Methods of Solving Problems in High-School Mathematics

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In this educational aid, intended for high-school students, an attempt has been made to classify the problems encountered in high-school mathematics by their solution methods. The goal of this book is a challenging one. On one hand, a detailed classification of problems by methods of solution would require the consideration of a large number of applied problems. On the other hand, a topical classification would not yield a useful aid for solving different kinds of problems. Therefore, alongside a large number of worked problems, the book includes about 2, 500 problems for the reader to solve. In addition to the traditional problems from the course of high-school mathematics, the book includes methods for solving simple differential and integral calculus problems as well as problems which require the use of coordinates and vector algebra. These sections only include problems whose solutions require knowledge that is beyond the scope of high-school mathematics. Some problems in the book can only be solved by a combined application of the knowledge from the traditional and new divisions of mathematics. These include, for instance, problems connected with the calculation of limits, derivatives and integrals of functions which must first be simplified by means of identity transformations. The authors consider all the most frequent methods of solving problems from the high-school course of mathematics. The fact that many problems are not followed by their solutions makes it possible to use the book to prepare for the entrance tests for higher educational establishments.