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1 IiFirst Print 2014 Second Print 2015 Third Print 2016 Fourth Print 2017 Fifth Print 2018 Sixth Print 2019 All Rights ReservedISBN 978-955-25-0188-3 State Printing CorporationPanaluwa, Padukkaiii ivvv Message from the Hon. Minister of Education The past two decades have been significant in the world history due to changes that took pl ace in technology. The present students face a lot of new challenges along with the rapid development of Information Technology, communication and other related fields. The manner of career opportunities are liable to change specifically in the near future. In such an environment, with a new technological and intellectual society, thousands of innovative career opportunities would be created. To win those challenges, it is the responsibility of Sri Lankan Government and myself, as the Minister of Education, to empower you all.

2 This book is a product of free education. Your aim must be to use this book properly and acquire the necessary knowledge out of it. The government in turn is able to provide free textbooks to you, as a result of the commitment and labour of your parents and elders. Since we have understood that the education is crucial in deciding the future of a country, the government has taken steps to change curriculum to suit the rapid changes of the technological world. Hence, you have to dedicate yourselves to become productive citizens. I believe that the knowledge this book provides will suffice your aim. It is your duty to give a proper value to the money spent by the government on your education. Also you should understand that education determines your future. Make sure that you reach the optimum social stratum through education. I congratulate you to enjoy the benefits of free education and bloom as an honoured citizen who takes the name of Sri Lanka to the world.

3 Akila Viraj Kariyawasam Minister of Education Being innovative, changing with right knowledge Be a light to the country as well as to the from the Hon. Minister of EducationThe past two decades have been significant in the world history due to changes that took place in technology. The present students face a lot of new challenges along with the rapid development of Information Technology, communication and other related fields. The manner of career opportunities are liable to change specifically in the near future. In such an environment, with a new technological and intellectual society, thousands of innovative career opportunities would be created. To win those challenges, it is the responsibility of the Sri Lankan Government and myself, as the Minister of Education, to empower you all. This book is a product of free education. Your aim must be to use this book properly and acquire the necessary knowledge out of it.

4 The government in turn is able to provide free textbooks to you, as a result of the commitment and labour of your parents and we have understood that the education is crucial in deciding the future of a country, the government has taken steps to change curriculum to suit the rapid changes of the technological world. Hence, you have to dedicate yourselves to become productive citizens. I believe that the knowledge this book provides will suffice your aim. It is your duty to give a proper value to the money spent by the government on your education. Also you should understand that education determines your future. Make sure that you reach the optimum social stratum through congratulate you to enjoy the benefits of free education and bloom as an honoured citizen who takes the name of Sri Lanka to the world. Being innovative, changing with right knowledgeBe a light to the country as well as to the and Supervision W.

5 M. Jayantha Wickramanayaka - Commissioner General of Educational Publications Educational Publications DepartmentDirection Nirmala Piyaseeli - Commissioner of Education Publications (Development) Educational Publications DepartmentCo-ordination Thanuja Maithrie Witharana - Assistant Commissioner Educational Publications DepartmentFinal Evaluation Kulathunga - Professor, Department of Mathematics, University of Kelaniya Board of EditorsDr. Romaine Jayewardene - Senior Lecturer, Department of MathematicsUniversity of ColomboDr. Mallawa Arachchi - Senior Lecturer, Department of Mathematics University of Pragnadarshana - Senior Lecturer, Faculty of Education, University of Biyanwila - Director of Education, Ministry Of Jagath Kumara - Senior Lecturer, National Institute of EducationS.

6 Rajendram - Lecturer, National Institute of EducationThanuja Maithrie Witharana - Assistant Commissioner, Educational Publications DepartmentBoard of WritersHemamali Weerakoon - Lecturer, Pasdunrata National College of Jayasena - In Service Adviser (Retired) Vitarama - In Service Adviser, Zonal Education Office, DehiowitaAjith Ranasinghe - In Service Adviser, Zonal Education Office, HomagamaAnura Weerasinghe - In Service Adviser, (Priven), Matara Lal Wijekantha - Teacher, St. Thomas College, Mt. Dharmarathna - Teacher, Sirimavo Bandaranaike Vidyalaya, Colombo Ranjani De Silva - Teacher, Dharmapala Vidyalaya, PannipitiyaN. Vakeeshamoorthi - Director of Education (Retired) Pushparajan - Assistant Director, Zonal Education Office, PuttalamK. Karuneshvaran - In Service Adviser, Zonal Education Office, Colombo Language EditingDr. J. Rathnayake - Senior Lecturer, Department of Mathematics University of ColomboProof Samurdhi - Teacher, Sirimavo Bandaranaike Vidyalaya, Colombo 07 Illustrations, Cover Page and Technical Chathurani Perera - Educational Publications Thilini Sewwandi - Educational Publications Departmentviii Message of the Board of CompilersThis textbook has been compiled in accordance with the new syllabus to be implemented from 2015.

7 Textbooks are compiled for students. Therefore, we have made an attempt to compile this textbook in a simple and detailed manner making it possible for you to read and understand it on your own. We have included descriptions, activities and examples to introduce the subject concepts in an attractive manner and to establish them. Moreover, activities are organized from simple to complex to develop an interest to do them. We have used the terms related to mathematical concepts in accordance with the glossary of technical terms of mathematics compiled by the Department of Official subject matter learnt during the earlier grades is necessary to learn the subject content in the grade 10 syllabus. Thus, review exercises are included at the begin-ning of each chapter to revise previous knowledge. You will be prepared by them for the subject content of grade will gain maximum benefit from this textbook by reading the chapters and do-ing the review exercises of each chapter even before your teacher teaches them in the hope that studying mathematics will be an interesting, joyful and productive of CompilersixContentsUnit Page19.

8 Logarithms I 120. Logarithms II 1021. Graphs 2022. Rate 4323. Formulae 5624. Arithmetic Progressions 6125. Algebraic Inequalities 7826. Frequency Distributions 8727. Chords of a Circle 10128. Constructions 11429. Surface Area and Volume 12830. Probability 14331. Angles in a Circle 16432. Scale Diagrams 189x1 For free distributionBy studying this lesson you will be able tosimplify numerical expressions using logarithms. Indices Review Exercise Logarithms I192 For free distribution2. Fill in the blanks. 3. Simplify each of the following expressions. 4. Simplify each of the following expressions and find its LogarithmsLet us now consider how simplifications are facilitated by using the properties of indices. To do this, let us use the table of powers of 2 given below.

9 Power of 22x212223242526272829210 Value1248163264 128 256512 1024 Let us consider how the value of is found using this , let us write these numbers as powers of the same base. 3 For free distributionIt can be seen that the above simplification was done easily and concisely by using the laws of indices. In the above example it was possible to write the numbers as powers of 2. Any expression containing the multiplication and division of numbers can easily be simplified using the logarithm tables. John Napier (1550 -1617 ) a Scottish mathematician is bestowed with the honour of introducing the logarithm tables first. Briggs another mathematician who was a contemporary of Napier developed logarithms further. Although the use of the logarithm tables has reduced in recent years due to the widespread use of calculators, it is very important to learn the mathematical concepts related to form and logarithm formWe know that 23 = 8.

10 Here 8 is expressed as a power with base 2 and index 3. Such expressions are defined as '' index form''. This can also be expressed as the logarithm of 8 to base 2 is 3. This is written as log28 = 3, which is defined as the ''logarithm form''. It must be clear to you that the same statement is written in index form and in logarithm , since 23 = 8, we also have log2 8 = 3. Similarly, log2 8 = 3, means 23 = 8. Let us consider several other examples. Since 32 = 9, the logarithm of 9 to base 3 is 2. That is, log3 9 = 2. Since 51 = 5, the logarithm of 5 to base 5 is 1. That is, log5 5 = 1. Since103 = 1000, the logarithm of 1000 to base 10 is 3. That is, log10 1000 = general, for a positive number a, If ax = N, then logaN = x If logaN = x, then ax = Nax = N is considered as the index form and loga N = x is considered as the logarithm form. Here a and N take only positive values.