*Features of the 3rd stage of the Olympiad**Requirements for the content, scope and level of complexity of tasks**Evaluation of works of participants of the 3rd stage of the Olympiad**Scientific and methodological support of the 3rd stage of the Olympiad*

The third stage of the All-Ukrainian Student Olympiad in Mathematics is held in January 2020. The 1st round is scheduled for Sunday, January 19, the 2nd round is scheduled for Sunday, January 26.

__Features of the 3rd stage of the Olympiad __

We recommend three options for the III stage of the Olympiad.

1 option. In accordance with paragraph 2.4.5 regulations, both rounds of the THIRD stage of the All-Ukrainian Student Olympiad in Mathematics should be carried out on tasks developed by the Institute for the Modernization of Educational Content (IZO). In this case, tours in the respective regions are held on January 19 and 26, 2020. The scheduled start of the Olympiad at 10:00 (the start date of the Olympiad may vary depending on the characteristics of each region). Tasks will be sent to the venues 1-2 hours before the start of the tour. Closer to the end of the Olympiad, conditions with complete solutions to problems will be sent out by region, and upon completion – posted on the website of matholymp.com.ua.

In each region, the jury develops criteria for evaluating each task. These criteria may vary by different areas.

2 option. Both tours of the Olympiad in the region are conducted on their own tasks and their own system of verification of works. In this case, the dates and number of tours are determined in the region.

3 option. Only the 1st (or 2nd) round of olympiads in the region are conducted on the tasks developed by the IZO, and the 2nd (1st) on their own tasks. Then, for a joint tour, the region must choose one of the above-mentioned dates of the Olympiad.

__Requirements for the content, scope and level of complexity of tasks__

The content of tasks for the 3rd stage of the Olympiad is based on the current curriculum, including taking into account the program of in-depth study of mathematics. Tasks include both tasks related to the sections of the school course of mathematics of the current academic year, and tasks that reflect the previously studied material.

The tasks of the 1st round consist of 4 (5) tasks for the 7th grade and 5 (6) tasks for grades 8-11, the tasks of the 2nd round consist of 4 tasks in each class. Among the tasks in each parallel, it is desirable to have at least one problem in algebra, geometry, number theory, and combinatorics.

The duration of the 1st round for the 7th grade is 3 astronomical hours, for all other classes and for all classes in the 2nd round – 4 astronomical hours.

For each of the parallels of 7-11 classes, different sets of tasks are used (although individual tasks can be offered simultaneously for several parallels).

Participants of the 3rd stage of the Olympiad should have not only methods directly provided for by the curriculum, but also special methods for solving Olympiad problems for the relevant age groups, additional theoretical knowledge provided for by the programs of elective courses, mathematical circles, established practice of mathematical Olympiads in Ukraine and the world, etc.

The Institute for The Modernization of Educational Content will develop the tasks of the 3rd stage of the All-Ukrainian Student Olympiad in Mathematics in three versions: level "A" (high), level "B" (average) and level "B" (sufficient).

Each region receives tasks at all levels. On the day of the 1st (2nd) round of the Olympiad, the text of the conditions will be sent to the specified e-mail address within a specified period. The jury and the organizing committee of the local Olympiad can use tasks of different levels in different parallels if it considers it appropriate. Typically, level B differs from level "A" in the last (most difficult) task. And the level "B" from the level "B" is characterized by the penultimate task.

In the case of the Olympiad, according to option 1 or 3 of the organizing committees of the 3rd stage of the All-Ukrainian Student Olympiad in Mathematics, who will decide to conduct the 1st and/or 2nd round on the tasks provided by the IZO, they had to send an application to the e-mail addresses of the persons responsible for the organizational and technical support of the 3rd stage of the Olympiad in mathematics according** to the**** s****ame tex****t****s:**

**A****n****dri**y.pankov@gmai.com (Senior Research Fellow, PhD, 0639933366);

rublyovbv@gmail.com (Professor of Taras **Shevchenko National Uni**versity of Kyiv, Doctor of Physical and Mathematical Sciences Rublev Bohdan Vladyslavovych, 0683892107, 0505613964);

anik_andrii@ukr.net (Associa**te Professor of Taras S**hevchenko National University of Kyiv, Candidate of Physical and Mathematical Sciences Aikoushin Andriy Valeriyovych, 0637103420).

Conditions will be provided only in Ukrainian. With the permission of the organizing committee and the jury of the Olympiad of the 3rd stage in the region, participants can perform the tasks of the Olympiad in another language convenient for themselves. Participants should be warned about this before the start of the Olympiad.

__Evaluation of works of participants of the 3rd stage of the Olympiad__

To evaluate works, a system is used in which each task is evaluated with an integer of points from 0 to 7**.** This corresponds to the practice of the jury of the IV stage of the All-Ukrainian Student Olympiad in Mathematics, the jury of international mathematical olympiads and most other mathematical olympiads in the world.

In general, a score of 5 to 7 points is set for the correctly solved task. For significant advancement, for the solution of several fundamental cases, for the task solved half a score of 3 or 4 points is set. For a total unsolved task, a score of 0 to 2 points can be scored.

- 7 points – complete and impeccable solution of the problem.
- 5-6 points – the solution contains minor shortcomings, errors, inaccuracies, etc.
- 3-4 points – if the problem is solved in half, depending on the progress towards a complete solution.
- 1-2 points is set with a slight but correct advance towards the correct solution.
- 0 points – there are no correct and meaningful advances towards the correct solution of the problem.

When evaluating Olympiad works, the rationality or irrationality of solutions, the method of solution, as well as the amount of written are not taken into account. If the jury is not able to disassemble the handwriting of the participant, where most of the words are written so inaudible that they can be read in several ways, then the jury can evaluate in this problem only the part of the solution that was able to disassemble. We are talking about understanding handwriting, and not the mathematical part written in legible handwriting. At the same time, on appeal, the student has no right to demand to "translate" the content of the written for the jury.

In order to carry out high-quality impartial verification of the tasks of the jury of the Olympiad of the 3rd stage in each region, it develops uniform evaluation criteria for each task, taking into account the different ways of solving tasks by the participants of the Olympiad. The evaluation criteria should reflect all the significant steps (promotion) of solving each problem. Separately, it is possible to specify the steps of the solution that were not evaluated (for example, the correct picture for the problem, the consideration of the trivial case, the use of the coordinate method without bringing to a final solution, etc.). The jury at the meeting discusses and approves criteria for assessing tasks and allied points.

The jury checks only the tasks recorded in the cleaner of the olympiad participant. The draft is not considered by the jury. As an exception, the jury can refer to the draft if most of the solution is written in the cleaner, and a link to the draft is made to the rest. In the draft, there may be some unwritten cases of the correct solution, proof of the auxiliary statement, the necessary picture, etc., which the participant simply did not have time to rewrite to the cleaner. In the latter case, for improper execution of the solution, the jury may (but not necessarily) make a separate decision to reduce the total score for the implementation of the relevant task. The jury should ensure that the same criteria are applied to the work of all participants. Upon completion of the inspection of the works, the developed criteria together with the results should be available to all participants of the Olympiad. On their basis, an appeal is made. All participants participating in the Olympiad of the 3rd stage, with their participation, agree to the disclosure of their personal data used by the organizing committee and the jury when summarizing the olympiad – full name, educational institution, teacher's full name, the result of the Olympiad and appeal, etc.

__Scientific and methodological support of the 3rd stage of the Olympiad__

When drawing up the tasks of the 3rd stage of the All-Ukrainian Student Olympiad in Mathematics, the topics and format of tasks of the 3rd and 4th stages of the Olympiad of previous years, published in the manuals, are taken into account:

- Mathematical Olympiad competitions of schoolchildren. 2006–2007. Aikoushin A.V., Arman A.R. and others – K.: Letter, 2008 – 224c.
- Mathematical Olympiad competitions of schoolchildren of Ukraine. 2006–2007. Aikoushin A.V., Arman A.R. and others – K.: Letter, 2008 – 135c.
- Mathematical Olympiad competitions of ukrainian schoolchildren: 2007-2008 and 2008-2009 (per edit. Would.In.Rublev). — Lviv: Kamenyar, 2010. — 549 p.
- Mathematical Olympiad competitions of schoolchildren of Ukraine: 2009-2010 (edit. Would.In.Rublev). — Kharkiv: Gymnasium, 2011. — 320 p.
- Mathematical Olympiad competitions of schoolchildren of Ukraine: 2010-2011 (edit. Would.In.Rublev). — Kharkiv: Gymnasium, 2013. — 368 p.
- Mathematical Olympiad competitions of schoolchildren of Ukraine: 2011-2012 (edit. Would.In.Rublev). — Kharkiv: Gymnasium, 2013. — 416 p.
- Mathematical Olympiad competitions of schoolchildren of Ukraine: 2012-2013 (edit. Would.In.Rublev). — Kharkiv: Gymnasium, 2014. — 401 p.
- Mathematical Olympiad competitions of schoolchildren of Ukraine: 2013-2014 (edit. Would.In.Rublev). — Kharkiv: Gymnasium, 2015. — 465 p.
- Mathematical Olympiad competitions of schoolchildren of Ukraine: 2014-2015 (edit. Would.In.Rublev). — Kharkiv: Gymnasium, 2016. — 464 p.
- Mathematical Olympiad competitions of schoolchildren of Ukraine: 2015-2016 (edit. Would.In.Rublev). — Kharkiv: Gymnasium, 2017. — 464 p.
- Mathematical Olympiad competitions of schoolchildren of Ukraine: 2016-2017 (edit. Would.In.Rublev). — Kharkiv: Gymnasium, 2018. — 464 p.
- Mathematical Olympiad competitions of schoolchildren of Ukraine: 2016-2017 (edit. Would.In.Rublev). — Kharkiv: Gymnasium, 2019. — 464 p.
- Ukrainian Mathematical Olympiads. handbook. V.A.Vyshensky, O.G.Hanyushkin and others. – K.: High School, 1993. – 415c.
- Kiev Mathematical Olympiads 1984-1993 biennium Collection of tasks. V.A.Vitshensky, M.V.Kartashov and others. – K.: Lybid, 1993. – 144c.
- Kyiv City Mathematical Olympiad 2003-2011 (per edit. Would.In.Rublev). — Kharkiv: Gymnasium, 2011. — 192 p.

It is also suggested that you use the following Internet sources:

**matholymp.com.ua**is a site of Kyiv and All-Ukrainian olympiads and tournaments in mathematics, where you can find the texts of tasks, results and conditions of mathematical competitions held in Ukraine over the past two years**http://imo-official.org –**site of international olympiads in mathematics

GLORY TO UKRAINE!!!

GLORY TO THE HEROES!!!

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