IOQM Syllabus 2025-26: Complete Subject-Wise Breakdown

The Indian Olympiad Qualifier in Mathematics (IOQM) is one of the most prestigious mathematics competitions in India, serving as the first step in the selection process for the International Mathematical Olympiad (IMO). Conducted by the Mathematics Teachers’ Association of India (MTA(I)), the IOQM 2025–26 exam is scheduled to be held on 7th September 2025.

Aspirants looking to participate in this rigorous mathematical journey must first understand the IOQM syllabus 2025–26 thoroughly. The syllabus not only helps in effective preparation but also provides a clear roadmap to master fundamental and advanced mathematical concepts.

IOQM 2025-26: Exam Overview

• Exam Name: Indian Olympiad Qualifier in Mathematics (IOQM)
• Exam Date: 7th September 2025
• Mode: Offline (Pen & Paper)
• Duration: 3 Hours
• Question Type: Subjective and Problem Solving-Based
• Official Website: www.mtai.org.in

IOQM Syllabus 2025–26: Subject-Wise Topics

Here’s a subject-wise breakdown of the official IOQM syllabus for the year 2025–26:

1. Basic Mathematics

• Number Systems
• Basic Inequality Concepts
• Modulus & Greatest Integer Functions
• Logarithmic Functions

2. Number Theory

• Prime Numbers, Prime Factorization
• Divisibility Rules, GCD, LCM, Euclidean Algorithm
• Modular Arithmetic (Congruences, Chinese Remainder Theorem)
• Diophantine Equations (Linear & Pell’s)
• Number Bases (Binary, Octal, Hexadecimal)
• Arithmetic Functions (Euler's Totient φ, Möbius μ, σ Functions)
• Fermat’s Little Theorem and Euler’s Theorem

3. Algebra

• Simplification & Factorization of Algebraic Expressions
• Inequalities (AM-GM, Cauchy-Schwarz, Rearrangement)
• Polynomials: Vieta’s Formulas, Newton’s Identities, Roots
• Complex Numbers: Operations, Roots of Unity, De Moivre's Theorem
• Sequences & Series (AP, GP, Convergence, Infinite Series)
• Functional Equations (Cauchy, Jensen, etc.)
• Binomial Theorem and Combinatorics

4. Combinatorics

• Counting Principles (Multiplication, Addition, Inclusion-Exclusion)
• Permutations and Combinations
• Pigeonhole Principle
• Recurrence Relations (Homogeneous, Non-Homogeneous)
• Principle of Inclusion and Exclusion (PIE)
• Graph Theory: Basics, Trees, Eulerian & Hamiltonian Paths
• Combinatorial Geometry & Theorems
• Generating Functions
• Combinatorial Identities (Catalan Numbers, Hockey Stick, Vandermonde’s)

5. Geometry

• Euclidean Geometry: Lines, Triangles, Circles, Quadrilaterals, Polygons
• Geometric Transformations: Reflections, Rotations, Translations, Dilations
• Coordinate Geometry: Distance, Midpoints, Slopes, Conic Sections
• Trigonometry: Trigonometric Functions, Identities, Applications in Geometry

How to Use the IOQM Syllabus Effectively?

Understanding the syllabus isn’t enough—here’s how to make the most of it:

• Create a Timetable around each topic.
• Prioritize Topics you are weak in or unfamiliar with.
• Solve Previous Year IOQM Papers to understand question patterns.
• Revise Regularly to retain important concepts.
• Join Olympiad Coaching (like Aakash Institute) for structured guidance.

Why is the IOQM Syllabus Important?

The IOQM syllabus lays the groundwork for advanced Olympiad stages like:

• RMO (Regional Mathematical Olympiad)
• INMO (Indian National Mathematical Olympiad)
• IMO (International Mathematical Olympiad)

Focusing on this syllabus ensures that students are not only prepared for IOQM but also for successive rounds in the Olympiad hierarchy.

Conclusion

The IOQM Syllabus 2025–26 acts as the blueprint for aspiring mathematicians aiming to represent India at the international stage. With the exam scheduled for 7th September 2025, students still have ample time to plan their preparation in a focused and strategic way.

Stay updated with any changes by regularly visiting the official MTA(I) website, and ensure that your preparation aligns with the topics mentioned above.

IOQM Syllabus 2025-26 FAQs

What is the official syllabus for IOQM 2025–26?

Answer: The official IOQM 2025–26 syllabus includes topics from five major areas of mathematics: Basic Mathematics, Number Theory, Algebra, Combinatorics, and Geometry. Topics range from number systems, inequalities, and modular arithmetic to Euclidean geometry, complex numbers, and combinatorics. These topics are chosen to test problem-solving and analytical thinking required for Olympiad-level exams.

Is the IOQM syllabus based on the NCERT curriculum?

Answer: While IOQM questions may overlap with topics from the NCERT curriculum (Classes 9 to 12), the syllabus is more advanced and designed for Olympiad-level difficulty. The exam includes higher-order problems in number theory, combinatorics, and functional equations, which are typically beyond the scope of regular school textbooks.

How can I effectively prepare for all topics in the IOQM 2025–26 syllabus?

Answer: Start by dividing the syllabus into weekly goals. Use Olympiad-specific books, attend coaching classes like Aakash Foundation programs, and solve past year papers. Regular practice of problems in each topic—especially from number theory, inequalities, and geometry—will help you master the concepts. Online mock tests and peer discussions can further improve your understanding and speed.

Has there been any change in the IOQM syllabus for the year 2025–26?

Answer: As of now, no major changes have been announced in the IOQM syllabus for 2025–26. The syllabus remains consistent with previous years and includes a wide range of topics from pure mathematics. Students are advised to keep checking the official MTA(I) website (mtai.org.in) for any syllabus updates or notifications.