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.