# CUET Exam Maths Syllabus 2024

## Maths Syllabus 2024

The National Testing Agency (NTA) has released the detailed syllabus for the CUET 2024 Mathematics exam on its official website. This syllabus is also provided here for your reference

The Mathematics syllabus is divided into two sections:

## Section A: Compulsory Section:

Unit 1: Algebra:

• Matrices: Introduction, types of matrices, equality, transpose, symmetric & skew-symmetric matrices, algebra of matrices, determinants, inverse of a matrix, solving simultaneous equations using the matrix method

Unit 2: Calculus:

• Higher-order derivatives, tangents & normals, increasing & decreasing functions, maxima & minima.

Unit 3: Integration and its Applications:

• Indefinite integrals of simple functions, evaluation of indefinite integrals, definite integrals, application of integration as the area under the curve.

Unit 4: Differential Equations:

• Order and degree of differential equations, formulating and solving equations with separable variables.

Unit 5: Probability Distributions:

• Random variables and their probability distributions, expected value, variance, and standard deviation of a random variable, binomial distribution.

Unit 6: Linear Programming:

• Mathematical formulation of linear programming problems, graphical solution method for problems with two variables, feasible and infeasible regions, optimal feasible solution

## Section B:

## Section B1:

Mathematics (focuses on theoretical and conceptual aspects of mathematics)##
UNIT: RELATIONS AND FUNCTIONS

CHAPTER: Relations and Functions

Sub-unit: Types of relations• Reflexive, symmetric, transitive, and equivalence relations.

• One-to-one and onto functions, composite functions, the inverse of a function.

• Binary operations

Sub-unit: Inverse Trigonometric Functions

• Definition, range, domain, principal value branches.

• Graphs of inverse trigonometric functions.

• Elementary properties of inverse trigonometric functions

##
UNIT: ALGEBRA

CHAPTER: Matrices

Sub-unit: Concepts of Matrices• Concept, notation, order, equality, types of matrices.

• Zero matrix, transpose of a matrix, symmetric and skew-symmetric matrices.

• Addition, multiplication, and scalar multiplication of matrices, simple properties.

• Non-commutativity of multiplication of matrices, existence of non-zero matrices whose product is the zero matrix (restricted to square matrices of order 2).

• Concept of elementary row and column operations.

• Invertible matrices and proof of the uniqueness of inverse

Sub-unit: Determinants

• Determinants of a square matrix (up to 3×3 matrices), properties of determinants, minors, co-factors.

• Applications of determinants in finding the area of a triangle.

• Adjoint and inverse of a square matrix.

• Consistency, inconsistency, and a number of solutions of a system of linear equations.

##
UNIT: CALCULUS

CHAPTER: Continuity and Differentiability

Sub-unit: Continuity and Differentiability• Derivative of composite functions, chain rules.

• Derivatives of inverse Trigonometric functions, implicit functions.

• Exponential, logarithmic functions, derivatives of log 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.

Sub-unit: Applications of Derivatives

• Rate of change, increasing/decreasing functions.

• Tangents and normals, approximation, maxima, and minima.

## CHAPTER: Integrals

Sub-unit: Integration• Integration as an inverse process of differentiation.

• Integration of various functions by substitution, partial fractions, and parts.

• Definite integrals as a limit of a sum.

• Fundamental Theorem of calculus (without proof), basic properties, and evaluation of definite integrals

Sub-unit: Applications of Integrals

• Finding the area under simple curves, area between curves

## CHAPTER: Differential Equations

Sub-unit: Basics of Differential Equations• Definition, order, and degree, general, and particular solutions.

• Formation of differential equations, methods of solution

##
UNIT: VECTORS & THREE - DIMENSIONAL GEOMETRY

CHAPTER: Vectors

Sub-unit: Basics of Vectors• Magnitude and direction, types of vectors.

• Scalar and vector products, projection of a vector

## CHAPTER: Three-dimensional Geometry

Sub-unit: Basics of Three-dimensional Geometry• Cartesian and vector equations of lines and planes.

• Angle between lines and planes, distance of a point from a plane.

##
UNIT: LINEAR PROGRAMMING

CHAPTER: Linear Programming

Sub-unit: Introduction to Linear Programming• Terminology, mathematical formulation, graphical method of solution.

##
UNIT: PROBABILITY

CHAPTER: Probability

Sub-unit: Basics of Probability• Multiplication theorem, conditional probability, independent events.

• Random variable and its probability distribution, mean, and variance.

• Binomial distribution, Baye’s theorem

## Section B2 : CUET 2024 Mathematics Syllabus: Section B2 (Applied Mathematics)

Unit 1: Numbers, Quantification, and Numerical Applications• Modulo Arithmetic: Definition and application of modulo arithmetic rules (congruence, allegation and mixture problems, numerical problems).

• Real-Life Applications: Solving problems involving boats and streams, pipes and cisterns, races and games, partnership, and numerical inequalities.

Unit 2: Algebra

• Matrices: Definitions and identification of different types of matrices (equality, transpose, symmetric & skew-symmetric matrices).

Unit 3: Calculus

• Higher Order Derivatives: Understanding differentiation of parametric and implicit functions, identifying dependent and independent variables.

• Marginal Cost & Marginal Revenue: Definitions, finding their values using derivatives.

• Maxima & Minima: Determining critical points, finding local/absolute maxima/minima values

Unit 4: Probability Distributions

• Probability Distribution: Understanding random variables and their probability distributions, finding the probability distribution of discrete random variables.

• Mathematical Expectation: Calculating expected value using the arithmetic mean of the frequency distribution.

• Variance: Calculating variance and standard deviation of a random variable.

Unit 5: Index Numbers and Time Based Data

• Index Numbers: Definition as a special type of average, constructing different types and applying time reversal test.

• Population & Sample: Definitions, differentiation, and identifying representative samples.

• Parameter & Statistics: Definitions and relation, limitations of statistics, interpretation of statistical significance and inferences, central limit theorem, and relation between population, sampling distribution, and sample.

• Time Series: Identifying time series data, distinguishing components, and analyzing univariate data based on statistical interpretation

Unit 6: Financial Mathematics

• Perpetuity & Sinking Funds: Explaining concepts and calculating perpetuities and differentiating between sinking funds and savings accounts.

• Valuation of Bonds: Defining valuation of bonds and related terms, calculating bond value using the present value approach.

• Calculation of EMI: Explaining the concept and calculating EMI using various methods.

• Linear Method of Depreciation: Defining the concept, interpreting cost, residual value, and useful life, and calculating depreciation.

Unit 7: Linear Programming

• Introduction & Terminology: Familiarizing with terms related to linear programming problems.

• Mathematical Formulation: Formulating linear programming problems.

• Types of Linear Programming Problems: Identifying and formulating different types of LPPs.

• Graphical Method: Drawing graphs and finding solutions for systems of linear inequalities in two variables.

• Feasible & Infeasible Regions/Solutions: Identifying feasible, infeasible, and unbounded regions and understanding feasible and infeasible solutions, finding the optimal feasible solution

## CUET Mathematics Exam Breakdown:

Section A:

o Compulsory for all candidates.

o 15 questions covering both Mathematics and Applied Mathematics

Section B:

o Section B1: Mathematics (25 out of 35 questions to be attempted).

o Section B2: Applied Mathematics (25 out of 35 questions to be attempted).

Candidates can choose which section (B1 or B2) to focus on and attempt more questions from