The selection process varies between countries, but typically involves several rounds of competition, each progressively more difficult, after which the number of candidates is repeatedly reduced until the final 6 are chosen.
Many countries also run training events for IMO potentials, with the aim of improving performance as well as assisting with team selection.
All students that took and passed the National Finals (fifth and last round of the competition) exams, usually held in November; and were born before July 1 21 years ago, are allowed to take two new written tests to be selected for IMO, usually in May.
From the results of that tests, six titular students and a number of substitutes are selected to represent Argentina at the International Mathematical Olympiad.
The French-speaking community selects their three participants through the [Olympiade Mathématique Belge] and additional tests at training weekends.
High school students must first write the Canadian Open Mathematics Challenge, which takes place around November.
The students with the top scores (conditions permitting) will make the Canadian team and travel to the location of the IMO in that year.
Top 15 contestants from the China Girls Mathematical Olympiad are invited to the CMO, as well as past national training squad members.
At the end of the second stage, the 6 students with the highest combined scores in the four selection tests will form the Chinese team.
In Cuba the selection process consists (depending on regional conditions of availability of resources, participants and organizers) six levels.
In a number of years the lack of financial support has allowed only the first member of the team to actually travel and compete in the International mathematical Olympiad.
On the last day they have to find the answers (this time in form of a number) to rather large set of shorter problems under significant time-pressure.
The Association Animath, and more precisely the Olympiade Française de Mathématiques prepares and selects the French IMO team.
[citation needed] Unlike mainland China and Taiwan, there are no specific policies for university admission for students representing Hong Kong SAR in the IMO and other mathematics competitions.
About 100-120 students who pass the province-level test will be eligible to participate in the National Mathematical Olympiad, which is held in August or September.
In Ireland, the top scorers in the Junior Certificate (a state exam taken around the age of 15-16) are invited by the various universities to take part in the Irish Mathematical Olympiad.
In Kosovo, there are many stages to the selection process: In Latvia a national contest open to all high school students takes place each year.
While usually the 3 best students are automatically chosen for the final team, the rest 3 are decided by their results in the Nordic Mathematical Contest, which they will compete in afterwards.
The process starts one and a half year before a particular IMO; and a test (also known as NMTC - National Mathematics Talent Contest) is taken by the high school students which is organized by the Higher Education Commission of Pakistan.
About fifty students out of a 4000 are selected which are called by Abdus Salam School of Mathematics, Government College University, Pakistan - usually in September.
Different aspects of solving mathematical problems are studied and revealed: combinatorics, logics, structural arrangement and proofs.
In South Africa those who would be members of the team must pass through a nationwide talent search by correspondence, after which the top fifty or so are selected for a camp (usually in the December holidays) at Stellenbosch University.
In Thailand, the selection of the IMO representatives is the responsibility of the organization "The Promotion of Academic Olympiad and The Development of Science Education Foundation".
The topics include Algebra, Geometry, Number Theory, and Combinatorics in an advanced level, Functional Equation, and Inequality.
After the two rounds of the BMO, 20 potential team members, chosen primarily based on BMO results, are invited to a training and selection camp held in Trinity College, Cambridge, during which further examinations are held, allowing the number of potential team members to be reduced to eight or nine.
In addition to this formal selection process, there is further training during the year for a squad of potential team members, including the 'Advanced Mentoring Scheme', practice exams and an annual training camp in Hungary; information from exams at the Hungary camp may be considered in selection where available.
[11][12] In the United States, the team is selected through a year-long process, starting with the American Mathematics Competitions (AMC) consisting of 25 multiple-choice questions in 75 minutes with increasing difficulty, with high-scoring individuals from the Year 10 (AMC10) and 12 (AMC12) divisions admitted into the American Invitational Mathematics Examination (AIME).
The AIME is invite-only and may also accept proficient takers from the United States of America Mathematical Talent Search.
In HSGQG, different aspects of solving mathematical problems are studied and revealed: combinatorics, logics, structural arrangement and proofs.
After VMO, the top 48 scorers, plus past IMO contestants who have not graduated from high school will participate in the international Olympiads selection tests, commonly called TST.