B U S I N E S S M A T H E M A T I C S

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2 B U S I N E S S M A T H E M A T I C S For Grade XII Ashok Kumar Chaudhary Global College of Management Uniglobe HSS, +2 Science Bijay Lal Pradhan Birendra Multiple Campus Apex Educational Academy Chitwan Mukund Jha Caspain Valley College, Lalitpur Global College of Management, Ramchandra Sigdel Caspain Valley HSS, Lalitpur Kumari Academy, Prakash Karki Pashupati Multiple Campus Unified City HSS/College Durga Prasad Bajgain Pashupati Multiple Campus Raphi Bhandari Tri Chandra Multiple Campus The Times Intl' College Kist College the publisher Samjhana Publication Pvt. Ltd. Minbhawan,, PH

3 Business Mathematics XII Edition : 2071 Publisher : Samjhana Publication Pvt. Ltd. Minbhawan, Campus Road, Phone No.: Copyright : Authors Price : Rs. 395 / ISBN : Computer : Ranjeet Shrestha

4 Preface There is a general feeling in the students of management stream that mathematics is tough and dry. But, in this book, it is not so. The concepts are made simple and interesting, so that students can solve the exercise easily. One can find a variety of exercises chosen to suit for the +2 level management students, which will help them even in further higher education. We shall reckon our labours simply rewarded if the readers find the book useful to them. Thanks to Samjhana Publication Pvt. Ltd.,, they had published our book within the period of a fortnight. The readers may come across differences in conception; they are free to express their criticism, correction and suggestion. We will consider your opinion as a support for the improvement of this book. June, 2014 The Authors

5 New Syllabus Full Marks: 100 Teaching Hrs: 150 Course Contents Unit 1: Number System LH 7 Review of system of Natural numbers, Integers, Rational and Irrational numbers, Real numbers, Concept of inequalities and their properties, Absolute values and their properties (verification only), Complex numbers and their properties (verification only) Unit 2: Sets and Relations LH 7 Review of sets, Euler-Venn diagram and operation on sets, Properties of algebra of sets and their verification only (without theoretical proof), Number of elements in a set and the problems relating upon 3 sets, Cartesian product of two sets, Relation and function, Domain and range (Excluding types of function, inverse and composite functions) Unit 3: Sequence and Series LH 7 Difference between sequence, series and progression, Finite and infinite series, Types of progression (A.P., G.P. and H.P.), n th term of an A.P., sum of the n terms of the series in A.P., Arithmetic means, n th term of G.P., sum of the n terms of the series reducible to G.P. of the type (excluding sum to n terms of the type ) Unit 4: Permutation and Combination LH 5 Basic principles of counting, Meaning of n P r, Permutation of things when some are alike (simple cases only), Meaning of n C r, problems relating to combination (simple cases only) (Avoid the problems relating to restricted permutation like "two things arranged together". not arranged together) Unit 5: Matrices and Determinants LH 12 Matrix and its size, Types of matrices, Algebra of matrices,

6 Determinants and its evaluation upto third order, Properties of determinants Solving simultaneous of two and three variables by using Cramer's rule, solution of verbal problems of two variables only. Unit 6: Co-ordinate Geometry LH 9 Rectangular coordinates systems, Slope of a straight line joining two points, Distance between two points, Coordinates of a point dividing a line joining two points in a given ratio, Locus and equation, Equation of a straight line in slope-intercept form, double intercepts forms, point slope form and two points form, The point of intersection of two straight lines. Unit 7: Logarithms LH 6 Logarithm and its basic properties, change of base, Common logarithm table, use of common logarithm table in finding logarithm of a number, Antilog table, finding antilog of logarithm of a number. Unit 8: Functions, Limit and Continuity LH 10 Constant and variable, Definition and notation of function, Types of function and its graphic representation, Computation of functional values, Application of functions to Commerce and Economics, An intuitive idea of limit of a function, Basic rules of limit; limit at infinity, Concept of continuity and discontinuity (Note: Algebraic only) Unit 9: Differentiation LH 10 Definition and notation of derivatives, Geometrical meaning of derivatives, Differentiation of a function by first principle of algebraic functions only, Methods of differentiation, Differentiation of implicit function and parametric function, Second order derivatives, (Note: Derivative of algebraic, logarithmic and exponential functions only) Unit 10: Application of Derivatives LH 6 Application of derivative of commerce and economics, Increasing and decreasing function, point of inflection,

7 Maximum and minimum of a function and its application (Algebraic only) Unit 11: Integration LH 9 Integration as an inverse process of differentiation, Methods of integration by substitution and by parts, Concept of definite integral, Methods of evaluating definite integrals, Application of integration to commerce and economics, (Note: Anti derivative of algebraic, logarithmic and exponential functions only) Unit 12: Linear Programming Problems LH 7 Linear inequality in two variables and its graphical solution, System of linear inequalities in two variables and its graphical solution, Meaning of L.P.P. and its importance, Constraints, objective function, optimization, Mathematical formulation of L.P.P., Graphic method of solving L.P.P. Unit 13: Measures of Dispersion LH 12 Review of measures of Central Tendency, Range, quartile deviation, mean deviation and standard deviation and their relative measures Unit 14: Probability LH 6 Concept of probability, Addition and multiplication theorems without proof (mutually exclusive and independent cases with simple problems only) Unit 15: Mathematics of Gain and Loss LH 15 Ratio and proportion, Profit and loss, Partnership Unit 16: Mathematics of Finance LH 22 Money and exchange (chain method), Present worth and discount, Compound interest and compound depreciation, Annuity and its terminology: (a) Immediate annuity and computation of amount, present value only, (b) Annuity due and computation of amount, present value only (excluding deferred cases)

8 Table of Contents 1. Number System Sets and Relations Sequence, Series and Progression Permutation and Combination Matrices and Determinants Co-ordinate Geometry Logarithms Functions, Limits and Community Differentiation Application of Derivatives Integration Linear Programming Measure of Dispersion Probability Ratio and Proportion Profit and Loss Partnership Money and Exchange Present Worth and Discount Compound Interest and Depreciation Annuities Bibliography 465 Model Questions HSEB Logarithms and Anti Logarithms Table

9 Evaluation Scheme Unit Title Short answer questions Marks Long answer questions Marks Total marks 1. Number system 1 13= Sets and 1 13=3 3 Relations 3. Sequence and 2 23=6 6 Series 4. Permutation and 1 13=3 3 combination 5. Matrices and 1 13=3 1 15=5 8 Determinants 6. Co-ordinate 2 23=6 6 Geometry 7. Logarithms 1 13= Functions, Limit 2 23=6 6 and Continuity 9. Differentiation 1 13=3 1 15= Application of 1 15=5 5 Derivatives 11. Integration 2 23= Linear 1 15=5 5 Programming Problem 13. Measures of 1 13=3 1 15=5 8 Dispersion 14. Probability 1 13= Mathematics of 2 23=6 1 15=5 11 Gain and Loss 16. Mathematics of 2 23= = Finance 17. Total