IOQM Syllabus 2024-25
India’s Olympiad qualification in the mathematics syllabus has
remained consistent. Some of the highest scoring areas on the
exam include number system, geometry and algebra.
Students can check IOQM Syllabus 2024-25 for class 8-11 from
the below table-
IOQM Syllabus 2024-25
Indian Olympiad
Classes Qualifier in Mathematics
Syllabus
Geometry
Rational Numbers
Linear Equations in
One Variable
Class 8 Syllabus of Indian Algebraic Expression
Olympiad Qualifier in Permutations and
Mathematics Combination
Square Root & Cube
Root
Factorization
Elementary Graph
Theory
Class 9 Syllabus of Indian Number System
Olympiad Qualifier in Polynomials
Mathematics Coordinate Geometry
Probability
Linear Equations in
two variables
Surface Area &
Volume
Circles
Areas of
Parallelograms and
triangles
Real Numbers
Trigonometry
Quadratic Equation
Arithmetic Progression
Class 10 Syllabus of Indian
Coordinate Geometry
Olympiad Qualifier in Inequalities
Mathematics Surface Area &
Volume
Circles
Linear Equation in two
variables
Permutations and
Combination
Trigonometric
Reasoning
Class 11 Syllabus of Indian
Quadratic Equations
Olympiad Qualifier in and Expressions
Mathematics Probability Theory
Number Theory
Factorization of
Polynomial
Coordinate Geometry
Class 12 Syllabus of Indian Coordinate Geometry
Olympiad Qualifier in Permutations and
Mathematics Combination
Trigonometric
Reasoning
Quadratic Equations
and Expressions
Probability Theory
Number Theory
Factorization of
Polynomial
Integers, geometry
Linear equations
Permutations and
combination
Factorization of
polynomial
Elementary
combinatorics
Probability theory and
number theory,
Finite series
IOQM Syllabus
You can get the complete details of the IOQM Syllabus from the
below section.
IOQM Syllabus
Topic Description
Basic arithmetic operations,
Arithmetic of Integers properties, and number theory
related to integers.
Properties and relations of
Geometry points, lines, surfaces, and
solids.
Study of angles, triangles, and
Trigonometry trigonometric functions and their
applications.
Mathematical expressions
Inequalities involving greater than, less than,
and equal to signs.
Geometry using a coordinate
Coordinate Geometry system, including lines, curves,
and shapes.
System of Linear Solutions and properties of linear
Equations equations and their systems.
Counting techniques involving
Permutations and
arrangement and selection of
Combinations
objects.
Techniques for breaking down
Factorization of
polynomials into simpler
Polynomials
components.
Solutions and properties of
Quadratic Equations
quadratic equations and related
and Expressions
expressions.
Elementary Basic principles of counting,
Combinatorics arrangements, and selections.
Study of series with a finite
Finite Series and number of terms and
Complex Numbers introduction to complex
numbers.
Concepts and applications of
Probability Theory
probability.
Properties and relationships of
Number Theory
numbers, especially integers.
Elementary Graph Study of graphs, nodes, edges,
Theory and their properties.
IOQM Syllabus – Number Theory
Sub-topic Concepts
Prime factorization, prime
counting functions, sieve
Prime Numbers methods (e.g., Eratosthenes’
sieve), properties of prime
numbers.
Divisibility rules, Greatest
Common Divisor (GCD), Least
Divisibility
Common Multiple (LCM),
Euclidean algorithm.
Modular Arithmetic Congruences and modular
arithmetic, residues and non-
residues, Chinese Remainder
Theorem.
Linear Diophantine equations,
Diophantine Equations Pell’s equation, Fermat’s Last
Theorem.
Binary, octal, hexadecimal, and
Number Bases
other bases, base conversion.
Euler’s totient function (φ),
Mobius function (μ), number of
divisors function (σ), sum of
Arithmetic Functions
divisors function (σ), Fermat’s
Little Theorem, Euler’s Totient
Theorem.
IOQM Syllabus – Algebra
Sub-topic Concepts
Simplification of algebraic
Basic Algebraic expressions, factorization of
Manipulations polynomials, solving algebraic
equations.
AM-GM inequality, Cauchy-
Schwarz inequality,
Inequalities
rearrangement inequality,
Jensen’s inequality.
Fundamental theorem of
algebra, Vieta’s formulas,
Polynomials
Newton’s identities,
Eisenstein’s criterion.
Operations with complex
Complex Numbers numbers, De Moivre’s
Theorem, roots of unity.
Arithmetic progressions,
geometric progressions,
convergent and divergent
Sequences and Series
series, infinite series
summation (e.g., geometric
series).
Cauchy’s functional equation,
Functional Equations Jensen’s functional equation,
other functional equations.
Binomial coefficients,
Binomial Theorem and
multinomial coefficients,
Combinatorics
combinatorial identities.
Roots and coefficients of
polynomial equations, factor
Polynomial Equations
theorem, rational root
theorem.
IOQM Syllabus – Combinatorics
Sub-topic Concepts
Multiplication principle, addition
Counting Principles principle, inclusion-exclusion
principle.
Arrangements (permutations),
Permutations and
selections (combinations),
Combinations
combinatorial identities.
Dirichlet’s principle, application
Pigeonhole Principle
in solving problems.
Linear recurrence relations,
homogeneous and non-
Recurrence Relations
homogeneous recurrences,
solving recurrence relations.
Basics of graph theory, graph
coloring, trees and spanning
Graph Theory trees, connectivity and Eulerian
graphs, Hamiltonian cycles and
paths.
Geometric counting problems,
Combinatorial Geometry theorems like the Sylvester-
Gallai theorem.
Generating Functions Generating functions for
combinatorial sequences,
operations on generating
functions.
Vandermonde’s identity,
hockey stick identity
Combinatorial Identities (combinatorial sum), Catalan
numbers and other
combinatorial sequences.
IOQM Syllabus – Geometry
Sub-topic Concepts
Points, lines, and planes; angle
measurement and properties;
congruence and similarity of
triangles; quadrilaterals
Euclidean Geometry (properties and theorems);
circles (tangents, secants,
angles, and theorems);
polygons (properties and
interior/exterior angles).
Reflection, rotation, translation,
Geometric and dilation; isometries and
Transformations similarities; symmetry and
tessellations.
Distance formula, slope and
equations of lines, midpoint
Coordinate Geometry
formula, conic sections
(parabola, ellipse, hyperbola).
Sine, cosine, tangent, and their
properties; trigonometric
Trigonometry
identities and equations;
applications in geometry.
