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Accounts

Applied & Core Mathematics

Economics

Economics/Statistics

- Meaning of Accounting
- Accounting as a Source of Information
- Objectives of Accounting
- Role of Accounting
- Basic Terms in Accounting

- Generally Accepted Accounting Principles (GAAP)
- Basic Accounting Concepts
- Systems of Accounting
- Basis of Accounting
- Accounting Standards

- Business Transactions and Source Document
- Accounting Equation
- Using Debit and Credit
- Books of Original Entry
- The Ledger
- Posting from Journal

- Cash Book
- Purchases (Journal) Book
- Purchases Return (Journal) Book
- Sales (Journal) Book
- Sales Return (Journal) Book
- Journal Proper
- Balancing the Accounts

- Need for Reconciliation
- Preparation of Bank Reconciliation Statement

- Meaning of Trial Balance
- Objectives of Preparing the Trial Balance
- Preparation of Trial Balance
- Significance of Agreement of Trial Balance
- Searching of Errors
- Rectification of Errors

- Depreciation
- Depreciation and other Similar Terms
- Causes of Depreciation
- Need for Depreciation
- Factors Affecting the Amount of Depreciation
- Methods of calculating Depreciation Amount
- Straight Line Method and Written Down Method: A Comparative Analysis
- Methods of Recording Depreciation
- Disposal of Asset
- Effect of any Addition or Extension to the Existing Asset
- Provisions
- Reserves
- Secret Reserve

- Meaning of Bill Exchange
- Promissory Note
- Advantages of Bill of Exchange
- Maturity of Bill
- Discounting of Bill
- Endorsement of Bill
- Accounting Treatment
- Dishonour of a Bill
- Renewal of the Bill
- Retiring of the Bill
- Bills Receivable and Bills Payable Books
- Accomodation of Bills

- Stakeholders and Their Information Requirements
- Distinction between Capital and Revenue
- Financial Statements
- Trading and Profit and Loss Account
- Operating Profit (EBIT)
- Balance Sheet
- Opening Entry

- Need for Adjustments
- Closing Stock
- Outstanding Expenses
- Prepaid Expenses
- Accrued Income
- Income Received in Advance
- Depreciation
- Bad Debts
- Provision for Bad and Doubtful Debts
- Provision for Discount on Debtors
- Manager's Commission
- Interest on Capital
- Methods of Presenting the Financial Statements

- Meaning of Incomplete Records
- Reasons of Incompleteness and its Limitations
- Ascertainment of Profit and Loss
- Preparing Trading and Profit and Loss Account and the Balance Sheet

- Economics: An introduction
- Meaning, Scope and Importance of Statistics

- Collection of Data
- Organisation of Data
- Tabular Presentation
- Diagrammatic Presentation
- Graphic Presentation

- Measures of Central Tendency - Arithmetic Mean
- Measures of Central Tendency - Median and Mode
- Measures of Dispersion
- Measures of Correlation
- Index Numbers

- Introduction

- Consumer's Equilibrium
- Demand
- Elasticity of Demand

- Production Function
- Cost
- Revenue
- Producer's Equilibrium
- Supply

- Main Market Forms
- Price Determination with Simple Applications

- Sets and their representations
- Empty set
- Finite and Infinite sets
- Equal sets
- Subsets
- Subsets of a set of real numbers especially intervals (with notations)
- Power set
- Universal set
- Venn diagrams
- Union and Intersection of sets
- Difference of sets
- Complement of a set
- Properties of Complement

- Ordered pairs
- Cartesian product of sets
- Number of elements in the Cartesian product of two finite sets
- Cartesian product of the set of reals with itself (upto R X R X R)
- Definition of relation, pictorial diagrams, domain, co-domain and range of a relation
- Function as a special type of relation
- Pictorial representation of a function, domain, co-domain and range of a function
- Real valued functions, domain and range of these functions, constant, identity, polynomial, rational, modulus, signum, exponential, logarithmic and greatesst integer functions, with their graphs
- Sum, difference, product and quotients of functions

- Positive and negative angles
- Measuring angles in radians and in degrees and conversion from one measure to another
- Definition of trigonometric functions with the help of unit circle
- Truth of the identity sin2x + cos2x = 1
- Signs of trigonometics functions
- Domain and range of trigonometric functions and their graphs
- Expressing sin (x±y) and cos (x±y) in terms of sin x, sin y, cos x and cos y and their simple applications
- Deducing identities like tan (x±y), cot (x±y), sin α ± sin β, cos α + cos β and cos α - cos β
- Identities related to sin 2x, cos 2x, tan 2x, sin 3x, cos 3x and tan 3x
- General solution of trigonometric equations of the type sin y = sin a, cos y = cos a and tan y = tan a

- Process of the proof by induction, motivating the application of the method by looking at natural numbers as the least inductive subset of real numbers
- The principle of mathematical induction and simple applications

- Need for complex numbers. especially √-1, to be motivated by inability to solve some of the quadratic equations
- Algebraic properties of complex numbers
- Agrand plane and polar representation of complex numbers
- Statement of Fundamental Theorem of Algebra, solution of quadratic equations (with real coefficients) in the complex number system
- Square root of a complex number

- Linear inequalities
- Algebraic solutions of linear inequalities in one variable and their representation on the number line
- Graphical solution of linear inequalities in two variables
- Graphical method of finding a solution of system of linear inequalities in two variables

- Fundamental principle of counting
- Factorial n
- (n!) Permutations and combinations
- derivation of Formulae for nCr and nPr and their connections, simple applications

- Historical perspective, statement and proof of the binomial theorem for positive integral indices
- Pascal's triangel
- General and middle term in binomial expansion, simple applications

- Sequence and Series
- Arithmetic Progression (A. P.)
- Arithmetic Mean (A. M.)
- Geometric Progression (G. P.), general term of a G. P., sum of n terms of a G. P., infinite G. P. and its sum, geometric mean (G. M.), relation between A. M. and G. M.
- Formulae for the following special sums: ∑k (n to k=1), ∑k² (n to k=1), ∑k³ (n to k=1)

- Brief recall of two dimensional geometry from earlier classes
- Shifting of origin
- Slope of a line and angle between two lines
- Various forms of equations of a line: parallel to axis, point-slope form, slope-intercept form, two-point form, intercept form and normal form
- General equation of a line
- Equation of family of lines passing through the point of intersection of two lines
- Distance of a point from a line

- Sections of a cone: circle, ellipse, parabola, hyperbola, a point, a straight line and a pair of intersecting lines as a degenerated case of a conic section
- Standard equations and simple properties of parabola, ellipse and hyperbola
- Standard equation of a circle

- Coordinate axes and coordinate planes in three dimensions
- Coordinates of a point
- Distance between two points and section formula

- Derivative introduced as rate of change both as that of distance function and geometrically
- Intuitive idea of limit
- Limits of polynomials and rational functions trigonometric, exponential and logarithmic functions
- Definition of derivative relate it to scope of tangent of the curve, derivative of sum, difference, product and quotient of function
- Derivatives of polynomial and trigonometric functions

- Mathematically acceptable statements
- Connecting words/phrases - consolidating the understanding of "if and only if (necessary and sufficient) condition", "implies", "and/or", "implied by", "and", "or", "there exists" and their use through variety of examples related to real life and Mathematics
- Validating the statements involving the connecting words, difference among contradiction, converse and contrapositive

- Measure of Dispersion: Range, Mean deviation, variance and standard deviation of ungrouped/grouped data
- Analysis of frequency distributions with equal means but different variances

- Random experiments; outcomes, sample spaces (set representation)
- Events; occurence of events, 'not', 'and' and 'or' events, exhaustive events, mutually exclusive events, Axiomatic 9set theoretic) probability, connections with other theories of earlier classes
- Probablity of an event, probability of 'not', 'and' and 'or' events

- Prime Numbers, Encryptions using Prime Numbers
- Binary Numbers
- Complex Numbers (Preliminary idea only)
- Indices, Logarithm and Antilogarithm
- Laws and properties of logarithms
- Simple applications of logarithm and antilogarithm
- Numerical problems on averages, calender, clock, time, work and distance, mensuration, seating arrangement

- Sets
- Types of sets
- Venn diagram
- De Morgan's laws
- Problem solving using Venn diagram
- Relations and types of relations
- Introduction of Sequences, Series
- Arithmetic and Geometric progression
- Relationship between AM and GM
- Basic concepts of Permutations and Combinations
- Permutations, Circular Permutations, Permutations with restrictions
- Combinations with standard results

- Mathematically acceptable statements
- Connecting words/phrases in Mathematical statement consolidating the understanding of "if and only if (necessary and sufficient) condition", "implies", "and/or", "implied by", "and", "or", "there exists" and their use through variety of examples related to real life and Mathematics
- Problems based on logical reasoning (coding-decoding, odd man out, blood relation, syllogism etc)

- Introducing functions
- Domain and Range of a function
- Types of function (Polynomial function; Rational function; Composite function; Logarithm function; Exponential function; Modulus function; Greatest integer function, Signum function)
- Graphical representation of functions
- Concept of limits and continuity of a function
- Instantaneous rates of change
- Differentiation as a process of finding derivative
- Derivatives of algebraic functions using Chain rule
- Tangent line and equations of tangents

- Random experiment, sample space, events, mutually exclusive events
- Independent and Dependent Events
- Law of Total Probability
- Bayes' Theorem

- Types of data (raw data, univariate data, bivariate and multi-variate data)
- Data on various scales (nominal, ordinal, interval and ratio scale)
- Data representation and visualization
- Data interpretation (central tendency, dispersion, deviation, variance, skewness and kurtosis)
- Percentile rank and quartile rank
- Correlation (Pearson and Spearman method of correlation)
- Applications of descriptive statistics using real time data

- Interest and interest rate
- Accumulation with simple and compound interest
- Simple and compound interest rates with equivalency
- Effective rate of interest
- Present value, net present value and future value
- Annuities, calculating value of regular annuity
- Simple applications of regular annuities (up to 3 period)
- Tax, calculation of tax and simple applications of tax calculation in Goods and service tax, Income tax
- Bills, tariff rates, fixed charge, surcharge, service charge
- Calculation and interpretation of electricity bill, water supply bill and other supply bills (Comparing interest rates on various types of savings; calculating income tax; electricity bills, water bills; surcharge using realistic data)

- Straight Line
- Circles
- Parabola (only standard forms and graphical representation on two-dimensional plane)

99.2%

AIR - 4, Accounts 100/100

2020 Batch