The monograph is devoted to teaching students to solve mathematical tasks on the updated program. From the standpoint of the activity approach, the manual presents a system of tasks, that have the properties of structural completeness, i.e., the construction of taking into account the principle of integrity (text tasks, equation (inequality) of all kinds), to master such important mathematical methods as geometric transformations, vector, coordinate. This monograph is addressed to specialists in the field of theory and methods of teaching mathematics, applicants engaged in the field of education, as well as teachers of mathematics in the secondary school system.