CUET Mathematics Syllabus 2025

topics mentioneThe National Testing Agency (NTA) administers the Common University Entrance Test (CUET), a nationwide entrance exam, to applicants for admission to a range of undergraduate programs at Indian universities. CUET evaluates candidates’ academic abilities in multiple subjects, including mathematics. For those opting for Mathematics in CUET, understanding the syllabus in detail is crucial for preparing effectively. Below is a comprehensive breakdown of the CUET Mathematics Syllabus for 2025, which is divided into various sections, covering the essential topics and concepts students need to focus on.

1. Algebra

Algebra is one of the most significant components of the CUET Mathematics syllabus. The concepts in this section are fundamental and form the base for other advanced topics.

  • Polynomials:
    • Zeroes of polynomials and their relationship with coefficients.
    • Remainder theorem and factor theorem.
    • Algebraic identities and their applications.
    • Factorization of quadratic polynomials and other polynomial identities.
  • Linear Equations:
    • Solutions of linear equations in two variables.
    • Pair of linear equations in two variables (both graphical and algebraic methods for solving them).
    • Consistency and inconsistency of linear systems.
  • Quadratic Equations:
    • Solutions of quadratic equations using factorization, completing the square, and the quadratic formula.
    • Nature of roots and discriminants.
    • a function’s continuity both at a point and throughout time. 
  • Matrices and Determinants:
    • Basics of matrices, types of matrices, matrix operations, and properties.
    • Determinants and their properties.
    • The inverse of a matrix and solving linear systems using matrix methods.

2. Calculus

Calculus is another essential section of the CUET Mathematics syllabus and is crucial for understanding the behavior of functions and their changes.

  • Limits and Continuity:
    • Concept of limit and its evaluation.
    • Continuity of functions at a point and in an interval.
    • Properties of continuous functions.
    • Limits of rational functions and their applications.
  • Differentiation:
    • Definition and basic rules of differentiation (product rule, quotient rule, chain rule).
    • Derivatives of standard functions (polynomial, trigonometric, exponential, logarithmic, etc.).
    • Application of differentiation in rate of change problems, tangents, and normals.
    • Higher-order derivatives.
  • Integration:
    • Indefinite integrals and basic integration rules (substitution, by parts, and partial fractions).
    • Definite integrals and their applications in area under curves.
    • Fundamental theorem of calculus.
    • Applications of integration in finding areas, volumes, and averages.
  • Applications of Calculus:
    • Maxima and minima of functions and their practical applications.
    • Optimization problems in economics and business.
    • Rate of change in physical and natural processes.

3. Geometry

The Geometry section in the CUET Mathematics syllabus focuses on shapes, their properties, and related theorems.

  • Coordinate Geometry:
    • Cartesian coordinates and the distance formula.
    • Section formula and the midpoint formula.
    • Equation of a line (slope-intercept form, point-slope form, general form).
    • Parallel and perpendicular lines.
    • Conic sections: equations of circles, parabolas, ellipses, and hyperbolas.
  • Euclidean Geometry:
    • Basic geometrical definitions: points, lines, angles, and planes.
    • Triangles, quadrilaterals, and their properties (congruence, similarity).
    • Pythagoras theorem and its applications.
    • Circles: tangents, secants, chords, and their properties.
  • Trigonometry:
    • Trigonometric ratios and their applications.
    • Trigonometric identities and equations.
    • Heights and distances problems using trigonometry.
    • Inverse trigonometric functions.

4. Statistics and Probability

This section covers concepts related to data analysis and probability, which are crucial for students who wish to pursue further studies in data science, economics, or social sciences.

  • Statistics:
    • Measures of central tendency: mean, median, and mode.
    • Measures of dispersion: range, variance, and standard deviation.
    • Histogram, frequency polygon, and cumulative frequency distribution.
    • Probability distribution and cumulative frequency.
    • Correlation and regression analysis.
  • Probability:
    • Basic concepts of probability (sample space, events).
    • Conditional probability and Bayes’ theorem.
    • Random variables, expectation, and variance.
    • Probability distributions (binomial and normal distributions).
    • Theorems and problems on probability.

5. Vector Algebra

Vector algebra plays a critical role in higher mathematics and applications such as physics, engineering, and computer graphics.

  • Vectors:
    • Definition of vectors, types of vectors (position, displacement, unit vectors).
    • Addition and subtraction of vectors, scalar multiplication.
    • Dot product and cross product of vectors and their properties.
    • Vector applications in geometry (finding areas, volumes, etc.).
  • Three-Dimensional Geometry:
    • Cartesian coordinates in 3D space.
    • Direction cosines and direction ratios.
    • Equation of a plane, line, and sphere in 3D space.
    • Angle between two lines, two planes, and line and plane.

6. Sets and Relations

This section focuses on the fundamental principles of set theory and relations, which form the foundation of logic and mathematical reasoning.

  • Sets:
    • Types of sets: finite, infinite, equal, singleton, etc.
    • Set operations: union, intersection, difference, and complement.
    • Venn diagrams and their applications.
    • Laws of set theory (De Morgan’s laws, distributive, associative, etc.).
  • Relations:
    • Definition of relations and types (reflexive, symmetric, transitive, etc.).
    • Equivalence relations and partitions.
    • Cartesian product of sets.

7. Miscellaneous Topics

Apart from the core topics, there are other miscellaneous areas in the CUET Mathematics syllabus that contribute to a holistic understanding of mathematics.

  • Sequences and Series:
    • Arithmetic Progression (AP) and Geometric Progression (GP).
    • Sum of the first n terms of AP and GP.
    • Infinite series, convergence, and divergence.
  • Complex Numbers:
    • Basic operations on complex numbers.
    • Argand plane and polar form of complex numbers.
    • Modulus and argument of complex numbers.
    • De Moivre’s theorem.
  • Permutations and Combinations:
    • Factorial notation and basic counting principles.
    • Permutations and combinations with and without repetition.
    • Binomial theorem and its applications.

Conclusion

The CUET Mathematics Syllabus 2025 is designed to evaluate a candidate’s overall understanding of mathematical concepts. By covering a wide range of topics such as algebra, calculus, geometry, statistics, probability, and more, the syllabus ensures that students develop both theoretical and practical skills. To excel in the CUET Mathematics exam, candidates need to not only understand the formulas and theorems but also develop problem-solving abilities through regular practice and application. Therefore, following a structured study plan and focusing on the importantd above will significantly increase the chances of scoring well in the exam.

Scroll to Top