CUET Mathematics Syllabus: Check Direct Link, Chapter-Wise Detailed Topics

Algebra

• Matrices and types of Matrices
• Algebra of Matrices
• Determinants
• Equality of Matrices, transpose of a Matrix, Symmetric, and Skew Symmetric Matrix
• Inverse of a Matrix
• Solving simultaneous equations using Matrix Method

Calculus

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

Applications of Integrations

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

Differential Equations

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

Distribution of Probabilities

• Random variables and their probability distribution
• Variance and Standard Deviation of a random variable
• Expected value of a random variable

Linear Programming

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

Relationships and Functions

• Functions of inverse trigonometry: Inverse trigonometric functions include several subjects, including determining range, domain, and principal value and creating graphs of inverse functions.
• Relations and functions: Included is a one-to-one mapping, composite functions, reflexive, transitive, symmetric, and equivalence relations, as well as binary operations.

Algebra

• Determinants: Significant properties of determinants, estimating cofactors, and employing properties of determinants in estimating a triangle's area are covered. The adjoint and inverse of the square matrix are discussed in the second section of the chapter, along with checking for consistent and inconsistent answers to linear equations and utilizing the inverse approach to solve equations involving more than two variables.
• Matrices: Fundamental ideas of matrices, notation, order of operations, zero matrices, and matrix transposition. Row and column operations knowledge, non-commutativity of matrix multiplication, and properties of addition and multiplication of scalar matrices are also covered in this chapter.

Calculus

• Continuity and Differentiability: The derivatives of composite functions, the derivative of inverse functions, the use of the chain rule approach, and determining the derivative of an implicit function are covered in the first few sections of the chapter. Exponential and logarithmic functions, logarithmic differentiation, derivatives of parametric functions, Rolle's and Lagrange's Mean Value Theorem, and their applications are covered in the chapter's latter sections.
• Integrals: The differentiation method and the integration approach are considered opposites. The two main ways of integration that can be used depending on convenience are integration by substitution and parts. This chapter also covers the basic characteristics of definite integrals and some of their uses.
• Application of Derivatives: The estimation of the rate of change of growing and decreasing functions, tangent and normal ideas, and maxima and minima functions, including the first and second derivative tests, are some of the subjects covered in the first section. This chapter's latter section has some problem sums on tangents and normals that are of an advanced level.
• Differential equations: The simple definition, degree, and order of equations, as well as the formulation of differential equations with indicated solutions, are covered in the first section of the differential equations chapter. Finding solutions to first-order homogeneous differential equations, solving linear differential equations, and the separation of variables approach are all included in the second section.
• Applications of Integrals: Integrals are used in this chapter to calculate the areas of circles, ellipses, and parabolas.

3-D Geometry and Vectors

• 3-D geometry: Estimating ratios, determining the shortest distance between any two lines, constructing cartesian and vector equations of a line, and calculating the angle between two lines, planes, and a line and a plane are all aspects of three-dimensional geometry.
• Vectors: Discusses vectors, including their magnitude and direction, direction cosines, collinearity, and the vectors' addition and multiplication by scalars. The next portion of the textbook covers scalar triple products, cross products of vectors, vector dot products, and problem sums on the projection of a vector on a straight line.

Linear Programming

• Finding the best solutions up to three non-trivial restrictions and identifying the feasible and infeasible solutions are included in the second section.
• The first section of Linear programming covers mathematically expressing linear programming issues, optimization strategies, and using graphical tools to solve equations with two variables.

Probability

• The Bayes theorem, conditional probability theorem, and multiplication theorem on probability are all included in the chapter's first section.
• The chapter's third section, which deals with problem sums, assumes that the reader has already read the first two sections.
• A random variable, its probability distribution, repeated independent trials, and binomial distribution are all included in the second section of the chapter.

Numbers, Quantification, and Numerical Applications

• Modulo Arithmetic
• Congruence Modulo
• Races and Games
• Partnership Inequalities
• Mixture and Allegation
• Numerical Problem Sums
• Boats and Streams
• Pipes and Cisterns

Algebra

• Matrices
• Symmetric and Skew-symmetric Matrix
• Transpose of a Matrix

Calculus

• Higher-order Derivatives
• Maxima and Minima
• Marginal Cost and Marginal Revenue

Probability Distributions

• Probability Distribution
• Variance
• Mathematical Distribution

Index Numbers and Time-Based Data

• Index numbers
• Application of time-reversal test
• Construction of Index Numbers

Probability

• Parameter and statistics and statistical inferences
• Population and sample

Time Series

• Components of time series using time series analysis for univariate data

Financial Mathematics

• Perpetuity
• Estimating EMI
• Bond valuation method
• Calculating depreciation through a linear method

Linear Programming

• Introduction and steps to form linear programming problems
• Graphical method for finding solutions
• Distinguishing between different types of linear programming problems
• Shading feasible, bounded, and infeasible region