The International Mathematical Olympiad is the largest and most influential mathematical competition for middle school students in the world. It was initiated by Professor Roman of Romania. Since 1959 held its first competition in Romania, it has been held once a year except 1980. Only seven or eight countries and regions participated in the first few sessions. At first, the organization work was undertaken by several participating countries in turn. By 1980, the International Commission for Mathematics Education had set up an IMO branch, seeking IMO sponsors every year.
IMO's test questions are not limited to the content of middle school mathematics, it contains the basic part of so-called pre-calculus mathematics, and even some calculus content. As time goes on, the test questions become more and more difficult. The difficulty of the test questions lies not in the need for a lot of profound knowledge to answer the test questions, but in the insight, creativity and mathematical wit of the essence of mathematics. Although the scope of the test questions has never been formally stipulated, it is mainly number theory, combinatorial mathematics, sequence, inequality, functional equation and geometry. In many test questions, interesting mathematical topics, including mathematics of that year, often appear, which shows the humor of mathematicians. Some topics give much broader conditions than the required conclusions, while some topics only allow you to draw a few powerful conclusions. Compared with the usual types of questions that draw appropriate conclusions from appropriate conditions, the real purpose of these questions is to test your flexibility and skills. Some topics have different styles and novel ways of thinking, which can only be solved by using certain skills. For such a topic, it is impossible for the usual way of thinking to guide the correct way of solving the problem. The solutions to some problems give us enlightenment, which is not limited to a specific skill for specific problems, but a profound mathematical way of thinking.
After more than 40 years of development, the operation of the International Mathematical Olympiad has gradually become institutionalized and standardized, and a set of established routines has been followed by previous hosts.
1, use
Stimulate teenagers' mathematical ability; Stimulate young people's interest in mathematics; Discover the reserve army of scientific and technological talents; Promote the exchange and development of mathematics education in various countries.
2. Time
It is held once a year in July.
Step 3 host
It is hosted by participating countries in turn, and the funds are provided by the host country.
4. Objectives
The contestants are middle school students, each team has 6 people, and 2 mathematicians are sent as the team leader.
Step 5 test questions
The test questions were provided by the participating countries, then selected by the host country and submitted to the examiners' committee for voting, resulting in six test questions. The host country does not provide test questions. After the test questions are determined, they will be written in English, French, German, Russian and other working languages, and the team leader will translate them into the national language. Step 6 check
The exam is divided into two days, 4.5 hours a day, and three questions are tested. Six players from the same team were assigned to six different examination rooms to answer questions independently. The answer sheet will be judged by the national team leader and then negotiated with the coordinator designated by the organizer. If there is any objection, it will be submitted to the examiner's Committee for arbitration. 7 points for each question, out of 42 points.
Step 6: Pay
There are first prize (gold medal), second prize (silver medal) and third prize (bronze medal) in the competition, and the ratio is roughly1:2: 3; About half of the contestants won the prize. The award criteria of each session are related to the results of the current exam.
IMO is not a competition between teams, so there is no team award, but all teams attach great importance to the ranking of team total scores. Judging from the situation in recent years, China, Russian, American, German, Romanian and other countries are stronger.
7. Main Review Committee
The examiners' committee is composed of leaders of various countries and the chairman designated by the host country. This chairman is usually the authority on mathematics in this country. The main review committee has six responsibilities:
1), multiple-choice questions;
2), determine the scoring standard;
3) Accurately express the test questions in the working language, and translate and approve the test questions translated into the languages of the participating countries;
4) During the competition, determine how to answer students' questions in writing;
5) Resolve the different opinions on grading between individual team leaders and coordinators;
6) Determine the number and scores of medals.
1-20th session of examination questions download:
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I. Development of the International Olympic Mathematics Competition
In the world, competitions based on numbers have a long history: there were competitions to solve geometric problems in ancient Greece; During the Warring States Period in China, horse racing between Qi Weiwang and Tian Ji was actually a game of game theory. /kloc-In the 6th century, there was a fierce competition in Italy about Tattaglia who stuttered to solve cubic equations. /kloc-in the 0/7th century, many mathematicians like to ask some questions to challenge other mathematicians, and Fermat of France is one of them. His Fermat's last theorem (when the integer n≥3, the equation Xn+Yn=Zn has no positive integer solution; .....) challenged the wisdom of mankind for 300 years; /kloc-in the 0 th and 8 th centuries, France once held an independent mathematics competition; /kloc-In the 9th century, the French Academy of Sciences collected answers to difficult mathematical problems by offering a reward, which often led to some important mathematical discoveries. The math prince Gauss is the winner of the contest ... However, all these facts are only partial in nature, limited to adults, and the math contest specifically for middle school students is a modern fashion.
The modern middle school mathematics competition (hereinafter referred to as the middle school mathematics competition) originated in Hungary. 1894, in order to commemorate the appointment of Evos, president of the Society of Mathematical Physics, as Minister of Education, the Society of Mathematical Physics passed a resolution: the mathematical competition named after Evos will be held every year 10, and will be completed in four hours, and any reference books are allowed. Problems usually involve advanced mathematics, but the solutions are completely elementary. Under the leadership of Evos, this mathematics competition has played a great role in the development of mathematics in Hungary. Many accomplished mathematicians and scientists are winners of previous Evos competitions, such as Fryer of 1897 and Von Kamen of 1898. After Hungary, Romania organized a competition in 1902 by a mathematical magazine. In the next 30 years, no other country has organized similar large-scale activities.
Until the 1930s, the former Soviet Union organized a large-scale mathematics competition, with more middle school students. 1934 and 1935 The title of "Mathematical Olympics" was first adopted in the mathematics competition for middle school students sponsored by Leningrad University and Moscow University. Compared with sports competitions, intellectual competitions also emphasize the spirit of persistent pursuit, which has gradually become a kind of worldwide knowledge. Today, many countries and regions have math competitions called "Olympics".
1949, Bulgaria held a math competition;
1950, Poland held a math competition;
195 1 year, the former Czechoslovakia held a mathematics competition;
1956, China held a math competition;
Then East Germany (196 1), Vietnam (1962), the former Yugoslavia (1962), the Netherlands (1962) and Finland (1962). Israel (1968), Canada (1969), Greece (1969), former west Germany (197 1), and the United States (1972). ...
The situation shows that since the 1950s, there has been a worldwide upsurge of holding middle school mathematics competitions, which not only prepared the conditions for the birth of the International Mathematical Olympics, but also provided the impetus for its development. 1956, after the active activities of Professor Roman from Romania, the Eastern European countries formally decided on the plan to launch an international mathematics competition. 1 IMO kicked off in July 1959 in Blaso, the ancient Romanian capital. At that time, there were 52 students from seven countries in Eastern Europe, including Romania, Bulgaria, Hungary, Poland, the former Czechoslovakia, the former German Democratic Republic and the former Soviet Union. Each country has 8 players, while the former Soviet Union sent only 4 players. This is the pioneering work of a cross-border mathematics competition, but from 1 to the 5th session, the participating countries were limited to several countries in Eastern Europe, which was actually only regional and not very international.
Since the 1960s, the International Mathematical Olympiad has gradually expanded and developed into a truly global middle school mathematics competition. From 65438 to 0967, teams from Britain, France, Italy, Sweden and other western European countries joined. After 1974, the United States also actively participated in this activity. The president of the United States once met and encouraged the American Mathematical Olympiad team that achieved good results. The most famous military academies in the United States (such as West Point Military Academy) have been providing training places for the Mathematical Olympiad American team for many years. 1986, China officially teamed up to participate in the International Mathematical Olympiad for the first time. By the late 1980s, with the participation of teams from many countries in Asia, Latin America and Africa, the International Mathematical Olympiad had developed into a large-scale activity. Japan emphasizes strict basic training in mathematics education, and is restricted by the almost harsh entrance examination system, so it is difficult to carry out the mathematical Olympic competition. However, since the 3 1 International Mathematical Olympiad in 1990, Japan has also actively participated in this worldwide activity. By 1997, the International Mathematical Olympiad had developed into a large-scale activity, with 460 athletes from 82 teams participating. Due to the enthusiasm of the bidders, the annual International Mathematical Olympiad has been arranged in 2006, which shows that people all over the world attach importance to and support this activity. Facing a wider range of teams and contestants, the competition style of Mathematical Olympics often has wider adaptability. It will be the future development trend to advocate mathematical inquiry questions that can arouse more participants' interest.
Nowadays, although not every country in the world participates in every session, most countries with developed economy and culture are among them. IMO has become the most influential academic competition in the world. At the same time, it is also recognized as the highest level of middle school mathematics competition.
Although more and more teams are participating in the International Mathematical Olympiad, and the scale of the competition is constantly expanding, before 1980, there was no unified international organization responsible for organizing and coordinating the work. At first, it was basically several eastern European countries that participated in international competitions to undertake the organization work and the required expenses in turn. With the increase of new countries, the burden cannot be placed on a few countries. 1976 Austria became the first western country to host IMO. Since then, Britain has held 2 1 IMO in 1979. However, 1980 IMO failed to be held because of the financial difficulties of Mongolia, the original host country, and the lack of an international coordinating body for IMO to let possible host countries and participating countries know about this situation, which made people clearly realize the necessity of establishing an international organization to coordinate and organize the annual IMO. 1980, the international mathematics education Committee decided to set up an IMO sub-committee (formally established in April, 198 1) to determine the host of each session. Therefore, since 198 1, the IMO tradition has been uninterrupted and gradually standardized.
Second, the articles of association of the International Olympic Mathematical Competition stipulate that:
1) The annual IMO host country is held by participating countries (or regions) in turn. The time is scheduled for July, and the required funds will be borne by the host country. The whole activity was hosted by the host country, presided by the examiners' committee composed of leaders of various countries, and the test questions and answers were provided by the participating countries. Each country has 3-5 questions (or none), and the host country does not provide test questions, but forms a topic selection Committee. The evaluation and primary selection of test questions provided by various countries mainly consider whether the test questions are repeated with previous test questions, and classify the test questions according to algebra, number theory, geometry, combinatorial mathematics and combinatorial geometry. , determine the difficulty of the test questions (A, B, C), and select about 30 questions. If there are new answers to these questions, it is also required to provide answers other than the original answers and translate them into English for the examiner to choose.
2) Each team will organize a team with no more than 8 players, including no more than 6 players (students from middle schools or schools at the same level), 65,438+0 captains and vice captains. The exam will be held in two days, with 3 questions each, 4.5 hours each and 7 points each, so the highest score of each player is 42 points.
The official languages of IMO are English, French, German and Russian, and participating countries need about 26 languages. At that time, the team leaders will translate the test papers into the national language and be approved by the Coordination Committee. The answers are judged by the team leaders and deputy team leaders of various countries, and then negotiated with the coordination committee (each coordinator is responsible for grading a test question). If there are differences, the arbitration shall be conducted by the presiding committee, and the negotiation shall be conducted in a trusting and friendly atmosphere.
IMO's winners account for about half of the participants, and the winners of the first, second and third prizes are awarded according to their scores, with an average ratio of 1:2:3. In addition, the examiner's committee can award special prizes to students who have made a very beautiful (meaning simple, ingenious and original) or mathematically meaningful answer to a question.
5) Main Review Committee
The examiners' committee is composed of leaders of various countries and the chairman designated by the host country. This chairman is usually the authority on mathematics in this country. The main review committee has six responsibilities:
A) selecting test questions;
B) Determine the scoring standard;
C) Accurately express the test questions in the working language, and translate and approve the test questions translated into the languages of the participating countries;
D) During the competition, determine how to answer the questions about the test questions put forward by students in written form;
E) Resolve the different opinions on grading between individual team leaders and coordinators;
F) Determine the number and scores of medals.
According to IMO regulations, the host of each session must send an invitation to all the participating countries in the previous session, and the new participating countries must show their willingness to participate in the competition to the host, and then the host will send an invitation.
The spirit of IMO is the Olympic spirit: "The important thing is not to win, but to participate." Accordingly, since the 24th 1983, although each team (6 people) has calculated their total scores and knows how many people rank according to the order of total scores, the organizing committee does not award prizes to the team winners, because IMO is only an individual competition, not a team competition.