Candidates applying for the CUET Examination 2022 can check out the topics and units included in the syllabus of Mathematics given below.

Table of Contents

**SECTION A**

- 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 (v) Inverse of a Matrix (vi) Solving of simultaneous equations using Matrix Method
- Calculus (i) Higher-order derivatives (ii) Tangents and Normals (iii) Increasing and Decreasing Functions (iv). Maxima and Minima
- Integration and its Applications (i) Indefinite integrals of simple functions (ii) Evaluation of indefinite integrals (iii) Definite Integrals (iv). Application of Integration as the area under the curve
- Differential Equations (i) Order and degree of differential equations (ii) Formulating and solving of differential equations with variable separable
- Probability Distributions (i) Random variables and their probability distribution (ii) Expected value of a random variable (iii) Variance and Standard Deviation of a random variable (iv). Binomial Distribution
- 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

*Note: There will be one Question Paper which will contain Two Sections i.e. Section A and Section B [B1 and B2]. Section A will have 15 questions covering both i.e. Mathematics/Applied Mathematics which will be compulsory for all candidates Section B1 will have 35 questions from Mathematics out of which 25 questions need to be attempted. Section B2 will have 35 questions purely from Applied Mathematics out of which 25 questions will be attempted.

**Section B1: Mathematics**

UNIT I: RELATIONS AND FUNCTIONS 1. Relations and Functions Typesofrelations:Reflexive,symmetric,transitive and equivalence relations.One toone and onto functions,compositefunctions,inverseofa function.Binaryoperations. 2. InverseTrigonometricFunctions Definition,range, domain, principal value branches. Graphs ofinverse trigonometric functions. Elementarypropertiesofinverse trigonometric functions.

UNITII: ALGEBRA 1. Matrices Concept, notation, order, equality,typesofmatrices, zero matrices, transpose of a matrix, symmetric and skewsymmetric 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 matrices (restrict to square matrices of order 2). Concept of elementary row and column operations. Invertible matrices and proof of the uniqueness of inverse exists;(Here all matrices will have real entries). 2. Determinants Determinant of a square matrix (upto3×3matrices), 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 linearequations by examples, solving system of linear equations in two or three variables(having unique solution)using the inverse of a matrix.

UNIT III: CALCULUS 1. Continuity and Differentiability Continuity and differentiability, a derivatives of composite functions, chain rules, derivatives of inverse trigonometric functions, and derivatives of implicit functions. Conceptsofexponential,logarithmic functions. Derivativesoflog x ande x .Logarithmic differentiation. Derivative of functions expressed in parametric forms. Second-order derivatives.Rolle’s and Lagrange’s Mean ValueTheorems(without proof) and their geometric interpretations. 2. 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 a well as real-life situations). Tangent and Normal. Integrals Integrationasinverseprocessofdifferentiation.Integration of a varietyof functionsbysubstitution, by partial fractions and by parts, only simple integrals of the type – 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. 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. DifferentialEquations 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 the method of separation of variables, homogeneous differential equations of the first order and first degree. Solutions of linear differential equation ofthe type – dy Py Q , where P and Q are functions of x or constant dx dx Px dy Q, where P and Q are functions of y or constant

UNITIV: VECTORS AND THREE-DIMENSIONAL GEOMETRY 1. 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, the 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. 2. Three-dimensional Geometry Direction cosines/ratios of a line joining two points.Cartesian and vector equation of a line, coplanar and skew lines, the shortest distance between two lines.Cartesian and vector equation of a plane.The angle between (i)two lines,(ii)two planes, and (iii) a line and a plane.Distance of a point from a plane.

UnitV:LinearProgramming Introduction,relatedterminologysuchas constraints,objective function,optimization,differenttypes oflinearprogramming(L.P.)problems,mathematicalformulationofL.P.problems,graphicalmethod ofsolution for problemsin two variables, feasible and infeasible regions, feasible and infeasible solutions,optimalfeasiblesolutions(uptothreenon-trivial constrains).

Unit VI: Probability Multiplicationstheoremonprobability.Conditional probability, independent events, total probability, Baye’s theorem.Randomvariable and its probability distribution, mean and variance of haphazard variable.Repeated independent(Bernoulli)trials and binomial distribution.

**Section B2: Applied Mathematics**

Unit I: Numbers, Quantification and Numerical Applications A. Modulo Arithmetic Define the 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 the rule of allegation D. Numerical Problems Solve real-life problems mathematically Mathematics/Applied Mathematics (319) 4 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 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 volume/surface area for solid formed using two or more shapes 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 skewsymmetric matrix

UNIT III: CALCULUS A. Higher OrderDerivatives 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 Minimal 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 ofRandom Variables and their Probability Distributions Find probability distribution of discrete random variable Mathematics/Applied Mathematics (319) 4 B. MathematicalExpectation 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

UNIT VI: INDEX NUMBERS AND TIME-BASED DATA 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 Interferences Define Parameter with reference to Population Define Statistics with reference to Sample Explain the relation between Parameter and Statistic Explain the limitation of Statisticto 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: INDEX NUMBERS AND TIME-BASED DATA A. Time Series Identify time series as chronological data B. Components of time Series Distinguish between different components of time series C. Time Series analysis for univariate data Solve practical problems based on statistical data and Interpret

UNIT VIII: 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 Mathematics/Applied Mathematics (319) 4 Calculate the value 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 IX: LINEAR PROGRAMMING A. Introduction and related terminology Familiarize with terms related toLinear Programming Problem B. Mathematicalformulation of Linear ProgrammingProblem Formulate Linear ProgrammingProblem 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 InfeasibleRegions Identify feasible, infeasible and bounded regions F. Feasible and infeasible solutions, optimal feasible solution Understand feasible and infeasible solutions Find the optimal feasible solution

**Download the CUET Mathematics Syllabus PDF here.**

**CUET Mathematics Syllabus – FAQs**

**What is the CUET Examination?**CUET is the Central Universities Entrance Test

**What is the last date to apply for the CUET Examination?**The last date to apply for the CUET Examination is 6 May 2022.

**How many questions are there in the CUET paper?**A total of 50 questions will be asked in the paper out of which 40 must be attempted by the candidates.

**What is the selection procedure for the CUET Examination?**The selection procedure for the CUET Examination is a written examination and an interview

**How many topics are there in the Mathematics subject of CUET?**A total of 3 topics are there.