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Government of Karnataka

MATHEMATICS

Karnataka Text Book Society (R.)100 Feet Ring Road,

Banashankari 3rd Stage, Bangalore - 85

2014

10Tenth Standard

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Preface

The Textbook Society, Karnataka has been engaged in producing new textbooks

according to the new syllabi which in turn are designed on NCF – 2005 since June 2010.

Textbooks are prepared in 12 languages; seven of them serve as the media of instruction.

From standard 1 to 4 there is the EVS, mathematics and 5th to 10th there are three core

subjects namely mathematics, science and social science.

NCF – 2005 has a number of special features and they are:

· connecting knowledge to life activities

· learning to shift from rote methods

· enriching the curriculum beyond textbooks

· learning experiences for the construction of knowledge

· making examinations flexible and integrating them with classroom experiences

· caring concerns within the democratic policy of the country

· make education relevant to the present and future needs.

· softening the subject boundaries- integrated knowledge and the joy of learning.

· the child is the constructor of knowledge

The new books are produced based on three fundamental approaches namely.

Constructive approach, Spiral Approach and Integrated approach

The learner is encouraged to think, engage in activities, master skills and competencies.

The materials presented in these books are integrated with values. The new books are

not examination oriented in their nature. On the other hand they help the learner in the

total development of his/her personality, thus help him/her become a healthy member of

a healthy society and a productive citizen of this great country, India.

Mathematics is essential in the study of various subjects and in real life. NCF 2005

proposes moving away from complete calculations, construction of a framework of concepts,

relate mathematics to real life experiences and cooperative learning.

Many students have a maths phobia and in order to help them overcome this phobia,

jokes, puzzles, riddles, stories and games have been included in textbooks. Each concept

is introduced through an activity or an interesting story at the primary level. The

contributions of great Indian mathematicians are mentioned at appropriate places.

Textbooks for students X have a special significance. As any other new textbook they help

learners’ master skills and competencies and at the same time there is going to be a

public examination based on them.

The Textbook Society expresses grateful thanks to the chairpersons, writers,

scrutinisers, artists, staff of DIETs and CTEs and the members of the Editorial Board and

printers in helping the Text Book Society in producing these textbooks.

Date: 1.3.2014

Y.T. Gurumurthy

Managing Director

Karnataka Textbook Society®

Bangalore, Karnataka

Prof G.S. Mudambadithaya

Coordinator

Curriculum Revision and Textbook Preparation

Karnataka Textbook Society®

Bangalore, Karnataka

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Chairperson’s note

This tenth standard mathematics textbook is prepared for the revised syllabus

of Karnataka State based on the recommendations made by NCF 2005. It is

designed to support the two major suggestions made by NCF 2005.

The higher aim of mathematics education should be to develop the inner

resources in children. That is, development of mental abilities such as logi-

cal and abstract thinking, reasoning, analysing, problem solving etc.

The mode of transaction should be based on contructivism, which facilitate

the learners to construct their own knowledge.

Conceptual understanding of basic ideas and problem solving are the two

main components of mathematics learning. Hence, this textbook is prepared in

such a way to facilitate mathematics learning by doing mathematics and well

balanced text and exercises.

The salient features of this text book are

Each unit begins with real life situations or activities that engage students

in learning tasks.

Each concept in each unit is provided with suitable exploring activities and

illustrations.

The text is presented in simple language and logical manner with suitable

hands on and minds on activities.

The units where theorems are included, both practical activity for stating the

theorem and logical proof for proving the theorem are discussed.

Each theorem is followed by numerical problems and riders. Equal

weightage is given to problems and riders on theorems, its converse and

corollories.

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Questions are raised wherever possible to promote thinking and do

analysis.

Additional information is provided in boxes with the heading “know this”.

This is to motivate students and create interest in the subject.

Questions and statements with headings “Try” and “Discuss” are given

for promoting inquiry and co-operative learning strategies.

Each unit ends with a flow chart where all the ideas learnt in the unit are

provided through concept mapping. Students with the guidance of teachers

can generate better concept maps.

This text book is made to be both learner friendly and teacher friendly. We,

the Tenth standard mathematics text book committee members hope that the

text book will pave a suitable path for making mathematics learning joyful and

meaningful.

We would be greatful for constructive suggestions and comments from

experts, teachers, students and parents for further improvement of this book.

Dr. G. Vijayakumari

Chairperson

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Text Book Committee

Chairperson :

Dr. Vijaya Kumari G. - Associate Professor, Vijaya Teachers College (CTE),4th block, Jayanagar, Bangalore - 11.

Members :

1) Dr. Y.B. Venkatesh - Lecturer, Govt. P.U. College, Bidadi, Ramanagara District.

2) Sri V. Ravikumar - Senior Lecturer, DIET, Ilakal, Bagalkot District.

3) Sri Narasappa - Head Master, Sri Saraswati Vidyaniketana, Dommasandra,Bangalore.

4) Sri T.K. Prasanna Murthy - Asst. teacher, Vijaya High School, Jayanagar,Bangalore.

5) Smt. M. N. Deepa Rao - Asst. Teacher, Sri. N.K.S.E.H.S, D.V.V. Gujarati Shala,Majestic Circle, Bangalore.

6) Sri Tharakesh (Artist) Drawing Teacher, Government High School,Bannitalapura, Gundlupet Taluk, Charamarajanagar Dt.

Scrutinizers :

1) Dr. B.J. Venkatachala, Prof. H.B.C.S.E (T.I.F.R) Mathematics Dept. IISC,Bangalore.

2) Sri K. Krishna Iyengar, Retired B.E.O., Bangalore.

Editorial Committee Members:

1) Dr. R. Raveendra - N.C.E.R.T Director (Retd.), Banashankari III stage, Bangalore.

2) Dr. B.S. Upadhyaya - Professor, Extension & Education Division, R.I.E., Mysore.

3) Dr. V.S. Prasad - Professor, Mathematics Department, R.I.E., Mysore.

4) Dr. Sharath Sure - Asst. Professor, Azim Premji University, P.E.S. School ofEngineering Campus, Electronics City, Bangalore.

Chief Advisor :

1) Sri Y.T. Gurumurthy, Managing Director, KTBS, Bangalore.

2) Sri Bella Setty, Joint Director, KTBS, Bangalore.

Chief Co-ordinator :

Prof. G.S. Mudambaditaya, Co-ordinator, Curriculum revision and textbookpreparation, KTBS, Bangalore.

Programme Co-ordinator :

Smt. Shashikala R.N. - Assistant Director, KTBS, Bangalore.

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CONTENT

1. Real Numbers 1 - 14 June - 4

2. Sets 15 - 26 June - 4

3. Progressions 27 - 64 July to Nov -20

4. Permutations and Combinations 65 - 90 Nov & Dec -12

5. Probability 91 - 122 Jan - 8

6. Statistics 123 - 152 Feb - 8

7. Surds 153 - 166 June - 4

8. Polynomials 167 - 192 Jun & July - 8

9. Quadratic Equations 193 - 228 July to Nov -24

10. Similar Triangles 229 - 268 June & July -16

11. Pythagoras Theorem 269 - 286 Aug & Sep -10

12. Trigonometry 287 - 322 Nov to Jan -16

13. Coordinate Geometry 323 - 342 Jan & Feb -12

14. Circle - Chord properties 343 - 350 Sep - 4

15. Circles - Tangent Properties 351 - 376 Nov & Dec -12

16. Mensuration 377 - 414 Dec & Jan -12

17. Graphs and Polyhedra 415 - 430 Feb - 6

S.L.No.

UNIT Page No. Months & Periods