CUET Mathematics Syllabus 2026: Topics, Exam Pattern & Preparation Guide

Introduction

The CUET Mathematics / Applied Mathematics syllabus 2026 is designed to assess a student’s mathematical reasoning, problem-solving ability, and application of concepts. Mathematics is a core domain subject for students seeking admission into undergraduate programmes such as B.Sc. Mathematics, Engineering-related courses, Economics, Statistics, Data Science, and Applied Sciences through CUET UG.

The syllabus is aligned with the Class 12 Mathematics and Applied Mathematics curriculum, with emphasis on conceptual clarity and numerical accuracy.

CUET Syllabus for Mathematics / Applied Mathematics 2026

Section A1

1. Algebra

• Matrices and types of Matrices
• Equality of Matrices, transpose of a Matrix, Symmetric and Skew Symmetric Matrix
• Algebra of Matrices
• Determinants
• Inverse of a Matrix
• Solving of simultaneous equations using Matrix Method

2. Calculus

• Higher order derivatives up to (second order)
• Increasing and Decreasing Functions
• Maxima and Minima

3. Integration and its Applications

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

4. Differential Equations

• Order and degree of differential equations
• Solving of differential equations with variable separable

5. Probability Distributions

• Simple Probability

6. Linear Programming

• Graphical method of solution for problems in two variables
• Feasible and infeasible regions
• Optimal feasible solution

Section B1: Mathematics

UNIT I: Relations and Functions

1. Relations and Functions

• Types of relations: Reflexive, symmetric, transitive and equivalence relations
• One to one and onto functions

2. Inverse Trigonometric Functions

• Definition
• Range
• Domain
• Principal value branches
• Graphs of 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
• Operations on matrices:
  • Addition
  • Multiplication
  • Multiplication with a scalar
• Simple properties of addition, multiplication and scalar multiplication
• Non-commutativity of multiplication of matrices
• 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)

2. Determinants

• Determinant of a square matrix (up to 3 × 3 matrices)
• Minors and cofactors
• 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

1. Continuity and Differentiability

• Continuity and differentiability
• Chain rule
• Derivatives of inverse trigonometric functions:
  • sin⁻¹x, cos⁻¹x, tan⁻¹x
• Derivative of implicit functions
• Concepts of exponential and logarithmic functions
• Derivatives of logarithmic and exponential functions
• Logarithmic differentiation
• Derivative of functions expressed in parametric forms
• Second-order derivatives

2. Applications of Derivatives

• Rate of change of quantities
• Increasing/decreasing functions
• Maxima and minima
  • First derivative test (motivated geometrically)
  • Second derivative test (provable tool)
• Simple problems based on real-life situations

3. 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/(x² + a²), ∫ dx/√(x² ± a²), ∫ dx/(a² − x²), ∫ dx/√(a² − x²), ∫ dx/(ax² + bx + c), ∫ dx/√(ax² + bx + c),

∫ (px + q) dx/(ax² + bx + c), ∫ (px + q) dx/√(ax² + bx + c), ∫ √(a² ± x²) dx, ∫ √(x² − a²) dx, ∫ √(ax² + bx + c) dx

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
• Area bounded by:
  • Straight lines
  • Circles
  • Parabolas
  • Ellipses (standard form only)

5. Differential Equations

• Definition of differential equation
• Order and degree of a differential equation
• General solution and particular solution
• Methods of solution:
  • Separation of variables
  • Homogeneous differential equations of first order and first degree
• Linear differential equations of the type:
  • dy/dx + P y = Q, where P and Q are functions of x or constants
  • dx/dy + P x = Q, where P and Q are functions of y or constants

UNIT IV: Vectors and Three-Dimensional Geometry

1. Vectors

• Vectors and scalars
• Magnitude and direction of a vector
• Direction cosines and direction ratios of a vector
• Types of vectors:
  • Equal vectors
  • Unit vectors
  • Zero vectors
  • Parallel vectors
  • 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:
  • Definition
  • Geometrical interpretation
  • Properties
  • Applications
• Vector (cross) product of vectors

2. Three-Dimensional Geometry

• Direction cosines and direction ratios of a line joining two points
• Cartesian equation of a line
• Vector equation of a line
• Skew lines
• Shortest distance between two lines
• Angle between two lines

UNIT V: Linear Programming

• Introduction to linear programming
• Related terminology:
  • Constraints
  • Objective function
  • Optimization
• Graphical method of solution for problems in two variables
• Feasible and infeasible regions:
  • Bounded regions
  • Unbounded regions
• Feasible and infeasible solutions
• Optimal feasible solutions (up to three non-trivial constraints)

UNIT VI: Probability

• Conditional probability
• Multiplication theorem of probability
• Independent events
• Total probability
• Bayes’ theorem

Section B2: Applied Mathematics

Unit I: Numbers, Quantification and Numerical Applications

A. Modulo Arithmetic

• Definition of modulus of an integer
• Arithmetic operations using modular arithmetic rules

B. Congruence Modulo

• Definition of congruence modulo
• Application of congruence modulo in problems

C. Allegation and Mixture

• Rule of allegation to produce a mixture at a given price
• Mean price of a mixture
• Applications of rule of allegation

D. Numerical Problems

• Solving real-life problems mathematically

E. Boats and Streams

• Difference between upstream and downstream
• Forming equations from given conditions

F. Pipes and Cisterns

• Time taken by two or more pipes to fill a tank
• Time taken by pipes to empty a tank

G. Races and Games

• Comparing performance of two players with respect to:
  • Time
  • Distance

H. Numerical Inequalities

• Basic concepts of numerical inequalities
• Writing and solving numerical inequalities

UNIT II: ALGEBRA

A. Matrices and Types of Matrices

• Definition of a matrix
• Identification of different kinds of matrices

B. Equality of Matrices, Transpose, Symmetric and Skew Symmetric Matrices

• Conditions for equality of two matrices
• Transpose of a given matrix
• Definition of symmetric matrix
• Definition of skew symmetric matrix

C. Algebra of Matrices

• Addition of matrices of same order
• Subtraction of matrices of same order
• Multiplication of two matrices of appropriate order
• Multiplication of a scalar with a matrix

D. Determinant of Matrices

• Determinant of a square matrix
• Elementary properties of determinants
• Singular matrix
• Non-singular matrix
• Property: |AB| = |A| |B|
• Simple problems to find determinant value

E. Inverse of a Matrix

• Definition of inverse of a square matrix
• Properties of inverse of matrices
• Inverse of a matrix using cofactors
• If A and B are invertible square matrices of same size:
  • (AB)⁻¹ = B⁻¹ A⁻¹
  • (A⁻¹)⁻¹ = A
  • (Aᵀ)⁻¹ = (A⁻¹)ᵀ

F. Solving System of Simultaneous Equations

• Solving non-homogeneous simultaneous equations
• Up to three variables only
• Matrix method for solution

UNIT III: CALCULUS

A. Higher Order Derivatives

• Determine second and higher order derivatives (up to second order)
• Differentiation of parametric functions
• Differentiation of implicit functions

B. Application of Derivatives

• Determine the rate of change of various quantities

C. Marginal Cost and Marginal Revenue Using Derivatives

• Definition of marginal cost
• Definition of marginal revenue
• Calculation of marginal cost
• Calculation of marginal revenue

D. Increasing / Decreasing Functions

• Determine whether a function is increasing or decreasing
• Conditions for a function to be increasing
• Conditions for a function to be decreasing

E. Maxima and Minima

• Determine critical points of a function
• Find points of local maxima and local minima
• Find corresponding local maximum and minimum values
• Find absolute maximum value of a function
• Find absolute minimum value of a function
• Solve applied problems

F. Integration

• Concept of indefinite integrals as anti-derivatives
• Determine indefinite integrals of simple functions

G. Indefinite Integrals as Family of Curves

• Evaluate indefinite integrals of simple algebraic functions using:
  • Method of substitution
  • Method of partial fractions
  • Method of integration by parts

H. Definite Integral as Area Under the Curve

• Definition of definite integral as area under the curve (non-trigonometric functions)
• Fundamental Theorem of Integral Calculus
• Evaluation of definite integrals using the theorem
• Properties of definite integrals and their applications

I. Application of Integration

• Graphical identification of consumer surplus and producer surplus regions
• Use of definite integrals to find consumer surplus
• Use of definite integrals to find producer surplus

J. Differential Equations

• Recognition of a differential equation
• Order of a differential equation
• Degree of a differential equation

K. Formulating and Solving Differential Equations

• Formulation of differential equations
• Verification of solutions of differential equations
• Solving simple differential equations

UNIT IV: PROBABILITY DISTRIBUTIONS

A. Probability Distribution

• Concept of random variables and their probability distributions
• Probability distribution of a discrete random variable

B. Mathematical Expectation

• Expected value using arithmetic mean of frequency distribution
• Expected value of a random variable

C. Variance

• Variance of a random variable
• Standard deviation of a random variable

D. Binomial Distribution

• Bernoulli trials and conditions
• Application of binomial distribution
• Mean of binomial distribution
• Variance of binomial distribution
• Standard deviation of binomial distribution

E. Poisson Distribution

• Conditions for Poisson distribution
• Mean of Poisson distribution
• Variance of Poisson distribution

F. Normal Distribution

• Normal distribution as a continuous distribution
• Standard normal variate (Z value)
• Area relationship between mean and standard deviation

UNIT V: TIME BASED DATA

A. Time Series

• Time series as chronological data

B. Components of Time Series

• Trend component
• Seasonal component
• Cyclical component
• Irregular component

C. Time Series Analysis for Univariate Data

• Solving practical problems using statistical time data
• Interpretation of results

D. Secular Trend

• Concept of long-term tendency

E. Methods of Measuring Trend

• Different methods of measuring trend
• Techniques for finding trend values

UNIT VI: INFERENTIAL STATISTICS

A. Population and Sample

• Definition of population
• Definition of sample
• Difference between population and sample
• Representative sample
• Non-representative sample
• Simple random sampling
• Systematic random sampling

B. Parameter, Statistic and Statistical Inference

• Parameter with reference to population
• Statistic with reference to sample
• Relationship between parameter and statistic
• Limitations of statistics for population generalization
• Statistical significance
• Statistical inference
• Central Limit Theorem
• Relationship: population → sampling distribution → sample

C. t-Test (One Sample t-Test for Small Sample)

• Definition of hypothesis
• Null hypothesis and alternative hypothesis
• Degree of freedom
• Testing null hypothesis using one-sample t-test
• Drawing inference using t-test statistic

UNIT VII: FINANCIAL MATHEMATICS

A. Perpetuity and Sinking Funds

• Concept of perpetuity
• Calculation of perpetuity
• Concept of sinking fund
• Difference between sinking fund and saving account

B. Calculation of EMI

• Concept of EMI
• EMI calculation methods

C. Returns and Nominal Rate of Return

• Rate of return
• Nominal rate of return
• Calculation methods

D. Compound Annual Growth Rate (CAGR)

• Concept of CAGR
• Difference between CAGR and annual growth rate
• CAGR calculation

E. Linear Method of Depreciation

• Concept of linear depreciation
• Cost, residual value, useful life
• Depreciation calculation

F. Valuation of Bonds

• Concept of bond and related terms
• Bond value using present value approach

UNIT VIII: LINEAR PROGRAMMING

A. Introduction and Terminology

• Terms related to Linear Programming Problem (LPP)

B. Mathematical Formulation of LPP

• Formulating linear programming problems

C. Types of LPP

• Identification and formulation of different LPP types

D. Graphical Method (Two Variables)

• Graphing linear inequalities in two variables
• Graphical solution of LPP

E. Feasible and Infeasible Regions

• Feasible region
• Infeasible region
• Bounded region

F. Feasible Solutions and Optimal Solution

• Feasible solution
• Infeasible solution
• Optimal feasible solution

CUET Mathematics / Applied Mathematics Exam Overview 2026

Below is an overview of the CUET UG Mathematics / Applied Mathematics examination:

• Exam Name: Common University Entrance Test (CUET UG)
• Subject: Mathematics / Applied Mathematics
• Conducting Authority: National Testing Agency (NTA)
• Exam Level: Undergraduate
• Mode of Examination: Computer-Based Test (CBT)
• Question Type: Multiple Choice Questions (MCQs)
• Medium of Paper: Multiple languages
• Syllabus Level: Class 12
• Focus Areas: Algebra, calculus, probability, statistics, and applied mathematics concepts

The paper tests a student’s logical reasoning, numerical ability, and conceptual understanding.

CUET Mathematics / Applied Mathematics Preparation Strategy

Follow these preparation tips to score well in Mathematics:

• Build Strong Conceptual Foundations: Understand formulas and derivations clearly.
• Practice Daily: Mathematics requires consistent problem-solving.
• Focus on High-Weightage Topics: Calculus and algebra usually carry significant weight.
• Revise Formulas Regularly: Maintain a formula sheet for quick revision.
• Attempt Mock Tests: CUET-style mocks help improve speed and accuracy.

Best Books for CUET Mathematics / Applied Mathematics 2026

NCERT books should be your primary resource, supported by CUET-focused practice material.

Recommended Books

Tip: Focus more on accuracy and speed rather than solving lengthy problems.

Topics to Refer for CUET Mathematics / Applied Mathematics

Students should prioritise the following important topics:

• Relations and functions
• Inverse trigonometric functions
• Matrices and determinants
• Continuity and differentiability
• Application of derivatives
• Integrals and differential equations
• Vectors and three-dimensional geometry
• Probability
• Linear programming (Applied Mathematics)
• Financial mathematics and statistics (Applied Mathematics)

These topics are frequently tested and conceptually important.

Conclusion

The CUET Mathematics / Applied Mathematics syllabus 2026 is problem-solving and concept-driven. With consistent practice, strong conceptual clarity, and regular mock tests, students can perform well in this subject.

Mathematics is a high-scoring subject for students who maintain accuracy, speed, and regular practice.

FAQs CUET Mathematics / Applied Mathematics 2026