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IOQM or the Indian Olympiad Qualifier in Mathematics ‌ is a prestigious national-level examination and a qualifying stage for the International Mathematical Olympiad (IMO), the most prestigious mathematics competition for high school students worldwide.




Who can participate –

Students from classes 8 to 11 are eligible to participate in IOQM. They need to clear this stage to advance to the next level of mathematics olympiads.


Exam Pattern

It is a written examination consisting of challenging mathematical problems . It also tests students’ problem-solving skills, mathematical reasoning, and creativity.

Syllabus –

Basic Maths– Number System
Basic Inequality
Log Concept
Modulus Concept
Greatest Integer

Number Theory- Prime Numbers:
Prime factorization
Prime counting functions
Sieve methods (e.g., Eratosthenes’ sieve)
Properties of prime numbers

Divisibility:
Divisibility rules
Greatest Common Divisor (GCD) and Least Common Multiple (LCM)
Euclidean algorithm

Modular Arithmetic:
Congruences and modular arithmetic
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 other bases
Base conversion

Arithmetic Functions:
Euler’s totient function (φ)
Mobius function (μ)
Number of divisors function (σ)
Sum of divisors function (σ)
Fermat’s Little Theorem and Euler’s Totient Theorem

Algebra– Basic Algebraic Manipulations:
Simplification of algebraic expressions
Factorization of polynomials
Solving algebraic equations

Inequalities:
Arithmetic Mean-Geometric Mean (AM-GM) inequality
Cauchy-Schwarz inequality
Rearrangement inequality

Polynomials:
Fundamental theorem of algebra
Vieta’s formulas
Newton’s identities
Eisenstein’s criterion

Complex Numbers:
Operations with complex numbers
De Moivre’s Theorem
Roots of unity

Sequences and Series:
Arithmetic progressions
Geometric progressions
Convergent and divergent series
Infinite series summation (e.g., geometric series)

Inequalities:
Arithmetic Mean-Geometric Mean (AM-GM) inequality
Cauchy-Schwarz inequality
Jensen’s inequality

Functional Equations:
Cauchy’s functional equation
Jensen’s functional equation
Other functional equations

Binomial Theorem and Combinatorics:
Binomial coefficients
Multinomial coefficients
Combinatorial identities

Polynomial Equations:
Roots and coefficients of polynomial equations
Factor theorem
Rational root theorem

Inequalities:
Triangle inequalities
Holder’s inequality
Muirhead’s inequality

Combinatorics– Counting Principles:
Multiplication principle
Addition principle
Inclusion-Exclusion principle

Permutations and Combinations:
Arrangements (permutations)
Selections (combinations)
Combinatorial identities

Pigeonhole Principle:
Dirichlet’s principle
Application in solving problems

Recurrence Relations:
Linear recurrence relations
Homogeneous and non-homogeneous recurrences
Solving recurrence relations

Principle of Inclusion and Exclusion:
Solving problems with PIE
Counting problems with constraints

Graph Theory:
Basics of graph theory
Graph coloring
Trees and spanning trees
Connectivity and Eulerian graphs
Hamiltonian cycles and paths

Combinatorial Geometry:
Geometric counting problems
Theorems like the Sylvester-Gallai theorem

Generating Functions:
Generating functions for combinatorial sequences
Operations on generating functions

Combinatorial Identities:
Vandermonde’s identity
Hockey stick identity (Combinatorial sum)
Catalan numbers and other combinatorial sequences

Geometry-Euclidean Geometry:
Points, lines, and planes
Angle measurement and properties
Congruence and similarity of triangles
Quadrilaterals (properties and theorems)
Circles (tangents, secants, angles, and theorems)
Polygons (properties and interior/exterior angles)

Geometric Transformations:
Reflection, rotation, translation, and 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


Duration –  3 hrs.

OMR (Optical Mark Recognition) technology is used for evaluation.

For every question, the response should be a whole number falling within the range of 00 to 99.

Marks pattern – One set consists of 10 questions, each carrying 2 marks; another set of 10 questions, each worth 3 marks; and finally, 10 questions that are valued at 5 marks each.



Date of Examination: 7th September 2025.

Student registration through centres:  09th June 2025 to 25th July 2025.

Individual student registration online: 30th June 2025 to 25th July 2025.

Center registration:  09th June 2025 to 28th June 2025.




Eligibility Check:

Typically, IOQM is open to students of class 8 to class 12.




Depending on your performance in IOQM, you may qualify for further rounds of the Mathematics Olympiad program.

Fees –

IOQM 2025 Registration Fee :
School Category Fee
Jawahar Navodaya Vidyalayas (JNV) ₹180
Kendriya Vidyalayas (KV) ₹180
Other Schools ₹300

Certificate –
National and Regional certificates are awarded based on IOQM performance.