IOQM Syllabus 2026: Subject-wise & Class-wise Topics, Exam Pattern & PDF

The IOQM syllabus 2026 covers high-level school mathematics designed to test deep conceptual understanding and Olympiad-style problem-solving. The Indian Olympiad Qualifier in Mathematics (IOQM) focuses on four core areas - Algebra, Number Theory, Geometry, and Combinatorics - spanning topics studied from Class 8 to Class 12, but excluding Calculus.

Instead of routine textbook problems, the IOQM tests creative reasoning through questions on the arithmetic of integers, quadratic equations, inequalities, coordinate geometry, probability, and elementary graph theory. Understanding the complete syllabus of IOQM, along with the exam pattern, helps students plan a focused and effective preparation strategy.

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IOQM 2026 Syllabus PDF Download

IOQM Syllabus 2026 - Subject-wise Topics

The IOQM 2026 syllabus includes a wide range of mathematical topics, excluding Calculus. The main topics covered under the basic mathematics section are:

• Arithmetic of Integers – operations, properties, and integer-based number theory

• Geometry – properties and relations of points, lines, surfaces, and solids

• Trigonometry – angles, triangles, and trigonometric functions

• Inequalities – expressions involving greater than, less than, and equality

• Coordinate Geometry – lines, curves, and shapes on a coordinate system

• System of Linear Equations – linear equations and their systems

• Permutations and Combinations – arrangement and selection of objects

• Factorisation of Polynomials – breaking polynomials into simpler factors

• Quadratic Equations and Expressions – solutions and properties

• Elementary Combinatorics – basic counting, arrangements, and selections

• Finite Series and Complex Numbers – finite-term series and complex numbers

• Probability Theory – concepts and applications of probability

• Number Theory – properties and relationships of integers

• Elementary Graph Theory – graphs, nodes, edges, and their properties

IOQM Number Theory Syllabus

Number Theory is a key part of the IOQM syllabus and frequently appears in the paper. The main subtopics are:

• Prime Numbers: Prime factorisation, prime counting functions, sieve methods (e.g., Eratosthenes' sieve), properties of prime numbers

• Divisibility: Divisibility rules, GCD, LCM, Euclidean algorithm

• Modular Arithmetic: Congruences, residues and non-residues, Chinese Remainder Theorem

• Diophantine Equations: Linear Diophantine equations, Pell's equation, Fermat's Last Theorem

• Number Bases: Binary, octal, hexadecimal, and base conversion

• Arithmetic Functions: Euler's totient function (φ), Mobius function (μ), number and sum of divisors functions, Fermat's Little Theorem, Euler's Totient Theorem

IOQM Algebra Syllabus

Algebra is a core area of the IOQM syllabus. The main subtopics are:

• Basic Algebraic Manipulations: Simplifying expressions, factorisation, solving equations

• Inequalities: AM-GM, Cauchy-Schwarz, rearrangement, and Jensen's inequality

• Polynomials: Fundamental theorem of algebra, Vieta's formulas, Newton's identities, Eisenstein's criterion

• Complex Numbers: Operations, De Moivre's Theorem, roots of unity

• Sequences and Series: Arithmetic and geometric progressions, convergent and divergent series, infinite series summation

• Functional Equations: Cauchy's and Jensen's functional equations, and others

• Binomial Theorem and Combinatorics: Binomial and multinomial coefficients, combinatorial identities

• Polynomial Equations: Roots and coefficients, factor theorem, rational root theorem

IOQM Combinatorics Syllabus

Combinatorics plays a major role in the IOQM question pattern. The key subtopics are:

• Counting Principles: Multiplication, addition, and inclusion-exclusion principles

• Permutations and Combinations: Arrangements, selections, and combinatorial identities

• Pigeonhole Principle: Dirichlet's principle and its applications

• Recurrence Relations: Linear, homogeneous, and non-homogeneous recurrences

• Graph Theory: Basics, graph colouring, trees and spanning trees, connectivity, Eulerian and Hamiltonian graphs

• Combinatorial Geometry: Geometric counting problems, Sylvester-Gallai theorem

• Generating Functions: Generating functions for sequences and their operations

• Combinatorial Identities: Vandermonde's identity, hockey stick identity, Catalan numbers

IOQM Geometry Syllabus

Geometry forms a major portion of the IOQM 2026 syllabus. The key subtopics are:

• Euclidean Geometry: Points, lines, and planes; angle properties; congruence and similarity of triangles; quadrilaterals; circles (tangents, secants, angles, theorems); polygons

• Geometric Transformations: Reflection, rotation, translation, dilation; isometries and similarities; symmetry and tessellations

• Coordinate Geometry: Distance formula, slope and equations of lines, midpoint formula, conic sections (parabola, ellipse, hyperbola)

• Trigonometry: Sine, cosine, tangent and their properties; trigonometric identities and equations; applications in geometry

IOQM Syllabus 2026 for All Classes (Class 8 to 12)

While the core IOQM chapters remain the same across all classes, the depth of problem-solving increases from Class 8 to Class 12. The class-wise IOQM syllabus 2026 is given below for reference.

IOQM Syllabus for Class 8

• Geometry

• Rational Numbers

• Linear Equations in One Variable

• Algebraic Expressions

• Permutations and Combinations

• Square Root and Cube Root

• Factorization

• Elementary Graph Theory

IOQM Syllabus for Class 9

• Number System

• Polynomials

• Coordinate Geometry

• Probability

• Linear Equations in Two Variables

• Surface Area and Volume

• Circles

• Areas of Parallelograms and Triangles

IOQM Syllabus for Class 10

• Real Numbers

• Trigonometry

• Quadratic Equations

• Arithmetic Progression

• Coordinate Geometry

• Inequalities

• Surface Area and Volume

• Circles

• Linear Equations in Two Variables

IOQM Syllabus for Class 11

• Permutations and Combinations

• Trigonometric Reasoning

• Quadratic Equations and Expressions

• Probability Theory

• Number Theory

• Factorisation of Polynomials

• Coordinate Geometry

IOQM Syllabus for Class 12

• Coordinate Geometry

• Permutations and Combinations

• Trigonometric Reasoning

• Quadratic Equations and Expressions

• Probability Theory

• Number Theory

• Factorisation of Polynomials

• Elementary Combinatorics

• Finite Series

• Linear Equations

• 
  

Note: These class-wise topics are indicative. Since IOQM is a single common paper for all classes, students of every class are advised to prepare the complete syllabus rather than limiting themselves to their class-specific topics.

IOQM Exam Pattern 2026

Understanding the IOQM paper format is important, along with the syllabus. The key details of the IOQM exam pattern 2026 are given below.

Each question requires a numerical answer between 00 and 99. Since there is no negative marking, students are encouraged to attempt all questions.

IOQM Syllabus 2026 PDF Download

Students can download the IOQM syllabus 2026 PDF for offline reference and easy revision. The PDF includes the complete subject-wise and class-wise topics along with the exam pattern, helping students plan their preparation systematically. To get the most accurate and updated syllabus, students should also refer to the official HBCSE Olympiad page and the MTAI website.

How to Prepare Using the IOQM 2026 Syllabus?

• Start with the four core areas — Algebra, Number Theory, Combinatorics, and Geometry — since they carry the most weight.

• Move beyond school textbooks and practise Olympiad-level problems that test creative reasoning.

• Solve the IOQM previous year question papers to understand the difficulty level and question style.

• Maintain a notebook of key theorems and formulas like the AM-GM inequality, Vieta's formulas, and the Pigeonhole Principle.

• Take regular timed mock tests to improve speed and accuracy for the 3-hour paper.