IISER Entrance Exam 2025 Mathematics Syllabus

IISER Entrance Exam 2025 will consist of 15 questions from the IAT 2025 Mathematics syllabus. Candidates preparing for the IISER exam 2025 must go to the Mathematics syllabus specified by the exam officials. Read this Shiksha article to learn about the IISER entrance exam 2025 Mathematics syllabus of class 11 and 12 NCERT books. Also, check out the weightage of Mathematics questions asked in the examination.

IAT 2025 Mathematics Syllabus

IISER Entrance Exam 2025 will be conducted to test candidates domain knowledge in Biology, Mathematics, Physics and Chemistry subjects. Among the diverse subjects tested, mathematics holds a pivotal role, evaluating a candidate's grasp of fundamental mathematical concepts and their ability to apply them. The IAT mathematics syllabus 2025 is meticulously designed to assess a student's proficiency in key areas, ensuring they possess the necessary mathematical foundation for advanced studies in science.

Also Read: IISER 2025 New Changes Introduced: Check for Newly Added Courses, Eligibility, Seat Intake Details 

IAT 2025 Mathematics syllabus encompasses a broad spectrum of topics typically covered in higher secondary education (Class 11 and 12). It delves into algebra, exploring concepts like sets, relations, functions, complex numbers, and quadratic equations. Trigonometry forms another significant component, examining trigonometric functions, inverse trigonometric functions, and their applications. Calculus, a cornerstone of higher-level mathematics, is thoroughly tested through limits, derivatives, integrals, and differential equations.

IISER Entrance Exam 2025 will be conducted on May 25, 2025, at various exam centres across the nation. Interested applicants will be able to fill out the IAT 2025 application form from March 5, 2025 onwards. Candidates are advised to check out the IISER 2025 eligibility criteria meticulously before applying to not lose their candidature at any stage of the admission process.

IISER Aptitude Test Mathematics Syllabus 2025

By mastering the IAT mathematics syllabus, candidates not only enhance their chances of securing a place in IISER participating institutes but also equip themselves with the mathematical tools essential for a successful scientific career. Success in this section demands not just rote memorization of formulas but a deep understanding of underlying principles and the ability to apply them creatively.

Check out the IAT 2025 Mathematics syllabus of class 11 & 12 NCERT of Mathematics domain from here:

Sets and Logic
Set: Representing sets in different ways. Subsets. Different types of sets e.g. universal set, finite or infinite sets, intervals in real line. Various operations on sets. Properties of various operations on sets. Venn diagram. Ordered pairs. Cartesian products.
Relations & functions: Type of relations. Equivalence relation. Functions. Types of functions. Composition of functions, inverse of a function. Real valued functions: algebraic operations of real valued functions, different types of real valued functions (e.g. polynomial, rational, modules, signum, etc), graphical representation of real valued functions.

Basic counting techniques
Permutations and Combinations: Fundamental principles of counting. Factorial n. Permutations and combinations- derivation of formulae and their connections. Applications.
Binomial Theorem: Binomial theorem for positive integral indices. Pascal’s triangle. General and middle term in binomial expansion. Applications.

Complex numbers, linear and quadratic equations
Complex Numbers: Motivation for complex numbers. Representation of complex numbers in the plane as a pair of real numbers and their representation of the form a+ib. Polar representation and the Argand plane. Algebra of complex numbers. Modulus and conjugate of a complex number. Statement of the Fundamental Theorem of Algebra.
Quadratic Equations: Quadratic equations and their solutions. Relation between roots and the coefficients of quadratic equations.
Linear Inequalities: Inequalities, Algebraic solution of linear inequalities in one variable and their graphical representation.

Trigonometric functions
Measures of angles and their conversions. Trigonometric functions, identities, and their geometric interpretations. Applications of trigonometric equations. Inverse trigonometric functions and properties. Graphs of trigonometric functions.

Also Read: IISER Aptitude Test Physics Syllabus 2025: Check Topic Wise Complete Syllabus Here 

Vectors
Vectors and scalars: Magnitude and direction of a vector. Direction cosines/ ratios. Types of vectors. Position vector. Negative and components of a vector. Addition of vectors. Multiplication of a vector by a scalar. Position vector of a point dividing a line segment in the given ratio. Dot and cross products of vectors. Projection of a vector on another vector/ line.

Matrices & determinants
Matrices: Concept, notation, order, equality, transpose of a matrix, types of matrices, simple properties of addition, multiplication, scalar multiplication, and multiplication of matrices. Concept of elementary row and column operations. Invertible matrices and proof of the uniqueness of inverse, if it exists. Applications of matrices.
Determinants: Determinant of a square matrix (up to 3 X 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. Applications of determinants.

Coordinate geometry
Cartesian system of rectangular coordinates in a plane. Shifting of origin.
Straight Lines: Slope of a line and angle between two lines. Various forms of equations of a line. General equation of a line. Distance of a point from a line.
Conic Sections: Sections of a cone: Circles, ellipse, parabola, hyperbola, a point, a straight line, and a pair of intersecting lines as a degenerated case of a conic section. Standard equations and simple properties of parabola, ellipse, and hyperbola. Standard equation of a circle, the general form of the equation of a circle.

Three-dimensional geometry
Coordinate axes and planes. Distance between points. Section formula. Direction cosines and direction ratios of a line. Various forms of the equation of a line. Angle between two lines and two planes. Shortest distance between two lines in three-dimensional space. Coplanar andskew line. Cartesian and vector equation of a plane. Distance of a point from a plane.

Also Read: IISER Aptitude Test 2025 Chemistry Syllabus 

Sequences & series
Arithmetic and Geometric progressions. Sums of finite and infinite geometric series. Sums of finite terms in arithmetic series. Arithmetic mean (A.M.) and geometric mean (G.M.). Relation between A.M and G.M. Sums of first n-terms of the special series, for example, ∑ n, ∑ n^2 and ∑ n^3.

Limit & continuity
Limits. Continuity. Algebraic properties of limits. Algebraic properties of continuous functions. Limits and continuity of real valued functions, polynomials, rational functions, trigonometric
functions, exponential functions, and inverse functions.

Differentiation
Differentiation: Definition of derivative and relating it to slope of tangent of the curve. Derivative of sum, difference, product, and quotient of functions. Derivative of some standard functione.g. polynomial, trigonometric, inverse trigonometric, exponential, and logarithmic functions. Derivative of composite functions via chain rule. Derivative of implicit functions and functions in parametric forms. Logarithmic derivative. Second order derivatives. 

Application of Derivatives: Rate of change, increasing/decreasing functions, tangents and normals maxima and minima.

Integration
Integration: Integration as inverse process of differentiation. Integrals involving algebraic, trigonometric, exponential, and logarithmic functions. Integration of a variety of functions by
substitution, by partial fractions, by parts and using trigonometric identities. Evaluation of integrals of some standard types. Fundamental theorem of calculus. Basic properties and evaluation of definite integrals.
Applications of Integration: Finding the area of region under simple curves. Finding the area of the region between two simple curves.

Differential equations
Definition, order, degree. Formation of a differential equation. Solution by separation of variables. Homogeneous differential equation of first order and degree. Solution of the equations dy/dx +P y=Q where P and Q are functions of x or constant and similarly for dx/dy +P x=Q where P and Q are functions of y or constant.

Statistics, Probability & Linear Programming
Statistics: Measure of dispersion; mean deviation, variance, and standard deviation of ungrouped/grouped data.
Probability: Random experiments: outcomes, sample spaces (set representation).

Events: Occurrence of events, ‘not’, ‘and’ & ‘or’ events, exhaustive events, mutually exclusive events. Axiomatic (set theoretic) probability. Probability of an event, probability of ‘not’, ‘and’, & ‘or’ events. Multiplication theorem on probability. Conditional probability, independent events, total probability, Baye’s theorem. 

Also Read: IISER Biology Syllabus 2025: Check Class 11 and Class 12 NCERT Biology Syllabus Here 

IISER Entrance Exam 2025: Subject Weightage

The IISER Entrance Exam Marking Scheme and subject weightage is as follows:

Marking scheme: Candidates will be awarded three marks for each correct answer. There will be negative marking of one mark for each incorrect answer.

Also Read: IISER Entrance Exam 2025 Pattern: Section-wise Paper Pattern, Marking Scheme 

Best IISER Aptitude Test Books for Mathematics

The most preferred books for the IISER Aptitude Test for Mathematics along with their authors are listed below.