Abstract and keywords
Abstract (English):
The article focuses on the application of tasks containing a variable under the sign of the module in problems of mathematical olympiads. The results are obtained: the topics of the section are determined, on the basis of which the conditions for the olympiad problems of the republican olympiad are compiled, the goals and requirements for studying the absolute value in the olympiad program are determined, 5 main methods for solving equations with a module are identified: methods for sequentially opening modules, intervals, graphical, determining the dependencies between numbers a and b, their modules and squares, geometric interpretation of the module. In the course of the study, conclusions were drawn: due to the increasing complexity of the olympiad problems, there is a need to familiarize students with different methods for solving the olympiad tasks with a module in the system of additional education.

olympiad, olympiad tasks, module of number, equation with module, inequality with module, graph, solution methods

1. Bajsalov Dzh.U., Keldibekova A.O. Metodicheskie priemy resheniya olimpiadnyh zadach po matematike [Methodological methods for solving olympiad problems in mathematics]. Osh: Book-dizajn Publ., 2018. 114 p.

2. Kostrikina N.P. Zadachi povyshennoj trudnosti v kurse algebry 7-9 klassov [Problems of increased difficulty in the course of algebra of grades 7-9]. Moscow: Prosveshchenie Publ., 1991. 239 p.

3. Okunev A.A. Spasibo za urok, deti! [Thanks for the lesson, kids!]. Moscow: Prosveshchenie Publ., 1988. 128 p.

4. Olimpiadnye zadachi po vsem razdelam matematiki. Edinaya kollekciya Cifrovyh obrazovatel'nyh resursov [Olympiad problems in all areas of mathematics. A single collection of Digital Educational Resources]. Available at: http://school-collection.edu.ru/catalog/rubr/1040fa23-ac04-b94b-4a41-bd93fbf0d55a/25352

5. Predmetnyj standart po predmetu «Matematika» dlya 10-11 klassov obshcheobrazovatel'nyh organizacij Kyrgyzskoj Respubliki [The subject standard for the subject “Mathematics” for grades 10-11 of educational institutions of the Kyrgyz Republic]. Bishkek, 2018. 71 p.

6. Ryazanovskij A.Ya. 500 sposobov i metodov resheniya zadach po matematike [500 ways and methods of solving problems in mathematics]. Moscow: Drofa Publ., 2001. 480 p.

7. Skopenkov A.B. Olimpiady i matematika [Olympiads and mathematics]. Mat. Prosveshcheniya [Mat. enlightenment]. 2006, I. 10, pp. 57-63. Available at: http://www.mathnet.ru/links/cb6d47b4ddb141a5aa75173332b15006/mp186.pdf

8. Cheung Pak-Hong Problem solving strategies - research findings from Mathematics Olympiad. Department of curriculum studies the university of Hong Kong. [Elektronnyj resurs]. Available at: https://kupdf.net/download/problem-solving-strategies-research-findings-from-mathematics-olympiad-ph-cheung-pdf_58fc5aa2dc0d60af27959eba_pdf

9. Moshe Stupel A special application of absolute value techniques in authentic problem solving//International Journal of Mathematical Education. 2013. I. 44 (4). DOI:https://doi.org/10.1080/0020739X.2012.729685

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