Saransk, Russian Federation
The article reveals the role of equations at the basic and profi le levels of teaching students mathematics at school. Various ways of solving rational equations of the third and fourth degree, based on the technique of the introduction of a new variable, are demonstrated. This technique is universal in mathematics. It fi nds its application both in algebra, in the solution of inequalities, in equations and their systems, and in geometry, where the additionally constructed geometric fi gure — a segment, an angle, a circle, a triangle — appears as a new variable. The methods of solving rational equations, shown by the author in this article, will be especially useful and interesting for students of profi le classes, as well as for applicants and students of higher educational institutions and mathematics teachers.
profi le teaching, equation, rational equation, introduction of a new variable.
Интеллектуальный потенциал общества, являющийся важнейшим фактором экономического роста и социального развития страны, ее политической самостоятельности, напрямую зависит от качества образования.
1. Kontseptsiya dolgosrochnogo sotsial’no-ekonomicheskogo razvitiya Rossiyskoy Federatsii na period do 2020 goda: rasporyazhenie Pravitel’stva RF ot 17.11.2008 № 1662-r (red. ot 10.02.2017): razrab. v sootvetstvii s porucheniem Prezidenta RF po itogam zasedaniya Gosudarstvennogo soveta RF, sostoyavshegosya 21 iyulya 2006 goda. Dostup iz elektronnogo fonda pravovoy i normativno-tekhnicheskoy dokumentatsii [The concept of long-term socio-economic development of the Russian Federation for the period up to 2020: the decree of the Government of the Russian Federation of November 17, 2008 No. 1662-r (as of 10.02.2017): developed. in accordance with the instruction of the President of the Russian Federation on the results of the meeting of the State Council of the Russian Federation, held on July 21, 2006. Access from electronic fund of legal and normative technical documentation]. Available at: http://docs.cntd.ru/document/902130343
2. Kontseptsiya profil’nogo obucheniya na starshey stupeni obshchego obrazovaniya: prilozhenie k prikazu Minobrazovaniya Rossii ot 18.07.2002 №2783: odobr. na zasedaniyakh Federal’nogo koordinatsionnogo soveta po obshchemu obrazovaniyu 24.04.2002 i 28.06.2002 : dorab. po otzyvam, postupivshim iz sub”ektov Rossiyskoy Federatsii (mayiyun’ 2002 goda), i rezul’tatam 2-go Vserossiyskogo soveshchaniya po profil’nomu obucheniyu (28.06.2002). Dostup iz elektronnogo fonda pravovoy i normativno-tekhnicheskoy dokumentatsii [The concept of profi le education at the higher level of general education: an annex to the order of the Ministry of Education of Russia from July 18, 2002 № 2783: approved. at the meetings of the Federal Coordinating Council for General Education on 24.04.2002 and 28.06.2002: dorab. according to the responses received from the subjects of the Russian Federation (May-June 2002), and the results of the 2 nd All-Russia meeting on profile training (28.06.2002). Access from electronic fund of legal and normative technical documentation]. Available at: http://docs.cntd.ru/document/901837067
3. Vasil’eva M.V., Bozhenkova L.I. Profi l’noe obuchenie matematike v kontekste realizatsii FGOS obshchego obrazovaniya [Specialized training in mathematics in the context of the implementation of the GEF of general education]. Profi l’naya shkola [Profile school]. 2016, V. 4, I. 5, pp. 21-30.
4. Ul’yanova I.V., Lyubimtseva T.V. Zadachi kak sredstvo obucheniya uchashchikhsya profi l’nykh klassov nachalam matematicheskogo analiza [Tasks as a means of teaching students of specialized classes the beginnings of mathematical analysis]. Uchebnyy eksperiment v obrazovanii [Educational experiment in education]. 2016, I. 1(77), pp. 31-35.
5. Grigoryan M.E., Boldyrevskiy P.B., Zalesskiy M.L., Troitskiy R.V. Teoriya i metodika obucheniya shkol’nikov resheniyu uravneniy [Th eory and Methods of Teaching Schoolchildren for Solving Equations]. Mezhdunarodnyy zhurnal eksperimental’nogo obrazovaniya [International Journal of Experimental Education]. 2017, I. 8, pp. 28-33.
6. Algebra i nachala matematicheskogo analiza. 11 klass [Algebra and the beginning of mathematical analysis. 11 class]. Moscow, Mnemozina Publ., 2010. 264 p.
7. Pratusevich M.Ya. Algebra i nachala matematicheskogo analiza. 10 klass. Profi l’nyy uroven’ [Algebra and the beginnings of mathematical analysis. Grade 10. Profi le level]. Moscow, Prosveshchenie Publ., 2009. 415 p.
