The proposed manual provides material for preparing for solving problems such as S5 on the exam in mathematics, devoted to equations, inequalities and systems with a parameter. On numerous examples with detailed solutions and justifications, various types of problems and methods for solving them are considered. For the convenience of using the book, a brief theory and reference materials are provided, and at the end of each paragraph - problems for self-solution. The manual is intended for high school students, applicants, mathematics teachers, students of pedagogical universities, students of preparatory departments of universities, methodologists and tutors.