Class 12 Business Mathematics

Secondary Education Curriculum
2076
Business Mathematics

Working hrs: 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 12 so as to prepare them for job market and for higher studies. The curriculum of Business Mathematics for Grade 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 field
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

1. Matrices and Determinants ( 21 Working hrs )

1.1 Matrices and Determinants

• Matrix and its Operations
• Laws of Matrix Algebra
• Transpose of a matrix
• Determinants (up to third order)
• Adjoint 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. Matrices and Determinants ( 40 Working hrs )

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 first order 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 ( 17 Working hrs )

3.1 Financial Mathematics

• Geometric sequence and series
• Compound Interest and Deprecation
• Net present value and internal rate of return
• Ordinary annuity
• Annuity due
• Deferred annuity
• Perpetuities
• Sinking funds

3.2 Comp. Work: Excel for financial mathematics

4. Linear Programming Problem ( 10 Working hrs )

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 ( 20 Working hrs )

5.1 Skewness

• Karl Pearson’s and Bowley’s coefficient of skewnes

5.2 Correlation

• Correlation Coefficient by Karl Pearson’s method and its Interpretations

5.3 Regression

• Regression lines of Y on X and X on Y by least square method

5.4 Comp. Work: Excel for Skewness, five number summary of raw data, Correlation and Regression

6. Probability ( 12 Working hrs )

6.1 Probability

• Conditional probability
• Multiplication Law of probability (dependent events only)
• 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