Business Mathematics Syllabus and Model Question  NEB Syllabus Management 12 includes Accounting, Economics, Finance, Business Maths, Business Studies, Marketing, Computer Science, Nepali, English, Life Skill Education
About NEB
National Examinations BoardNEB (formerly Higher Secondary Education BoardHSEB) is the only one education board of Nepal Government.
The Board has a separate seal for its own work implementation purpose.
The examination related tasks of Grade 10 (Secondary Education Examinations (SEE) and class 11 and 12 (School Leaving Certificate Examination (SLCE) have now been affiliated to the jurisdiction of NEB as integrated components.
The examinations of class 10 will be brought into operation in the regional/provincial level.
Compulsory Subjects, Grade 12
Nepali
English
Social Studies and Life Skills Education
Optional Subjects Group 1, Grade 12
Physics
Accounting
Rural Development
Nepalese Legal System
Health and Physical Education
Sports Science
Instructional Pedagogy and Evaluation
Psychology
History
Gender Studies
Hospitality Management
Agronomy
Naturopathy
Human Value Education
Sculpture
Optional Subjects Group 2, Grade 12
Biology
Education and Development
Geography
Procedural Law
Sociology
Ayurveda
Business Studies
Linguistics
Political Science
Philosophy
Population Studies
Horticulture (Fruits, Vegetable, Floriculture, and Mushroom farming)
Food and Nutrition
Dance
Computer Science
Optional Subjects Group 3, Grade 12
Chemistry
Economics
Tourism and Mountaineering Studies
Marketing
Gerontology and Caretaking Education
Yog
Vocal / Instrumental
Sweing and Knitting
Criminal Law and Justice
Culinary Arts
Culture
Fashion Designing
Film and Documentary
Animal Husbandry, Poultry, and Fisheries
Nepali Major
English Major
Maithali
Newari
Hindi
Chinese
German
Japanese
Korean
Urdu
French
Hebrew
Arabic
Sanskrit
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Share (Accounting for Share) 

Share in Nepali 

Debentures 

Final Account: Class 12 

Final Account in Nepali 

Work Sheet 

Ratio Analysis (Accounting Ratio) 

Fund Flow Statement 

Cash Flow Statement 

Theory Accounting Xii 

Theory: Cost Accounting 

Cost Accounting 

LIFO−FIFO 

Cost Sheet, Unit Costing 

Cost Reconciliation Statement 
#####
Optional Subjects Group 4, Grade 12
Mathematics
Applied Mathematics
Business Mathematics
Human Rights
Library and Information Science
Home Science
Environment Science
General Law
Finance
Cooperative Management
Buddhist Studies
Applied Arts
Singing
Painting
Sericulture and Bee Keeping
Beautician and Hair Dressing
Medicinal Herbals
Plumbing and Wiring
Internal Decoration
Hotel Management
Mass Communication
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Business Mathematics
Grades: 12
Subject code: Bmt. 406
Credit hours: 5
Working hours: 160
1. Introduction
Business primarily revolves around the financial transaction or products that have some monetary value. Involvement of finance makes it extremely important to have sufficient knowledge about the basics of calculations. This is where business mathematics comes into play. It deals with the fundamental topics that one needs to carry out business related calculations. Realizing the necessity to impart the same on students, the curriculum has been developed for Grades 11 and 12 so as to prepare them for job market and for higher studies.
The curriculum of Business Mathematics for Grade 11 and 12 is designed to equip the students with mathematical and statistical concepts applicable in business and economics. The purpose of this course, then, is to present mathematical and statistical skills and concepts so that the students will be able to use them in management, economics, and social sciences. As mathematics and statistics are widely used in economics, business and finance, the students need a certain level of skill and understanding of the basic mathematical and statistical methods. The pedagogical approaches in delivering the course should consider the balance between theory and practice. In doing so, students should provide ample opportunities of working actively in realworld problems. The same applies in case of student evaluation procedure too.
The curriculum has different sections: levelwise competencies, gradewise learning outcomes, contents and their elaboration, suggested project works, learning facilitation process and the assessment procedure. The major content areas included in this course are: algebra, calculus, financial mathematics, linear programming, statistics and probability.
2. Levelwise Competencies
By the end of the grade 12, the students will have the following competencies.
1. Understand the concepts of algebra and employ a variety of thinking processes and strategies to truly understand the concepts that underlie the business problems.
2. Apply calculus in business and economics fields.
3. Apply partnership, present worth and discount, arithmetic sequence and series, geometric sequence and series, compound interest and depreciation, NPV and IRR, annuity in business and many other fields.
4. Maximize the profit and minimize the cost under very limited resources used.
5. Apply statistical knowledge and skills for their personal development and future career pathways, and analyze the data using Ms. Excel.
6. Develop appropriate process skills for the acquisition and application of mathematical concepts and skills.
7. Apply mathematical and statistical knowledge and skills for their personal development and future career pathways.
8. Apply modern technology to solve problems related to business and economic fields.
3. Gradewise Learning Outcomes
1.1 Perform matrix operations.
1.2 Use laws of matrix algebra.
1.3 Find the transpose of a matrix.
1.4 Evaluate determinants (up to third order).
1.5 Find ad joint and inverse of a matrix.
1.6 Solve system of linear equations by Cramer’s rule, inverse matrix method and Gauss elimination method.
1.7 Solve problems of input/output analysis.
1.8 Use excel in solving problems of matrix algebra.
2.1 Define monotonic functions and test the monotonicity.
2.2 Identify stationary point and point of inflection.
2.3 Solve problems related elasticity of demand.
2.4 Acquaint with relation between the marginal revenue, average revenue and elasticity of demand.
2.5 Optimize functions of one variable using derivative.
2.6 Define the definite integral using the Fundamental Theorem of Calculus.
2.7 Find the area under a curve (simple problems only).
2.8 Solve problems of marginal analysis, consumer and producer surplus.
2.9 Solve firstorder linear differential equations with constant coefficient and constant term.
2.10 Solve differential equations for limited and unlimited growth.
2.11 Dynamics of market price function (Dynamic analysis)
3.1 Solve problems of geometric sequence and series.
3.2 Solve problems of compound interest and depreciation.
3.3 Find net present value and internal rate of return.
3.4 Compare investment projects.
3.5 Solve problems of ordinary annuity, annuity due, deferred annuity, perpetuities and sinking funds.
3.6 Use excel in solving problems of financial mathematics.
4.1 Define standard LP Problems.
4.2 Solve LP Problems by simplex method and its application in business and economics.
4.3 Solve standard minimization LP Problems using duality.
5.1 Find Karl Pearson’s and Bowley’s coefficient of skewness.
5.2 Find the five number summaries of raw data.
5.3 Define correlation and find correlation coefficient by Karl Pearson’s method and interpret the result.
5.4 Define regression and find regression lines of Y on X and X on Y using least square method.
5.5 Use excel in solving problems of Skewness, Correlation and Regression.
6.1 Define conditional probability and solve the related problems.
6.2 Use multiplication law of probability for dependent events.
6.3 State and apply the Bayes’ theorem (simple problems only).
6.4 Define mathematical expectation and variance of a discrete random variable and solve related problems.
6.5 Define binomial distribution.
6.6 Use characteristics of the binomial distribution to solve the simple problems only.
6.7 Find mean and standard deviation of the binomial distribution.
6.8 Use excels in solving problems of conditional probability, Bayes’ theorem, Expected Value, Binomial Probability.
4. Scope and Sequence of Contents
1. Algebra LH21
1.1 Matrices and Determinants
Matrix and its Operations
Laws of Matrix Algebra
Transpose of a matrix
Determinants (up to third order)
Ad joint and Inverse of a matrix
Elementary row operations
Solving System of linear equations (Up to three variables by using Cramer’s rule, inverse matrix method and Gauss elimination method)
Input/output analysis
1.2 Comp. Work: Excel for matrix algebra
2. Calculus LH40
2.1 Applications of Derivatives
Monotonic functions
Stationary point and Point of inflection
Elasticity of demand and the derivatives
Relation between the marginal revenue, average revenue and elasticity of demand
Optimization of functions of one variable
Economic application of maximum and minimum points (Algebraic function only)
2.2 Definite Integral and its Applications
Definite Integral using the Fundamental Theorem of Calculus
Area under a Curve (simple problems only)
Marginal analysis
Consumer and Producer Surplus
2.3 Differential equations and Applications
Differential equations and necessary terminologies
Solution of firstorder linear differential equations with constant coefficient and constant term
Differential equations for limited and unlimited growth
Dynamics of market price functions (Dynamic analysis)
3. Financial Mathematics LH17
3.1 Financial Mathematics
Geometric sequence and series
Compound Interest and Deprecation
Net present value and internal rate of return
Ordinary annuity o Annuity due
Deferred annuity
Perpetuities
Sinking funds
3.2 Comp. Work:
Excel for financial mathematics
4. Linear Programming Problem LH10
4.1 Linear Programming Problem
Standard LP Problems
Simplex method of solving linear programming problem (two decision variables only)
Duality and Standard Minimization LP Problems
4.2 Comp. Work:
Online Simplex Method
5. Statistics LH20
5.1 Skewness o Karl Pearson’s and Bowley’s coefficient of skewness
5.2 Correlation o Correlation Coefficient by Karl Pearson’s method and its Interpretations
5.3 Regression o Regression lines of Y on X and X on Y by least square method
5.4 Comp. Work: Excel for Skewness, five number summaries of raw data, Correlation and Regression
6. Probability LH12
6.1 Probability
Conditional probability
Multiplication Law of probability (dependent events only) o
Bayes’ theorem
6.2 Random Variables
Mathematical expectation and Variance of Discrete Random Variable
6.3 Binomial Distribution
Binomial distribution
Characteristics of the Binomial Distribution
Mean and Standard Deviation of the Binomial Distribution
6.4 Comp. Work:
Excel for Conditional probability, Bayes’ theorem, Expected Value, Binomial Probability
5. Suggested Practical/Project Activities
During project works, students learn by actively engaging in realworld. Project work allows the students to study, do research and act by themselves using their abilities, interests, personal experience and aptitudes. Doing the computer works using excel requires students solve and analyze mathematical and statistical problems.
Each Student should do one project work or computer work (in the given table below, the second row in each content areas contains the project works and content areas where there is only one row the task is designed for project work) from each of six content areas and should give a 15minute presentation. The project works or computer works will be documented in a file and will be submitted at the time of practical evaluation. Out of the project works, anyone can be presented at the time of practical evaluation. Whatever the style, the project work should include the following points:
· Historical background
· Description
· Key features or properties
· Relationship with others
· Geometrical illustrations
· Practical significance
· Varieties of examples other than those given in the textbook
· Limitations
· Varieties of problems with solutions other than those given in the textbook
· Use in everyday life, business, economics, finance, etc.
· Conclusion
The project works will be evaluated on the basis of clarity of aims, originality, presentation style and the skills demonstrated.
SN 
Content Area 
Task 
LH 
1 
Algebra 
o Performing basic operations on matrices using excel. o Evaluating a determinant of a Matrix using excel. o Solving system of linear equations using matrices. o Solving problems involving a Leontief inputoutput model using excel. o Applications of matrices in real life. o Methods of solving system of linear equations by using Cramer’s rule, inverse matrix method and Gauss elimination method. 
7 
2 
Calculus 
o Applications of maxima and minima of one variable in daily life. o Calculating consumer surplus and producer surplus using definite integral. o Applications of differential equations with constant coefficient and constant term in economics. 
7 
3 
Financial Mathematics 
o Solving some problems of geometric sequence and series using excel. o Solving some problems of compound interest and depreciation using excel. o Solving some problems of net present value and internal rate of return using excel. o Solving some problems on amount of immediate annuity and annuity due using excel. o Solving some problems on present value of immediate annuity and annuity due using excel. o Solving some problems on present value of deferred annuity using excel. o Solving some problems on present value of perpetual annuity using excel. o Investigation on geometric sequence and series can be applied in real life situations. o Applying the concept of compound interest and depreciation in all areas of life. o Net present value (NPV) and internal rate of return (IRR) methods for project evaluation. o Calculating amount and present values of annuities in real life situations. 

4 
Linear Programming 
o Simplex method of solving linear programming problem(LPP) o Simplex method of solving linear programming problem(LPP) 
5 
5 
Statistics 
o Calculating Karl Pearson’s and Bowley’ coefficient of skewness for individual series, discrete series and continuous series using excel. o Calculating five number summary for individual series, discrete series and continuous series using excel. o Calculating Karl Pearson’s correlation coefficient using excel. o Estimating regression lines of Y on X and that of X on Y using excel. o Skewness in statistics. o Calculating correlation coefficient by Karl Pearson’s method and its interpretation in real life situations. o Estimating simple regression lines of Y on X and X on Y in real life situations. 
11 
6 
Probability 
o Solving some problems on conditional probability and Bayes’ theorem using excel. o Finding expected value and variance of discrete random variable using excel. o Finding the probability of an event of binomial distribution using excel. o Finding the mean and standard deviation of binomial distribution using excel. o Developing conceptual understanding of Conditional Probability and Bayes’ theorem through explanation. o Developing conceptual understanding of Binomial distribution through explanation. 
4 

Total 

40 
Prerequisites for computer based tasks: Spreadsheets Introduction, Files, Cells, Cell Address, Cell Format, Cell Content, Cell Value, Formulas, Copy, Paste, Fill, Charts, Conclusion.
6. Learning Facilitation Methods and Process
The following principles should guide the learning facilitation of business mathematics:
· One of the most important principles in teaching mathematics is “Let It Make Sense”. The course assumes minimal mathematical background but includes the usefulness and relevance of basic mathematics in economics, finance, and business.
· Students need to be able to navigate their lives in this eversocomplex modern world. This involves dealing with interest, annuities, taxes, loans, purchases, budgeting etc. Our youngsters need to be able to handle money wisely. All that requires good understanding of parts, proportions, and percentages.
· Another very important approach of mathematics education as a whole is to enable the students to understand information around us. In today’s world, this includes quite a bit of scientific information. Being able to read through it and make sense of it requires knowing statistics and probability.
· We need to prepare our students for further studies. Not everyone ultimately needs algebra, calculus, linear programming, but many do, and teens don’t always know what profession they might choose or end up with.
· Let students see some beauty of mathematics and learn to like it, or at the very least, make sure they don’t have negative felling towards mathematics.
· Finally, let students be familiar with modern computation skill. This involves working with excel.
It’s important to learn how to use any tool the student might acquire. Quantity won’t equal quality. Knowing a few “math tools” inside out is more beneficial than a mindless dashing to find the newest activity to spice up the math lessons. In this course, we do not show how the mathematical results have been obtained and proved, but we show how they may be used in reallife economics and business.
Gaining purposeful learning experiences through solving problems in relevant and meaningful contexts allows students to view mathematics in a practical setting relevant to their intended careers, and also motivates them to move on to increasingly more abstract concepts.
Teacher has to analyze and diagnose the weakness of the students and create appropriate learning environment to solve mathematical problems in teaching learning process. The following are some of the methods and techniques which can be used in delivering this course.
· Problem solving
· Case study
· Project work
· Question answer
· Discussion
· Discovery
· ICT
· Cooperative learning
· Lecture
7. Student Assessment
Continuous assessment of students for formative purpose will be an integral part of teaching learning process. Student’s summative evaluation will be done using both internal (25%) and external examination (75%).
(a) Internal Evaluation
Practical evaluation includes written tests (first term, second term), classroom participation and project work including presentation /excels lab work. The scores of evaluation will be used for providing feedback and to improve their learning. The criteria for internal evaluation are shown in the following table:
SN 
Criteria 
Marks 
1 
Classroom participation (Daily attendance, home assignment and classwork, participation in learning, participation in other activities) 
3 
2 
Trimester exam (3 marks from each trimester exam) 
6 
3 
Project work, project report and presentation 
16 

Total 
25 
(b) External Evaluation
External evaluation of the students will be based on the written examination. It carries 75 percent of the total weightage. The types and number questions will be as per the test specification chart developed by the Curriculum Development Centre.
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