Mathematics Syllabus
Section A
Topic  Subtopic 

1. Algebra  
(i) Matrices and Types of Matrices  
(ii) Equality of Matrices  
 Transpose of a Matrix  
 Symmetric and Skew Symmetric Matrix  
(iii) Algebra of Matrices  
(iv) Determinants  
 Inverse of a Matrix  
 Solving Simultaneous Equations using Matrix Method  
2. Calculus  
(i) Higher Order Derivatives  
(ii) Tangents and Normals  
(iii) Increasing and Decreasing Functions  
(iv) Maxima and Minima  
3. Integration and its Applications  
(i) Indefinite Integrals of Simple Functions  
(ii) Evaluation of Indefinite Integrals  
(iii) Definite Integrals  
4. Differential Equations  
(i) Order and Degree of Differential Equations  
(ii) Formulating and Solving Differential Equations  
 Variable Separable  
5. Probability Distributions  
(i) Random Variables and its Probability Distribution  
(ii) Expected Value of a Random Variable  
(iii) Variance and Standard Deviation of a Random Variable  
(iv) Binomial Distribution  
6. Linear Programming  
(i) Mathematical Formulation of Linear Programming Problem  
(ii) Graphical Method of Solution for Problems in Two Variables  
(iii) Feasible and Infeasible Regions  
(iv) Optimal Feasible Solution 
Section B1: Mathematics
UNIT I: RELATIONS AND FUNCTIONS

Relations and Functions
 Types of relations: Reflexive, symmetric, transitive and equivalence relations.
 One to one and onto functions, composite functions, inverse of a function.
 Binary operations.

Inverse Trigonometric Functions
 Definition, range, domain, principal value branches.
 Graphs of inverse trigonometric functions.
 Elementary properties of inverse trigonometric functions.
UNIT II: ALGEBRA

Matrices
 Concept, notation, order, equality, types of matrices, zero matrix, transpose of a matrix, symmetric and skew symmetric matrices.
 Addition, multiplication and scalar multiplication of matrices, simple properties of addition, multiplication and scalar multiplication.
 Noncommutativity of multiplication of matrices and existence of nonzero matrices whose product is the zero matrix (restrict to square matrices of order 2).
 Concept of elementary row and column operations.
 Invertible matrices and proof of the uniqueness of inverse, if it exists; (Here all matrices will have real entries).

Determinants
 Determinant of a square matrix (up to 3 × 3 matrices), properties of determinants, minors, cofactors and applications of determinants in finding the area of a triangle.
 Adjoint and inverse of a square matrix.
 Consistency, inconsistency and number of solutions of system of linear equations by examples, solving system of linear equations in two or three variables (having unique solution) using inverse of a matrix.
UNIT III: CALCULUS

Continuity and Differentiability
 Continuity and differentiability, derivative of composite functions, chain rule, derivatives of inverse trigonometric functions, derivative of implicit function.
 Concepts of exponential, logarithmic functions.
 Derivatives of log x and e^x.
 Logarithmic differentiation.
 Derivative of functions expressed in parametric forms.
 Secondorder derivatives.
 Rolle’s and Lagrange’s Mean Value Theorems (without proof) and their geometric interpretations.

Applications of Derivatives
 Applications of derivatives: Rate of change, increasing/decreasing functions, tangents and normals, approximation, maxima and minima (first derivative test motivated geometrically and second derivative test given as a provable tool).
 Simple problems (that illustrate basic principles and understanding of the subject as well as reallife situations).
 Tangent and Normal.

Integrals
 Integration as inverseprocess of differentiation.
 Integration of avarietyof functions bysubstitution, bypartial fractions andbyparts, only simple integrals ofthetype –
$$\int \frac{dx}{x^2 \pm a^2}, \quad \int \frac{dx}{\sqrt{x^2 \pm a^2}}, \quad \int \frac{dx}{\sqrt{a^2  x^2}}, \quad \int \frac{dx}{ax^2 + bx + c}, \quad \int \frac{dx}{\sqrt{ax^2 + bx + c}},$$
$$\int \frac{(px + q)}{ax^2 + bx + c} , dx, \quad \int \frac{(px + q)}{\sqrt{ax^2 + bx + c}} , dx, \quad \int \sqrt{a^2 \pm x^2} , dx \quad \text{and} \quad \int \sqrt{x^2  a^2} , dx,$$
$$\int \sqrt{ax^2 + bx + c} , dx \quad \text{and} \quad \int (px + q) \sqrt{ax^2 + bx + c} , dx $$
to be evaluated.
 Definite integrals as a limit of a sum.
 Fundamental Theorem of Calculus (without proof).
 Basic properties of definite integrals and evaluation of definite integrals.

Applications of the Integrals
 Applications in finding the area under simple curves,
 especially lines,
 arcs of circles/parabolas/ellipses (in standard form only),
 area between the two above said curves (the region should be clearly identifiable).

Differential Equations
 Definition, order and degree, general and particular solutions of a differential equation.
 Formation of differential equation whose general solution is given.
 Solution of differential equations by method of separation of variables, homogeneous differential equations of first order and first degree.
 Solutions of linear differential equation of the type –
$$\frac{dy}{dx} + Py = Q, \text {where P and Q are functions of x or constant}$$
$$\frac{dx}{dy} + Px = Q, \text{where P and Q are functions of y or constant.} $$
UNIT IV: VECTORS AND THREEDIMENSIONAL GEOMETRY

Vectors
 Vectors and scalars, magnitude and direction of a vector.
 Direction cosines/ratios of vectors.
 Types of vectors (equal, unit, zero, parallel and collinear vectors),
 position vector of a point,
 negative of a vector,
 components of a vector,
 addition of vectors,
 multiplication of a vector by a scalar,
 position vector of a point dividing a line segment in a given ratio.
 Scalar (dot) product of vectors, projection of a vector on a line.
 Vector (cross) product of vectors, scalar triple product.

Threedimensional Geometry
 Direction cosines/ratios of a line joining two points.
 Cartesian and vector equation of a line,
 coplanar and skew lines,
 shortest distance between two lines.
 Cartesian and vector equation of a plane.
 Angle between (i) two lines, (ii) two planes, (iii) a line and a plane.
 Distance of a point from a plane.
Unit V: Linear Programming
 Introduction, related terminology such as constraints, objective function, optimization,
 different types of linear programming (L.P.) problems,
 mathematical formulation of L.P. problems,
 graphical method of solution for problems in two variables,
 feasible and infeasible regions,
 feasible and infeasible solutions,
 optimal feasible solutions (up to three nontrivial constraints).
Unit VI: Probability
 Multiplication theorem on probability.
 Conditional probability, independent events, total probability, Baye’s theorem.
 Random variable and its probability distribution, mean and variance of a random variable.
 Repeated independent (Bernoulli) trials and Binomial distribution.
Section B2: Applied Mathematics
Unit I: Numbers, Quantification and Numerical Applications
A. Modulo Arithmetic
 Define modulus of an integer
 Apply arithmetic operations using modular arithmetic rules
B. Congruence Modulo
 Define congruence modulo
 Apply the definition in various problems
C. Allegation and Mixture
 Understand the rule of allegation to produce a mixture at a given price
 Determine the mean price of a mixture
 Apply rule of allegation
D. Numerical Problems
 Solve real life problems mathematically
E. Boats and Streams
 Distinguish between upstream and downstream
 Express the problem in the form of an equation
F. Pipes and Cisterns
 Determine the time taken by two or more pipes to fill or drain
G. Races and Games
 Compare the performance of two players w.r.t. time, distance taken/distance covered/ work done from the given data
H. Partnership
 Differentiate between active partner and sleeping partner
 Determine the gain or loss to be divided among the partners in the ratio of their investment with due consideration of the time
I. Numerical Inequalities
 Describe the basic concepts of numerical inequalities
 Understand and write numerical inequalities
UNIT II: ALGEBRA
A. Matrices and Types of Matrices
 Define matrix
 Identify different kinds of matrices
B. Equality of Matrices, Transpose of a Matrix, Symmetric and Skew Symmetric Matrix
 Determine equality of two matrices
 Write transpose of given matrix
 Define symmetric and skew symmetric matrix
UNIT III: CALCULUS
A. Higher Order Derivatives
 Determine second and higher order derivatives
 Understand differentiation of parametric functions and implicit functions
 Identify dependent and independent variables
B. Marginal Cost and Marginal Revenue Using Derivatives
 Define marginal cost and marginal revenue
 Find marginal cost and marginal revenue
C. Maxima and Minima
 Determine critical points of the function
 Find the point(s) of local maxima and local minima and corresponding local maximum and local minimum values
 Find the absolute maximum and absolute minimum value of a function
UNIT IV: PROBABILITY DISTRIBUTIONS
A. Probability Distribution
 Understand the concept of Random Variables and its Probability Distributions
 Find probability distribution of discrete random variable
B. Mathematical Expectation
 Apply arithmetic mean of frequency distribution to find the expected value of a random variable
C. Variance
 Calculate the Variance and S.D. of a random variable
UNIT V: INDEX NUMBERS AND TIME BASED DATA
A. Index Numbers
 Define Index numbers as a special type of average
B. Construction of Index Numbers
 Construct different types of index numbers
C. Test of Adequacy of Index Numbers
 Apply time reversal test
D. Time Series
 Identify time series as chronological data
E. Components of Time Series
 Distinguish between different components of time series
F. Time Series Analysis for Univariate Data
 Solve practical problems based on statistical data and interpret
UNIT VI: INFERENTIAL STATISTICS
A. Population and Sample
 Define Population and Sample
 Differentiate between population and sample
 Define a representative sample from a population
B. Parameter and Statistics and Statistical Inferences
 Define Parameter with reference to Population
 Define Statistics with reference to Sample
 Explain the relation between Parameter and Statistic
 Explain the limitation of Statistic to generalize the estimation for population
 Interpret the concept of Statistical Significance and Statistical Inferences
 State Central Limit Theorem
 Explain the relation between PopulationSampling DistributionSample
UNIT VII: FINANCIAL MATHEMATICS
A. Perpetuity, Sinking Funds
 Explain the concept of perpetuity and sinking fund
 Calculate perpetuity
 Differentiate between sinking fund and saving account
B. Valuation of Bonds
 Define the concept of valuation of bond and related terms
 Calculation of Bond Using Present Value Approach
C. Calculation of EMI
 Explain the concept of EMI
 Calculate EMI using various methods
D. Linear Method of Depreciation
 Define the concept of linear method of Depreciation
 Interpret cost, residual value and useful life of an asset from the given information
 Calculate depreciation
UNIT VIII: LINEAR PROGRAMMING
A. Introduction and Related Terminology
 Familiarize with terms related to Linear Programming Problem
B. Mathematical Formulation of Linear Programming Problem
 Formulate Linear Programming Problem
C. Different Types of Linear Programming Problems
 Identify and formulate different types of LPP
D. Graphical Method of Solution for Problems in Two Variables
 Draw the Graph for a system of linear inequalities involving two variables and to find its solution graphically
E. Feasible and Infeasible Regions
 Identify feasible, infeasible and bounded regions
F. Feasible and Infeasible Solutions, Optimal Feasible Solution
 Understand feasible and infeasible solutions
 Find optimal feasible solution