MATHEMATICS (3 11)

During modern period, Srinivasa Ramanujan was one of India’s greatest Mathematical geniuses.Ramanujan’s contribution was mostly on Number theory and he had obtained over mastery thenumber 1729. Ramanujan discovered that 1729 is the smallest number which could be representedin two different ways as a sum of two cubes. After that,1729 has been called “Ramanujan-Hardynumber”. Shakuntala Devi is a world renowned Indian Mathematician. She has been nicknamed‘Human Computer” because of her innate ability to solve complex mathematical problems withoutusing any kind of aid.The main goal of Mathematics education in schools is the Mathematisation of the child’s thinking.Clarity of thought and pursuing assumptions to logical conclusions is central to the Mathematicalenterprise. There are many ways of thinking, and the kind of thinking one learns in Mathematicsis an ability to handle abstractions, and an approach to problem solving. The procedural knowledgei.e. to solve problems for getting answers only is not enough. At the Senior Secondary stage oneneeds to develop both procedural as well as conceptual knowledge for better understanding ofMathematics. Success in Mathematics requires more than just computational skills. It also requiresthe ability to apply Mathematics in solving problems, to more information from a variety ofsources. Senior Secondary stage is the launching pad from which the learner is guided towardscareer choices, whether learners aspire in university education or otherwise. By this time, thelearners’ interests and aptitude have been largely determined, and Mathematics education inthese two years can help in sharpening their abilities.Many university degrees require Mathematics as a pre requirement. Learners who choose not totake Mathematics seriously or to ignore it in secondary and senior secondary level forfeit manyfuture career opportunities that they could have. They essentially turn their backs on more thanhalf the job market. The importance of mathematics for potential careers cannot be overemphasized. To get degrees in the following areas i.e. the Physical Sciences (Chemistry, Physics,Engineering), the life and health sciences (Biology, Psychology, Pharmacy, Nursing, Optometry),Social Sciences, including Anthropology, Communications, Economics, Linguists, Education,Geography the Tech Sciences, like Computer Science, Networking, Software development,Business and Commerce Medicine, Actuarial science, used by insurance companies, one needto have good knowledge of Mathematics and Statistics. Learning Mathematics at SeniorSecondary stage helps to choose a career in several areas. The diagram below depicts some ofthese ematicsCareersComputingEngineeringMathematicsOther CareersE.g. Sales/HR/AdministrationStatisticianActuary /InsuranceOperationalResearcherPostgraduateStudy

How to Use the Study MaterialsYou should note that taking admission in the National Institute of Open Schooling (NIOS), youhave entered in a system where studying is different than in a formal school.You Are a Self Learner NowIn a school, a teacher is always available to take classes, clarify doubts, guide and encourage.There you also must be discussing with your peer-group, going to the library, doing practicals,participate in co-curricular activities, watching educational TV, Radio programmes etc. All thiswas also contributing to your learning.However, in the NIOS, there is no teacher available and you have to learn on your own, It meansthat you have become a self-learner. Responsibilities of a self-learner are much more than anormal learner who is dependent on a teacher; but at the same time it is also challenging. Here itis solely you, who is responsible for your learning. It means that you have to organize your study,learn regularly, keep up your motivation and achieve your goal.Understanding Your Learning MaterialThe NIOS will help you by providing learning material, part of which is in your hands at thismoment. We call them learning materials because these are different from the textbooks youhave read in your schools. Here the textbooks and the teachers have been put together. You willfind that the contents, concepts and topics have been explained here in a way the teacher does ina classroom. You will also find examples and illustrations to help you understand the thingsproperly.This is the reason you will find them bulky, but let this shall not frighten you. You will find a fewsections in your lessons. Let us know the purpose of these:Introduction: It introduces the topic to you.Objectives: Here you will find the list of objectives, which you shall achieve afterlearning the lesson. You can actually check whether or not you have achieved thesebecause these are presented in measurable terms.1A%CCheck Your Progress: These will appear after every section of the lesson. They willcontain objective, very short answer, short answer and long answer type questionsbased on each lesson. This will help you to find whether you have learnt the section ornot. Your will find the key to these questions at the end of the lesson. If you are ableto answer the questions, then you can proceed further otherwise you should learn thesection again. Let us Sum up: Here you will find the summary of the main concepts of the lessonfor recapitulation and revision.Terminal Exercise: Here short answer and long answer type questions are given tohelp you enhance your learning and give you an opportunity to practice for examination.Answers: Answers of all “Check Your Progress” and “Terminal Exercise” are givenat the end of each lesson. Some hints are also given in case of difficult questions.Apart from the learning material, you will also get, sample papers, previous yearquestion papers, etc., for help in your studies and for practice for examination.

Personal Contact ProgrammesA few sessions/ classes would be provided to you at the center. You should, however, note thatthose are not meant for teaching you as it happens in a normal school. Here you will have anopportunity to clarify your doubts, solve your problems and get guidance and advice on yourstudy. So go to the classes well prepared to get maximum benefit.Use of Audio and Video ProgrammesNIOS has also developed a few audio and video programmes, which will be very interesting foryou and will help you in your studies. You can take copies of this from your Center.Planning and Organizing Your StudyLet me also give you some tips for planning and organizing your study.First of all, you need to understand that there is no substitute for hard work. Harder you workbetter you achieve. Also, there are no short cuts to success. If someone has given you assuranceof helping you in passing, then that will not work as there will be strict checking and vigilance inthe exam. Even if you are able to get through somehow, you will not gain any learning. So in orderto succeed in an honest way and get benefit of your learning in your life, you need to learn.As you must have understood by now, the NIOS provides a lot of freedom and flexibilities inyour study. For example, there is no need to take examination in all the subjects simultaneously.So, first of all, think about the time available with you and decide whether you wish to study allthe subjects together or you wish to learn them one after the other. Just gambling in all thesubjects will bring you to a situation where you will not be able concentrate on any subject.Now fix up a time for study, evening, morning or daytime whichever is convenient Draw atimetable giving justified time to the subjects you have taken up for study and follow this as far aspossible. While you study, underline the concepts you feel are important. You should study fromNIOS learning material. In addition you may read other-books, if you have time. However, foryour purpose, this material will be sufficient. Keep a copy each for the subjects you are preparing.Note down the points you did not understand. Discuss these with your parents, friends or teachersat the centres.Solve all the exercises, and practice exercises of each module appearing in the material. Thiswill not only help you in learning, but also provide practice for your examination. You may alsolike to solve sample papers and previous years’ question papers. Show your answers to yourparents and friends and discuss with them.These were a few hints to help you. You may find some other techniques which may workbetter with you. Follow those, if you like. I am sure you will be successful in your endeavor.

Course OverviewPart-1: [For Tutor Marked Assignment]Module-I: Sets, Relations and Functions1.Sets2.Relations and Functions-I3.Trigonometric Functions-I4.Trigonometric Functions-II5.Relation between Sides and Angles of A triangleModule- II: Sequences and Series6.Sequences and Series7.Some Special SequencesModule -III: Algebra-I8.Complex Numbers9.Quadratic Equations and Linear inequalities10.Principle of Mathematical Induction11.Permutations and Combinations12.Binomial TheoremModule-IV: Co-ordinate Geometry13.Cartesian System of Rectangular Co-ordinates14.Straight Lines15.Circles16.Conic SectionsModule-V: Statistics and Probability17.Measures of Dispersion18.Random Experiments and Events19.ProbabilityIMPORTANT NOTE: All contents of Part-1 will be assessed/examined through Tutor MarkedAssignment (TMA). TMA is compulsory and contains 20% marks as weightage. The Marks/Grades of TMA will be reflected in the mark sheet.

Part-2: [For Public Examination]Module-VI: Algebra-II20.Matrices21.Determinants22.Inverse of a Matrix and its ApplicationsModule-VII: Relations and Functions23.Relations and Functions-II24.Inverse Trigonometric FunctionsModule-VIII: Calculus25.Limits and Continuity26.Differentiation27.Differentiation of Trigonometric functions28.Differentiation of Exponential and Logarithmic functions29.Application of Derivatives30.Integration31.Definite Integrals32.Differential EquationsModule-IX: Vectors and Three Dimensional Geometry33.Introduction to Three Dimentional Geometry34.Vectors35.Plane36.Straight LineModule-X: Linear Programming and Mathematical Reasoning37.Linear Programming38.Mathematical ReasoningIMPORTANT NOTE: All Contents of Part-2 will be assessed/examined through Public/FinalExamination. Public Examination is compulsory and contains 80% marks as weightage.

CONTENTSModule-I: Sets, Relations and Functions1. Sets .01-242. Relations and Functions-I .25-583. Trigonometric Functions-I .59-944. Trigonometric Functions-II .95-1265. Relation between Sides and Angles of a Triangle .127-138Module- II: Sequences and Series .139-1406. Sequences and Series .141-1687. Some special sequences .169-178Module -III: Algebra-I .179-1808. Complex Numbers .181-2089. Quadratic Equations and Linear Inequalities .209-23410. Principle of Mathematical Induction .235-24611. Permutations and Combinations .247-27012. Binomial Theorem .271-284Module-IV: Co-ordinate Geometry .285-28613. Cartesian System of Rectangular Co-ordinates .287-31614. Straight Lines .317-34415. Circles .345-35216. Conic Sections .353-370Module-V: Statistics and Probability .371-37217. Measures of Dispersion .373-41018. Random Experiments and Events .411-42019. Probability .421-466Curriculum . i-viiiFeedback form . ix-x

NIOS Curriculum for Senior Secondary CourseCURRICULUM OF SENIOR SECONDARY COURSEIN MATHEMATICS (311)1.RATIONALEMathematics is an important discipline of learning at the Senior Secondary stage. It helps the learner inacquiring decision making ability through its applications to real life both in familiar and unfamiliar situations.It predominantly contributes to the development of precision, rational reasoning and analytical thinking. Inthe Senior Secondary stage is most crucial where learners for the first time move towards diversification.At this stage, the learners start thinking to take important decisions concerning their future career bychoosing suitable courses. It is the stage, from where learners would either go for higher academic educationin Mathematics or for Professional courses or it may be the end of their academic career. One of the basicaims of learning Mathematics at Senior Secondary level is to be developed problem solving skills andquantificational experiences around the learners. It includes a way of doing things, and the ability andattitude to formulate and solve problems (NCF, 2005). The idea is to allow the learner to realize how andwhy Mathematics is all around us. In view of these facts, it is important to make Mathematics Education atthis level broad based and meaningful. The revised curriculum in Mathematics has been designed to meetthe needs of diversity of learners. The contents and design of the revised curriculum broadly based on thecommon curriculum suggested by Council of Boards of School Education in India (COBSE). In order torelate Mathematics to real life and work situations of NIOS learners, greater emphasis has been put onapplications of various concepts.2.OBJECTIVESThe main objectives of learning Mathematics at Senior Secondary level are to enables the learners to: acquire knowledge and understanding of basic concepts, facts, principles, terms, symbols andprocesses of Mathematics. acquire the skills of quantification of experiences around them and make linkage with their life. articulate logically and use the same to prove results. convert the word problems in the mathematical forms and solve them. introduce learners to different ways of processing the given data and help them in arriving atconclusions provide learners with an appreciation of the wide variety of application of Mathematics and equipthem with the basic device that enable such application develop appreciation for the influence and exquisiteness of Mathematics for its applications inScience, Commerce, Economics and daily life apply mathematical knowledge and skills to solve variety problems. develop positive attitude towards Mathematics and its application.3.COURSE STRUCTURE:The present curriculum in Mathematics has been distributed into two parts and ten modules. Part-1 consistsof five modules namely as: Sets; Relation and Function; Sequences and Series; Algebra-I; Co-ordinateGeometry; Statistics and Probability. Similarly five modules are inside the Part-2 namely as: Algebra-II;Relations and Functions; Calculus; Vectors and Three Dimensional Geometry; Linear Programming andMathematical Reasoning. Each module has been divided further into different lessons.The number of Lesson and suggested study time allotted for each module is as follows:iMathematics (311)

NIOS Curriculum for Senior Secondary CoursePart-1Module/ LessonNo. of LessonsModule-I: Sets, Relations and FunctionsStudy Time (in hours)05300215053004300315191201. Sets2. Relations and Functions-I3. Trigonometric Functions-II4. Trigonometric Functions-II5. Relation between Sides and Angles of a TriangleModule- II: Sequences and Series6. Sequences and Series7. Some Special SequencesModule -III: Algebra-I8. Complex Numbers9. Quadratic Equations and Linear Inequalities10. Principle of Mathematical Induction11. Permutations and Combinations12. Binomial TheoremModule-IV: Co-ordinate Geometry13 Cartesian System of Rectangular Co-ordinates14 Straight Lines15 Circles16 Conic SectionsModule-V: Statistics and Probability17 Measures of Dispersion18.Random Experiments and Events19.ProbabilityTotaliiMathematics (311)

NIOS Curriculum for Senior Secondary CoursePart-2Module/ LessonNo. of LessonsModule-VI: Algebra-IIStudy Time (in hours)033002300860043020. Matrices21. Determinants22. Inverse of a Matrix and its ApplicationsModule-VII: Relations and Functions23. Relation and Functions-II24. Inverse Trigonometric FunctionsModule-VIII: Calculus25. Limits and Continuity26. Differentiation27. Differentiation of Trigonometric Functions28. Differentiation of Exponential and Logarithmic Functions29. Application of Derivatives30. Integration31.Definite Integrals32. Differential EquationsModule-IX: Vectors and Three Dimensional Geometry33. Introduction to Three Dimensional Geometry34. Vectors35. Plane36. Straight LineModule-X: Linear Programming and Mathematical Reasoning023037. Linear Programming38. Mathematical ReasoningTotal 19Mathematics (311)180iii

NIOS Curriculum for Senior Secondary Course4.COURSE DESCRIPTIONPart-1Module I : Sets, Relation and Function.Lesson 1 : SetsSets and their representations, Classification of Sets, Sub- sets, Intervals as subsets of real numbers,Power Set , Universal set, Venn Diagram, Difference of sets, Complement of a set and its properties,Union and Intersection of sets,Lesson 2 : Relations and Functions -ICartesian product of two sets, Cartesion product of the reals with itself, Definition of relation, Domain,Co-domin and range of a relation, Definition of a Function, Domain and Co-domain and Range of aFunction, Graphical representation of a function, some special functions, sum, difference, product and quotient of functions.Lesson 3 : Trigonometric Functions -ICircular measure of angle, Trigonometric functions, Trigonometric functions of some specific real numbers,Graphs of Trigonometric functions, Periodicity of the Trigonometric functions,Lesson 4 : Trigonomertic Functions-IIAddition and Multiplication of Trigonometric Functions, Trans formation of products into sums and viceversa, Trigonometric functions of multiples a

NCERT, New Delhi PG DAV College Dept. of Maths Nehru Nagar, New Delhi Jamia Milia Islamia University, New Delhi Prof. D.P. Shukla Prof. V.P. Gupta Prof. C.P.S. Chauhan Dept. of Maths Dept. of Measurement Dept. of Education Lucknow University & Evaluation, NCE