This article describes the selection process, by country, for entrance into the International Mathematical Olympiad.
The International Mathematical Olympiad (IMO) is an annual mathematics olympiad for students younger than 20 who have not started at university.
Each year, participating countries send at most 6 students. 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 potential participants, with the aim of improving performance as well as assisting with team selection.
IMO selection process by country
Argentina In Argentina, the Olimpíada Matemática Argentina is organized each year by Fundación Olimpíada Matemática Argentina. 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.
Australia In Australia, selection into the IMO team is determined by the Australian Mathematics Trust and is based on the results from the following exams: The Australian Mathematics Olympiad The Asian Pacific Mathematics Olympiad IMO selection exams in the AMOC Selection School in April
The Australian Mathematical Olympiad (AMO) is held annually in the second week of February. It is composed of two four-hour papers held over two consecutive days. There are four questions in each exam for a total of eight questions. Entry is by invitation only, with approximately 200 candidates per year from Australia and New Zealand.
The top 25 from the AMO are invited to sit the Asian Pacific Mathematics Olympiad, a four-hour exam with five questions held a month after the AMO.
About 80 students are chosen for the AMOC Selection School which is held in April of each year. Students are invited to either the Senior, Intermediate, or Junior Stream. At this school, the Senior students take Team Selection Tests (consisting of 12 questions with 3 in each 4.5-hour test) and 6 students plus one reserve are selected for the International Mathematical Olympiad (IMO). There is a mentor program for the Australian teams prior to the EGMO and IMO.
Bangladesh The selection process is organised by Bangladesh Mathematical Olympiad. There are four levels of selection in Bangladesh. The students can participate in four academic categories: primary, junior, secondary and higher secondary.
Preliminary Selection: This is the first step of the selection. This is mainly done in district level. The selected contestants then go for the divisional round. Students are given 7 problems and have to solve them with in 1hr 15mins. Divisional: Currently (2011) the country is divided in 13 regions for divisional Olympiad. The number of divisions may increase later. Roughly 5,500 students participate each of the divisional Olympiads and 40 are selected for the next level. In Dhaka division, where number of students are more than the others, 11,000 students participate and 60 to 70 students are selected. All problems in the divisional test are "To find" problems. The students need not to write down the solution, only the answer is necessary. The test is usually one hour long. National: The national Olympiad is a 3-4 hour test depending on the category. In this test the students must write down the solutions of the problems. Some of the winners from junior, secondary and higher secondary categories of this level are selected for the next level. Cut-marks depend on overall performance of every participants in this level. The camps: More than one camps are arranged to select students for IMO. The selection process in the camps isn't as straight forward as it is in the Olympiads. The students in the camps are closely monitored by the previous campers and coaches and four to six students are selected for IMO.
Brazil The Brazilian participants are selected in a two phase process:
The contestants, from 8th grade onwards, that are awarded medals or honorable mentions in the Brazilian Mathematical Olympiad (OBM) (Olimpíada Brasileira de Matemática) of the year before the IMO are selected to participate in a training process. The contestants then take a series of tests, which are of similar level to the IMO, and the six students who perform best are invited to join the Brazilian team that goes to IMO.
Belgium The Belgian team is bilingual. The Dutch-speaking community selects three participants during the Vlaamse Wiskunde Olympiade. The French-speaking community selects their three participants through the [Olympiade Mathématique Belge] and additional tests at training weekends.
Canada High school students must first write the Canadian Open Mathematics Challenge, which takes place around November. If they score high enough in the COMC(normally 60+), they will be invited to write the Canadian Mathematics Olympiad (CMO), Asian Pacific Mathematics Olympiad (APMO), IMO TST, and unofficially write the USAMO.
The students with the top scores (conditions permitting) will make the Canadian team and travel to the location of the IMO in that year. Although the team is made up of students from all over Canada, Toronto and its suburbs have produced the most people for the team due to its high population density. The Canadian Mathematical Society is the organization which selects team leaders and members for the IMO team.
China In mainland China, high school students can participate in the annual National High School Mathematics Competition held on the second Sunday of September. However, unofficial provincial preliminary tests may be held to pre-select students for the competition.
The competition consists of two tests: the first test is 80 minutes long and covers the high school mathematics syllabus, while the second test is 170 minutes long, consists of 4 proof questions, and covers topics in contest mathematics. The top-scoring competitors from each province, usually 3 to 5 (but for very strong provinces, it can be up to 15), will be invited to participate in the Chinese Mathematical Olympiad held in November or December.
In recent years, the provincial quotas have increased; for instance, the quotas for CMO 2023 ranged from 6 to 26. Top 15 contestants from the China Girls Mathematical Olympiad are invited to the CMO, as well as past national training squad members.
The CMO has the same format as the IMO but is graded in 3-point increments to give a total score of 126 points. Approximately the top 60 competitors of CMO will be selected for the national training squad and attend the training camp, which is divided into two separate stages, each 8 to 9 days long. All national training squad members are exempted from Gaokao to let them focus on competition preparation. During the first stage of the camp, they will take two sets of IMO-style selection tests, with 4 papers in total. Then the top 15 competitors in the first stage will be selected for the second stage of the camp held at a different place some time later, during which they will take another two sets of IMO-style selection tests. 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.
Colombia In Colombia the selection and preparation of students for math competitions is organized by Olimpiadas Colombianas de Matemáticas. Students are split into levels based on their age and grade, splitting them into Primer Nivel(Grades 6-7), Nivel Intermedio(Grades 8-9) and Nivel Superior(Grades 10-11). The process begins with the regional competitions which are held in October and November. The best students of these competitions are invited to the January Training Session. In early March the National Competition or Olimpiada Colombiana de Matemáticas begins. It consists of a sequence of four examinations: the clasificatoria, the selectiva, the semifinal(now the final for Primer Nivel students) and the ronda final. The latter contains a (prior) training session and then two days of IMO-style papers.
Every Colombian high school student can take part in the first "classifying" examination but afterwards students are invited to compete according to their results on the previous examination. The three best students of the three different high school levels of the final round examination are the winners of the Colombian Math Olympiad. Although in principle students of the lower levels may be selected to go to the IMO, it generally takes many years before they can compete with students of the highest level or nivel superior. After the National Competition the twenty best students of each level are invited to the June Training Session where students undergo the IMO selection process.
Croatia Hrvatsko matematičko društvo invites about 20 contestants who performed best at the national level (national level competition is separated by age) to the Croatian Mathematical Olympiad (Hrvatska matematička olimpijada, HMO) which consists of 2 days, 4 problems each. The best ~10 are invited to the IMO test, the rest to the MEMO test. The best six at the IMO test and HMO combined are selected for IMO.
Cuba In Cuba the selection process consists (depending on regional conditions of availability of resources, participants and organizers) six levels. Competitions are held to select the best candidates from each school, then from each municipality, then from each province who then are allowed to take part in the National Competition (Concurso Nacional in Spanish). The gold and silver medals (around 20 participants) take a number of further exams closer to the level of International competitions. Thirteen of these are selected to form the National Pre-Selection that trains for up to three months taking also exams out of which the best 6 are selected to form the National team. 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.
Cyprus
In Cyprus four provincial competitions and a national (Pancyprian) competition are held every year. During this procedure 30 students are selected and four Team Selection Tests are held to determine who will be the six members of the national team. In every competition or test there are four problem usually covering geometry, number theory, algebra, and combinatorics (elementary level) and last four hours each.
Czech Republic After successfully completing the school and regional rounds, roughly 50 best participants are invited to the national round, where 10 best students are selected to participate in a week-long selection campus. Each day they solve a set of 3-4 problems, taken mainly from the past national olympiads of various countries. 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. After that the team is selected and before the actual IMO, it competes in traditional Czech-Slovak-Polish Mathematical Contest where the participants can practise their skill under almost identical conditions to IMO.
Denmark In Denmark a national contest open to all high school students is held every year called "Georg Mohr-Konkurrencen" (the Georg Mohr Contest) named after a Danish mathematician. The top scorers are invited to the winner seminar test. The top 20 students are invited to the NMC. After this a preliminary team is chosen for the IMO-TST.
France