(0) HSS Math Orientation Programme Basic Math XI

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NAMASTE GOOD MORNING g d :t] Nxf:;f], k\mofk'mNhL, ;nfdflnsd HjHjNkf

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NMC ... ... ... 2068 On Behalf of Please allow me to welcome you all at Today's Basic Mathematics Orientation Programme (NA MA S TE)

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? What Do We Do Today?

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We begin by asking questions like: Who Are We? What We Do? How We Go?

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Who Are We?

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D.A.O.K. Regd. No. 146/2067 NMC NEPAL MATHEMATICS CENTRE 2009 @)^^ We represent

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Makalu [left (8,462 m; 27,765 ft)], Everest [middle (8,848 m; 29,035 ft)] , Lhotse [middle (8,516 m; 27,939 ft)] and Cho Oyu [right (8,201 metres; 26,906 ft)] - from International Space Station NA MA S TE National Mathematical Sciences Team ECMAT PRIMAT SECMAT HISMAT GRAMAT REMAT (Special Teams ) Our collective name is

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Nepal Mathematics Centre is a non-profit service oriented educational foundation/Trust dedicated to the improvement of teaching, learning, evaluation, research and applications of mathematics in Nepal. Its short form is NMC. In Vernacular , it will be called “ g]kfn ul0ft s]Gb|” -g]us]_ . NMC

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NMC's main objectives are To launch a nationwide Mathematics Awareness Movement in order to convince the public in recognizing the need for better mathematics education for all children, To initiate a campaign for the recruitment, preparation, training and retaining teachers with strong background in mathematics,

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NMC's main objectives are To help promote the development and dissemination of innovative ideas, methods and materials in the teaching, learning and research in mathematics and mathematics education, To provide a forum for free discussion on all aspects of mathematics education,

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NMC's main objectives are To facilitate the development of consensus among diverse groups with respect to possible changes , and To work for the implementation of such changes.

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How We Go?

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Basic Mathematics, one of the basic components of Higher Secondary School Level Education, is now being taught on the basis of newly designed courses of study. Just A Few Words

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The present science and technology dominated 21st century world of work demands an increasingly improved teaching and learning environment.

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We have also initiated 1. the preparation of some kind of teaching materials and aids such as ppt , charts, worksheet, model questions and answers in order to facilitate teaching, learning and evaluation., 2. orientation programmes for students, teachers, various categories of stke-holders and Higher Secondary School mangers to convey the message that teaching, learning, evaluation and use of mathematics can be done in a comfortably easy and c ongenial atmosphere without any kind of tension.

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What Is There?

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Basic Mathematics XI There is

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I. Introduction: This course deals with the fundamentals of advanced mathematical concepts. It also tries to consolidate the concepts and skills learnt in Mathematics course in school level. It is desirable at the end of each unit sufficient related problems be solved. Mathematics 11 Higher Secondary School Curriculum (2067/2010) Full Marks 100 Teaching hours 150

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II. Specific Objectives: On completion of this course students will be able to: 1. use principles of elementary logic to find the validity of statement; 2. state field and order axioms of Real number system; 3. define functions and illustrate them graphically; 4. sketch the curves;

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II. Specific Objectives : 5. use trigonometrical relations to find the general values, understand inverse circular functions and their properties and to find property & solution of triangle; 6. state properties of A.S., G.S. and H.S. Understand infinite series and use method of mathematical induction to establish the result; 7. define transpose, adjoint and inverse of matrix, state properties of determinants; 8. use matrix and determinant to solve system of linear equations;

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9. explain the idea of a complex number, verify their properties, prove De-Moivre's theorem and use it; 10. define polynomial equations, establish fundamental theorem of algebra and quadratic equation, and find relation between roots and coefficients of a quadratic polynomials; 11. define straight lines, pair of lines in terms of co-ordinates and establish their properties; 12. define circle in terms of coordinates and establish their properties;

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13. define limit of a function, establish properties of limits; 14. define continuity of a function using the concept of limit; 15. define derivative of a function and give its geometrical interpretation as rate of change; 16. use derivative to determine the nature of the function and determine the maxima and minima of a function and apply differentiation to find tangent & normal, increasing & decreasing function; 17. define anti-derivative as an inverse process of derivative and use various methods of negation; and 18. define integration as the area of the sum, and apply definite integral to find the area between the curves.

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III. Course Contents: Unit 1: Sets, Real Number System and Logic 10 hrs Sets: Sets and set operations, Theorems based on set operations. Real Number System: Real numbers, Field axioms, Order axioms, Interval, Absolute value, Geometrical representation of the real numbers. Logic: Introduction, statements, Logical connectives, Truth tables, Basic laws of logic.

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Unit 2: Relations, Functions and Graphs 12 hrs Relations: Ordered pair, Cartesian product, Geometrical representation of Cartesian product, relation, Domain and range of a relation, Inverse of a relation. Functions: Definition, Domain and range of a function, Functions defined as mappings, Inverse function, Composite function, functions of special type (Identity, Constant, Absolute value, Greatest integer), Algebraic (Linear, quadratic and cubic), Trigonometric, Exponential logarithmic functions and their graphs.

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Unit 3: Curve Sketching 10 hrs Odd and even functions, Periodicity of a function, symmetry (about x – axis, y – axis and origin) of elementary functions, Monotonocity of a function, Sketching graphs of polynomial functions , Trigonometric, exponential, logarithmic functions (Simple cases only)

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Unit 4: Trigonometry 10 hrs Inverse circular functions, Trigonometric equations and general values, properties of a triangle (sine law, Cosine law, tangent law, Projection laws, Half angle laws), the area of a triangle. Solution of a triangle (simple cases)

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Unit 5: Sequence and Series, and Mathematical Induction 12 hrs Sequence and Series: Sequence and series, type of sequences and series (Arithmetic, Geometric, Harmonic), Properties of Arithmetic, Geometric, and Harmonic sequences, A.M., G.M. And H.M. Relation among A.M., G.M. and H.M., Sum of infinite geometric series. Mathematical Induction: Sum of finite natural numbers, Sum of the squares of first n – natural numbers, Sum of cubes of first n – natural numbers. Intuition and induction, principle of mathematical induction

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Unit 6: Matrices and Determinants 8 hrs Matrices and operation on matrices (Review), Transpose of a matrix and Its properties, Minors and Cofactors, (Adjoint ) Inverse matrix. Determinant of a square matrix, properties of determinants (Without proof) upto 3 × 3.

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Unit 7: System of Linear Equations 8 hrs Consistency of system of linear equations, solution of a system of linear equations by Cramer's rule, Matrix method (row – equivalent and Inverse) up to three variables.

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Unit 8: Complex Number 12 hrs Definition of a complex number, Imaginary unit, Algebra of complex numbers, Geometric representation of a complex number, Conjugate and absolute value (Modulus) of a complex numbers and their properties, Square root of a complex number, Polar form of a complex number, Product and Quotient of complex numbers. De Moivre's theorem and its application in finding the roots of a complex number, properties of cube roots of unity.

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Unit 9: Polynomial Equations 8 hrs Polynomial function and polynomial equations, Fundamental theorem of algebra (without proof), Quadratic equation Nature and roots of a quadratic equation, Relation between roots and coefficients, Formation of a quadratic equation, Symmetric roots, one or both roots common.

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Unit 10: Co-ordinate Geometry 12 hrs Straight line: Review of various forms of equation of straight lines, Angle between two straight lines, condition for parallelism and perpendicularity, length of perpendicular from a given point to a given line, Bisectors of the angles between two straight lines. Pair of lines: General equation of second degree in x and y, condition for representing a pair of lines, Homogeneous second degree equation in x and y, Angle between pair of lines, Bisectors of the angles between pair of lines.

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Unit 11: Circle 10 hrs Equation of a circle in various forms (Centre at origin, centre at any point, General equation of a circle, circle with a given diameter), Condition of Tangency of a line at a point to the circle, Tangent and normal to a circle.

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Unit 12: Limits and Continuity 10 hrs Limits of a function, Indeterminate forms, Algebraic properties of limits (without proof), Theorem on limits of algebraic, Trigonometric, Exponential and logarithmic functions Continuity of a function, Types of discontinuity, Graph of discontinuous function.

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Unit 13: The Derivatives 8 hrs Derivative of a function, Derivatives of algebraic, trigonometric, exponential and logarithmic functions by definition (simple forms), Rules of differentiation, Derivatives of parametric and implicit functions, Higher order derivatives

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Unit 14: Applications of Derivatives 12 hrs. Geometric interpretation of derivative, Monotonocity of a function, Interval of monotonocity, Extrema of a function, Concavity, Points of inflection, Derivative as rate measure.

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Unit 15: Anti-derivatives and its Applications 10 hrs Anti-derivative, Integration using basic integrals, Integration by substitution and by parts method, the definite integral, The definite integral as an area under the given curve, Area between two curve

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V. Reference books: 1. Adhikari, D.B. and et.al. Element of Mathematics Part I . Himalayan Book Stall. 2. Bajracharya, D.R. Higher Secondary Level Basic Mathematics Shreshtha, R.M. and et.al . ( For Grade XI) . Sukunda Pustak Bhawan. Kathmandu: 3. Bajracharya, P.M. and . Fundamentals of Mathematics for Grade XI . Basnet, G. Buddha Academic Publishers & Distributor P. Ltd. Kathmandu: 4. Koirala, S. and et.al. Fundamentals of Mathematics . Nepal Sahitya Prakashan Kendra. Kathmandu: 5. Pant, S.R. and et.al. A Text-Book of Higher Secondary Mathematics (For Grade XI). Buddha Academic Publishers and Distributors P.Ltd. Kathmandu: 6. Uprety, K.N. and., Foundation of Mathematics, (For Grade XI) . Ghimire, K.P . Pigeon Educational Publisher .

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