CUET Maths Syllabus 2023: Download Free Syllabus Pdf Here!

CUET Maths Syllabus 2023

Section

Topics

A

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

Calculus 

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

Integration and its Applications 

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

Differential Equations 

• Order and degree of differential equations 
• Formulating and solving of differential equations with variable separable 

Probability Distributions 

• Random variables and its probability distribution 
• Expected value of a random variable 
• Variance and Standard Deviation of a random variable 
• Binomial Distribution 

Linear Programming 

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

B1

Relationsand Functions 

Relations and Functions: Types of relations Reflexive, symmetric, transitive and equivalence relations. Toone and onto functions, composite functions,inverseofa function.Binaryoperations. 

InverseTrigonometricFunctions: Definition,range, domain, principal value branches. Graphs ofinverse trigonometric functions. Elementarypropertiesofinverse trigonometric functions.

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 of addition, multiplication, and scalar multiplication. Non-commutativity of multiplication of matrices and existence of non-zero matrices whose product is the zero matrices (restrict to square matrices of order 2). Concept of elementary row and column operations. Invertible matrices and proof of the uniqueness of inverse, if it exists; (Here all matrices will have real entries).

Determinants: Determinants of a square matrix (up to 3 × 3 matrices), properties of determinants, 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 a system of linear equations by examples, solving system of linear equations in two or three variables (having unique solution) using the inverse of a matrix.

Calculus

Continuity and Differentiability: Continuity and differentiability, derivative of composite functions, chain rule, derivatives of inverse trigonometric functions, derivative of implicit function. Concepts of 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.

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

Integrals: Integration as inverse process of differentiation. Integration of a variety of functions by substitution, by partial fractions, and by parts, only simple integrals of the type – to be evaluated, Definite integrals as a limit of a sum. 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, arcs of circles/parabolas/ellipses (in standard form only), and area between the two above said curves (the region should be clearly identifiable).

Differential Equations: Definition, order and degree, general and particular solutions of a differential equation. Formation of differential equation whose general solution is given. Solution of differential equations by the method of separation of variables, homogeneous differential equations of the first order and first degree. Solutions of linear differential equation of the type dy + Py = Q , where P and Q are functions of x or constant dy dx + Px = Q , where P and Q are functions of y or constant.

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

Three-dimensional Geometry: Direction cosines/ratios of a line joining two points. Cartesian and vector equation of a line, coplanar and skew lines, the shortest distance between two lines. Cartesian and vector equation of a plane. The angle between (i) two lines, (ii) two planes, (iii) a line and a plane. Distance of a point from a plane.

Linear Programming: Introduction, related terminology such as constraints, objective function, optimization, different types of linear programming (L.P.) problems, mathematical formulation of L.P. problems, graphical method of solution for problems in two variables, feasible and infeasible regions, feasible and infeasible solutions, optimal feasible solutions (up to three non-trivial constraints).

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

B2

Numbers, Quantification, and Numerical Applications

Allegation andMixture

• Understand the rule of allegation to produce a mixture at a given price
• Determine the mean price of a mixture
• Apply rule of the allegation

Modulo Arithmetic

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

Congruence Modulo

• Define congruence modulo
• Apply the definition in various problems

Numerical Problems

• Solve real-life problems mathematically

Boats and Streams

• Express the problem in the formof an equation
• Distinguish between upstream and downstream

Partnership

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

Pipes and cisterns

• Determine the time taken by two or more pipes to fill or

Boats and Streams

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

Races and games

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

Numerical Inequalities

• Describe the basic concepts of numerical inequalities
• Understand and write numerical inequalities

Algebra

Matrices and types of matrices

• Define matrix
• Identify different kinds of matrices

Equality of matrices, Transpose of a matrix, Symmetric and skew symmetric matrix

• Determine equality of two matrices
• Write transpose of a given matrix
• Define symmetric and skew symmetric matrix

Calculus

Higher Order Derivatives

• Determine second and higher-order derivatives
• Understand differentiation of parametric functions and implicit functions Identify 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

• 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

Probability Distributions

• Probability Distribution
• Understand the concept of random Variables and its Probability Distributions
• Find the probability distribution of the discrete random variable
• MathematicalExpectation
• Apply arithmetic mean of frequency distribution to find the expected value of a random variabl
• Variance
• Calculate the Variance and S.D.of a random variable

Index Numbers And Time-Based Data

• Construct different types of index numbers
• Construction of index numbers
• Index Numbers
• Define Index numbers as a special type of average
• Test of Adequacy of Index Numbers
• Apply time reversal test

Index Numbers And Time-Based Data

Population And Sample

• Define Population and Sample
• Differentiate between population and sample
• Define a representative sample from a population
• 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 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

Index Numbers And Time-Based Data

•  Distinguish between different components of time series
• Components of Time Series
• Time Series
• Identify time series as chronological data
• Time Series analysis for univariate data
• Solve practical problems based on statistical data and Interpret

Financial Mathematics

• Calculation of EMI
• Explain the concept of EMI
• Calculate EMI using various methods
• Perpetuity, Sinking Funds
• Explain the concept of perpetuity and sinking fund
• Calculate perpetuity
• Differentiate between sinking fund and saving account
• Valuation of bonds
• Define the concept of valuation of bonds and related terms
• Calculate the value of the bond using the present value approach
• Linear method of Depreciation
• Define the concept of linear method of Depreciation
• Interpret the cost, residual value, and useful life of an asset from the given information
• Calculate depreciation

Linear Programming

• Feasible and InfeasibleRegions
• Identify feasible, infeasible and bounded regions
• Different types of Linear Programming Problems
• Identify and formulate different types of LPP
• Introduction and related terminology
• Familiarize with terms related toLinear Programming Problem
• Mathematicalformulation ofLinear ProgrammingProblem
• Formulate Linear ProgrammingProblem
• 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
• Feasible and infeasible solutions, optimal feasible solution
• Understand feasible and infeasible solutions
• Find the optimal feasible solution