CUET UG 2027 / Maths syllabus
CUET UG 2027 · Paper 319
CUET Maths Syllabus 2027: Units, Chapters and Books
The official CUET UG Mathematics / Applied Mathematics syllabus (paper 319), unit by unit, with the book chapter each unit comes from, links to our class 12 notes for every chapter, what changed from 2025 to 2026, and where to practise.
2027 status: NTA has not released the CUET UG 2027 syllabus. This page shows the official CUET UG 2026 Maths syllabus, the latest available, and will be updated when NTA publishes the 2027 version.
CUET Maths at a glance
- Paper code
- 319 (Mathematics / Applied Mathematics)
- Questions
- 50 multiple-choice questions, all compulsory
- Time
- 60 minutes
- Marking
- +5 for a correct answer, minus 1 for a wrong answer; 250 maximum
- Syllabus
- 20 units, 23 chapters in our chapter map
How the CUET Maths paper is structured
Paper 319 covers both Mathematics and Applied Mathematics. Section A1 is a common core for every candidate: matrices and determinants, derivatives up to second order, maxima and minima, integration and area, variable-separable differential equations, simple probability and linear programming.
You then attempt either Section B1 Mathematics, which is the rationalised NCERT class 12 book, or Section B2 Applied Mathematics, which follows the CBSE Applied Mathematics course. Neither the syllabus nor the bulletin says how the 50 questions split between A1 and B1 or B2. The Mathematics chapters below link to our class 12 notes.
CUET Maths syllabus, unit by unit
Unit titles and topics as printed in NTA’s CUET UG 2026 syllabus PDF.
Section A1: common core for all candidates
Unit 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
- (v) Inverse of a Matrix
- (vi) Solving of simultaneous equations using Matrix Method
Unit 2
Calculus
- (i) Higher order derivatives upto (second order)
- (ii) Increasing and Decreasing Functions
- (iii) Maxima and Minima
Unit 3
Integration and its Applications
- (i) Indefinite integrals of simple functions
- (ii) Evaluation of indefinite integrals
- (iii) Definite Integrals
- (iv) Application of Integration as area under the curve (simple curve)
Unit 4
Differential Equations
- (i) Order and degree of differential equations
- (ii) Solving of differential equations with variable separable
Unit 5
Probability Distributions
- Simple Probability
Unit 6
Linear Programming
- (i) Graphical method of solution for problems in two variables
- (ii) Feasible and infeasible regions
- (iii) 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.
- Inverse Trigonometric Functions: Definition, range, domain, principal value branches. Graphs 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. Operations on matrices: Addition, multiplication and multiplication with a scalar. 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). 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 x 3 matrices), 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, chain rule, derivatives of inverse trigonometric functions, like sin^-1 x, cos^-1 x and tan^-1 x, derivative of implicit functions. Concepts of exponential, logarithmic functions. Derivatives of logarithmic and exponential functions. Logarithmic differentiation, derivative of functions expressed in parametric forms. Second-order derivatives.
- Applications of derivatives: Rate of change of quantities, increasing/decreasing functions, maxima and minima (first derivative test motivated geometrically and second derivative test given as provable tool). Simple problems (that illustrate basic principles and understanding of the subject as well as real-life situations).
- Integrals: Integration as inverse process of differentiation. Integration of a variety of functions by substitution, by partial fractions and by parts, Evaluation of simple integrals of the following types and problems based on them: dx/(x^2+a^2), dx/sqrt(x^2+-a^2), dx/(a^2-x^2), dx/sqrt(a^2-x^2), dx/(ax^2+bx+c), dx/sqrt(ax^2+bx+c), (px+q)dx/(ax^2+bx+c), (px+q)dx/sqrt(ax^2+bx+c), sqrt(a^2+-x^2)dx, sqrt(x^2-a^2)dx, sqrt(ax^2+bx+c)dx. 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, circles/parabolas/ellipses (in standard form only)
- Differential Equations: Definition, order and degree, general and particular solutions of a differential equation. Solution of differential equations by method of separation of variables, solutions of homogeneous differential equations of first order and first degree. Solutions of linear differential equation of the type: dy/dx + Py = Q, where P and Q are functions of x or constants; dx/dy + Px = Q, where P and Q are functions of y or constants
Unit IV
Vectors and Three-Dimensional Geometry
- Vectors: Vectors and scalars, magnitude and direction of a vector. Direction cosines and direction ratios of a vector. 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. Definition, Geometrical interpretation, properties and application of scalar (dot) product of vectors, vector (cross) product of vectors.
- Three-dimensional Geometry: Direction cosines and direction ratios of a line joining two points. Cartesian equation and vector equation of a line, skew lines, shortest distance between two lines. Angle between two lines.
Unit V
Linear Programming
- Introduction, related terminology such as constraints, objective function, optimization, graphical method of solution for problems in two variables, feasible and infeasible regions (bounded or unbounded), feasible and infeasible solutions, optimal feasible solutions (up to three non-trivial constraints).
Unit VI
Probability
- Conditional probability, Multiplications theorem on probability, independent events, total probability, Baye's theorem.
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 empty the tank
- G. Races and Games: Compare the performance of two players w.r.t. time, distance
- H. 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
- C. Algebra of Matrices: Perform operations like addition & subtraction on matrices of same order; Perform multiplication of two matrices of appropriate order; Perform multiplication of a scalar with matrix
- D. Determinant of Matrices: Determinant of a square matrix; Use elementary properties of determinants; Singular matrix, Non-singular matrix; |AB|=|A||B|; Simple problems to find determinant value
- E. Inverse of a Matrix: Define the inverse of a square matrix; Apply properties of inverse of matrices; Inverse of a matrix using: a) cofactors; If A and B are invertible square matrices of same size, i) (AB)^-1 = B^-1 A^-1 ii) (A^-1)^-1 = A iii) (A^T)^-1 = (A^-1)^T
- F. Solving system of simultaneous equations (upto three variables only (non-homogeneous equations))
Unit III
Calculus
- A. Higher Order Derivatives: Determine second and higher order derivatives upto second order derivatives; Understand differentiation of parametric functions and implicit functions
- B. Application of Derivatives: Determine the rate of change of various quantities
- C. Marginal Cost and Marginal Revenue using derivatives: Define marginal cost and marginal revenue; Find marginal cost and marginal revenue
- D. Increasing/Decreasing Functions: Determine whether a function is increasing or decreasing; Determine the conditions for a function to be increasing or decreasing
- E. 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; Solve applied problems
- F. Integration: Understand and determine indefinite integrals of simple functions as anti-derivative
- G. Indefinite integrals as family of curves: Evaluate indefinite integrals of simple algebraic functions by methods of (i) substitution (ii) partial fraction (iii) by parts
- H. Definite Integral as area under the curve: Define definite integral as area under the curve (non-trigonometric function); Understand fundamental theorem of integral calculus and apply it to evaluate the definite integral; Apply properties of definite integrals to solve problems
- I. Application of Integration: Identify the region representing C.S. and P.S. graphically; Apply the definite integral to find consumer surplus-producer surplus
- J. Differential Equations: Recognize a differential equation; Find the order and degree of a differential equation
- K. Formulating and solving differential equations: Formulate differential equations; Verify the solution of differential equation; Solve simple differential equation
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
- D. Binomial Distribution: Identify the Bernoulli Trials and apply Binomial Distribution; Evaluate Mean, Variance and S.D. of a Binomial Distribution
- E. Poisson Distribution: Understand the conditions of Poisson Distribution; Evaluate the Mean and Variance of Poisson distribution
- F. Normal Distribution: Understand normal distribution is a continuous distribution; Evaluate value of Standard normal variate; Area relationship between Mean and Standard Deviation
Unit V
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
- D. Secular trend: Understand the long term tendency
- E. Methods of Measuring trend: Demonstrate the techniques of finding trend by different methods
Unit VI
Inferential Statistics
- A. Population and Sample: Define Population and Sample; Differentiate between population and sample; Define a representative sample from a population; Differentiate between a representative and a non-representative sample; Draw a representative sample using simple random sampling; Draw a representative sample using a systematic random sampling
- 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 Statistic to generalize the estimation for population; Interpret the concept of Statistical Significance and Statistical Inferences; Central Limit Theorem; Explain the relation between Population-Sampling Distribution-Sample
- C. t-Test (one sample t-test for a small group sample): Define a hypothesis; Differentiate between Null and Alternate hypothesis; Define and calculate degree of freedom; Test Null hypothesis and make inferences using t-test statistic for one group.
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. Calculation of EMI: Explain the concept of EMI; Calculate EMI using various methods
- C. Calculation of Returns, Nominal Rate of Return: Explain the concept of rate of return and nominal rate of return; Calculate rate of return and nominal rate of return
- D. Compound Annual Growth Rate: Understand the concept of Compound Annual Growth Rate; Differentiate between Compound Annual Growth rate and Annual Growth Rate; Calculate Compound Annual Growth Rate
- E. Linear method of Depreciation: Concept of linear method of Depreciation; Interpret cost, residual value and useful life of an asset from the given information; Depreciation
- F. Valuation of Bonds: Concept of bond and related terms; Value of bond using present value approach
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
Chapter map
Each row is one chapter of study, with the book it comes from. Where a syllabus topic is missing from that book, the row says so. Every NCERT chapter links to our class 12 notes for it.
Mathematics (Sections A1 and B1)
- Relations and FunctionsNCERT Mathematics Part I Class 12, chapter 1Class 12 notes
- Inverse Trigonometric FunctionsNCERT Mathematics Part I Class 12, chapter 2Class 12 notes
- MatricesNCERT Mathematics Part I Class 12, chapter 3Class 12 notes
- DeterminantsNCERT Mathematics Part I Class 12, chapter 4Class 12 notes
- Continuity and DifferentiabilityNCERT Mathematics Part I Class 12, chapter 5Class 12 notes
- Application of DerivativesNCERT Mathematics Part I Class 12, chapter 6Class 12 notes
- IntegralsNCERT Mathematics Part II Class 12, chapter 7Class 12 notes
- Application of IntegralsNCERT Mathematics Part II Class 12, chapter 8Class 12 notes
- Differential EquationsNCERT Mathematics Part II Class 12, chapter 9Class 12 notes
- Vector AlgebraNCERT Mathematics Part II Class 12, chapter 10Class 12 notes
- Three Dimensional GeometryNCERT Mathematics Part II Class 12, chapter 11Class 12 notes
- Linear ProgrammingNCERT Mathematics Part II Class 12, chapter 12Class 12 notes
- ProbabilityNCERT Mathematics Part II Class 12, chapter 13Class 12 notes
Applied Mathematics (Sections A1 and B2)
- Numbers, Quantification and Numerical ApplicationsCBSE Applied Mathematics Class XII e-support material (Manuals)
- Algebra: Matrices and DeterminantsCBSE Applied Mathematics Class XII e-support material (Manuals)
- Differentiation and its ApplicationsCBSE Applied Mathematics Class XII e-support material (Manuals)
- Integration and its ApplicationsCBSE Applied Mathematics Class XII e-support material (Manuals)
- Differential Equations and ModelingCBSE Applied Mathematics Class XII e-support material (Manuals)
- Probability DistributionsCBSE Applied Mathematics Class XII e-support material (Manuals)
- Inferential StatisticsCBSE Applied Mathematics Class XII e-support material (Manuals)
- Time Based Data (Time Series)CBSE Applied Mathematics Class XII e-support material (Manuals)
- Financial MathematicsCBSE Applied Mathematics Class XII e-support material (Manuals)
- Linear Programming (Applied)CBSE Applied Mathematics Class XII e-support material (Manuals)
What changed from 2025 to 2026
Mathematics (B1) essentially unchanged apart from dropping 'Random variable'; Applied Mathematics trimmed (tangents/normals, growth-decay DEs, index numbers, two-sample t-test out) and gained bond valuation.
Added
- B1 Integrals: integral of sqrt(ax^2+bx+c) dx added to the list of standard forms
- B2 Unit VII F: Valuation of Bonds (present value approach)
- B2 Unit III H: definite integral restricted to non-trigonometric functions
- A1 2(i): 'upto (second order)' qualifier
Removed
- A1 unit 5 'Random variable' (replaced by 'Simple Probability')
- B1 Unit VI 'Random variable'
- B2 Unit III: tangents and normals (gradient of tangent, equations of tangent and normal)
- B2 Unit III L: Application of differential equations - growth and decay models
- B2 Unit V: Index Numbers (unit renamed 'Index Numbers and Time Based Data' -> 'Time Based Data')
- B2 Unit VI C: two independent groups t-test (only one-sample t-test now)
Compared against NTA’s CUET UG 2025 syllabus PDF. When the 2027 syllabus is out, this section will compare 2027 with 2026.
Books to study from
- NCERT Mathematics Part I and Part II (class 12), for Section B1 and A1
- NCERT Mathematics class 11, Probability chapter (simple probability in A1)
- CBSE Applied Mathematics class 12 support material, for Section B2
NCERT books are on ncert.nic.in; NIOS course material is on nios.ac.in.
Practise CUET Maths chapter by chapter
The Study OS CUET track follows the chapter map above. Choose Maths as one of your papers, revise a chapter, then test it with exam-style questions and read the explanation after every answer.
Frequently asked questions
What is the exam pattern of the CUET Maths paper?
CUET UG Maths (paper code 319) has 50 compulsory multiple-choice questions to be answered in 60 minutes. A correct answer earns 5 marks and a wrong answer costs 1 mark, so the paper is out of 250. This is the CUET UG 2026 pattern; NTA has not announced any change for 2027.
Has NTA released the CUET Maths syllabus for 2027?
Not yet. The syllabus on this page is the official CUET UG 2026 Maths syllabus, which is the latest one NTA has published. This page will be updated when the 2027 syllabus is released.
Which books should I study for CUET Maths?
Study from: NCERT Mathematics Part I and Part II (class 12), for Section B1 and A1; NCERT Mathematics class 11, Probability chapter (simple probability in A1); CBSE Applied Mathematics class 12 support material, for Section B2.
What changed in the CUET Maths syllabus?
Mathematics (B1) is essentially unchanged apart from dropping random variables. Applied Mathematics lost tangents and normals, index numbers and the two-sample t-test, and gained bond valuation. This compares the 2025 and 2026 syllabi; the 2027 syllabus is not out yet.
What is the difference between CUET Mathematics and Applied Mathematics?
Both are paper 319. Everyone answers the common Section A1. After that, Section B1 follows the NCERT class 12 Mathematics book and Section B2 follows the CBSE Applied Mathematics course, which adds financial mathematics, time series and inferential statistics.
Is Random Variable in the CUET Maths syllabus?
No. The 2026 syllabus removed random variables from both Section A1 and Section B1. A1 now has simple probability instead.
Other CUET UG 2027 syllabi
EnglishAccountancyAgricultureAnthropologyBiologyBusiness StudiesChemistryEnvironmental ScienceComputer ScienceEconomicsFine ArtsGeographyHistoryHome ScienceKTPIMass MediaPerforming ArtsPhysical EducationPhysicsPolitical SciencePsychologySanskritSociologyGeneral Test
CUET UG 2027 overview: exam pattern, dates and how to choose subjects