*Features of the 3rd stage of the Olympiad**Table of contents, scope, and difficulty of shared 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 will be held in January 2022, the 1st round is scheduled for Sunday, January 23, the 2nd round – on Sunday, January 30.

*1.Features of the 3rd stage of the Olympiad *

For organizing committees and jury of iii stages of All-Ukrainian Olympiads in the regions and the city of Kyiv we recommend three options for the III stage of the Olympiad.

1 option. In accordance with the "Regulations on olympiads …" both tours of the 3rd stage of the All-Ukrainian Student Olympiad in Mathematics to conduct according to the tasks developed by the Institute for the Modernization of Educational Content (IZO). In this case, tours in the respective regions are held on January 23 and 30, 2022. 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. At approximately 14:00 conditions with complete solutions to the problems of the third stage of the Olympiad in mathematics will be sent to the regions, and at 16:00 – posted on the website of matholymp.com.ua.

In each region, the jury independently develops criteria for evaluating each task, according to which the participants check the solution of tasks. 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 only the 2nd round of olympiads in the region are conducted on the tasks developed by the IZO, and the other tour – on their own tasks. Then, for a joint tour, the region must choose the appropriate period of the Olympiad.

*Remarks .* Under any conditions, we ask the jury and the organizing committee of the Olympiads of the THIRD stage in the regions to prepare alternative tasks for both rounds. Due to the fact that it is guaranteed to predict the spread of the COVID-19 virus both in the world and in Ukraine, it is necessary to be prepared for various surprises (not always pleasant) regarding quarantine restrictions that can be introduced in certain regions or throughout the country. This may make it impossible to hold an Olympiad on common texts in some areas. Let's hope it doesn't happen, but it's better to be prepared for any adversity.

*2.Content, scope and level of complexity of joint 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 based on the previously studied material.

The tasks of the 1st round consist of 4 tasks for the 7th grade and 5 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 (180 minutes), for all other classes and for all classes in the 2nd round – 4 astronomical hours (240 minutes).

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, the established practice of conducting mathematical Olympiads in Ukraine and the world.

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, which will work on the common texts of the Olympiad of the THIRD stage, will receive tasks of 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, a Level B task differs from the A-level tasks in the last task, and the B-level task differs from the B-level tasks in the penultimate task.

In the case of the 3rd stage of the All-Ukrainian Olympiad under option 1 or 3 of the organizing committees and/or the jury of the 3rd stage, which decided to conduct the 1st and/or 2nd round on the tasks provided by the IZO, they must 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 a single text:

**rublyovbv@gmail.com** (Bogdan Rublev, Chairman of the Jury of the 3rd Stage of the All-Ukrainian Olympiads in Kyiv, 0683892107, 0505613964);

**kodzarina16@gmail.com** (Kodyrova Zarina, member of the organizing committee of the 3rd stage of the All-Ukrainian Olympiads, 0951285223);

**anik_andrii@ukr.net** (Andriy Aikoushin, member of the Task Commission of the 3rd stage of the All-Ukrainian Olympiads, 0637103420).

Conditions will be provided 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.

*3. Evaluation of works of participants of the 3rd stage of the Olympiad*

To evaluate the work, 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 are set at a certain meaningful advance towards the correct solution.
- 0 points – there are no correct and meaningful advances towards the correct solution of the problem.

The jury checks only the tasks recorded in the cleaner of the olympiad participant. The draft is not considered by the jury. When evaluating Olympiad works, rationality or irrationality of solutions, method and way of solution, as well as the volume of written are not taken into account. If the jury cannot disassemble the participant's handwriting (the words are written completely inaudible or can be read in several ways, etc.), then the jury should evaluate in this problem only the part of the solution that could be dismantled. 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 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.

*4. 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 ukrainian schoolchildren: 2017-2018 (edit. Would.In.Rublev). — Kharkiv: Gymnasium, 2019. — 464 p.
- Mathematical Olympiad competitions of ukrainian schoolchildren: 2018-2019 (edit. Would.In.Rublev). — Kharkiv: Gymnasium, 2020. — 464 p.
- Mathematical Olympiad competitions of ukrainian schoolchildren: 2019-2020 (edit. Would.In.Rublev). — Kharkiv: Gymnasium, 2021. — 496 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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