CUET Maths Syllabus 2023: Download Topic-wise Syllabus PDF

CUET Mathematics Syllabus

RELATIONS AND FUNCTIONS

(a) Relations and Functions.
– Types of relations: Reflexive, symmetric, transitive, and equivalence.
– One-to-one and on-to functions, composite functions, the inverse of a function.
– Binary operations.

(b) Inverse Trigonometric Functions
– Definition, range, domain, principal value branches.
– Graphs of inverse trigonometric functions.
– Elementary properties of inverse trigonometric functions.

ALGEBRA

– Matrices Concept, notation, order, equality, types of matrices, zero matrices, 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.
– Concept of elementary row and column operations.
– The invertible matrices and proof of the uniqueness of inverse fit exist.

– 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 several solutions of a system of linear equations by examples, solving a system of linear equations in two or three variables using the inverse of a matrix.

CALCULUS

(a) Continuity and Differentiability:
– A derivative of composite functions, chain rules, inverse trigonometric functions, and a derivative of implicit functions.
– Concepts of exponential and 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 and their geometric interpretations.

(b) Applications of Derivatives:
– Rate of change, increasing/decreasing functions, tangents and normals, approximation, maxima, and minima.
– Simple problems.
– Tangent and Normal.

(c) Integration is an inverse process of differentiation:
– Integration of various functions by substitution, partial fractions, and parts. Only simple integrals of the type are to be evaluated.
– Definite integrals as a limit of a sum.
– Fundamental Theorem of Calculus.
– Basic properties of definite integrals and evaluation of definite integrals. 

(d) Applications of the Integrals.
– Applications in finding the area under simple curves, especially lines, arcs of circles/parabolas/ellipses, and the area between the above-said curves. 

(e) Differential Equations
– Definition, order, degree, general and particular differential equation solutions.
– Formation of differential equation whose general solution is given.
– Solution of differential equations by separating variables, homogeneous differential equations of the first order, and first degree.
– Solutions of linear differential equation of the type.

VECTORS & THREE-DIMENSIONAL GEOMETRY

(a) Vectors and scalars, magnitude, and direction of a vector.
– Direction cosines/ratios of vectors.
– Types of 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.
– The scalar product of vectors, projection of a vector on a line.
– Vector product of vectors, scalar triple product.

(b) 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, and
(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 problems, mathematical formulation of L.P.
– Problems, graphical method of solving problems in two variables, feasible and infeasible regions, feasible and infeasible solutions, optimal feasible solutions.

PROBABILITY

– Multiplications theorem on probability.
– Conditional probability, independent events, total probability, Bayes theorem.
– Random variable and its probability distribution, mean, and variance of haphazard variable.
– Repeated independent trials and binomial distribution.