This textbook provides the foundation for a second-year high school mathematics course. It aims to teach "how to study" as well as the "content" of a second unit of secondary mathematics through the nature and form of the material, explicit exhibits, formulated tests of both sound and unsound reasoning, through study-helps, directions for working, and systematic chapter summaries. "Second-Year Mathematics" may be used successfully in classes that have had only algebra during the first year. The syllabus at the beginning of the book gives all the theorems and axioms taught in "First-Year Mathematics," indicating the order in which they were given.