CUET (UG) Mathematics Syllabus 2025 PDF Download
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CUET (UG) Mathematics Syllabus 2025
The CUET (UG) Mathematics Syllabus for the CUET (UG) 2025 is available by the National Testing Agency. The CUET (UG) Mathematics Syllabus is available for review from the link below. The CUET (UG) 2025 Mathematics syllabus defines and describes each unit covered on the CUET (UG) 2025 Mathematics exam.
Academic year:
NTA Entrance Exam Mathematics Revised Syllabus
Units and Topics
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Syllabus
1: Mathematics
NTA Entrance Exam Mathematics Syllabus
1 Relations and Functions
- Fundamental Concepts of Ordered Pairs and Relations
- Definition of Relation
- Domain
- Co-domain and Range of a Relation
- Functions
- Ways of Representing Functions
- Tabular Representation of a Function
- Graphical Representation of a Function
- Analytical Representation of a Function
- Some Elementary Functions
- Types of Functions
- Operations on Functions
- Inverse of a Function
- Algebra of Functions
- Some Special Functions
- Types of Relations
- Empty Relation
- Universal Relation
- Trivial Relations
- Identity relation
- Symmetric relation
- Transitive relation
- Equivalence Relation
- Antisymmetric relation
- Inverse relation
- One-One Relation (Injective)
- Many-one relation
- Into relation
- Onto relation (Surjective)
- Concept of Binary Operations
- Commutative Binary Operations
- Associative Binary Operations
- Identity Binary Operation,
- Invertible Binary Operation
2 Inverse Trigonometric Functions
- Properties of Inverse Trigonometric Functions
Inverse of Sin, Inverse of cosin, Inverse of tan, Inverse of cot, Inverse of Sec, Inverse of Cosec
- Inverse Trigonometric Functions
- Introduction of Inverse Trigonometric Functions
- Graphs of Inverse Trigonometric Functions
3 Matrices
- Concept of Matrices
- Matrices
- Determinants
- Cramer’s Rule
- Application in Economics
- Types of Matrices
- Row Matrix
- Column Matrix
- Zero or Null matrix
- Square Matrix
- Diagonal Matrix
- Scalar Matrix
- Unit or Identity Matrix
- Upper Triangular Matrix
- Lower Triangular Matrix
- Triangular Matrix
- Symmetric Matrix
- Skew-Symmetric Matrix
- Determinant of a Matrix
- Singular Matrix
- Transpose of a Matrix
- Equality of Matrices
- Determine equality of two matrices
- Operation on Matrices
- Properties of Matrix Addition
- Commutative Law
- Associative Law
- Existence of additive identity
- The existence of additive inverse
- Properties of Matrix Multiplication
- Negative of Matrix
- Transpose of a Matrix
- Symmetric and Skew Symmetric Matrices
- Define symmetric and skew symmetric matrix
- Elementary Transformations of a Matrix
- Elementary row and column operations
- Row-Echelon form
- Rank of a Matrix
- Gauss-Jordan Method
- Invertible Matrices
4 Determinants
- Determinant Method (Cramer’s Rule)
- Determinants
- Determinants of Matrices of different order
- Properties of Determinants
- Application of Factor Theorem to Determinants
- Product of Determinants
- Relation between a Determinant and its Cofactor Determinant
- Area of a Triangle
- Singular and non-singular Matrices
- Determinants of Matrix of Order One and Two
- Determinant of a Matrix of Order 3 × 3
- 1st, 2nd and 3rd Row
- 1st, 2nd and 3rd Columns
- Expansion along the first Row (R1)
- Expansion along the second row (R2)
- Expansion along the first Column (C1)
- Properties of Determinants
- Property 1 - The value of the determinant remains unchanged if its rows are turned into columns and columns are turned into rows.
- Property 2 - If any two rows (or columns) of a determinant are interchanged then the value of the determinant changes only in sign.
- Property 3 - If any two rows ( or columns) of a determinant are identical then the value of the determinant is zero.
- Property 4 - If each element of a row (or column) of a determinant is multiplied by a constant k then the value of the new determinant is k times the value of the original determinant.
- Property 5 - If each element of a row (or column) is expressed as the sum of two numbers then the determinant can be expressed as the sum of two determinants
- Property 6 - If a constant multiple of all elements of any row (or column) is added to the corresponding elements of any other row (or column ) then the value of the new determinant so obtained is the same as that of the original determinant.
- Property 7 - (Triangle property) - If all the elements of a determinant above or below the diagonal are zero then the value of the determinant is equal to the product of its diagonal elements.
- Application of Determinants
- Area of a Triangle Using Determinants
- Minors and Co-factors
- Adjoint of a Matrix
- Properties of Matrix Multiplication
- Applications of Determinants and Matrices
- Consistent System
- Inconsistent System
- Solution of a system of linear equations using the inverse of a matrix
5 Continuity and Differentiability
- Introduction of Continuity and Differentiability
- Concept of Continuity
- Algebra of Continuous Functions
- Concept of Differentiability
- Derivatives of Composite Functions - Chain Rule
- Derivatives of Implicit Functions
- Derivatives of Inverse Trigonometric Functions
- Exponential and Logarithmic Functions
- Logarithmic Differentiation
- Derivatives of Functions in Parametric Forms
- Second Order Derivative
- Mean Value Theorem
- Rolle’s Theorem
- Lagrange’s Mean Value Theorem
- Applications
6 Applications of Derivatives
- Introduction to Applications of Derivatives
- Rate of Change of Bodies or Quantities
- Increasing and Decreasing Functions
- Tangents and Normals
- Approximations
- Maxima and Minima
- First and Second Derivative test
- 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
- Maximum and Minimum Values of a Function in a Closed Interval
- Graph of Maxima and Minima
- Simple Problems on Applications of Derivatives
Simple problems (that illustrate basic principles and understanding of the subject as well as real-life situations)
7 Integrals
- Introduction of Integrals
- Integration as an Inverse Process of Differentiation
Derivatives Integrals
(Anti derivatives)`d/(dx) (x^(n+1)/(n+1)) = x^n` `int x^n dx = x^(n+1)/(n+1) + "C"`, n ≠ –1 `d/(dx)`(x) = 1 `int dx` = x + C `d/(dx)`(sin x) = cos x `int` cos x dx = sin x +C `d/(dx)` (-cos x) = sin x `int`sin x dx = -cos x +C `d/(dx)` (tan x) = sec2x `int sec^2 x` dx = tanx + C `d/(dx)`(-cot x) = `cosec^2x ` `int cosec^2x` dx = -cot x +C `d/(dx)` (sec x) = sec x tan x `int` sec x tan x dx = sec x +C `d/(dx)` (-cosecx) = cosec x cot x `int` cosec x cot x dx = -cosec x +C `d/(dx) (sin^-1) = 1/(sqrt(1-x^2))` `int (dx)/(sqrt(1-x^2))= sin^(-1) x +C ` `d/(dx) (-cos^(-1)) = 1/(sqrt (1-x^2))` `int (dx)/(sqrt (1-x^2))= -cos^(-1) x + C ` `d/(dx) (tan^(-1) x) = 1/(1+x^2)` `int (dx)/(1+x^2)= tan^(-1) x + C ` `d/(dx) (-cot^(-1) x) = 1/(1+x^2)` `int (dx)/(1+x^2)= -cot^(-1) x + C ` `d/(dx) (sec^(-1) x) = 1/(x sqrt (x^2 - 1))` `int (dx)/(x sqrt (x^2 - 1))`= `sec^(-1)` x + C `d/(dx) (-cosec^(-1) x) = 1/(x sqrt (x^2 - 1))` `int (dx)/(x sqrt (x^2 - 1))=-cosec^(-1) x + C ` `d/(dx)(e^x) = e^x` `int e^x dx = e^x + C` `d/(dx) (log|x|) = 1/x` `int 1/x dx = log|x| +C` `d/(dx) ((a^x)/(log a)) = a^x` `int a^x dx = a^x/log a` +C - Integration
- Some Properties of Indefinite Integral
- Comparison Between Differentiation and Integration
- Methods of Integration: Integration by Substitution
- Methods of Integration: Integration Using Partial Fractions
- Integrals of Some Particular Functions
1) `int (dx)/(x^2 - a^2) = 1/(2a) log |(x - a)/(x + a)| + C`
2) `int (dx)/(a^2 - x^2) = 1/(2a) log |(a + x)/(a - x)| + C`
3) `int (dx)/(x^2 - a^2) = 1/a tan^(-1) (x/a) + C`
4) `int (dx)/sqrt (x^2 - a^2) = log |x + sqrt (x^2-a^2)| + C`
5) `int (dx)/sqrt (a^2 - x^2) = sin ^(-1) (x/a) +C`
6) `int (dx)/sqrt (x^2 + a^2) = log |x + sqrt (x^2 + a^2)| + C`
7) To find the integral `int (dx)/(ax^2 + bx + c)`
8) To find the integral of the type `int (dx)/sqrt(ax^2 + bx + c)`
9) To find the integral of the type `int (px + q)/(ax^2 + bx + c) dx`
10) For the evaluation of the integral of the type `int (px + q)/sqrt(ax^2 + bx + c) dx`
- Methods of Integration: Integration by Parts
- Integration Using Trigonometric Identities
- Definite Integrals
- Definite Integral as the Limit of a Sum
- Fundamental Theorem of Calculus
Area function, First fundamental theorem of integral calculus and Second fundamental theorem of integral calculus
- Evaluation of Definite Integrals by Substitution
- Properties of Definite Integrals
8 Applications of the Integrals
- Introduction of Applications of the Integrals
- Area Under Simple Curves
- Simple curves: lines, parabolas, polynomial functions
- Area of the Region Bounded by a Curve and a Line
- Area of the Region Bounded by a Curve & X-axis Between two Ordinates
- Area of the Region Bounded by a Curve & Y-axis Between two Abscissa
- Circle-line, elipse-line, parabola-line
- Area Between Two Curves
9 Differential Equations
- Introduction of Differential Equations
- Differential Equations
- Order and Degree of a Differential Equation
- General and Particular Solutions of a Differential Equation
- Formation of a Differential Equation Whose General Solution is Given
- Procedure to Form a Differential Equation that Will Represent a Given Family of Curves
- Methods of Solving First Order, First Degree Differential Equations
- Solutions of Linear Differential Equation
- 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.
- Differential equations, order and degree.
- Solution of differential equations.
- Variable separable.
- Homogeneous equations
- Linear form `dy/dx` + Py = Q where P and Q are functions of x only. Similarly, for `dx/dy`.
10 Vectors
- Basic Concepts of Vector Algebra
- Position Vector
- Direction Cosines and Direction Ratios of a Vector
- Vector Analysis
- Vector
- Definition: Vector
- Representation of vector
- Types of Vectors
- Examples of Vector Quantities
- Vector
- Vector Operations>Addition and Subtraction of Vectors
- Statement
- Vector Addition: Parallel Vectors
- Vector Subtraction: Anti-Parallel Vectors
- Real-Life Applications
- Properties of Vector Addition
- Vector Operations>Multiplication of a Vector by a Scalar
- Introduction: Vector Operations
- Statement: Multiplication of a Vector by a Scalar
- Example
- Components of Vector
- Vector addition using components
- Components of a vector in two dimensions space
- Components of a vector in three-dimensional space
- Vector Joining Two Points
- Section Formula
- Formula
- Division of Line Segment
- Proof
- Examples
- Product of Two Vectors
- Magnitude and Direction of a Vector
- Position Vector of a Point Dividing a Line Segment in a Given Ratio
- Scalar Triple Product of Vectors
11 Three-dimensional Geometry
- Introduction of Three Dimensional Geometry
- Direction Cosines and Direction Ratios of a Line
- Direction cosines of a line passing through two points.
- Equation of a Line in Space
- Equation of a line through a given point and parallel to a given vector `vec b`
- Equation of a line passing through two given points
- Angle Between Two Lines
- Shortest Distance Between Two Lines
- Coplanar
- Skew lines
- Distance between two skew lines
- Distance between parallel lines
- Equation of a Plane
- Forms of the Equation of a Straight Line
- y = mx+c
- Coplanarity of Two Lines
- Angle Between Two Planes
- Distance of a Point from a Plane
- Angle Between Line and a Plane
- Vector and Cartesian Equation of a Plane
- Vector and Cartesian Equations of a Line
- Equation of a line passing through a given point and parallel to given vector
- Equation of a line passing through given two points
12 Linear Programming
- Introduction of Linear Programming
- Definition of related terminology such as constraints, objective function, optimization.
- Linear Programming Problem and Its Mathematical Formulation
- Mathematical Formulation of Linear Programming Problem
- Graphical Method of Solving Linear Programming Problems
- Graphical method of solution for problems in two variables
- Feasible and infeasible regions and bounded regions
- Feasible and infeasible solutions
- Optimum feasible solution
- Different Types of Linear Programming Problems
- Different types of linear programming (L.P.) problems
- Manufacturing problem
- Diet Problem
- Transportation problem
13 Probability
- Concept of Probability
- Conditional Probability
- Independent Events
- Properties of Conditional Probability
- Multiplication Theorem on Probability
- Bayes’ Theorem
- Partition of a sample space
- Theorem of total probability
- Random Variables and Its Probability Distributions
- Probability distribution of a random variable
- Mean of Grouped Data
- Variance of a Random Variable
- Bernoulli Trials and Binomial Distribution
- Independent Events
- Binomial Distribution
2: Applied Mathematics
NTA Entrance Exam Mathematics Syllabus
14 Numbers, Quantification and Numerical Applications
- Modulo Arithmetic
- Define the modulus of an integer
- Apply Arithmetic Operations Using Modular Arithmetic Rules
- Apply the Definition of Congruence Modulo in Various Problems
- Allegation and Mixture
- Rule of Allegation to Produce a Mixture at a Given Price
- Determine the Mean Price of Amixture
- Apply Rule of Allegation
- Solve Real Life Problems Mathematically
- Boats and Streams (Entrance Exam)
- Distinguish between upstream and downstream
- Express the Boats and Streams Problem in the Form of an Equation
- Pipes and Cisterns (Entrance Exam)
- Determine the time taken by two or more pipes to fill
- Races and Games
- Compare the performance of two players w.r.t. time
- distance taken/ distance covered/ Work done from the given data
- Differentiate Between Active Partner and Sleeping Partner
- Determination of Partner's Ratio
- Determine the gain or loss to be divided among the partners in the ratio of their investment with due
- Surface Area of a Combination of Solids
- Numerical Inequalities
- Describe the basic concepts of numerical inequalities
- Understand and write numerical inequalities
15 Algebra
- Concept of Matrices
- Matrices
- Determinants
- Cramer’s Rule
- Application in Economics
- Types of Matrices
- Row Matrix
- Column Matrix
- Zero or Null matrix
- Square Matrix
- Diagonal Matrix
- Scalar Matrix
- Unit or Identity Matrix
- Upper Triangular Matrix
- Lower Triangular Matrix
- Triangular Matrix
- Symmetric Matrix
- Skew-Symmetric Matrix
- Determinant of a Matrix
- Singular Matrix
- Transpose of a Matrix
- Equality of Matrices
- Determine equality of two matrices
- Transpose of a Matrix
- Symmetric and Skew Symmetric Matrices
- Define symmetric and skew symmetric matrix
16 Calculus
- Second Order Derivative
- Higher Order Derivative
- Derivative of Functions Which Expressed in Higher Order Derivative Form
- Derivatives of Functions in Parametric Forms
- Derivatives of Implicit Functions
- 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
- First and Second Derivative test
- 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
17 Probability Distributions
- Probability Distribution
- Expected Value, Variance and Standard Deviation of a Discrete Random Variable
- Apply arithmetic mean of frequency distribution to find the expected value of a random variable
- Calculate the Variance and S.D. of a random variable
- Expected Value, Variance and Standard Deviation of a Discrete Random Variable
- Random Variables and Its Probability Distributions
- Probability distribution of a random variable
- Probability Distribution of Discrete Random Variables
18 Index Numbers and Time Based Data
- Index Numbers
- Introduction
- Origin
- Terminologies
- Definition: Index Number
- Test of Adequacy of Index Numbers
- Apply time reversal test
- Population and Sample
- Define Population and Sample
- Differentiate Between Population and Sample
- Representative Sample from a Population
- Define a representative sample from a population
- Parameter
- Define Parameter with reference to Population
- Concepts of Statistics
- Relation Between Parameter and Statistic
- Limitations of Statistics to Generalize the Estimation for Population
- Statistical Significance and Statistical Inferences
- Interpret the concept of Statistical Significance and Statistical Inferences
- Central Limit Theorem
- State Central Limit Theorem
- Relation Between Population, Sampling Distribution, and Sample
- Explain the relation between Population-Sampling Distribution-Sample
- Time Series Analysis
- Meaning, Uses and Basic Components
- Why should we learn Time Series?
- Components of Time Series
- Secular Trend
- Seasonal variations
- Cyclic variations
- Irregular variations
- Measurements of Trends
- Freehand or Graphic Method
- Method of Semi-Averages
- Method of Moving Averages
- Method of Least Squares
- Method of Moving Averages
- Method of Least Squares
- Methods of measuring Seasonal Variations By Simple Averages
- Components of a Time Series
- Secular Trend
- Seasonal Variation
- Cyclical Variation
- Irregular Variation
- Time Series Analysis for Uni-variate Data
- Solve practical problems based on statistical data and Interpret
19 Financial Mathematics
- Perpetuity Fund
- Concept of perpetuity
- Sinking Fund
- Concept of sinking fund
- Calculate Perpetuity
- Differentiate Between Sinking Fund and Saving Account
- Valuation of Bond
- Define the concept of valuation of bonds and related terms
- Calculate Value of Bond Using present Value Approach
- Concept of EMI
- Calculation of EMI
- Calculate EMI using various methods
- Methods of Depreciation
- Fixed Instalment Method
- Definition: Fixed Instalment Method
- Overview
- Advantages and Disadvantages
- Formula: When Scrap Value is Given
- Example: When Scrap Value is Given
- Formula: When Rate of Depreciation is Given
- Example: When Rate of Depreciation is Given
- Key Takeaways
- Fixed Instalment Method
- Interpretation Cost, Residual Value and Useful Life of an Asset
- Interpret cost, residual value and useful life of an asset from the given information
20 Linear Programming
- Linear Programming Problem (L.P.P.)
- Meaning of Linear Programming Problem
- Mathematical formulation of a linear programming problem
- Familiarize with terms related to Linear Programming Problem
- Mathematical Formulation of Linear Programming Problem
- Different Types of Linear Programming Problems
- Different types of linear programming (L.P.) problems
- Manufacturing problem
- Diet Problem
- Transportation problem
- Graphical Solution of Linear Inequalities in Two Variables
Linear Inequalities - Graphical Representation of Linear Inequalities in Two Variables
- Graphical Method of Solving Linear Programming Problems
- Graphical method of solution for problems in two variables
- Feasible and infeasible regions and bounded regions
- Feasible and infeasible solutions
- Optimum feasible solution
