10th Maths EM Inner Text Pages 2015-16

INSTRUCTIONS TO STUDENTSPictures/figures are provided for many items/situations for better understanding ofthe concepts in the text book.You have to read them carefully in relation with theconcepts.Clarify your doubts with the help of your teachers while you are doing the activitesrelated to the concepts time to time.''Do thisProblems are meant to test your progress immediately after learning aconcept.So you have to do these problems on your own.Check these with your teacher.Try theseitems in every chapter are provided to sharpen your ideas andthoughts.some logic will be there behind these questions.You have to try all thesequestions with out fail.Do this and Try these problems are meant to solve in the class room under theguidance of your teacher.Do not leave them at all.The questions under Think discuss and write are given to test your analytical ability.Youcan answer these questions by discussing in groups.The exercises given at the end of some sub topics arerelated to the concepts learnedto a particular level.You try to solve these problems on your own.Do not copy themfrom guides and from other sources.Some projects given in in the textbook are meant to be done with proper plan andguidance with the teacher.you can do this in a group.A report is to be submitted at theend of the project.Some blank spaces are provided in tables,try these exercises to facilitate you toanswer quickely.You can fill it in the text book it self.Every student is required to finish the day's work on the same day it self.Donot postpone it.You may feel burden later.Try to collect some more information to create some similar problems based on theconcepts you have learned.Ask your friends to solve your questions.Games,Puzzles provided in the textbooks shall encourage you to feel joy in doingmaths.For recreation collect some more .You should always connect the concepts learned in the class with other subject ar-eas and situations out side the class room.You have to develop abilities with regard to academic standards prescribed at theend of the text book based on the syllabus .The academic standards at the second-ary level are based on a) Problem solving 2)Reasoning and Proof 3)Mathematicalcommunication 4)Connections 5)Representation.You have to go through various reference books,Internet,Forums for finding differentways of solutions for a problem and for better understanding of the concepts.Optional exercises are provided to think critically to solve certain problems.Theseexercises will help you to face Talent tests conducted at national level on par withother students.The appendix chapter Mathematical modelling will help you to know modelling ofmathematical concepts in the fields of business,Agriculture,Stock markets etc,Youcan see the connection of mathematics with different areas.Syllabus is also provided at the end of the textbook for your reference that how youare making your progress.You can also compare with others.

We wish you all the best

SIGNS AND SYMBOLS OF SCHOOL MATHEMATICSSign/symbol Read as Mathematical meaning

plus or minus Either positive or negative not equal to unequal therefore logical flow of a statement infinite uncountable,not defined is similar to 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 square root of a number3

cube root of cube root of a number cup of union of sets cap of intersection of sets phi symbol for empty set% percent of per hundredo degree angle measure delta / triangle symmetric difference in sets/symbol of triangle belongs to an element belong to a particular set equivilent to one to one correspondence

, , alfa,beta,gamma greek lettetrs to represent coefficients mue universal set symbol pi irrational number equal to 3.14159....app=22/7 sigma sum of scores

sin , cos , tan sin theta,cos theta,tan theta trigonometric ratiosx x bar arithmetic mean

loga x log x to the base a logarthemic function(a, b) point (a, b) ordered pair a,b

|x| mod x absolute value of a real numberP(x) P of x a polynomial function in xP(E) P of e probability of an event Since reasoning at a stage` rupee symbol of Indian rupee| | is parallel to parallel property of lines is perpendicular to making 90 degree with a line

{ } flower bracket used to set notationPQ arc PQ arc of acircle a2 a square square of a number angle symbol of angle theta measurement of an angle

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Mathematics Class-X

10th Maths EM Inner Text Pages 21 1 1 1 - 0 2 - 2 0 1 5 1 6 : 5 9 : 2 3

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Foreword ! " # $ % " & ' $ " % " " % ( " ! % " ) * " ' + ' $ " " ! % " & # " , & & ! ' ! " - " " " $ - " % % " $ " % " & - " $ " . - " ! & + # & " % " ! / ( $ ! ' " " ! % ! - "0 & / " & & ) 1 ! # , - " ! & + # 2 " ! / $ ' " % % " % )3 $ " " ! / ' " , $ " 4 " ' ' # $ " ! # ! % # & % $ " % " $ " ! % ! / ' " $ " / # % $ " % & " 5 " & " )6 $ " & ' & ! # # ! , $ " ! " % " ) ! " ! " $ ' " ) 1 ! # ! %4 " ' " # 4 7 " , " " $ " ! 4 7 " - & - ' & / $ ! ' $ % % " $ ) 3 % ! $ $ & ! " # $ $ " " ! / & " - " & ( $ $ " " " # # " " " % $ " % ! ' ' " 8 " ! " " % - " & " ! ' 9 ' $ & " - " & 4 " % " ' + " # 3 )3 % # " $ $ " $ & ! " ! " 6 " & ' & " ! " 7 / % $ " % ,% 5 " % $ " % ! # $ " ! & # " " 8 " ! " " , " & - " % " ' # & ! 4 & " % , " ! $ " 4 ! ! " # % $ " % 4 / ! " ' $ " 8 4 5 ): ! " $ " ! , " ! 4 ! 4 ! & " ! ! & ! " ' ' " ! " - " & / # ' & " ! ' & " # % ! 5 , $ " " " # $ " $ ! ) 1 & ' ( $ % 8 " & ! % " - ! % " " " & & / ! " 0 ! " # ! " # # " - " ! # ! ! & % " $ ' & " ! ' ! " ) ; ! ! ' & ! % & ! " & " - " " ! " % ' $ & ! " ( $ # # " ! " " ! " % # & # " / & " , # " & # " 5 ( & " ' " $ ! $ " " $ ' 7 4 )6 $ " # ! " - # % $ " % " $ ' ! " " " 2 " < ! ! & % : ! % "( ! 5 = 2 < : > ? @ A A B $ 4 " " " & 4 ! " % $ " % " ! ( $ $ & & " ! & / & / ( $ " " % ! # % $ " % " $ ' $ " " ) 6 $ " " 8 4 5 % 5 " " % ! " + " & & $ " " % " )6 $ " 2 " < & # ! * " " ! $ 6 ! ' 6 " & ' ! " " $ "$ ! ( ! 5 # $ " " 8 4 5 " - " & % " % % " " " - " ! & " $ " ! # ! % & & - " ! $ " " ( $ $ - " ! 4 " $ " " - " & % " # $ " 8 4 5 ) 3 % $ 5 # & $ "C ! & D # # " ! , E & & D # # " ! $ " " $ " ! # ! % 5 ' $ 4 & " ) 3 & $ 5 $ " ! ' + ( $ $ $ - " ' - " $ " ! % " $ " " - " & % " # $ " 8 4 5 ) 3 % ' ! " # & $ " # # " # $ " < % % " ! C ! " ! # 2 $ & # ! " 8 " ' > " ! " - " & ' $ " 8 4 5 ) 3 $ " " " - ! & / % ! - " $ " 0 & / # ! ( ! 5 , ( " ( " & % " / ! % % " ' ' " $ ! " ' ! )F & " G 9 / " ! 4 H I J K L M N JC " G A O D 4 " ! , ? @ A P 2 < * 6 , 9 / " ! 4 Q 10th Maths EM Inner Text Pages 24 4 1 1 - 0 2 - 2 0 1 5 1 6 : 5 9 : 2 3

R $ $ E $ " % 4 5 , $ & ! " ( & $ - " % & " " $ " $ ! " " / " ! #& " ! ' $ " " & % " ! / & " " / " ! # " ! / & ) R " $ " $ E $ " % & " ! ' " # ! & & $ & ! " & S & $ ( " - " ! , $ " ! " % / 4 " % " $ & ! " # ! % ( $ % $ ( & 4 " $ " & / " ! # $ & ) 3 , $ " ! " # ! " , % ! $ $ & ! " # $ $ " " ! / & " - " & ( $ " " # # " " " E $ " % ! ' + ' " 8 " ! " " % - " & " ! ' )E $ " % " " & # ! " - " ! / " ! # $ " % & ! / ! ' ! % # ! $ & " & & $ " " ! / ' " ) 9 ( " - " ! , ! " " , E $ " % & " ! ' " & & # " " & ' # % # ! # " " $ & ! " & ) 3 " ! " 4 "" 8 ! " % " & / # # & & / # ! # " ( ) 6 $ " # " ! # E $ " % " ! - " 7 $ & ! " " $ " ! 4 ! " ! " " / ) 3 " 8 ( $ " ! " E $ " % ! " ' ! # ! & - " % ! # ! # ! $ " ! ' ! & " ! ' , $ # " ! $ 4 " ! " % - " ) 6 $ "" # # ! $ & $ & 4 " " % ( " ! $ & ! " % 5 " $ " % # " " & 4 & " # & " ! ' ' E $ " % ) 6 $ " / $ & & / 4 " % # ! 4 & " ( $ $ " E $ " % $ " & ! % 4 $ & 4 " 4 & " " $ " ( " ! ( ! & 4 / ! " & ' " " #E $ " % # ! % & " $ " ! " ! ' # $ " ( ! & )D " # $ " $ & & " ' " $ E $ " % " $ ' # " $ " ( / " # " )6 $ " - & + # E $ " % ! " % " " ! " ! % 4 " ! , % & " & & , & ' ! $ % , " # % " % ! + # # , $ ! > & & ' ! # ) ' ' ' ( $ " 8 & ! " ( $ ' $ ! ' " $ " % % 4 " & " # $ $ " ! " 4 " & / " ! ! " ( / & - " ! 4 & " % $ E $ " % " $ - " 4 & " # % & & " & )6 $ ! ' $ $ 4 5 ( " ( " % $ + " $ " " " # ! % & & " ( / # " % ' ! 4 & " % , " ! ' $ E $ " % 4 " 8 & ! ' " ! , - " ! '! " & $ 4 & ' & ' ) R " ( & & 5 " & & " $ " ! " ' ' " " ! " ' $ " 4 5 $ " & $ " % # ! % & ' ! & ' $ " ! " ! ' # # # " ! " " ( " & & # ' - ! " / # & # ! " $ ! 4 & " % ) 6 $ " " % $ $ 4 5 & & & ( ' $ & ! " ( ! 5 ( $ " $ $ " ! ' ! % 5 " " % & - " ! 4 & " % & & " - " & / ) R " ( $ " % & 5 " $ $ " ! 4 E $ " % ! " " ! 4 & " % 4 " $ " " $ $ - " & " ! ) R " ( " - " ! / 4 / ! " ' + " $ E $ " % & / 4 & - ' ! 4 & " % " 4 / $ " ! ! & " ! ' ! # % " $ $ ! " " - " & " 4 / $ " ! , 4 4 " 8 & ! 4 & ' " ( ! ' % " )C ' & " ! ' E $ " % $ " ! " # ! " 4 " $ " ! % ' ( $ $ " ! ( % " $ ( ! & " )

Preface

Q 10th Maths EM Inner Text Pages 25 5 1 1 - 0 2 - 2 0 1 5 1 6 : 5 9 : 2 3

< & S $ " # & / " ! # " ! / & " - " & " $ " ! $ - " & ! " / " & 4 $ " & # ) 6 $ " / $ - " & ! " / & " ! & " ! $ E $ " % # " $ ! " & " & # " 4 " " ! & / ! " # ! % & # " ) R " ( & & & 5 " $ & ! " 4 " " 8 " $ " # ! # ! " ' + " $ ! " " ' " 8 % & " " 0 - & " ! # ( $ % " & ' " )6 $ " ! " # E $ " % ( " $ - " ! " " $ " ! " # " ( " & & $ " 4 5 $ ( " " & " " 8 & ! ' % $ " % + # " 8 " ! " " ) 6 $ % " $ " 4 " ' ! " & " $ " " " % ' & / 4 ! " $ " / & " ! $ " & ! % $ " ! ( " 8 " ! " " ! ' + " $ " ! " 8 " ! " " ' $ " " " ) 6 $ ! " 0 ! " $ " % $ - " ! / ! " # & " " 8 ! " 4 $ $ " ! " ( # ! % & ( " & & $ " ! $ " " % % $ " % + ' " - " ! $ " % ) R " $ - " & ( / " % $ + " $ " % ! " # & ' ' " E $ " % " ! & / ) R $ & " ( " $ - " ! " " % / & " $ " ! / $ $ 4 " ! - " $ & ! " ! " # & " " & ' ' " )R " ( & " % $ " $ " " " % 5 " % ! " # $ 4 & " $ " & ! % ) R "$ - " & ! " 5 " " $ " & ' ' " % & " & " $ " & ' ' " $ $ " $ & ! % & & / " ) R " $ " $ " $ " ! $ " ( $ # ! % & " " % " 5 ( & ! " ' + " $ " ! # $ " 4 5 ) 6 $ " 4 5 $ 4 " " " - " & " ( $ ( " & 3 % $ 5 & & $ " ( $ $ - " ! 4 " " - " & % " ) 6 $ " ' ! # $ ! ! ( # ! % # # " ! " " 8 " ! " " $ - " ( ! 5 " ! " & & / $ ! ' " $ " ! " % ) 3 & " " $ # $ " % & 5 # ! ( ! % % " ' ' " # $ " ( $ ( & 4 " " ! # $ 4 5 )

Q 10th Maths EM Inner Text Pages 26 6 1 1 - 0 2 - 2 0 1 5 1 6 : 5 9 : 2 3

Mathematics Class-X

Q

W T U V W X Y W Z [ W X [ W \ 5 Z Z ] ^ _ _ U ` a \ W Z ` X < U b X5 a c ` X Y < X Y d Z e \ W Z f X Y X e e a Y d [ b 5 a c ` X Yg h i j k l m n o p j q r h s t n u j h v w xg w y j z r g { t n l | w s v x }g ~ l | u o k l r g { t n l | n n r z x v wg x k q u j k q n k z u r u h s z p j q ~ v h g g k q k p l j rg s n k q k z n k z u r h w m Q j o p j q h g h v h w xg } q q j r r u r h h t k u n k q | j p q n k q | h w s v h s {g q u k z j j o j z q | h w j j o p j q h s v h gg { y o l k q q k u l j r h { n n r z h h v w w xg k u j u z r k u y j k u z r z k q l j h s m Q j o p j q w w s v w x xh g j u r n q k z u h g y j z j o p j q z p j q w x s v w } {h h q u o j z q | h s y j z j o p j q w } v w ~h w l k z u r q u o j z q | g { t k u n k q | w x v ~ g xh ~ q p k p l z | h g j p q n k q | ~ g s v ~ w wh x y z k z r z r h s t n l | ~ w ~ v ~ s w j u k z j o k z k l j l l u g { j p q n k q | ~ s ~ v ~ } s u r j q r ~ } } v ~ { x10th Maths EM Inner Text Pages 27 7 1 1 - 0 2 - 2 0 1 5 1 6 : 5 9 : 2 4

OOOOOURURURURUR N N N N NAAAAATIONTIONTIONTIONTIONALALALALAL A A A A ANTHEMNTHEMNTHEMNTHEMNTHEM

Jana-gana-mana-adhinayaka, jaya he

Bharata-bhagya-vidhata.

Punjab-Sindh-Gujarat-Maratha

Dravida-Utkala-Banga

Vindhya-Himachala-Yamuna-Ganga

Uchchala-Jaladhi-taranga.

Tava shubha name jage,

Tava shubha asisa mage,

Gahe tava jaya gatha,

Jana-gana-mangala-dayaka jaya he

Bharata-bhagya-vidhata.

Jaya he, jaya he, jaya he,

Jaya jaya jaya, jaya he!

India is my country. All Indians are my brothers and sisters.

I love my country, and I am proud of its rich and varied heritage.

I shall always strive to be worthy of it.

I shall give my parents, teachers and all elders respect,

and treat everyone with courtesy. I shall be kind to animals

To my country and my people, I pledge my devotion.

In their well-being and prosperity alone lies my happiness.

PPPPPLEDGELEDGELEDGELEDGELEDGE

1.1 I1.1 I1.1 I1.1 I1.1 INTRODUCTIONNTRODUCTIONNTRODUCTIONNTRODUCTIONNTRODUCTION

Real Numbers1


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10th Maths EM Inner Text Pages 2015-16