Introduction. The degree of mathematical culture is determined by the level of correct perception and mastering of the studied material. The article considers the expediency of using the synthetic method in solving problems in mathematics.

Materials and Methods. The study defines the level of complexity and difficulty of the problem for correct choice of the method of its solving. Special attention is given to the development of logic of thinking in the application of synthesis. As a main method, the authors suggest synthetic method of problem solving, which is inextricably linked with analytical method. They are often combined into a single whole and called analytical-synthetic.

Results. The research includes tasks included in the base of Unified State Exam (USE) and their solutions by means of synthetic method. The solution to any task should be brought to a logical perception of all the work done on the optimal use of all data, not only numerical, but also textual, tasks. The results show the necessity of increasing use of mathematical data of the task based on the fundamental knowledge of basic terms and theorems of classical mathematical education in Russia. Choosing a solution method is always a creative process. It can reveal the existence and, at the same time, improve the knowledge not only in algebra and geometry, but in other subjects which are being studied and have been already learned.

Discussion. The starting point in the choosing the method for problem solving is the conditions of a problem. While the analytical method usually requires the conditions themselves, the question of the problem.

Conclusion. The synthetic method in problem solving, considered in this article, can be applied to various tasks in physics, chemistry, geography, and other subjects.