Each state sets its own curricular standards and details are usually set by each local school district.
In the United States, mathematics curriculum in elementary and middle school is integrated, while in high school it traditionally has been separated by topic, like Algebra I, Geometry, Algebra II, each topic usually lasting for the whole school year.
Algebra I, also known as elementary algebra or beginning algebra, is the first course students take in algebra. Historically, this class has been a high school level course that is often offered as early as the seventh grade but more traditionally in eighth or ninth grades. The course is also offered in community colleges as a basic skills or remedial course.
Geometry is usually taken in a student’s 2nd year of high school. The course introduces concepts such as basic trigonometry, angles of elevation and depression, and methods of proving triangle congruence.
Algebra II, advanced Algebra or intermediate algebra has a prerequisite of Algebra I. Historically, intermediate algebra has been a high school level course.
The Common Core mathematical standards recognize both the sequential as well as the integrated approach to teaching high-school mathematics, which resulted in increased adoption of integrated math programs for high school. Accordingly, the organizations providing post-secondary education updated their enrollment requirements. For example, University of California requires three years of “college-preparatory mathematics that include the topics covered in elementary and advanced algebra and two- and three-dimensional geometry” to be admitted. After California Department of Education adopted Common Core, the University of California clarified that “approved integrated math courses may be used to fulfill part or all” of this admission requirement.
The above three-course sequence is followed by a course often called pre-calculus for college-bound students. Pre-calculus usually combines advanced algebra (or “Algebra III”) and geometry with trigonometry.