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)
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)
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)
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)
http://samacheerkalvi.net/ CONTENTS1. 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 202. 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 493. 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 1014. 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)
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 1646. GEOMETRY 171-195 6.1 Introduction 171 6.2 Similar Triangles 182 6.3 Circles and Tangents 1897. TRIGONOMETRY 196-218 7.1 Introduction 196 7.2 Trigonometric Identities 196 7.3 Heights and Distances 2058. MENSURATION 219-248 8.1 Introduction 219 8.2 Surface Area 219 8.3 Volume 230 8.4 Combination of Solids 2409. 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 25910. GRAPHS 267-278 10.1 Introduction 267 10.2 Quadratic Graphs 267 10.3 Some special Graphs 27511. STATISTICS 279-298 11.1 Introduction 279 11.2 Measures of Dispersion 28012. PROBABILITY 299 - 316 12.1 Introduction 299 12.2 Classical Definition of Probability 302 12.3 Addition theorem on Probability 309 (x)
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 wasa close analogy between symbols that denote all positive integers (natural numbers) by N and allrepresent logical interactions and real numbers by R .algebraic symbols. 1.2 Sets He used mathematical symbols Definitionto express logical relations. Althoughcomputers did not exist in his A set is a collection of well-defined objects. The objectsday, 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 foris 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” incomputer logic - Boole is regarded in Chennai does not form a set, because here, the deciding criteriahindsight as a founder of the field of “tall people” is not clearly defined. Hence this collection doescomputer science. not define a set.