Kvant
Information

Correspondence mathematics school

Раббот Ж. М.

Kvant 1970, No. 1p. 55-57Tag SBM8

Rough automatic draft, low quality: expect mistakes and awkward wording. It will be replaced by a better translation. Original →

55

CORRESPONDENCE MATH SCHOOL

There is probably no larger school in the Soviet Union than this: after all, about ten thousand people study in it, living in different cities and villages of the country. We are talking about a correspondence mathematical school (CMS) at the Faculty of Mechanics and Mathematics of Moscow State University.

It was organized on the basis of the Moscow Secondary Mathematical School No. 2 in 1964 on the initiative of the famous Soviet mathematician, corresponding member of the USSR Academy of Sciences I. M. Gelfand, who heads the scientific council of the school. Its main goal is to help schoolchildren better master the school mathematics curriculum, develop their abilities, and teach them how to work with a book.

Once a month, schoolchildren receive assignments - brochures that outline some sections of mathematics adjacent to the school curriculum and contain many interesting problems *). Having independently studied the brochure, the student completes the test task and sends it to the ZMSH. About 500 teachers, students and graduate students of Moscow State University check and solve these works.

*) Some tasks compiled at the ZMSH were printed in the form of separate brochures from the series “Library of Physics and Mathematics Schools” (Nauka Publishing House): these are “Coordinate Method” by I. M. Gelfand, E. G. Glagoleva, A. A. Kirillova, “Functions and Graphs” by I. M. Gelfand, E. G. Glagoleva, E. E. Shnolya, “Limits” by A. A. Kirillov, “Straights and Curves” by N. B. Vasilyev and V. L. Gutenacher and others. Many of «Kvant»’s readers have seen these brochures with colored covers and drawings in the margins.

ZMSH does not have a special goal of preparing university students, but along with general assignments, ZMSH students are also sent materials to prepare for entrance exams. Almost all graduates of ZMSh after graduating from school successfully take entrance exams in mathematics in various.by. Many of them choose mathematics as their profession. For example, a quarter of second-year students at the Faculty of Mechanics and Mathematics of Moscow State University are recent graduates of the ZMSH.

There are 29 films in ZMSH. They are organized at pedagogical institutes and universities and work according to a general program. In addition, there is another form of ZMS work, which is called “collective student”. This is a school math circle, working under the guidance of a teacher according to the ZMS program. The tasks are divided into busy circles, then each participant completes a test, which is checked by the teacher. After this, the circle draws up one common “collective work” and sends it to the ZMS. Currently, there are about 350 such circles at the ZMS.

In 1965, the Northwestern Correspondence School of Mathematics at Leningrad University began its work. Both ZMSH - Moscow and Leningrad - maintain mutual contact and “divided” among themselves those entering the ZMSH on a territorial basis (see admission rules). Now there is a correspondence school of physics and mathematics at the Moscow Institute of Physics and Technology, a ZPS at the Faculty of Physics of Moscow State University, etc.

ZMSH methodologist J.M. Rabbom

56

Only eighth grade students are accepted to ZMSH. Schoolchildren living in Moscow, Leningrad and their suburbs are not accepted into ZMSH. Classes at the school will begin on September 1.

ZMSH has two courses. Students who successfully complete school will receive a certificate of completion. School education is free.

This issue «Kvant» offers problems that serve as an introductory test for correspondence mathematics schools at Moscow State University and Leningrad State University. Those who want to enter the ZMSH must submit solutions to these problems no later than March 10, 1970. After checking the work (around June 1970), you will be informed whether you have been accepted into the ZMSH.

Although some of the introductory problems differ in appearance from the general school ones, no additional knowledge of mathematics is required to solve them.

In order to be accepted at school, it is not necessary to solve all problems without exception. When evaluating work, it will take into account not only the number of problems solved, but also the quality of the solution. The solution to each problem must be justified. An answer without any obligations may not be read. If there are several possible answers to a task, then all of them must be indicated.

Work must be completed in Russian in a student notebook. Entry papers will not be sent back.

Please do not roll the notebooks into a tube when sending them. In the envelope along with the notebook you need to put a piece of paper measuring 14 cm × 6 cm with your postal address written on it (we will stick it on the envelope when we send the answer).

Glue a sheet of checkered paper onto the cover of your notebook, drawing and writing it according to the following pattern (otherwise your work will not be checked!):

Region:
Last name, first name, year of birth:
School [full name]:
Class:
Last name, first name, patronymic teacher
mathematics:
Place of work and position of the parent:
Popular postal address:

Volododskaya.
Ivanov Peter, 1952
School No. 2 Tomma.
8th grade “B”.

Nikanorov Nikolay Alekseevich.
Father is the driver of bus no. 3,
mother is a housewife.
Tomma, st. Lenina, 3, apt. 8.

CHECK RESULTS
(to be completed by the inspector)

Schoolchildren living in the Arkhangelsk, Vologda, Kaliningrad, Leningrad, Murmansk, Novosibirsk, Pskov regions, Komi and Karelian Autonomous Soviet Socialist Republics, Belarusian, Latvian, Lithuanian and Estonian SSRs must send work to the address: Leningrad, P-228, st. Savushkina, 61, Specialized School at Leningrad State University. Correspondence school. To the competition.

Schoolchildren living in other regions and resource areas of the USSR must send work to the address: Moscow, V-234, Moscow State University, Mechanics and Mathematics, ZMSH. To the competition.

57

ENTRANCE CONTROL TEST OF ZMSH 1970

  1. The mathematician walked home along the bank of the stream upstream at a speed one and a half times greater than the speed of the stream, and held a stick and a hat in his hands. At some points, he threw his hat into the stream, confusing it with a stick, and continued up the stream at the same speed. After a while he noticed the mistake, threw the stick into the stream and ran back at twice the speed of the hats in the mess. Having caught up with the plum hat, he instantly fished it out of the water, turned and walked along the current at its original speed. 10 minutes later he met a stick floating in the stream. How much earlier would he have gotten home if he had not confused the stick with the hat?

  2. For every triangle ABC, is there a point P such that all three points, symmetrical points P with respect to the lines AB, BC and AC, lie on the circumcircle of triangle ABC?

  3. For what values ​​of a is the difference between the roots of the equation ax² + x - 2 = 0 equal to 3?

  4. The student took 31 exams over five years of study. In each subsequent year he passed more exams than in the previous one. In the fifth year there are more second exams than in the first. How many exams are there in the fourth year?

  5. The bases of an equal-volume trapezoid are 4 cm and 8 cm, its area is 21 cm². Which side does the bissertis of the angle intersect with a larger base—the smaller base or the lateral side of the trapezoid?

  6. All digits of a four-digit number that is a perfect square can be reduced by the same number so that the result is a four-digit number that is also a perfect square. Find all such numbers.

  7. Is it possible for the sum of the distances from a point lying inside a convex quadrilateral to all its vertices to be greater than its perimeter?

  8. One of the three gangsters, known in the city of Ch. under the nicknames Archie, Boss and Wesley, stole a briefcase with money. During interrogation, each of them made three statements:

    Archie: 1) I didn’t take the briefcase.
    2) On the day of the theft, I left the city of Ch.
    3) Wesley stole the briefcase.

    Boss: 1) Wesley stole the briefcase.
    2) Even if I had taken it, I would not have confessed.
    3) I already have a lot of money.

    Wesley: 1) I didn’t take the briefcase.
    2) I’ve been looking for a good briefcase for a long time.
    3) Archie is right in saying that he got out of Ch.

During the investigation, it was found that out of the three statements of each gangster, two were true and one was incorrect. Who stole the briefcase?

  1. Find integers x and y such that x > y > 0 and x³ + 7y = y³ + 7x.

  2. A square area measuring 100 m × 100 m is lined with 1 m × 1 m square tiles in four colors: white, red, black and gray - so that no two tiles of the same color collide with each other (i.e., do not have a common side or top). How many red litas can there be?

  3. Solve the equation (x² + 6x - 4) (x² + 6x - 3) = 12.

  4. Given triangle ABC. Find points K and H, lying respectively on sides AB and BC, such that BK = KH = HC.

  5. Find all numbers p such that p² + 13 is also prime.