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CUET
Mathematics Syllabus

1.0CUET UG 2025 Maths Syllabus 

Aiming to continue your education in the field of mathematics at the graduate level? If yes then the Common University Entrance Test (CUET) UG – a gateway examination to get admission into various degree programs in some of India’s most prestigious universities and institutions – is the cornerstone for your career and academic goals. The right preparation and a clear knowledge of the CUET Maths Syllabus will help you set yourself ready for success in the field of mathematics. 

2.0CUET UG 2025 Maths Exam Overview 

The National Testing Agency, with the guidance of the University Grants Commission, conducts the CUET UG examination once every year. It is conducted in 3 sections: 

  • Section I includes the test of language in two subsections, namely 1A and 1B, 
  • Section II includes the domain-specific test and 
  • Section III is a General Aptitude Test or GAT.  

Mathematics is one of the 23 domain-specific subjects offered by CUET UG. A total of 50 compulsory questions will be asked this year in the maths paper in a timeframe of 1 hour. The CUET mathematics syllabus is divided into two sections, namely Section A and Section B (this section B is further divided into B1 and B2).   

3.0CUET UG 2025 Maths Exam Pattern

CUET UG Maths Pattern 2025

Language of Exam 

13 languages 

Difficulty level

10+2 

Type of Questions

Multiple Choice Questions (MCQ)

Duration of Exam 

60 minutes 

Total number of Questions 

50 (all compulsory)

Scheme of Marking 

+5 for every correct answer

–1 for every incorrect one

No marks or penalty for unattempted questions

Maximum Marks 

250

4.0CUET 2025 Mathematics Syllabus: Detailed

As mentioned earlier, the CUET UG mathematics syllabus is divided into two subsections, namely Section A and Section B, as given below: 

Section A

Chapter Name 

Topics included 

Algebra 

  • Matrices & Types of Matrices 
  • Equality of matrices, transpose of a matrix, & symmetric and skew-symmetric matrix.
  • Algebra of Matrices 
  • Determinants
  • The inverse of a matrix 
  • Solving the simultaneous equations using the matrix method 

Calculus 

  • Higher order derivatives
  • Tangents and Normals 
  • Increasing and Decreasing Functions 
  • Maxima and Minima 

Integration and its Applications 

  • Indefinite integrals of simple functions 
  • Definite integrals
  • Evaluation of indefinite integrals 
  • Application of Integration as area under the curve. 

Differential Equations

  • Order & Degree of differential equations 
  • Formulating & Solving differential equations with variable separable 

Probability Distributions 

  • Random variables; their probability distribution 
  • Expected value of a random variable 
  • Variance & Standard Deviation of a random variable 
  • Binomial Distribution 

Linear Programming 

  • Mathematical formulation of problems related to Linear Programming 
  • Graphical method of solution for the problems in two variables
  • Feasible and infeasible regions 
  • Optimal feasible solution 

Section B1: Mathematics 

Units 

Sub Units 

UNIT I: Relations and Functions

1. Relations and Functions

  • Types of relations: Reflexive, transitive, symmetric, & equivalence relations. 
  • One-to-one & onto functions, composite functions, and the inverse of a function. 
  • Binary operations.

2. Inverse Trigonometric Functions

  • Definition, range, domain, principal value branches. Graphs of inverse trigonometric functions.
  • Elementary properties- inverse trigonometric functions.

UNIT II: ALGEBRA

1. Matrices

  • Concept, order, notation, equality, types of matrices, zero matrices, transpose of a matrix, symmetric & skew-symmetric matrices. 
  • Simple properties of addition, multiplication, & scalar multiplication. 
  • Concept of elementary row & column operations. Invertible matrices and stating proof of the uniqueness of inverse, if it exists;(all matrices will have real entries).
  • Non-commutativity of multiplication of matrices along with the existence of non-zero matrices whose product is the 0 (Zero) matrix (restricted to square matrices of 2nd Order).

2. Determinants

  • Determinant of a square matrix (up to 3 × 3 matrices), cofactors, minors, & properties of determinants
  • Applications of determinants in finding the area of a triangle. 
  • Adjoint & Inverse of a square matrix. 
  • Consistency, inconsistency, & number of solutions of system of linear equations by examples
  • Solving a system of linear equations in two(2) or three(3) variables (having unique solutions) using the inverse of a matrix.

UNIT III: Calculus

1. Continuity & Differentiability

  • Continuity and differentiability, chain rule,  derivative of composite functions, derivatives of inverse trigonometric functions, derivative of implicit function. Concepts of logarithmic & exponential functions.
  • Derivatives of logx and Logarithmic differentiation. Derivative functions expressed in different parametric forms. Also, Second-order derivatives. 
  • Rolle’s and Lagrange’s Mean Value Theorems (no proof required) and & geometric interpretations.

2. Applications of Derivatives

  • Applications of derivatives: Rate of change, increasing/decreasing functions, tangents & normals, approximation, maxima, and minima (the first derivative test is motivated geometrically, & second derivative test is given as a proving tool). 
  • Simple problems (illustrating all basic principles & understanding of the subject as well as real-life situations). Tangent & Normal.

3. Integrals

  • Integration (the inverse process of differentiation).
  • Definite integrals as a limit of a sum. 
  • Basic properties of definite integrals and evaluation of definite integrals.
  • Fundamental Theorem of Calculus (without any proof).
  • Integration of a variety of functions by substitution, by partial fractions & by parts, only simple integrals of the type to be evaluated are –

∫x2±a2dx​,∫x2±a2​dx​,∫ax2+bx+cdx​,∫ax2+bx+c​dx​

∫ax2+bx+c(px+q)​dx,∫ax2+bx+c​(px+q)​dx,∫a2±x2​dxand∫x2−a2​dx

∫ax2+bx+c​dxand∫(px+q)ax2+bx+c​dx

4. Applications of Integrals: 

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

5. Differential Equations: 

  • Definition, order & 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 & first degree. 
  • Solutions of linear differential equations such as – 

dxdy​+Py=Q, where P and Q are the functions of x or constant. 

dydx​+Px=Q, where P and Q are the functions of y or constant. 

UNIT IV: Vectors and three-dimensional Geometry

1. Vectors

  • Vectors & scalars, magnitude and direction of a vector. Direction cosines/ratios of vectors. 
  • Types of vectors (equal, unit, zero, parallel, & collinear vectors), 
  • The position vector of a point, the 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.

2. Three-dimensional Geometry

  • Direction cosines/ratios of a line joining two points.
  • Cartesian and vector equation of a line, coplanar & skew lines, the shortest distance between two lines. Vector & Cartesian equation of a plane.
  • The angle between (i) 2 lines,(ii) 2 planes, (iii) a line & a plane. Distance of a point from a plane.

Unit V: Linear Programming

  • Introduction, related terminologies, such as constraints, objective function, & optimisation. 
  • Different types of L.P. (linear programming) problems,
  • Mathematical formulation of L.P. problems. 
  • Feasible and infeasible regions, feasible and infeasible solutions, optimal feasible solutions(up to three non-trivial constraints)
  • Graphical method of solution for problems in two variables.

Unit VI: Probability

  • Multiplications theorem on probability. 
  • Conditional probability, independent events, and total probability.
  • Baye’s theorem. 
  • Random variable & its probability distribution, mean, & variance of haphazard variable. 
  • Repeated independent (Bernoulli) trials & binomial distribution.

Section B2: Applied Mathematics 

Unit I: Numbers, Quantification and Numerical Applications

A. Modulo Arithmetic

  • Define the modulus of an integer
  • Applying arithmetic operations while using modular arithmetic rules

B. Congruence Modulo

  • Define congruence modulo
  • Applying the definition to its various problems

C. Allegation and Mixture

  • Understand the rule of allegation to produce any mixture at any given price
  • Determine the mean price of any mixture. Applying the rule of allegation

D. Numerical Problems

  • Solve real-life problems mathematically

E. Boats & Streams

  • Distinguish between upstream and downstream flows
  • Expressing the problem in the form of an equation

F. Pipes and Cisterns

  • Determine the time taken by two or more pipes to fill or empty a tank/container

G. Races and games

  • Compare the performance of two players w.r.t. Time, distance covered/ Work done from the given data

H. Partnership

  • Differentiate between active partner & sleeping partner
  • Determine the gain or loss to be divided among the partners in the ratio of their investments with due consideration of the time volume/surface area for a solid formed using 2 or more shapes

I. Numerical Inequalities

  • Describe the basic concepts of general numerical inequalities
  • Understand & 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 & Skew symmetric matrix

  • Determine the equality of two matrices
  • Write transpose of the given matrix
  • Define symmetric & skewsymmetric matrix

UNIT III: Calculus

A. Higher Order Derivatives

  • Determine second & higher-order derivatives
  • Understand the differentiation of parametric functions and implicit functions 
  • Identify dependent & independent variables

B. Marginal Cost & Marginal Revenue using derivatives

  • Define marginal cost along with marginal revenue
  • Find marginal cost and related marginal revenue

C. Maxima & Minima

  • Determine critical points of the function
  • Find the point(s) of local maxima and local minima and the corresponding local maximum and local minimum values
  • Find the absolute maxima and absolute minima values of any given function

UNIT IV: Probability Distributions

A. Probability Distribution

  • Understand the concept of Random Variables & Probability Distributions
  • Find the probability distribution of any discrete random variable

B. Mathematical Expectation

  • Apply the 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 the time series

F. Time Series Analysis for Univariate Data

  • Solve practical problems based on statistical data and Interpret

UNIT VI: Inferential Statistics

A. Population & Sample

  • Define Population & 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 the 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: Financial Mathematics

A. Perpetuity, Sinking Funds

  • Explain the concept of perpetuity and sinking fund
  • Calculate perpetuity
  • Differentiate between sinking funds & savings account

B. Valuation of bonds

  • Define the concept of valuation of bonds and related terms
  • Calculate the value of the  bond using the 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 the linear method of Depreciation
  • Interpret the cost, residual value, & 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 ProgrammingProblem

C. Different types of Linear Programming Problems

  • Identify & formulate different types of LPP

D. Graphical Method of Solution for problems in 2 Variables

  • Draw the Graph for a system of linear inequalities involving 2 variables and find a solution graphically

E. Feasible & Infeasible Regions

  • Identify feasible, infeasible, & bounded regions

F. Feasible & infeasible solutions, optimal feasible solution

  • Understand feasible & infeasible solutions
  • Find the optimal feasible solution

Table of Contents


  • 1.0CUET UG 2025 Maths Syllabus 
  • 2.0CUET UG 2025 Maths Exam Overview 
  • 3.0CUET UG 2025 Maths Exam Pattern
  • 4.0CUET 2025 Mathematics Syllabus: Detailed

Frequently Asked Questions

You can download the CUET maths syllabus pdf from the official website by visiting the link https://exams.nta.ac.in/CUET-UG/images/mathematics.pdf

Focus on core concepts of Mathematics and practice sample papers. Take mock tests to work on speed and max accuracy.

A strong foundation in Mathematics helps you attain a career in science, technology, management, and data analysis.

Time management can be improved by practising with mock tests and setting time limits while solving problems.

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