CUET Mathematics Syllabus 2024: Chapterwise Syllabus, Exam Pattern, Books, Previous Year Papers

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.

Matrices
Concept, notation, order, equality, types of matrices, zero matrix, transpose of 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).

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 number of solutions system of linear equations examples, solving system of linear equations in two or three variables (having unique solution) using inverse of amatrix.

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. Derivativesoflog x and ex. 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.

Applications of Derivatives
Applications of derivatives: Rate of change, increasing/decreasing functions, tangents and normals, approximation,maxima and minima (firstderivativetestmotivatedgeometricallyandsecondderivative test given as aprovabletool). Simple Problems (that illustrate basic principles and understanding of the subject as well as real-life situations). Tangent and Normal.

Integrals
Integration as an inverse process of differentiation. Definite integrals as a limit of a sum. Fundamental Theorem of Calculus. Basic properties of definite integrals and evaluation of definite integrals.

Application 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 differential equations. 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.

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.

Three-Dimensional 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 point from a plane.

Modulo Arithmetic
Define modulus of an integer Apply arithmetic operations using modular arithmetic rules

Congruence Modulo
Define congruence modulo Apply the definition in various problems

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

Numerical Problems
Solve real life problems mathematically

Boats and Streams
Distinguish between upstream and downstream Express the problem in the form of an equation

Pipes and Cisterns
Determine the time taken by two or more pipes to fill or

Races and Games
Compare the performance of two players w.r.t. time, distance taken/distance covered/ Work done from the given data

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

Numerical Inequalities
Describe the basic concepts of numerical inequalities Understand and write numerical inequalities

Matrices and types of matrices
Define matrix Identify different kinds of matrices

Equality of matrices,
Transpose of matrix, Symmetric andSkew symmetric matrix Determine equality of two matrices Write transpose of given matrix Define symmetric and skew symmetric matrix

Higher Order Derivatives
Determine second and higher order derivatives Understand differentiation of parametric functions and implicit functions Identify dependent and independent variables

Marginal Cost and Marginal Revenue using derivatives Define marginal cost and marginal revenue Find marginal cost and marginal revenue

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

Probability Distribution
Understand the concept ofRandom Variables and its Probability Distributions Find probability distribution of discrete random variable

Mathematical Expectation
Apply arithmetic mean of frequency distribution to find the expected value of a random variable

Variance Calculate the Variance and S.D.of a random variable

Index Numbers
Define Index numbers as a special type of average

Construction of Index numbers Construct different type of index numbers

Test of Adequacy of Index Numbers
Apply time reversal test

Time Series
Identify time series chronological data

Components of Time Series
Distinguish between different components of time series

Time Series analysis for univariate data

Solve practical problems based on statistical data and Interpret

Population and Sample
Define Population and Sample Differentiate between population and sample Define a representative sample from a population

Parameter andStatistics and Statistical Inferences
Define Parameter with reference to Population Define Statistics with reference to Sample Explain the relation betweenParameter and Statistic Explain the limitation of Statistics To generalise the estimation for population Interpret the concept of Statistical Significance andStatistical Inferences State Central Limit Theorem Explain the relation betweenPopulation-Sampling Distribution-Sample

Perpetuity, Sinking Funds
Explain the concept of perpetuity and sinking fund Calculate perpetuity Differentiate between sinking fund and saving account

Valuation of Bonds Define the concept of valuation of bond and related terms Calculate value of bond using present value approach

Calculation of EMI
Explain the concept of EMI Calculate EMI using various methods

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

Introduction And related terminology Familiarise with terms related toLinear Programming Problem

Mathematical Formulation of Linear Programming Problem
Formulate Linear ProgrammingProblem

Different types of Linear Programming Problems
Identify and formulate different types of LPP

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

Feasible and Infeasible Regions Identify feasible, infeasible and bounded regions

Feasible and infeasible solutions, optimal feasible solution Understand feasible and infeasible solutions Find optimal feasible solution