This article continues the author's description of three years of experience with the elective course "Solving Problems with Parameters." This course was piloted as part of a science club for cadets, students, and students of the Economics Department of the Academy of the Federal Penitentiary Service of Russia. The course content was tailored to the specifics of the second part of the Unified State Exam in advanced mathematics and will be of interest to high school students aiming to score over 80 points on this exam. The article describes the most visual way to develop students' understanding of absolute value through the properties of symmetry, using a system of specially selected examples that gradually increase in complexity and abstractness. At the same time, students' knowledge of the main topics of the school mathematics curriculum is reviewed and systematized.
elective course, problem solving with parameters, visual-figurative thinking, symmetry, graphs of functions containing expressions under the modulus sign
1. Pozdnev M.M. Kniga sochinitelya [The Author’s Book]. St. Petersburg, Amphora, 2008. 319 p. EDN: https://elibrary.ru/QTQINH
2. Hermann Weyl. Symmetry. Princeton, Princeton University Press, 1952.
3. Maskina M.S. Introduction propaedeutic course visual geometry to ensure the requirements of the FSES. Profil'naya shkola [Profession-Oriented School], 2017, V. 5, I. 1, p. 44-49. DOI: https://doi.org/10.12737/24367; EDN: https://elibrary.ru/YHOJEL
4. Maskina M.S., Vidov S.V. Consideration of specific psychological features of cadets of FPS of Russia academy when training in disciplines of information and technical and mathematical orientation. Vedomosti ugolovno-ispolnitelnoj sistemy [Journal of the penitentiary system], 2019, no. 8 (207), p. 22-29. EDN: https://elibrary.ru/OGUQLY
5. Maskina M.S. Use of algorithmic method of teaching when organizing classes in the mathematical disciplines. Standarty i monitoring v obrazovanii [Standards and Monitoring in Education], 2020, V. 8, I. 5, p. 43-48. DOI: https://doi.org/10.12737/1998-1740-2020-43-48; EDN: https://elibrary.ru/WYOHRW
6. Maskina M.S., Kuptsov M.I. Generalization and systematization of knowledge in preparation for solving the most complex problems of the Unified State Exam in advanced mathematics Standarty i monitoring v obrazovanii [Standards and Monitoring in Education], 2024, V. 12, I. 1, p. 18-23. DOI: https://doi.org/10.12737/1998-1740-2024-12-1-18-23; EDN: https://elibrary.ru/KHEWCY
7. Bank zadanij EGE` i OGE` po vsem osnovny`m predmetam [Bank of tasks for the Unified State Examination and the OGE in all major subjects] Available at: https://bank-ege.ru/ege/matematika-oge/tasks/task22/223-funkcii-s-modulem (accessed 25 October 2025).
8. EGE`. Matematika. Profil`ny`j uroven`: tipovy`e e`kzamenacionny`e varianty: 36 variantov [Unified State Exam. Mathematics. Profile level: standard examination options: 36 options]. Edited by I.V. Yashchenko. Moscow, Narodnoe obrazovanie, 2026. 224 p.
9. Kolmogorov A.N. Matematika – nauka i professiya [Mathematics is a science and a profession]. Moscow, Nauka, 1988. 288 p.
10. Maskina M.S., Davydochkina S.V. On the development of synthetic thinking in scientific circle classes with cadets of the Academy of the Federal Penitentiary Service of Russia. Vedomosti ugolovno-ispolnitelnoj sistemy [Journal of the penitentiary system], 2023, no. 8, p. 73-80. DOI: https://doi.org/10.51522/2307-0382-2023-255-8-73-80; EDN: https://elibrary.ru/DNZNRJ
11. Sbornik zadanij osnovnoj volny` EGE`-2024 po matematike [Collection of tasks for the main wave of the 2024 Unified State Exam in Mathematics] Available at: https://4ege.ru/matematika/70666-sbornik-zadanij-osnovnoj-volny-ege-2024-po-matematike.html (accessed 25 October 2025).
12. Kuptsov M.I., Maskina M.S., Moiseev S.A. Edinyy gosudarstvennyy ekzamen kak instrument monitoringa sostoyaniya shkolnogo matematicheskogo obrazovaniya [The Unified state exam as a tool for monitoring the state of school mathematics education]. Nauchnoe obozrenie. Seriya 2. Humanitarniye nauki [Science review. Series 2: Humanitarian science], 2014, I. 4-5, p. 132-134. EDN: https://elibrary.ru/TAHCZL
