores

sin theta,cos theta,tan theta trigonometric ratios

x

log a

x

(a, b)

|x|

P(x)

P(E)

`

| |

x bar log x to the base a

point (a, b) mod x P of x P of E Since rupee is parallel to

arithmetic mean logarthemic function

ordered pair (a, b) absolute value of a real number a polynomial function in x probability of an event reasoning at a stage symbol of Indian rupee parallel lines

{ }

PQ

a2

is perpendicular to flower bracket arc PQ

a square

making 90 degree with a line used to set notation arc of a circle

square of a number

angle

theta

symbol of angle measurement of an angle

SCERT TELANGANA

Mathematics

Class-X

Textbook Development & Publishing Committee

Chief Production Officer

: Sri. G. Gopal Reddy, Director, SCERT, Hyderabad.

Executive Chief Organiser : Sri. B. Sudhakar, Director, Govt. Text Book Press, Hyderabad.

Organising Incharge

: Dr. Nannuru Upender Reddy, Prof. & Head, Curriculum & Text Book Department, SCERT, Hyderabad.

CHAIRPERSON FOR POSITION PAPER AND MATHEMATICS CURRICULUM AND TEXTBOOK DEVELOPMENT

Prof. V.Kannan

Department of Mathematics and Statistics, HCU, Hyderabad

Sri Chukka Ramaiah

Eminent Scholar in Mathematics,

Telangana, Hyderabad.

CHIEF ADVISORS

Dr. H.K.Dewan

Educational Advisor, Vidya Bhavan Society Udaipur, Rajasthan

Published by:

The Government of Telangana, Hyderabad

Respect the Law Get the Rights

Grow by Education

(i)

Behave Humbly

SCERT TELANGANA

? Government of Telangana, Hyderabad.

First Published 2014 New Impressions 2015, 2016, 2017, 2018, 2019

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 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 subsequent purchaser. The copy right holder of this book is the Director of School Education, Hyderabad, Telangana.

This Book has been printed on 70 G.S.M. Maplitho Title Page 200 G.S.M. White Art Card

Free distribution by T.S. Government 2019-20

Printed in India at the Telangana Govt. Text Book Press,

Mint Compound, Hyderabad, Telangana. (ii)

Text Book Development Committee

SCERT TELANGANA

Sri Tata Venkata Rama Kumar

H.M., ZPHS, Mulumudi, SPS Nellore

WRITERS Sri Gottumukkala V.B.S.N. Raju

SA, Mpl. High School, Kaspa, Vizianagaram.

Sri Soma Prasada Babu

PGT. APTWRS, Chandrashekarapuram, SPS Nellore

Sri Padala Suresh Kumar

SA,GHS, Vijayanagar Colony, Hyderabad.

Sri G. Anantha Reddy

Retd. Headmaster, Ranga Reddy

Dr. Poondla Ramesh

Lecturer, Government lASE, SPS Nellore

Sri Komanduru Sreedharacharyulu

SA, ZPHS, Rangaipally, Medak

Sri Peddada D.L.Ganapati Sharma

SA,GHS, Zamisthanpur, Manikeshwar Nagar, Hyd.

Sri Sardar Dharmendra Singh

SA, ZPHS, Dannur (B), Adilabad

Sri Nagula Ravi

SA, ZPHS, Lokeshwaram, Adilabad

Sri Kandala Ramaiah

SA, ZPHS, Kasimdevpet, Warangal

Sri Kakulavaram Rajender Reddy

Co-ordinator, SCERT, T.S., Hyderabad.

Sri Ramadugu Lakshmi Narsimha Murthy

SA, ZPHS, Thupranpet, Nalgonda

CHIEF EDITOR

Dr. H.K.Dewan

Educational Advisor, Vidya Bhavan Society Udaipur, Rajasthan

Prof. V. Shiva Ramaprasad

Retd. Dept. of Mathematics, Osmania University, Hyderabad

EDITORS

Prof. N.Ch.Pattabhi Ramacharyulu

Retd., National Institute of Technology, Warangal

Sri A. Padmanabham (Rtd.)

Dr. G.S.N. Murthy (Rtd.)

Head of the Dept. of Mathematics

Reader in Mathematics

Maharanee College,

Rajah R.S.R.K.Ranga Rao College,

Peddapuram, East Godavari Dist.

Bobbili, Vizianagaram Dist. (A.P.)

C O - O R D I N AT O R S

Sri Kakulavaram Rajender Reddy

Sri K. Narayan Reddy

Co-ordinator, SCERT, Hyderabad.

Lecturer, SCERT, Hyderabad

ACADEMIC SUPPORT GROUP MEMBERS

Sri Hanif Paliwal

Ms. Preeti Mishra

Vidya Bhawan Education Resource Centre, Udaipur

Vidya Bhawan Education Resource Centre, Udaipur

Mrs. Snehbala Joshi

Vidya Bhawan Education Resource Centre, Udaipur

Ms. Tanya Saxena

Vidya Bhawan Education Resource Centre, Udaipur

Ms. M. Archana

Department of Mathematics and Statistics, University of Hyderabad

ILLUSTRATIONS AND DESIGN TEAM

Sri. Prashant Soni

Illustrator, Vidya Bhawan Education Resource Centre, Udaipur

Sri S. M. Ikram

Sri Bhawani Shanker

DTP Operator,

DTP Operator,

Vidya Bhawan Education Resource Centre, Udaipur

Vidya Bhawan Education Resource Centre, Udaipur

Sri Sunkara Koteswara Rao

Smt. Sunkara Sunitha

DTP Operator,

DTP Operator,

Pavan Graphics, Vignanpuricolony,Vidyanagar, Hyderabad. Pavan Graphics, Vignanpuricolony,Vidyanagar, Hyderabad.

Sri Kannaiah Dara, DPO,

SCERT, Telangana, Hyderabad.

COVER PAGE DESIGNING Sri. K. Sudhakara Chary, HM, UPS Neelikurthy, Mdl.Maripeda, Dist. Warangal

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SCERT TELANGANA

Foreword

Education is a process of human enlightenment and empowerment. Recognizing the enormous potential of education, all progressive societies have committed themselves to the Universalization of Elementary Education with a strong determination to provide quality education to all. As a part of its continuation, universalization of Secondary Education has gained momentum.

In the secondary stage, the beginning of the transition from functional mathematics studied upto the primary stage to the study of mathematics as a discipline takes place. The logical proofs of propositions, theorems etc. are introduced at this stage. Apart from being a specific subject, it is connected to other subjects involving analysis and through concomitant methods. It is important that children finish the secondary level with the sense of confidence to use mathematics in organising experience and motivation to continue learning in High level and become good citizens of India.

I am confident that the children in our state 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 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 in to knowledge is a thrust in the teaching job.

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. The text books make an attempt to concretize all the sentiments.

The State Council for Education Research and Training Telangana appreciates the hard 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 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 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.

Place : Hyderabad Date : 17 October, 2013

Director SCERT, Hyderabad

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SCERT TELANGANA

Preface

With this Mathematics book, children would have completed the three years of learning in the elimentary classes and one year of secondary class. We hope that Mathematics learning continues for all children in class X also however, there may be some children from whom this would be the last year of school. It is, therefore, important that children finish the secondary level with a sense of confidence to use Mathematics in organizing experience and motivation to continue learning.

Mathematics is essential for everyone and is a part of the compulsory program for school education till the secondary stage. However, at present, Mathematics learning does not instill a feeling of comfort and confidence in children and adults. It is considered to be extremely difficult and only for a few. The fear of Mathematics pervades not just children and teachers but our entire society. In a context where Mathematics is an increasing part of our lives and is important for furthering our learning, this fear has to be removed. The effort in school should be to empower children and make them feel capable of learning and doing Mathematics. They should not only be comfortable with the Mathematics in the classroom but should be able to use it in the wider world by relating concepts and ideas of Mathematics to formulate their understanding of the world.

One of the challenges that Mathematics teaching faces is in the way it is defined. The visualization of Mathematics remains centered around numbers, complicated calculations, algorithms, definitions and memorization of facts, short-cuts and solutions including proofs. Engaging with exploration and new thoughts is discouraged as the common belief is that there can be only one correct way to solve a problem and that Mathematics does not have possibilities of multiple solutions.

Through this book we want to emphasize the need for multiple ways of attempting problems, understanding that Mathematics is about exploring patterns, discovering relationships and building logic. We would like all teachers to engage students in reading the book and help them in formulating and articulating their understanding of different concepts as well as finding a variety of solutions for each problem. The emphasis in this book is also on allowing children to work with each other in groups and make an attempt to solve problems collectively. We want them to talk to each other about Mathematics and create problems based on the concepts that have learnt. We want everybody to recognize that Mathematics is not only about solving problems set by others or learning proofs and methods that are developed by others, but is about exploration and building new arguments. Doing and learning Mathematics is therefore about each person coming up with her own methods and own rules.

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SCERT TELANGANA

Class X is the final year of secondary level students and their have already dealt about the consolidation of initiations. They have already learnt also to understand that Mathematics consists of ideas that are applied in life situations but do not necessarily arise from life. We would also like children to be exposed to the notion of proof and recognize that presenting examples is not equivalent to proof with modeling aspects.

The purpose of Mathematics as we have tried to indicate in the preface as well as in the book has widened to include exploring mathematization of experiences. This means that students can begin to relate the seemingly abstract ideas they learn in the classrooms to their own experiences and organize their experiences using these ideas. This requires them to have opportunity to reflect and express both their new formulations as well as their hesitant attempt on mathematizing events around them. We have always emphasized the importance of language and Mathematics interplay. While we have tried to indicate at many places the opportunity that has to be provided to children to reflect and use language. We would emphasise the need to make more of this possible in the classrooms. We have also tried to keep the language simple and close to the language that the child normally uses. We hope that teachers and those who formulate assessment tasks would recognize the spirit of the book. The book has been developed with wide consultations and I must thank all those who have contributed to its development. The group of authors drawn from different experiences have worked really hard and together as a team. I salute each of them and look forward to comments and suggestions of those who would be users of this book.

Text Book Development Committee

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