In this article we consider some fractional-irrational expressions and prove the assertion that reduce them to fractional-rational expressions and also consider one general lower-and-upper bound (two-sided estimate) for one numerical series.

The article deals with the geometric interpretation of complex numbers, the possibilities of applying a transformation of the plane, and examples of solving problems.

This article reveals the possibility of solving life situations with combinatorial coefficients and shows the practicality of applying formulas on the theory of probability and mathematical statistics. The solution of tasks with combinatorial coefficients consists mainly in the decomposition of these coefficients by the basic formulas and their manipulations.

This article describes the ways in which students can develop logical thinking skills. Currently, any form of the exam takes precedence over logic. Accordingly, the article grouped logical tasks and provided their solutions.

The article presents the results of studies conducted at the veterinary clinic «Jean» in the city of Pavlodar. It is noted, that for the period 2013-2017. 348 cases of disease in dogs were registered by pyroplasmosis – a protozoal disease caused by parasitic organs of the genus Piroplasma. The authors described the clinical symptoms of disease in animals, as well as the nature of the flow of infectious diseases.