What is dvi in \u200b\u200bMGU. Additional entrance test, conducted at the Moscow State University. What tasks does the DWI in mathematics consist of at Moscow State University

Many people know that ordinary USE scores are not enough for admission to Moscow State University. Here we will talk about what "DWI" or "additional entrance tests" are. Such tests are held in various subjects. We are interested, of course, in mathematics.

As a DVI, it is passed upon admission to 17 out of 64 directions of Moscow State University. These are the Faculty of Mechanics and Mathematics, the Faculty of Computational Mathematics and Cybernetics, the Faculty of Geology, the Faculty of Materials Science, the Faculty of Economics, the Faculty of Bioengineering and Bioinformatics, the direction "Applied Mathematics and Physics" at the Faculty of Fundamental Physical and Chemical Engineering, the direction "Economics" of the Higher School of State audit, "Management" of the Higher School of Modern Social Sciences, all areas, except for "Political Science" of the Faculty of Public Administration, as well as the Higher School of Business and the Moscow School of Economics.

In 4 hours, applicants must solve several tasks. In recent years, these are usually eight problems, the first four of which are easier, and the last four are very difficult, presenting significant difficulty even for graduates of special schools, for these problems there is a competition for mathematical directions. The exam results are evaluated on a 100-point scale. Moreover, 100 points can be given not only for all 8, but also for 7 (and in some years even for 6) correctly solved problems. This is due to the fact that all 8 problems are solved extremely rarely, only a few among thousands of applicants are usually capable of this, these units can be safely called unique.

In order for a sufficiently high USE results to be guaranteed to enter the budget places of most of the named faculties, it is necessary to write a DVI for 75-80 points.

Consider the results of the recent DWI MSU (data taken from the website of Moscow State University, page http://pk.cmc.msu.ru/node/1063 and http://pk.cmc.msu.ru/sites/pk.cmc.msu.ru/files/dvi_sayt_0.pdf).

Among all MSU applicants, 3732 people took an additional entrance exam in mathematics. Of these: 340 people passed on "2", on "30" - 125, on "35" - 154, "40" - 125, on "45" - 134, on "50" - 436, on "55" - 456, "60" - 801, "65" - 572, "70" - 222, "75" - 105, "80" - 85, "85" - 89, "90" - 46, "95" - 30, "100" - 12.

Those. we see that only 10-15% of applicants with high USE scores, having written a DVI in mathematics, no doubt had real chances to enter budget places, and only 7% of applicants wrote mathematics for 80 or more points (for the maximum score - 0.3%).

Results of DWI MSU in mathematics

Now we will consider the results of the DVI among applicants of the Faculty of Computational Mathematics and Cybernetics (CMC). People go to this prestigious faculty only after special mathematical training (study in special schools, classes in courses and with tutors).

Among those who entered the VMK of Moscow State University, there were 128 people who received the highest score according to the results of the Olympiads, and among those 751 who wrote the DVI upon admission, the results are as follows:

"2" -17, "30" - 5, "35" - 9, "40" - 9, "45" - 11, "50" - 47, "55" - 74, "60" - 166, "65 "- 184," 70 "- 73," 75 "- 45," 80 "- 36," 85 "- 35," 90 "- 16," 95 "- 16," 100 "- 8 (i.e. we see that two-thirds of the applicants who wrote the DVI for 100 points applied to the VMC).

Thus, among specially prepared applicants, the percentage of really applying for the budget turns out to be only slightly higher: 15-20% (moreover, 70-75 points can only be afforded by guys with a superbly passed USE, because the passing score on the VMC is very high). And even among such an elite - only 1% of those who passed the DVI for the maximum score.

Results of DVI Faculty of CMC MSU in mathematics

So, we see that it is not so easy to pass the DVI in mathematics at Moscow State University, and special preparation is required for it.

Many of the graduates of "Mathematica" entered the selected faculties of Moscow State University based on the results of the Olympiads (victories at "Lomonosov", the Olympiad "Conquer the Sparrow Hills" and other mathematical competitions among the students of "Mathematica" are not uncommon).

However, some of the graduates nevertheless passed additional entrance examinations and looked more than worthy on them. Let's take the results of recent years, when the Unified State Exam was already introduced and the DWI began to pass in one subject according to the current scheme.

This year, new high school students are preparing to conquer the "mathematical horizons".

Applicants to the Faculty of History who enter the History direction undergo a written additional entrance test (ADI), and those entering the History of Arts direction pass a creative entrance test consisting of written and oral parts.

The terms of the entrance examinations for applicants to the history faculty of Moscow State University are announced after the start of the work of the selection committee and are indicated in the "Applicant's Calendar" and on the website of the Central Admissions Committee of Moscow State University.

The forms of additional admissions tests and admissions tests of creative orientation are established by the Central Admissions Committee of Moscow State University and become known on the day of the admissions tests.

The results of these introductory tests are added to the USE and individual achievement scores. The final value is the total score on the basis of which the applicant participates in the competition.

General information about DWI by history

An additional entrance test (ADT) in history is held at Moscow State University in a centralized manner - on the same day for applicants from all faculties.

Each of the faculties of Moscow State University organizes a DVI on its site for those applicants for whom this faculty is the base. The base is the faculty of Moscow State University, to which the applicant applied for the first time among all faculties with the same DVI.

Consultation before the DVI is held the previous day at 16:00 for applicants of all faculties in the classrooms Shuvalov building of Moscow State University.

The results are assessed on a 100-point scale and are credited at all faculties of Moscow State University, where history is passed in the form of a written exam as DVI.

On the day of the exam, applicants from the Faculty of History should get together in advance (no later than an hour before the start of the exam) in front of the central entrance to the Shuvalov building (Lomonosovskiy prospect, 27, building 4).

The exam starts at 10:00... Exam duration - 4 astronomical hours (240 minutes) .

Applicants who submitted an application by mail must receive a pass to the exam from the admissions office of the Faculty of History in advance (at least a day or two before the exam).

The distribution of applicants to audiences is carried out by the staff of the selection committee. Applicants who are late for the start of the exam are not allowed into the classroom.

• the passport,

• several pens in blue or black (you should be careful to ensure that the entire work is written in the same ink),

• being in the classroom with cell phones, pocket computers, electronic dictionaries, communication devices and other radio-electronic equipment, even if this equipment is off;
• take examination materials out of the audience;
• talk to each other;
• exchange any materials and items with each other
• arbitrarily leave the classroom and move around the building without being accompanied by an admissions officer
• In case of violation of these rules the applicant is removed from the exam, and his work is not checked.

  You can go to the toilet only when accompanied by an admissions officer, no earlier than an hour after the start of the exam and no later than an hour before its end.

  On the day of the exam, parents are not allowed into the building.

Order of conduct
the oral part of the additional entrance test
creative focus
for applicants for the direction " Art history"

Applicants in the History of Arts direction pass the oral part of the additional entrance test of a creative orientation in the auditorium on the 6th floor of the Shuvalov building of Moscow State University. The exam starts at 10:00.

On the day of the exam, applicants should get together in advance (no later than 9:30) in front of the central entrance to the Shuvalov building (Lomonosovsky prospect, 27, building 4).

Persons who did not appear for the exam for a good reason (illness or other circumstances confirmed by documents) are allowed to take it on a reserve day.

The staff of the admissions committee first gather applicants into the classroom to wait in line for the exam, and then, as the answers of the applicants who came earlier are completed, they accompany them to the examination room.

To participate in the exam, you must have the following documents with you:

• the passport,
• pass issued when submitting documents.

In addition to the named documents, applicants can bring the following subjects with them to the examination room:

• a blue or black pen to fill in the Oral Answer Sheet,
• non-carbonated mineral water in a transparent plastic bottle with a volume of no more than 0.6 l.

It is strictly forbidden to be in the classroom with cell phones, pocket computers, electronic dictionaries, communication devices and other radio electronic equipment, even if this equipment is turned off. If an applicant violates this rule, he is removed from the examination room.

During the exam, the applicant is required to give an oral answer to one question on the history of art indicated on the selected ticket and the accompanying envelope with illustrative material. After preliminary preparation using the "Oral Answer Sheet", the applicant demonstrates his knowledge to the members of the examination committee under a video recording conducted in the audience.

The maximum score for the oral part of the creative orientation test is 30 points. The score received is summed up with the mark for the written part (maximum -70 points), and on this basis, the overall final mark is given for the entrance test as a whole (maximum mark - 100 points).

Announcement of results and minimum score

The dates and times of the announcement of the results and the display of written works are communicated to applicants in the audience during the entrance examinations, and are also published in the "Applicant's Calendar" on the website of the Faculty of History.

The minimum number of points confirming the successful completion of the entrance examinations and entrance examinations of a creative orientation conducted by Moscow State University is set at the level of the minimum number of points required for admission to undergraduate programs and established by the federal executive body exercising control and supervision functions in the field of education.

Moscow State University them. M.V. Lomonosov

additional entrance test in mathematics

2014 variants

A task 1 .

Find explicitly natural numbergiven by the expression:

A task 2 .

Find the maximum value of the function:

a) log 1/2 ( x 2 - 6x + 17)

b) log 1/3 ( x 2 + 4x + 31)

a) log 1/2 ( x 2 - 8x + 20)

a) log 1/3 ( x 2 + 10x + 34)

A task 3 .

Find all positive x satisfying the inequality:

a) x 3x + 7\u003e x 12.

b) x -5x-7< х -7 .

c) x 4x-5\u003e x -2.

d) x -7x + 5< х -4 .

A task 4 .

Solve the equation:

A task 5 .

a) Circles W 1 and W 2 with centers at points O 1 and O 2 touch externally at point A. The common external tangent to these circles touches W 1 and W 2, respectively, at points B 1 and B 2. The common tangent to the circles passing through point A intersects the segment B 1 B 2 at point C. The straight line dividing the angle ACO 2 in half intersects the lines O 1 B 1, O 1 O 2, O 2 B 2 at points D 1, L , D 2, respectively. Find the ratio LD 2: O 2 D 2 if it is known that CD 1 \u003d CO 1.

b) Circles W 1 and W 2 with centers at points O 1 and O 2 touch externally at point A. The common external tangent to these circles touches W 1 at point B and intersects at point C the common tangent of these circles passing through point A The straight line dividing the angle АСО 1 in half intersects the lines О 1 О 2, BO 1 at points L and D, respectively. Find СО 2 if it is known that LO 1 \u003d 2, and the lines CO 2 and DO 2 are perpendicular.

c) Circles W 1 and W 2 with centers at points O 1 and O 2 touch externally at point A. The common external tangent to these circles touches W 1 and W 2, respectively, at points B 1 and B 2. The common tangent to the circles passing through point A intersects the segment B 1 B 2 at point C. The straight line dividing the angle ACO 2 in half intersects the straight lines O 1 B 1, O 1 O 2, O 2 B 2 at points D 1, L , D 2, respectively. Find the ratio CD 1: CO 1 if it is known that LD 2 \u003d O 2 D 2.

d) Circles W 1 and W 2 with centers at points O 1 and O 2 touch externally at point A. The common external tangent to these circles touches W 1 at point B and intersects at point C the common tangent of these circles passing through point A The straight line dividing the angle АСО 1 in half intersects the lines О 1 О 2, BO 1 at points L and D, respectively. Find LO 1 if it is known that CO 2 \u003d 2, and lines CO 2 and DO 2 are perpendicular.

A task 6 .

Find all the positive x, atsatisfying the system of equations:

Find all x, at on the interval (0, π / 2), satisfying the system of equations:

A task 7 .

a) At the base of a straight prism lies a regular triangle with side 1. The height of the prism is. Find the distance between the crossing diagonals of the side faces.

b) At the base of the straight prism lies a square with side 1. The height of the prism is equal to. Find the distance between the large diagonal of the prism and the diagonal of the side face that crosses it.

c) At the base of a straight prism lies a regular triangle with side 2. The height of the prism is. Find the distance between the crossing diagonals of the side faces.

d) At the base of the straight prism lies a square with side 1. The height of the prism is. Find the distance between the large diagonal of the prism and the diagonal of the side face that crosses it.

A task 8 .

Find all values \u200b\u200bthat at least one of the functions can take:

As you can see, the problems are certainly solvable, but they require very serious mathematical training and a fair amount of experience in solving problems of a high level of complexity.

Of course, it is impossible to prepare for such an exam from scratch in a month and a half. However, for an applicant who has a sufficient basic level of knowledge in mathematics (and who else will enter such serious faculties?), Purposeful preparation for an additional entrance test can be very, very useful. The logic of such an exam is very different from the Unified State Exam, and you need to prepare for it using a completely different method. Problems require more volumetric transformations and involve more logical branches during the solution.

Let's try to analyze some tasks:

Problem number 1.

Explicitly find the natural number given by the expression.