Elementary algebra that is studied in secondary schools focuses on explaining the basic techniques of manipulating equations, figures, numbers, unknowns, as well as abstractions such as fields and sets. Arithmetic, which is sometimes confused with algebra, works with numbers and direct operations where as algebra finds itself surrounded by letters which can represent a huge array of values. It is also an improvement over the earlier use of words and figures in place of equations.
Most students find themselves studying everything from finding x values, solving equations, determining sets, composing and breaking apart functions, on top of discovering real life applications of these methods. The most common topic studied is the quadratic equation. Along with this equation comes factoring, FOIL, roots, parabola graphing, quadratic formula, and future application in geometry and trigonometry.