As an international competition, the International Mathematical Olympiad was put forward by international mathematical education experts, which exceeded the level of compulsory education in various countries and was much more difficult than the college entrance examination. According to experts, only 5% of children with extraordinary intelligence are suitable for learning the Olympic Mathematics, and it is rare to reach the top of the international mathematical Olympics all the way. On August 2, 2065438+021day, Beijing took a number of measures to resolutely control the link between Olympic math scores and further studies.
1 Introduction to the Grand Prize
The International Olympic Mathematics Competition is an international mathematics competition for middle school students, which has great influence in the world. The purpose of international Olympic competition is to discover and encourage young people with mathematical talent in the world, create conditions for scientific education exchanges among countries, and enhance the friendly relationship between teachers and students in various countries. This contest (1959) was initiated by Eastern European countries and funded by UNESCO. The first competition was hosted by Romania and held in Bucharest from July 22 to 30. 1959. Bulgaria, Czechoslovakia, Hungary, Poland, Romania and the Soviet Union participated in the competition. After that, the International Olympic Mathematics Competition was held in July every year (1980 only once), and the participating countries gradually expanded from Eastern Europe to Western Europe, Asia and America, and finally expanded from 1967 to the whole world. In 20 13, more than 80 teams participated in this competition. The United States entered the competition in 1974 and China entered the competition in 1985. 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.
The International Olympic Mathematics Competition is hosted by participating countries in turn, and the funds are provided by the host country; However, the travel expenses are borne by the participating countries. Participants must be middle school students under the age of 20, with 6 people in each team; Two other mathematicians were appointed as team leaders. 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. 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.
2 responsibilities of the Committee
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.
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.
3 Award setting
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; The total number of winners cannot exceed half of the students participating in the competition. The award criteria of each session are related to the results of the current exam.
4 history of international competitions
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. In the 16 and 17 centuries, many mathematicians liked to ask questions to challenge other mathematicians, and sometimes they held some open competitions. In several open equation competitions, there is one of the most famous Fermat's Theorem: when the integer n≥3, the equation has no positive integer solution.
Modern mathematics competition is still a problem-solving competition, but it is mainly held among students (especially senior high school students). The purpose is to discover and cultivate talents.
Mathematics competition in the modern sense began in Hungary. 1894, in order to commemorate the appointment of Evos, President of the Society of Mathematics and Physics, as Minister of Education, the Society of Mathematics and Physics passed a resolution: a math contest named after Evos will be held every year 10, with 3 questions each time and a time limit of 4 hours. Any reference books are allowed. These problems are good at mysterious and strange forms, and generally have concise solutions and creative characteristics. 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.
Influenced by Hungary, Eastern European countries vigorously held math competitions:1Romania in 902, the former Soviet Union in 1934, Bulgaria in 1949, Poland in 1950, and Czechoslovakia in195 years ago.
It was the former Soviet Union that named the middle school students' mathematics competition "Mathematical Olympics". The name is adopted because there are many similarities between mathematics competition and sports competition, both of which advocate the Olympic spirit. The result of the competition is surprising, and it is often found that a powerful country in mathematics competition is also a powerful country in sports competition, which gives some enlightenment.
1934 in Leningrad, 1935 in Moscow, the relevant state universities organized regional mathematics competitions, which were called "Middle School Mathematics Olympics". At that time, famous mathematicians in Moscow took part in this work. The mathematical Olympics in the former Soviet Union were divided into five levels: school Olympics, county Olympics, regional Olympics, Republic Olympics and national Olympics, and then six representatives were elected to participate in the international mathematical Olympics.
The most enthusiastic about organizing the international mathematics competition is Romanian professor Roman. After his planning, the first International Mathematical Olympiad (IMO) was held in July 1959 in Blaso, the ancient Romanian capital, which opened the curtain of the international mathematical competition. At that time, 52 students took part in the competition. They came 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. It will be held once a year in the future (except 1980, which was suspended due to the financial difficulties of the host Mongolia). By the time 1990 3 1 was held in China, it had grown to 308 contestants from 54 countries and regions. By 1995, when the 36th tournament is held in Canada, the number of doubles will increase to 73 countries and regions, with more than 400 participants.
5 Competition laws and regulations
(1) The host country of IMO in the year is held by the participating countries (or regions) in turn, and the required funds are borne by the host country. The whole activity was hosted by the host country, presided by the examiners committee composed of national leaders, 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 to evaluate and preliminarily screen the test questions provided by each country. Mainly consider whether the test questions are repeated before, and classify the test questions according to algebra, number theory, geometry, combinatorial mathematics, combinatorial geometry and so on. , 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 shall organize a team with no more than 8 members, including no more than 6 members (students from middle schools or schools at the same level), 1 team leader and deputy team leader. 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.
(3) 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 get the approval of the coordination Committee. The marking is first judged by leaders and deputy leaders of various countries, and then negotiated with the Coordination Committee (each coordinator is responsible for marking a test question). If there are differences, the examiners' committee will arbitrate, and the negotiation will be conducted in a trusting and friendly atmosphere.
(4) The number of winners of IMO accounts for about half of the participants, and the winners of the first, second and third prizes are awarded in order of 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.
In order to avoid the interruption of 1980 again, IMO set up a special committee (some translated as venue committee) to determine the host of each session.
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.
Among the countries outside Eastern Europe, Finland was the first to join (1965 7th), and France, Britain, Italy, Sweden and the Netherlands joined in succession in 1960s. 1974, the United States and Vietnam joined. Since then, the number of participating countries has increased year by year, covering Europe, the United States, Asia, Africa and Oceania, and IMO has become a truly global mathematics competition.
1988 In the 29th session, IMO set up an honorary prize for the first time at the suggestion of Hong Kong, and awarded it to those players who got full marks in at least one question although they didn't win gold, silver or bronze medals. This measure greatly mobilized the enthusiasm of all participating countries and their players.
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.
198 1 22nd, the United States is the host of IMO. Greitzer, chairman of the American Mathematical Olympiad Committee, sent a letter inviting China to participate, and chinese mathematical society wrote back and agreed to participate. Later, he failed to make the trip and only sent visiting scholars from the United States as observers.
1984, at the first meeting of chinese mathematical society's popularization work held in Ningbo, it was decided to send two contestants to participate in the 26th IMO in 1985, so as to learn about the situation and accumulate experience. Due to the hasty selection time, only 1 outstanding students from Beijing and Shanghai were arranged to participate. Results 1 person won the third prize, and their average score with Israel was 17, while their total score was 32. Starting from 1986, China sent six players to participate in the competition.
The brilliant achievements of China athletes have greatly stimulated the enthusiasm of millions of middle school students to learn scientific and cultural knowledge, and also greatly enhanced the national vanity of Chinese people.
6 domestic competition situation
It's not too late to hold a math contest in China. After liberation, under the initiative of Professor Hua and other mathematicians of the older generation, middle school mathematics competitions were held from 65438 to 0956, and resumed in Beijing, Shanghai, Fujian, Tianjin, Nanjing, Wuhan, Chengdu and other provinces and cities, and high school mathematics leagues were also held jointly by Beijing, Tianjin, Shanghai, Guangdong, Sichuan, Liaoning and Anhui. From 65438 to 0979, 29 provinces, municipalities and autonomous regions in Chinese mainland held middle school mathematics competitions. Since then, the enthusiasm for developing mathematics competitions all over the country has never been higher. 1980, at the first national conference on the popularization of mathematics held in Dalian, it was decided to take the mathematics competition as a regular work of the Chinese Mathematical Society and the mathematical societies of all provinces, municipalities and autonomous regions, and hold the "National Senior High School Mathematics Joint Competition" 10 on the first Sunday in mid-June every year. At the same time, the mathematical circles in China are actively preparing to send athletes to participate in the International Mathematical Olympics. 1985, the national junior high school mathematics league was held; 1986 held the "Huajin Cup" Youth Mathematics Invitational Tournament; 199 1 year, the national primary school mathematics league was held.
China's high school mathematics competition is divided into three levels: the national league tournament in mid-June every year is 65438+ 10; The following year 1 month CMO (winter camp); The training and selection of the national training team began in March of the following year.
The American Middle School Mathematics Competition has a great influence on the middle schools in China. The competition is also divided into three rounds: AHSME, with 30 multiple-choice questions, which should be completed within 90 minutes; There are 15 empty questions in the American Mathematics Invitational Tournament (AIMS), and the answers are all positive integers not exceeding 999, which should be completed within 3 hours; The American Mathematical Olympiad (USAMO), the highest mathematics competition in the United States, has five questions each time and takes 3.5 hours to complete.
Our country has taken a series of effective measures to make our country's mathematics competition activities extensive, orderly, in-depth and lasting, and do a good job in the training and selection of all kinds of mathematics competitions at all levels. First, create a good scene for the math competition; Primary and secondary schools organize teaching interest group activities every year, and set the time, place, tutor and auxiliary content; There are plans to provide intensive counseling and training for some math "seedlings" in order to establish a math Olympic amateur school. Secondly, strengthen the counseling power of mathematics competition; Mathematical Olympic coaches at all levels should constantly improve their teaching and teaching quality. Third, optimize the mathematics competition counseling system; Compile and publish basic mathematics competition training materials or counseling books, collect and sort out domestic and foreign mathematics competition materials, study and refine the thinking methods and skills of solving problems in mathematics competitions, and improve and perfect the selection mechanism and counseling methods of mathematics competitions.
The "National Primary School Mathematics Olympics" (founded in 199 1) is a popular activity, which is divided into preliminary competition (March every year) and summer camp (summer every year).
The "National Junior Middle School Mathematics League" (founded in 1984) is held by the mathematics competition organizations of all provinces, municipalities and autonomous regions in the form of "taking turns to host", which is held in April every year, with a trial and a second trial.
The National High School Mathematics League (founded in 198 1) is held in the same way as the junior high school league. It is divided into initial test and second test. About 90 students who have achieved excellent results in this competition are eligible to participate in the "China Mathematical Olympics (CMO) and the National Winter Camp for Middle School Students" hosted by chinese mathematical society (every year 1 month).
The World Olympic Forest Mathematics Competition (China District) is held twice a year, and is undertaken by the Education Development Center of China Care for the Next Generation Committee and other institutions. Participants are children aged 10- 16, that is, seven grade groups from the third grade of primary school to the third grade of junior high school. The purpose of the competition is to select China, an outstanding mathematician from China, to participate in the global finals of the World Olympic Mathematics Competition. [ 1]
Under the guidance of the policy of "improving on the basis of popularization", the national mathematics competition is in the ascendant. Especially in recent years, Chinese athletes have made gratifying achievements in the international mathematics Olympics, which has aroused the enthusiasm of teachers, students and mathematicians in primary and secondary schools, and the mathematics competition has entered a new stage. In order to make the national mathematics competition sustainable, healthy and in-depth, the outline of mathematics competition is formulated at the request of teachers, students and mathematicians at all levels in middle schools.
This syllabus is based on the spirit and foundation of the "Full-time Middle School Mathematics Syllabus" formulated by the State Education Commission. The syllabus is pointed out in the column of teaching purpose; To realize the four modernizations, we must cultivate students' interest in mathematics and stimulate them to learn mathematics well. The specific measures are: "Students who have spare capacity for study should fully develop their mathematical talents through extracurricular activities or offering elective courses", "We should pay attention to the cultivation of their abilities …" and focus on cultivating students' computing ability, logical thinking ability and spatial imagination ability, so that students can gradually learn important thinking methods such as analysis, synthesis, induction, deduction, generalization, abstraction and analogy. At the same time, we should pay attention to cultivating students' independent thinking and self-study ability. "
The contents listed in the syllabus are the requirements of teaching and the minimum requirements of the competition. In the competition, there are higher requirements for the understanding and flexible application of the same knowledge content, especially the proficiency of methods and skills. And "classroom teaching. Priority of extracurricular activities is a principle that must be followed. Therefore, the content of extracurricular lectures listed in this syllabus must fully consider the actual situation of students, so that students can master it step by step and at different levels, implement the principle of "less but better", strengthen the foundation and constantly improve.
7 examination form
Just try it.
The outline of the preliminary test competition of the national senior high school mathematics league matches the teaching requirements and contents stipulated in the full-time middle school mathematics syllabus, that is, the knowledge scope and methods stipulated in the college entrance examination are slightly improved, and the preliminary test of probability and calculus is not taken.
Second division
plane geometry
Basic requirements: master all the contents determined by the junior high school competition outline.
Supplementary requirements: area and perimeter methods.
Several important theorems: Menelius Theorem, Seva Theorem, Ptolemy Theorem and siemsen Theorem.
Several important extreme values: fermat point, the point with the smallest sum of the distances to the three vertices of a triangle. The center of gravity is the point where the sum of squares of the distances to the three vertices of a triangle is the smallest. The point in a triangle with the largest product of the distances from three sides-the center of gravity.
Geometric inequality.
Simple isoperimetric problem. Understand the following theorem:
In the set of N-polygons with a certain circumference, the area of the regular N-polygon is the largest.
In a set of simple closed curves with a certain perimeter, the area of the circle is the largest.
In a group of N-sided polygons with a certain area, the perimeter of the regular N-sided polygon is the smallest.
In a set of simple closed curves with a certain area, the circumference of a circle is the smallest.
Motion in geometry: reflection, translation and rotation.
Complex number method, vector method.
Planar convex set, convex hull and their applications.
algebra
Other requirements based on the first test outline:
Image of periodic function and periodic and absolute value function.
Triple angle formula, some simple identities of triangle, triangle inequality.
The second mathematical induction.
Recursion, first and second order recursion, characteristic equation method.
Function iteration, find n iterations *, simple function equation *.
N-element mean inequality, Cauchy inequality, rank inequality and their applications.
Exponential form of complex number, Euler formula, Demefer theorem, unit root, application of unit root.
Cyclic arrangement, repeated arrangement, combination. Simple combinatorial identities.
The number of roots of an unary n-degree equation (polynomial), the relationship between roots and coefficients, and the pairing theorem of imaginary roots of real coefficient equations.
Simple elementary number theory problems should include infinite descent method, congruence, Euclid division, nonnegative minimum complete residue class, Gaussian function [x], Fermat's last theorem, Euler function *, Sun Tzu's theorem *, lattice points and their properties.
solid geometry
Polyhedral angle, properties of polyhedral angle. Basic properties of trihedral angle and straight trihedral angle.
Regular polyhedron, euler theorem.
Proof method of volume.
Sections, sections, and surface flat patterns will be made.
plane analytic geometry
Normal formula of straight line, polar coordinate equation of straight line, straight line bundle and its application.
The region represented by binary linear inequality.
The area formula of triangle.
Tangents and normals of conic curves.
Power and root axis of a circle.
other
Dove cage principle
Exclusion principle.
Extreme principle.
Division of sets.
Cover.