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Business Mathematics | NEB Syllabus and Model Question | Grade 12

Published on: August 14, 2021

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 Board-NEB (formerly Higher Secondary Education Board-HSEB) 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)	http://tiny.cc/889jkz
Share in Nepali	http://tiny.cc/k99jkz
Debentures	http://tiny.cc/yeakkz
Final Account: Class 12	http://tiny.cc/e89jkz
Final Account in Nepali	http://tiny.cc/w89jkz
Work Sheet	http://tiny.cc/579jkz
Ratio Analysis (Accounting Ratio)	http://tiny.cc/4fakkz
Fund Flow Statement	http://tiny.cc/wiakkz
Cash Flow Statement	http://tiny.cc/8gakkz
Theory Accounting Xii	http://tiny.cc/nfakkz
Theory: Cost Accounting	http://tiny.cc/tfakkz
Cost Accounting	http://tiny.cc/p29jkz
LIFO−FIFO	http://tiny.cc/dgakkz
Cost Sheet, Unit Costing	http://tiny.cc/w49jkz
Cost Reconciliation Statement	http://tiny.cc/829jkz

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Optional Subjects Group 4, Grade 12

Mathematics

Applied Mathematics

Business Mathematics

Human Rights

Library and Information Science

Home Science

Environment Science

General Law

Finance

Co-operative 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 Syllabus, Grade 12

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 real-world problems. The same applies in case of student evaluation procedure too.

The curriculum has different sections: level-wise competencies, grade-wise 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. Level-wise 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. Grade-wise Learning Outcomes

1. Algebra

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. Calculus

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 first-order 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. Financial Mathematics

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. Linear Programming Problem

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. Statistics

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. Probability

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 real-world. 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 15-minute 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 input-output 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

Pre-requisites 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 ever-so-complex 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 real-life 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

· Co-operative 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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