IOQM Syllabus 2026-27 PDF (OUT): Complete Subject-Wise Breakdown

The IOQM Syllabus 2026-27 covers four core areas — Algebra, Plane Geometry, Combinatorics, and Number Theory — built on top of NCERT Class VIII, IX, and X mathematics. I

OQM 2026 is scheduled for 6 September 2026, a Sunday, and individual online registration is open until 25 July 2026. This is the first stage of India's Mathematical Olympiad pathway, conducted jointly by the Mathematics Teachers' Association of India MTA(I) and HBCSE.

Most students search for the IOQM syllabus without realising the registration window, and the syllabus is tightly linked this year. Centre registration already closed on 29 June 2026, and individual enrollment is closing fast. This page walks through the exact subject-wise IOQM syllabus 2026-27, the exam pattern, key dates, and how to apply before the window shuts.

What Is IOQM and Who Conducts the IOQM 2026-27 Exam?

IOQM (Indian Olympiad Qualifier in Mathematics) is the first-stage qualifying exam of India's Mathematical Olympiad programme, conducted by MTA(I) in association with HBCSE, which operates under the Tata Institute of Fundamental Research. Students who clear IOQM move to the Regional Mathematical Olympiad (RMO), then the Indian National Mathematical Olympiad (INMO), and finally the International Mathematical Olympiad Training Camp (IMOTC) — the pathway that selects India's team for IMO, EGMO, and APMO.

IOQM replaced the earlier two-stage Pre-RMO and RMO system starting in 2021, combining them into one national qualifier. Let us be clear about this — the IOQM syllabus 2026-27 itself has not changed structurally from previous cycles; what changes each year is the exam date, registration timeline, and centre approvals.

IOQM 2026-27: Exam Overview

• Exam Name: Indian Olympiad Qualifier in Mathematics (IOQM)
• Exam Date: 6th September 2026
• Mode: Offline (Pen & Paper)
• Duration: 3 Hours
• Question Type: Subjective and Problem-Solving-Based
• Official Website: ioqm.mtai.org.in

IOQM 2026-27 Key Dates You Cannot Miss

The official IOQM 2026-27 registration schedule has been released by MTA(I), and every date below is sourced directly from ioqm.mtai.org.in.

Who Is Eligible for the IOQM Syllabus 2026-27?

Students currently studying in Classes 8 to 12 are eligible for IOQM 2026-27, subject to the participation rules issued by MTA(I) and age/academic conditions confirmed in the official notification. Class 8 students can appear, but since the IOQM syllabus 2026-27 extends well past Class 8 textbooks, younger aspirants should plan a longer preparation runway rather than attempting it cold. Candidates who have already completed Class 12 board exams before the exam year are generally not eligible — always confirm the exact clause on the HBCSE eligibility page before registering, since MTA(I) finalizes wording closer to the exam.

IOQM Syllabus 2026-27: Subject-Wise Breakdown

The official IOQM syllabus 2026-27, published by MTA(I) in the syllabus PDF, requires every aspirant to first be familiar with all topics covered in NCERT Mathematics Class VIII, IX, and X. Beyond that base, the IOQM syllabus 2026-27 is built around four specialised areas — Algebra, Plane Geometry, Combinatorics, and Number Theory — and the difficulty of problems from this syllabus rises step by step as students move from IOQM to RMO to INMO to IMO. Below is the complete topic-by-topic breakdown of the IOQM syllabus 2026-27, explained in plain language so you know exactly what to study under each head.

Algebra — IOQM Syllabus 2026-27

Algebra is one of the heavily weighted sections of the IOQM syllabus 2026-27, and it blends closely with number theory in actual exam questions. The topics under this part of the IOQM syllabus are as follows.

• Inequalities — comparing algebraic expressions and proving one quantity is always greater than, less than, or equal to another under given conditions.
• Progressions (A.P., G.P., H.P.) — arithmetic, geometric, and harmonic sequences, including how to find sums, general terms, and relationships between them.
• Theory of Indices — laws of exponents and powers, including fractional and negative indices, used to simplify complex algebraic terms.
• System of Linear Equations — solving two or more equations with multiple unknowns simultaneously, a recurring building block in IOQM problems.
• Theory of Equations — the relationship between the roots and coefficients of polynomial equations, and how to construct or transform equations from given roots.
• Binomial Theorem and Properties of Binomial Coefficients — expanding expressions of the form (a + b)^n and using coefficient identities to solve combinatorial-style algebra problems.
• Complex Numbers — numbers involving the imaginary unit i, their algebraic operations, and geometric interpretation on the Argand plane.
• Polynomials in One and Two Variables — factorisation, degree, and root-finding techniques for single- and multi-variable polynomial expressions.
• Functional Equations — equations where the unknown is a function itself, and the goal is to determine all functions satisfying a given condition.
• Sequences — ordered lists of numbers following a defined rule, tested through pattern recognition and proof-based reasoning.

Plane Geometry — IOQM Syllabus 2026-27

Plane Geometry in the IOQM syllabus 2026-27 tests construction-based and proof-based thinking rather than formula recall alone. This section of the IOQM syllabus includes the following topics.

• Triangles, Quadrilaterals, Circles and Their Properties — core Euclidean shapes and the theorems that govern their angles, sides, and areas.
• Standard Euclidean Constructions — classical compass-and-straightedge construction methods used to build and verify geometric figures.
• Concurrency and Collinearity (Theorems of Ceva and Menelaus) — theorems that determine when three lines meet at one point or when three points lie on one straight line.
• Basic Trigonometric Identities, Compound Angles, Multiple and Submultiple Angles, General Solutions — trigonometric relationships and equation-solving techniques frequently combined with geometry problems.
• Sine Rule and Cosine Rule — formulas linking a triangle's sides and angles, essential for solving non-right-angled triangle problems.
• Properties of Triangles and Polygons — deeper theorems on angle sums, symmetry, and area relationships in multi-sided figures.
• Coordinate Geometry (Straight Line, Circle, Conics, 3-D Geometry) — representing geometric figures using coordinates and equations, including conic sections and three-dimensional geometry.
• Vectors — quantities with both magnitude and direction, used to solve geometry problems algebraically.

Combinatorics — IOQM Syllabus 2026-27

Combinatorics is the shortest listed section of the IOQM syllabus 2026-27 on paper, but it produces some of the most challenging problems because it combines counting with logical constraints. The topics under this part of the IOQM syllabus are as follows.

• Basic Enumeration — systematic counting techniques for arrangements, selections, and outcomes without listing every case manually.
• Pigeonhole Principle and Its Applications — a logical principle stating that if more items are placed into fewer containers than items, at least one container must hold more than one item, used to prove existence-type results.
• Recursion — defining a sequence or problem in terms of its own earlier values, common in counting problems with repeating structure.
• Elementary Graph Theory — the basics of graphs made up of points (vertices) and connecting lines (edges), used to model relationships and paths.

Number Theory — IOQM Syllabus 2026-27

Number Theory is consistently one of the highest-weightage areas across past IOQM papers, and it forms a core pillar of the IOQM syllabus 2026-27. This section of the IOQM syllabus covers the following topics.

• Divisibility Theory in the Integers — including the Division Algorithm, the Greatest Common Divisor, the Euclidean Algorithm, and the Diophantine equation ax + by = c, all used to study how integers divide one another.
• Fundamental Theorem of Arithmetic — the rule that every integer greater than 1 can be written as a unique product of prime numbers.
• Basic Properties of Congruence and Linear Congruences — a system for comparing remainders when integers are divided by a fixed number, used to simplify large-number problems.
• Chinese Remainder Theorem — a method for solving systems of simultaneous congruences with different moduli.
• Fermat's Little Theorem and Wilson's Theorem — classical results connecting prime numbers with modular arithmetic, frequently used to simplify large exponents.
• Euler's Phi Function and Euler's Generalisation of Fermat's Theorem — a function that counts integers coprime to a given number, extended into a broader theorem used in advanced number theory problems.
• Pythagorean Triples (Definition and Properties) — sets of three positive integers that satisfy the Pythagorean equation, along with the patterns used to generate them.
• Diophantine Equations — equations where only integer solutions are sought, a recurring problem type across the IOQM syllabus.