International Mathematical Olympiad (IMO)
The content ranges from extremely difficult algebra and precalculus problems to problems on branches of mathematics not conventionally covered in secondary or high school and often not at university level either, such as projective and complex geometry, functional equations, combinatorics, and wellgrounded number theory, of which extensive knowledge of theorems is required. Calculus, though allowed in solutions, is never required, as there is a principle that anyone with a basic understanding of mathematics should understand the problems, even if the solutions require a great deal more knowledge. Supporters of this principle claim that this allows more universality and creates an incentive to find elegant, deceptively simplelooking problems which nevertheless require a certain level of ingenuity, often times a great deal of ingenuity to net all points for a given IMO problem.
The selection process differs by country, but it often consists of a series of tests which admit fewer students at each progressing test. Awards are given to approximately the topscoring 50% of the individual contestants. Teams are not officially recognized—all scores are given only to individual contestants, but team scoring is unofficially compared more than individual scores. Contestants must be under the age of 20 and must not be registered at any tertiary institution. Subject to these conditions, an individual may participate any number of times in the IMO.
The International Mathematical Olympiad is one of the most prestigious mathematical competitions in the world. In January 2011, Google sponsored €1 million to the International Mathematical Olympiad organization.
We have tried to answer all the common questions which might be in minds of the participants of IMO (International Mathematical Olympiad). We have started questions from scratch such as What is IMO, Syllabus, Eligibility Criteria, Exam Pattern, Application form, Application form Fee, Admit card and Results. We have also given study material of Maths (PDF) for IMO, which is strictly according to IMO Syllabus 2022 along with Official Sample Papers released by SOFIMO.
If any questions are haunting in your minds, feel free to contact us. We will try to resolve all queries related to IMO.
What is IMO?
The International Mathematical Olympiad (IMO) is the world championship mathematics competition for high school students and is held annually in a different country.
The first IMO was held in 1959 in Romania, with 7 countries participating. It has gradually expanded to over 100 countries from 5 continents.
The IMO Board ensures that the competition takes place each year and that each host country observes the regulations and traditions of the IMO.
Headquartered in London, United Kingdom, the IMO currently has 174 member states and three associate members.
IMO Eligibility Criteria 2022
 IMO Level 1 Eligibility
 Students from class 1 12 can apply for the Level 1 exam irrespective of their academic marks. The eligibility criterion is beneficial in increasing the participation of a large number of students. Class 1 to 12 school students pursuing education within the country or abroad can be a part of the International Mathematics Olympiad (IMO) Level 1 exam.
 IMO Level 2 Eligibility
 Only the students who performed well in the Level 1 exam get shortlisted for the Level 2 exam. The following students will be eligible:
 From each class, the top 5% of students will qualify for the Level 2 exam.
 Full 25 zone wise and category wise rank holders will also be eligible.
 Class toppers from each school participating should enroll at least ten students from a class in the exam and score 50% qualifying marks.
 In case of sectionwise registration, the top rank holder will be eligible for Level 2
 Only the students who performed well in the Level 1 exam get shortlisted for the Level 2 exam. The following students will be eligible:
However, note that the Class 1 and 2 students don’t need to appear for the Level 2 exam. They judge the pupil’s performance based on the Level 1 exam only.
IMO Exam Pattern 2022: The SOF International Mathematics Olympiad (IMO) consist of two levels:
 Level – 1
 The level 1^{st} of the test will be organized in the participating school during the school hour.
 The duration of the examination will be 60 minutes.
 There will be 35 objective type multiple choice questions in the exam for class 1^{st} to 4^{th}. Students from class 5^{th} to 12^{th} need to answer 50 objective type multiple choice questions in the examination.
 There are separate question papers for each class.
 The questions will be asked in English language only.
Detailed Examination pattern for Class 1^{st} to 4^{th}
[wptb id=34360] Detailed Examination pattern for Class 5^{th} to 12^{th}
[wptb id=34361]
 Level 2
 The level 2 will be conducted only for the students 3^{rd} to 12^{th}.
 The qualifiers to 2^{nd} round would including the following:
 At school level: topper of the class where at least 10 students from the class appear in the examination & score a minimum of 50% qualifying marks.
 At zone/ state level: Top 25 rank holders from each class and each zone.
 At international level: Classwise top 5% of the candidates who take the 1^{st} level of the exam internationally.
Application Form (Registration)
The details regarding the registration process of the 16th International Mathematics Olympiad (IMO) 2022 are given below:
 The students who want to participate in the 16th International Mathematics Olympiad (IMO) need to register through their respective schools only.
 The Science Olympiad Foundation does not accept individual registrations by the students.
 At least 10 students from a school are required in order to register for SOF IMO.
 The Principals/ teachers should know that any school can be registered as a center for 16th International Mathematics Olympiad (IMO) Level 1. There is absolutely no fee is required from the school.
 Registration forms and prospectus will be sent by the SOF to the school.
 Students need to collect the registration form from the school and fill the details carefully.
 All the students need to submit the registration form to their school.
 Then, the school will return the duly filled and completed registration forms to the SOF before the last date.
 Please note that the incorrect or incomplete application forms will be rejected.
 The registration fee for the Indian schools is Rs.125 (including GST).
 The registration fee for International schools is USD($) 9 (including GST).
 Schools may collect an additional amount of Rs.25. USD($) 1 for International schools per student towards honorarium in charge, guide using study material supplied by SOF, remuneration to teachers for teaching and other miscellaneous expenses.
IMO Application Fee 2022
The registration fee applicable for the 16^{th} International Mathematics Olympiad (IMO) is as follows:
 India, Bangladesh, Bhutan & Nepal: Rs. 125/ (including GST) per student.
 Students suffering from any major physical disability: Nil
 Students whose parent was martyred during defence operations: Nil
 Fees for the students of other countries: US$9
IMO Admit Card 2022
 Admit cards for IMO 2022 exam will be issued by the Science Olympiad Foundation.
 You can download your admit card from the SOF official website.
 IMO admit card has details like your name, venue of the exam etc.
 It is a compulsory document that has to be carried to the exam center.
Follow the steps mentioned here to download the IMO Admit Cards:
 Go to sofworld.org or the window given above.
 Click On the “1st/2nd Level Admit Card” button in the sidebar as per the requirement.
 Select IMO.
 Enter the Roll Number. It should be entered as School CodeClass CodeRoll Number.
 Click “Download” & Print a copy of Admit Card.”
 Admit Card & Guidelines will be generated and shown on your screen.
The tentative schedule of the 16^{th} International Mathematics Olympiad (IMO) is given in the table below: [wptb id=34387]
Class 10
IMO Syllabus 2022
Class 10
 Section – I (Logical Reasoning)
 Direction Sense Test,
 Mathematical Operations,
 Number Ranking & Time Sequence Test,
 CodingDecoding,
 Distance,
 Speed,
 Time,
 General Reasoning
 Section – II (Mathematical Reasoning)
 Real Numbers
 Polynomials
 Pair of Linear Equations in Two Variables
 Quadratic Equations
 Arithmetic Progressions
 Triangles
 Coordinate Geometry
 Introduction to Trigonometry
 Some Applications of Trigonometry
 Circles
 Constructions
 Areas Related to Circles
 Surface Areas and Volumes
 Statistics
 Probability
 Section – III (Everyday Mathematics)
 The syllabus of this section will be based on the syllabus of Mathematical Reasoning.
 Section IV  (Achievers Section)
 Higher Order Thinking Questions (HOTS) of the syllabus of Section II.
 Questions of levelI Olympiad exams will be 60% from the current class syllabus and 40% from the previous class syllabus, e.g. Class10 IMO exam will have 60% questions from class10 syllabus and 40% questions from class 9 syllabus.
 Questions of levelII Olympiad exams will be from current class syllabus only.
 Questions in ACHIEVERS SECTION will be from current class syllabus only.
Class 9
IMO Syllabus 2022
Class 9
 Section – I (Logical Reasoning)
 Mathematical Operations
 Series Completion
 Arithmetical Reasoning
 Problems on Cubes and Dice
 Number Ranking & Time
 Sequence Test
 Inserting Missing Character
 General Reasoning Based on Prescribed Syllabus
 Section – II (Mathematical Reasoning)
 Number Systems
 Polynomials
 Coordinate Geometry
 Linear Equations in Two Variables
 Introduction to Euclid’s Geometry
 Lines and Angles
 Triangles
 Quadrilaterals
 Areas of Parallelograms and Triangles
 Circles
 Constructions
 Heron’s Formula
 Surface Areas and Volumes
 Statistics
 Probability
 Section – III (Everyday Mathematics)
 The syllabus of this section will be based on the syllabus of Mathematical Reasoning.
 Section IV  (Achievers Section)
 Higher Order Thinking Questions (HOTS) of the syllabus of Section II.

 Number Systems
 Polynomials
 Coordinate Geometry
 Linear Equations in Two Variables
 Introduction to Euclid’s Geometry
 Lines and Angles
 Triangles
 Quadrilaterals
 Areas of Parallelograms and Triangles
 Circles
 Constructions
 Heron’s Formula
 Surface Areas and Volumes
 Statistics
 Probability
Class 8
IMO Syllabus 2022
Class 8
 Section – I (Logical Reasoning)
 Mathematical Operations
 Series Completion
 Direction Sense Test
 Analytical Reasoning
 Problems on Cubes and Dice
 Number Ranking and Time Sequence Test
 General Reasoning Based on Prescribed Syllabus
 Section – II (Mathematical Reasoning)
 Rational Numbers
 Squares and Square Roots
 Cubes and Cube Roots
 Exponents and Powers
 Comparing Quantities
 Algebraic Expressions and Identities
 Linear Equations in One Variable
 Understanding Quadrilaterals
 Constructions
 Mensuration
 Visualising Solid Shapes
 Data Handling
 Direct and Inverse Variations
 Factorization
 Introduction to Graphs
 Playing with Numbers
 Section – III (Everyday Mathematics)
 The syllabus of this section will be based on the syllabus of Mathematical Reasoning.
 Section IV  (Achievers Section)
 Higher Order Thinking Questions (HOTS) of the syllabus of Section II.
 Rational Numbers
 Squares and Square Roots
 Cubes and Cube Roots
 Exponents and Powers
 Comparing Quantities
 Algebraic Expressions and Identities
 Linear Equations in One Variable
 Understanding Quadrilaterals
 Constructions
 Mensuration
 Visualising Solid Shapes
 Data Handling
 Direct and Inverse Variations
 Factorization
 Introduction to Graphs
 Playing with Numbers
Class 7
IMO Syllabus 2022
Class 7
 Section1 (Logical Reasoning)
 Problems Based on Figures
 Odd One Out
 Series Completion
 CodingDecoding
 Mathematical Reasoning
 Mirror Images
 Embedded Figures
 Patterns
 Direction Sense
 Number Ranking and Alphabetical Test
 Section2 (Mathematical Reasoning)
 Integers
 Fractions and Decimals
 Exponents and Powers
 Algebraic Expressions
 Simple Linear Equations
 Lines and Angles
 Comparing Quantities
 The Triangle and its Properties
 Symmetry
 Congruence of Triangles
 Rational Numbers
 Perimeter and Area
 Data Handling
 Visualizing Solid Shapes
 Practical Geometry
 Section3 (Everyday Mathematics)
 The Syllabus of this section will be based on the syllabus of Mathematical Reasoning.
 Section – 4 (Achievers Section)
 Higher Order Thinking Questions  Syllabus as per Section – 2
 Integers
 Fractions and Decimals
 Practical Geometry
 Perimeter and Area
 Data Handling
 Rational Numbers
 Simple Linear Equations
 Exponents and Powers
 Algebraic Expressions
 Percentage and Its Applications
 Lines and Angles
 The Triangle and its Properties
 Congruence of Triangles
 Visualising 3DShapes
 Symmetry
 Circumference and Area of circles
Class 6
IMO Syllabus 2022
Class 6
 Section1 (Logical Reasoning)  Verbal and NonVerbal Reasoning.
 Problems Based on Figures
 Odd One Out
 Series Completion
 CodingDecoding
 Mathematical Reasoning
 Mirror Images
 Embedded Figures
 Patterns
 Direction Sense
 Number Range
 Section2 (Mathematical Reasoning)
 Knowing our Numbers
 Whole Numbers
 Playing with Numbers
 Basic Geometrical Ideas
 Understanding Elementary Shapes
 Integers
 Fractions
 Decimals
 Data Handling
 Mensuration
 Algebra
 Ratio and Proportion
 Symmetry
 Practical Geometry
 Section3 (Everyday Mathematics)
 Refer to the mathematical reasoning section
 Section 4 (Achievers Section)
 Higher Order Thinking Questions  Syllabus as per Section – 2.
 Knowing our Numbers
 Whole Numbers
 Playing with Numbers
 Basic Geometrical Ideas
 Understanding Elementary Shapes
 Integers
 Fractions
 Decimals
 Data Handling
 Mensuration
 Algebra
 Ratio and Proportion
 Symmetry
 Practical Geometry
Class 5
IMO Syllabus 2022
Class 5
 Section – 1 : (Logical Reasoning)
 Patterns
 Analogy and Classification
 Geometrical Shapes
 Mirror and Water Images
 Direction Sense Test
 Ranking Test
 Alphabet Test
 Logical Sequence of Words
 Puzzle Test
 CodingDecoding
 Section – 2 : (Mathematical Reasoning)
 Numerals
 Number names and Number Sense (7 and 8 digit numbers)
 Computation Operations
 Fractions and Decimals
 Measurement of Length
 Weight
 Capacity
 Time
 Temperature and Money
 Conversions
 Geometrical Shapes and Solids
 Angles
 Perimeter of Various Shapes & Area of Rectangle and Square,
 Symmetry,
 Data Handling.
 Section – 3 : (Everyday Mathematics)
 The syllabus of this section will be based on the Syllabus of Mathematical Reasoning.
 Section – 4 : (Achievers Section)
 Higher Order Thinking Questions  Syllabus as per Section2.
 Number Sense
 Computation Operations
 Fractions and Decimals
 Measurements
 Angles
 Perimeter & Area
 Symmetry
 Data Handling
Class 4
IMO Syllabus 2022
Class  4
 Section – 1 : (Logical Reasoning)
 Patterns,
 Alphabet Test
 CodingDecoding
 Ranking Test
 Mirror Images
 Geometrical Shapes and Solids
 Embedded Figures
 Direction Sense Test
 Days and Dates & Possible Combinations
 Analogy and Classification.
 Section – 2 : (Mathematical Reasoning)
 Numerals and Number Names
 Number Sense (more than 4digit numbers)
 Computation Operations
 Fractions
 Length
 Weight
 Capacity
 Time
 Money
 Geometry
 Perimeter of Various Shapes
 Symmetry
 Conversions
 Data Handling.
 Section – 3 : (Everyday Mathematics)
 The Syllabus of this section will be based on the Syllabus of Mathematical Reasoning.
 Section – 4 : (Achievers Section)
 Higher Order Thinking Questions  Syllabus as per Section–2
Class 3
IMO Syllabus 2022
Class  3
 Section – 1 : (Logical Reasoning)
 Patterns
 Analogy and Classification
 Alphabet Test
 CodingDecoding
 Ranking Test
 Grouping of Figures and Figure Matrix
 Mirror Images
 Geometrical Shapes
 Embedded Figures
 Days and Dates & Possible Combinations.
 Section – 2 : (Mathematical Reasoning)
 Numerals
 Number names and Number Sense (4digit numbers)
 Computation Operations
 Fractions
 Length
 Weight
 Capacity
 Temperature
 Time
 Money
 Geometry
 Data Handling.
 Section – 3 : (Everyday Mathematics)
 The Syllabus of this section will be based on the Syllabus of Mathematical Reasoning.
 Section – 4 : (Achievers Section)
 Higher Order Thinking Questions  Syllabus as per Section – 2.
 Number Sense
 Computation Operations
 Fractions
 Money
 Length, Weight, Capacity, Time and Temperature
 Geometry
 Data Handling.