Algebra II textbooks illustrate the fundamental principles of algebra, which include the mathematical study of symbols and the manipulation of symbolic equations. Symbolic equations can be used to describe problems important for diverse topics in many practical fields, including science, technology, economics and engineering.
Arithmetic deals with the manipulation of numbers and equations involving numbers, and algebra builds upon this by introducing abstract symbols as mathematical objects. Algebra II is meant to cover all of the most important topics within the study of algebra and prepare a student for higher level topics in mathematics that require a background in algebra, such as calculus and analysis.
Most Algebra II textbooks explain the most common types of algebraic equations and functions, including equations and functions with quadratic, polynomial, logarithmic, exponential, radical and trigonometric components. Real and complex functions as well as the relevance of algebra for trigonometry and probability are also typically taught. Real-world applications, such as exponential growth in biology, are also introduced.
Sequences and series are explained in Algebra II as well, which gives the student a good foundation for understanding calculus. Also, matrices and linear systems are usually introduced, which is especially useful if a student goes on to study linear algebra and differential equations.
Another important aspect of Algebra II is the understanding of graphs. Graphs can be used to visualize and interpret most of the functions that algebraic equations describe.