Mathematics

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

  1. Relations and Functions

  2. Inverse Trigonometric Functions

UNIT II: ALGEBRA

  1. 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.
    • Non-commutativity of multiplication of matrices and existence of non-zero 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).
  2. Determinants

UNIT III: CALCULUS

  1. 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.
    • Second-order derivatives.
    • Rolle’s and Lagrange’s Mean Value Theorems (without proof) and their geometric interpretations.
  2. Applications of Derivatives

  3. 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.

  4. 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).
  5. Differential Equations

    $$\frac{dy}{dx} + Py = Q, \text {where P and Q are functions of x or constant}$$

    $$\frac{dx}{dy} + Px = Q, \text{where P and Q are functions of y or constant.} $$

UNIT IV: VECTORS AND THREE-DIMENSIONAL GEOMETRY

  1. Vectors

  2. Three-dimensional Geometry

Unit V: Linear Programming

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 Population-Sampling Distribution-Sample

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

CUET (UG)

CUET (UG)

CUET Syllabus

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