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X Std.                                                           SYLLABUS
                                                                                                      Transactional
                                                                     Expected Learning                                   No. of
      Topic                                Content                                                      Teaching
                                                                        Outcomes                                        Periods
                                                                                                         Strategy
                                i. Introduction                 •	 To	revise	the	basic	con-        Use Venn
                                ii. Properties of operations on    cepts on Set operations         diagrams for all
                                     sets                       •	 To	understand	the	proper-       illustrations
                                iii.	De	Morgan’s	laws-verifi-      ties of operations of sets
                                     cation using example Venn     - commutative, associative,
                                     diagram                       and	distributive	restricted	    Give examples
                                                                   to	three	sets.
       I. Sets and Functions




                                iv. Formula for                                                    of functions from
                                v. Functions                    •	 To	understand	the	laws	of	      economics, medi-
                                                                   complementation of sets.        cine, science etc.
                                                                •	 To	understand	De	Mor-
                                                                   gan’s laws and demonstrat-
                                                                   ing	them	by	Venn	diagram	                              26
                                                                   as well.
                                                                •	 To	solve	word	problems	
                                                                   using	the	formula	as	well	
                                                                   as Venn diagram.
                                                                •	 To	understand	the	defini-
                                                                   tion	,	types	and	representa-
                                                                   tion of functions.
                                                                •	 To	understand	the	types	
                                                                   of	functions	with	simple	
                                                                   examples.
                                i. Introduction                 •	 To	understand	to	identify	      Use pattern ap-
                                ii. Sequences                      an	Arithmetic	Progression	      proach
                                iii.	Arithmetic	Progression	       and a Geometric Progres-
  II. Sequences and Series of




                                     (A.P)                         sion.                           Use dot pattern as
                                iv. Geometric Progression       •	 Able	to	apply	to	find	the	      teaching	aid
        Real	Numbers




                                     (G.P)                         nth	term	of	an	Arithmetic	
                                v. Series                          Progression and a Geomet-       Use patterns to
                                                                   ric Progression.                derive formulae        27
                                                                •	 To	determine	the	sum	of	
                                                                   n	terms	of	an	Arithmetic	       Examples	to	be	
                                                                   Progression and a Geomet-       given from real
                                                                   ric Progression.                life situations
                                                                •	 To	determine	the	sum	of	
                                                                   some	finite	series.

                                i. Solving linear equations     •	 To	understand	the	idea	about	   Illustrative
                                ii.	 Polynomials                   pair of linear equations in     examples –
                                iii.	Synthetic	division            two unknowns. Solving a
                                iv. Greatest common divisor        pair of linear equations in     Use	charts	as	
         III.	Algebra




                                     (GCD)                         two	variables	by	elimination	   teaching	aids
                                      and Least common mul-        method	and	cross	multipli-
                                     tiple (LCM)                   cation	method.		                Recall GCD and
                                v. Rational expressions         •	 To	understand	the	relation-     LCM	of	numbers	
                                vi. Square root                    ship	between	zeros	and	co-      initially
                                vii. Quadratic Equations           efficients	of	a	polynomial	
                                                                   with	particular	reference	to	
                                                                   quadratic	polynomials.	

                                                                       (v)
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                                                   •	 To	determine	the	remain-        Compare	with	
                                                      der	and	the	quotient	of	        operations on
                                                      the	given	polynomial	           fractions
                                                      using	Synthetic	Division	
                                                      Method.
                                                   •	 To	determine	the	factors	
                                                      of	the	given	polynomial	
                                                      using	Synthetic	Division	
                                                      Method.
                                                   •	 Able	to	understand	the	dif-
                                                      ference	between	GCD	and	        Compare	with	the	
                                                      LCM, of rational expres-        square root opera-
                                                      sion.                           tion on numerals.
                                                   •	 Able	to	simplify	rational	
                                                      expressions	(Simple	Prob-       Help students
                                                                                      visualize	the	
                                                      lems),
 III.	Algebra




                                                                                      nature of roots
                                                   •	 To	understand	square	
                                                                                      algebraically	and	
                                                      roots.
                                                                                      graphically.
                                                   •	 To	understand	the	standard	
                                                                                                           40
                                                      form of a quadratic equa-
                                                      tion .
                                                   •	 	To	solve	quadratic	equa-
                                                      tions	(only	real	root)	-	by	
                                                      factorization,	by	complet-
                                                      ing	the	square	and	by	using	
                                                      quadratic formula.
                                                   •	 Able	to	solve	word	prob-
                                                      lems	based	on	quadratic	
                                                      equations.
                                                   •	 Able	to	correlate	relation-
                                                      ship	between	discriminant	
                                                      and nature of roots.
                                                   •	 Able	to	Form	quadratic	
                                                      equation	when	the	roots	
                                                      are given.
                   i. Introduction                 •	 Able	to	identify	the	order	     Using of rect-
                   ii.	 Types	of	matrices             and formation of matrices       angular	array	of	
                   iii.	Addition	and	subtraction   •	 Able	to	recognize	the	types	    numbers.
                   iv. Multiplication                 of matrices
                   v. Matrix equation              •	 Able	to	add	and	subtract	       Using real life
                                                      the	given	matrices.             situations.
                                                   •	 To	multiply	a	matrix	by	a	
    IV. Matrices




                                                      scalar,	and	the	transpose	of	   Arithmetic	opera-
                                                      a matrix.                       tions	to	be	used     16
                                                   •	 To	multiply	the	given		
                                                      matrices (2x2; 2x3; 3x2
                                                      Matrices).
                                                   •	 Using	matrix	method	solve	
                                                      the	equations	of	two	vari-
                                                      ables.




                                                          (vi)
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                          i. Introduction                •	 To	recall	the	distance	           Simple geometri-
                          ii.	 Revision	:Distance	be-       between	two	points,	and	          cal result related
                               tween two points             locate	the	mid	point	of	two	      to triangle and
                          iii. Section formula, Mid         given points.                     quadrilaterals to
                               point formula, Centroid   •	 To	determine	the	point	           be	verified	as	ap-
                               formula                      of division using section         plications.
                          iv. Area of a triangle and        formula (internal).
                               quadrilateral             •	 To	calculate	the	area	of	a	       the	form
                          v.	 Straight	line                 triangle.                          y = mx + c	to	be	
 V.	Coordinate	Geometry




                                                         •	 To	determine	the	slope	of	        taken	as	the	start-
                                                            a	line	when	two	points	are	       ing point
                                                            given, equation is given.                               25
                                                         •	 To	find	an	equation	of	line	
                                                            with	the	given	information.
                                                         •	 Able	to	find	equation	of	
                                                            a line in: slope-intercept
                                                            form, point -slope form,
                                                            two -point form, intercept
                                                            form.
                                                         •	 To	find	the	equation	of	
                                                            a	straight	line	passing	
                                                            through	a	point	which	is	(i)	
                                                            parallel (ii) perpendicular
                                                            to	a	given	straight	line.

                          i.			Basic	proportionality	theo- •	 To	understand	the	theo-         Paper folding
                                rem	(with	proof)              rems	and	apply	them	to	         symmetry	and	
                          ii. Converse of Basic propor-       solve	simple	problems	          transformation
                                tionality	theorem	            only.                           techniques	to	be	
                          					(with	proof)                                                   adopted.
                          iii.	Angle	bisector	theorem	
                                                                                              Formal proof to
                                (with	proof	-	internal	case	
 VI.	Geometry




                                                                                              be	given	
                                only)
                          iv.		Converse	of	Angle	bisec-                                       Drawing of            20
                                tor	theorem	(with	proof	                                      figures
                                -	internal	case	only)
                          	v.		Similar	triangles	(theo-                                       Step	by	step	
                                rems	without	proof)                                           logical	proof	with	
                                                                                              diagrams	to	be	
                                                                                              explained and
                                                                                              discussed



                          i. Introduction                •	 Able	to	identify	the	             By	using	Alge-
                          ii. Identities                       Trigonometric	identities	      braic	formulae	
 VII.	Trigonometry




                          iii.	Heights	and	distances           and	apply	them	in	simple	
                                                               problems.                      Using trigonomet-
                                                         •	 To	understand	trigonomet-         ric identities.       21
                                                               ric	ratios	and	applies	them	
                                                               to	calculate	heights	and	      The	approximate	
                                                               distances.                     nature of values
                                                         					(not	more	than	two	right	       to	be	explained
                                                               triangles)


                                                                (vii)
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                           i. Introduction                  •	 To	determine	volume	and	          Use 3D models to
                           ii. Surface Area and Volume         surface	area	of	cylinder,	        create	combined	
      VIII. Mensuration         of	Cylinder,	Cone,	Sphere,	    cone,	sphere,	hemisphere,	        shapes
                                Hemisphere,	Frustum		          frustum
                           iii. Surface area and volume     •	 Volume	and	surface	area	          Use models and
                                of	combined	figures            of	combined	figures	(only	        pictures	ad	teach-
                           iv. Invariant volume                two).                             ing aids.              24
                                                            •	 Some	problems	restricted	
                                                               to constant Volume.               Choose	examples	
                                                                                                 from real life situ-
                                                                                                 ations.
                           i. Introduction                    •	   Able	to	construct	tangents	 To	introduce	
                           ii. Construction of tangents            to circles.                   algebraic	verifica-
                                to circles                    •	   Able	to	construct	triangles,	 tion	of	length	of	
 IX.	Practical		Geometry




                           iii.	Construction	of	Triangles          given	its	base,	vertical	     tangent segments.
                           iv.	 Construction	of	cyclic	            angle	at	the	opposite	vertex	
                                quadrilateral                      and                           Recall related
                                                                   (a) median                    properties of
                                                                   (b)	altitude		                angles in a circle     15
                                                                   (c)	bisector.                 before	construc-
                                                              •	   Able	to	construct	a	cyclic	 tion.
                                                                   quadrilateral
                                                                                                 Recall relevant
                                                                                                 theorems	in	theo-
                                                                                                 retical	geometry
                           i. Introduction                    •	   Able	to	solve	quadratic	      Interpreting skills
                           ii.	 Quadratic	graphs                   equations	through	graphs      also	to	be	taken	
                           iii.	Some	special	graphs           •	   To	solve	graphically	the	     care	of	graphs	
 X.	Graphs




                                                                   equations                     of quadratics to
                                                               .                                 precede	algebraic	
                                                              •	   Able	to	apply	graphs	to	      treatment.             10
                                                                   solve	word	problems
                                                                                                 Real life situa-
                                                                                                 tions	to	be	intro-
                                                                                                 duced.
                           i. Recall Measures of central •	        To	recall	Mean	for	grouped	 Use real life situa-
                                tendency                           and ungrouped data situa- tions like perfor-
                           ii. Measures of dispersion              tion	to	be	avoided).          mance in exami-
      XI. Statistics




                           iii.	Coefficient	of	variation •	        To	understand	the	concept	 nation, sports, etc.
                                                                   of	Dispersion	and	able	                              16
                                                                   to	find	Range,	Standard	
                                                                   Deviation and Variance.
                                                              •	   Able	to	calculate	the	coef-
                                                                   ficient	of	variation.
                           i. Introduction                    •	   To	understand	Random	         Diagrams and
                           ii.	 Probability-theoretical	ap-        experiments, Sample space investigations
                                proach                             and	Events	–	Mutually	        on coin tossing,
 XII.	Probability




                           iii.		Addition	Theorem	on	              Exclusive, Complemen-         die	throwing	and	
                                Probability                        tary,	certain	and	impossible	 picking	up	the	
                                                                   events.                       cards from a deck      15
                                                              •	   To	understand	addition	       of	cards	are	to	be	
                                                                   Theorem	on	probability	       used.
                                                                   and	apply	it	in	solving	
                                                                   some	simple	problems.



                                                                     (viii)
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                           CONTENTS
1.   SETS   AND FUNCTIONS                                       1-33
     1.1     Introduction                                          1
     1.2.    Sets                                                  1
     1.3.    Operations on Sets                                    3
     1.4.    Properties of Set Operations                          5
     1.5.    De Morgan’s Laws                                     12
     1.6.    Cardinality of Sets                                  16
     1.7.    Relations                                            19
     1.8.    Functions                                            20

2.   SEQUENCES AND SERIES OF REAL NUMBERS                      34-67
     2.1. Introduction                                            34
     2.2. Sequences                                               35
     2.3. Arithmetic Sequence                                     38
     2.4. Geometric Sequence                                      43
     2.5. Series                                                  49

3.   ALGEBRA                                                  68-117
     3.1 Introduction                                             68
     3.2 System of Linear Equations in Two Unknowns               69
     3.3 Quadratic Polynomials                                    80
     3.4 Synthetic Division                                       82
     3.5 Greatest Common Divisor and Least Common Multiple        86
     3.6 Rational Expressions                                     93
     3.7 Square Root                                              97
     3.8 Quadratic Equations                                     101

4.   MATRICES                                                118-139
     4.1 Introduction                                            118
     4.2 Formation of Matrices                                   119
     4.3 Types of Matrices                                       121
     4.4 Operation on Matrices                                   125
     4.5 Properties of Matrix Addition                           128
     4.6 Multiplication of Matrices                              130
     4.7 Properties of Matrix Multiplication                     132



                                     (ix)
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5.    COORDINATE GEOMETRY                                140-170
      5.1 Introduction                                       140
      5.2 Section Formula                                    140
      5.3 Area of a Triangle                                 147
      5.4 Collinearity of Three Points                       148
      5.5 Area of a Quadrilateral                            148
      5.6 Straight Lines                                     151
      5.7 General form of Equation of a Straight Line        164

6.    GEOMETRY                                           171-195
      6.1 Introduction                                       171
      6.2 Similar Triangles                                  182
      6.3 Circles and Tangents                               189
7.    TRIGONOMETRY                                       196-218
      7.1 Introduction                                       196
      7.2 Trigonometric Identities                           196
      7.3 Heights and Distances                              205
8.    MENSURATION                                        219-248
      8.1 Introduction                                       219
      8.2 Surface Area                                       219
      8.3 Volume                                             230
      8.4 Combination of Solids                              240

9.    PRACTICAL GEOMETRY                                249- 266
      9.1 Introduction                                       249
      9.2 Construction of Tangents to a Circle               250
      9.3 Construction of Triangles                          254
      9.4 Construction of Cyclic Quadrilaterals              259

10.   GRAPHS                                             267-278
      10.1 Introduction                                      267
      10.2 Quadratic Graphs                                  267
      10.3 Some special Graphs                               275

11.   STATISTICS                                         279-298
      11.1 Introduction                                      279
      11.2 Measures of Dispersion                            280

12.   PROBABILITY                                       299 - 316
      12.1 Introduction                                       299
	     12.2		 Classical	Definition	of	Probability	             302
      12.3 Addition theorem on Probability                    309


                                        (x)
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      1                                    SETS AND
                                                 FUNCTIONS
                                                        A set is Many that allows itself to be thought of as a One
                                                                                                   - Georg Cantor
    Introduction
    Sets                                  1.1    Introduction
                                                   The concept of set is one of the fundamental concepts
    Properties of set operations
                                           in mathematics. The notation and terminology of set theory
    De Morgan’s Laws
                                           is useful in every part of mathematics. So, we may say that
    Functions                             set theory is the language of mathematics. This subject, which
                                           originated from the works of George Boole (1815-1864) and
                                           Georg Cantor (1845-1918) in the later part of 19th century,
                                           has had a profound influence on the development of all
                                           branches of mathematics in the 20th century. It has helped
                                           in unifying many disconnected ideas and thus facilitated the
                                           advancement of mathematics.
                                                   In class IX, we have learnt the concept of set, some
       GeorGe Boole
                                           operations like union, intersection and difference of two sets.
                                           Here, we shall learn some more concepts relating to sets and
            (1815-1864)
              England                      another important concept in mathematics namely, function.
                                           First let us recall basic definitions with some examples. We
      Boole believed that there was
a close analogy between symbols that       denote all positive integers (natural numbers) by N and all
represent logical interactions and         real numbers by R .
algebraic symbols.                         1.2 Sets
        He used mathematical symbols       Definition
to express logical relations. Although
computers did not exist in his                A set is a collection of well-defined objects. The objects
day, Boole would be pleased to                in a set are called elements or members of that set.
know that his Boolean algebra                      Here, “well-defined” means that the criteria for
is the basis of all computer arithmetic.   deciding if an object belongs to the set or not, should be
       As the inventor of Boolean          defined without confusion.
logic-the basis of modern digital                  For example, the collection of all “tall people” in
computer logic - Boole is regarded in
                                           Chennai does not form a set, because here, the deciding criteria
hindsight as a founder of the field of
                                           “tall people” is not clearly defined. Hence this collection does
computer science.
                                           not define a set.

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Samacheer kalvi syllabus for 10th maths

  • 1. http://samacheerkalvi.net/ X Std. SYLLABUS Transactional Expected Learning No. of Topic Content Teaching Outcomes Periods Strategy i. Introduction • To revise the basic con- Use Venn ii. Properties of operations on cepts on Set operations diagrams for all sets • To understand the proper- illustrations iii. De Morgan’s laws-verifi- ties of operations of sets cation using example Venn - commutative, associative, diagram and distributive restricted Give examples to three sets. I. Sets and Functions iv. Formula for of functions from v. Functions • To understand the laws of economics, medi- complementation of sets. cine, science etc. • To understand De Mor- gan’s laws and demonstrat- ing them by Venn diagram 26 as well. • To solve word problems using the formula as well as Venn diagram. • To understand the defini- tion , types and representa- tion of functions. • To understand the types of functions with simple examples. i. Introduction • To understand to identify Use pattern ap- ii. Sequences an Arithmetic Progression proach iii. Arithmetic Progression and a Geometric Progres- II. Sequences and Series of (A.P) sion. Use dot pattern as iv. Geometric Progression • Able to apply to find the teaching aid Real Numbers (G.P) nth term of an Arithmetic v. Series Progression and a Geomet- Use patterns to ric Progression. derive formulae 27 • To determine the sum of n terms of an Arithmetic Examples to be Progression and a Geomet- given from real ric Progression. life situations • To determine the sum of some finite series. i. Solving linear equations • To understand the idea about Illustrative ii. Polynomials pair of linear equations in examples – iii. Synthetic division two unknowns. Solving a iv. Greatest common divisor pair of linear equations in Use charts as III. Algebra (GCD) two variables by elimination teaching aids and Least common mul- method and cross multipli- tiple (LCM) cation method. Recall GCD and v. Rational expressions • To understand the relation- LCM of numbers vi. Square root ship between zeros and co- initially vii. Quadratic Equations efficients of a polynomial with particular reference to quadratic polynomials. (v)
  • 2. http://samacheerkalvi.net/ • To determine the remain- Compare with der and the quotient of operations on the given polynomial fractions using Synthetic Division Method. • To determine the factors of the given polynomial using Synthetic Division Method. • Able to understand the dif- ference between GCD and Compare with the LCM, of rational expres- square root opera- sion. tion on numerals. • Able to simplify rational expressions (Simple Prob- Help students visualize the lems), III. Algebra nature of roots • To understand square algebraically and roots. graphically. • To understand the standard 40 form of a quadratic equa- tion . • To solve quadratic equa- tions (only real root) - by factorization, by complet- ing the square and by using quadratic formula. • Able to solve word prob- lems based on quadratic equations. • Able to correlate relation- ship between discriminant and nature of roots. • Able to Form quadratic equation when the roots are given. i. Introduction • Able to identify the order Using of rect- ii. Types of matrices and formation of matrices angular array of iii. Addition and subtraction • Able to recognize the types numbers. iv. Multiplication of matrices v. Matrix equation • Able to add and subtract Using real life the given matrices. situations. • To multiply a matrix by a IV. Matrices scalar, and the transpose of Arithmetic opera- a matrix. tions to be used 16 • To multiply the given matrices (2x2; 2x3; 3x2 Matrices). • Using matrix method solve the equations of two vari- ables. (vi)
  • 3. http://samacheerkalvi.net/ i. Introduction • To recall the distance Simple geometri- ii. Revision :Distance be- between two points, and cal result related tween two points locate the mid point of two to triangle and iii. Section formula, Mid given points. quadrilaterals to point formula, Centroid • To determine the point be verified as ap- formula of division using section plications. iv. Area of a triangle and formula (internal). quadrilateral • To calculate the area of a the form v. Straight line triangle. y = mx + c to be V. Coordinate Geometry • To determine the slope of taken as the start- a line when two points are ing point given, equation is given. 25 • To find an equation of line with the given information. • Able to find equation of a line in: slope-intercept form, point -slope form, two -point form, intercept form. • To find the equation of a straight line passing through a point which is (i) parallel (ii) perpendicular to a given straight line. i. Basic proportionality theo- • To understand the theo- Paper folding rem (with proof) rems and apply them to symmetry and ii. Converse of Basic propor- solve simple problems transformation tionality theorem only. techniques to be (with proof) adopted. iii. Angle bisector theorem Formal proof to (with proof - internal case VI. Geometry be given only) iv. Converse of Angle bisec- Drawing of 20 tor theorem (with proof figures - internal case only) v. Similar triangles (theo- Step by step rems without proof) logical proof with diagrams to be explained and discussed i. Introduction • Able to identify the By using Alge- ii. Identities Trigonometric identities braic formulae VII. Trigonometry iii. Heights and distances and apply them in simple problems. Using trigonomet- • To understand trigonomet- ric identities. 21 ric ratios and applies them to calculate heights and The approximate distances. nature of values (not more than two right to be explained triangles) (vii)
  • 4. http://samacheerkalvi.net/ i. Introduction • To determine volume and Use 3D models to ii. Surface Area and Volume surface area of cylinder, create combined VIII. Mensuration of Cylinder, Cone, Sphere, cone, sphere, hemisphere, shapes Hemisphere, Frustum frustum iii. Surface area and volume • Volume and surface area Use models and of combined figures of combined figures (only pictures ad teach- iv. Invariant volume two). ing aids. 24 • Some problems restricted to constant Volume. Choose examples from real life situ- ations. i. Introduction • Able to construct tangents To introduce ii. Construction of tangents to circles. algebraic verifica- to circles • Able to construct triangles, tion of length of IX. Practical Geometry iii. Construction of Triangles given its base, vertical tangent segments. iv. Construction of cyclic angle at the opposite vertex quadrilateral and Recall related (a) median properties of (b) altitude angles in a circle 15 (c) bisector. before construc- • Able to construct a cyclic tion. quadrilateral Recall relevant theorems in theo- retical geometry i. Introduction • Able to solve quadratic Interpreting skills ii. Quadratic graphs equations through graphs also to be taken iii. Some special graphs • To solve graphically the care of graphs X. Graphs equations of quadratics to . precede algebraic • Able to apply graphs to treatment. 10 solve word problems Real life situa- tions to be intro- duced. i. Recall Measures of central • To recall Mean for grouped Use real life situa- tendency and ungrouped data situa- tions like perfor- ii. Measures of dispersion tion to be avoided). mance in exami- XI. Statistics iii. Coefficient of variation • To understand the concept nation, sports, etc. of Dispersion and able 16 to find Range, Standard Deviation and Variance. • Able to calculate the coef- ficient of variation. i. Introduction • To understand Random Diagrams and ii. Probability-theoretical ap- experiments, Sample space investigations proach and Events – Mutually on coin tossing, XII. Probability iii. Addition Theorem on Exclusive, Complemen- die throwing and Probability tary, certain and impossible picking up the events. cards from a deck 15 • To understand addition of cards are to be Theorem on probability used. and apply it in solving some simple problems. (viii)
  • 5. http://samacheerkalvi.net/ CONTENTS 1. SETS AND FUNCTIONS 1-33 1.1 Introduction 1 1.2. Sets 1 1.3. Operations on Sets 3 1.4. Properties of Set Operations 5 1.5. De Morgan’s Laws 12 1.6. Cardinality of Sets 16 1.7. Relations 19 1.8. Functions 20 2. SEQUENCES AND SERIES OF REAL NUMBERS 34-67 2.1. Introduction 34 2.2. Sequences 35 2.3. Arithmetic Sequence 38 2.4. Geometric Sequence 43 2.5. Series 49 3. ALGEBRA 68-117 3.1 Introduction 68 3.2 System of Linear Equations in Two Unknowns 69 3.3 Quadratic Polynomials 80 3.4 Synthetic Division 82 3.5 Greatest Common Divisor and Least Common Multiple 86 3.6 Rational Expressions 93 3.7 Square Root 97 3.8 Quadratic Equations 101 4. MATRICES 118-139 4.1 Introduction 118 4.2 Formation of Matrices 119 4.3 Types of Matrices 121 4.4 Operation on Matrices 125 4.5 Properties of Matrix Addition 128 4.6 Multiplication of Matrices 130 4.7 Properties of Matrix Multiplication 132 (ix)
  • 6. http://samacheerkalvi.net/ 5. COORDINATE GEOMETRY 140-170 5.1 Introduction 140 5.2 Section Formula 140 5.3 Area of a Triangle 147 5.4 Collinearity of Three Points 148 5.5 Area of a Quadrilateral 148 5.6 Straight Lines 151 5.7 General form of Equation of a Straight Line 164 6. GEOMETRY 171-195 6.1 Introduction 171 6.2 Similar Triangles 182 6.3 Circles and Tangents 189 7. TRIGONOMETRY 196-218 7.1 Introduction 196 7.2 Trigonometric Identities 196 7.3 Heights and Distances 205 8. MENSURATION 219-248 8.1 Introduction 219 8.2 Surface Area 219 8.3 Volume 230 8.4 Combination of Solids 240 9. PRACTICAL GEOMETRY 249- 266 9.1 Introduction 249 9.2 Construction of Tangents to a Circle 250 9.3 Construction of Triangles 254 9.4 Construction of Cyclic Quadrilaterals 259 10. GRAPHS 267-278 10.1 Introduction 267 10.2 Quadratic Graphs 267 10.3 Some special Graphs 275 11. STATISTICS 279-298 11.1 Introduction 279 11.2 Measures of Dispersion 280 12. PROBABILITY 299 - 316 12.1 Introduction 299 12.2 Classical Definition of Probability 302 12.3 Addition theorem on Probability 309 (x)
  • 7. http://samacheerkalvi.net/ 1 SETS AND FUNCTIONS A set is Many that allows itself to be thought of as a One - Georg Cantor  Introduction  Sets 1.1 Introduction The concept of set is one of the fundamental concepts  Properties of set operations in mathematics. The notation and terminology of set theory  De Morgan’s Laws is useful in every part of mathematics. So, we may say that  Functions set theory is the language of mathematics. This subject, which originated from the works of George Boole (1815-1864) and Georg Cantor (1845-1918) in the later part of 19th century, has had a profound influence on the development of all branches of mathematics in the 20th century. It has helped in unifying many disconnected ideas and thus facilitated the advancement of mathematics. In class IX, we have learnt the concept of set, some GeorGe Boole operations like union, intersection and difference of two sets. Here, we shall learn some more concepts relating to sets and (1815-1864) England another important concept in mathematics namely, function. First let us recall basic definitions with some examples. We Boole believed that there was a close analogy between symbols that denote all positive integers (natural numbers) by N and all represent logical interactions and real numbers by R . algebraic symbols. 1.2 Sets He used mathematical symbols Definition to express logical relations. Although computers did not exist in his A set is a collection of well-defined objects. The objects day, Boole would be pleased to in a set are called elements or members of that set. know that his Boolean algebra Here, “well-defined” means that the criteria for is the basis of all computer arithmetic. deciding if an object belongs to the set or not, should be As the inventor of Boolean defined without confusion. logic-the basis of modern digital For example, the collection of all “tall people” in computer logic - Boole is regarded in Chennai does not form a set, because here, the deciding criteria hindsight as a founder of the field of “tall people” is not clearly defined. Hence this collection does computer science. not define a set.