States and school districts generally follow The National Council of Teachers
of Mathematics "Principles and Standards for School Mathematics"
(http://standards-e.nctm.org/1.0/89ces/Table_of_Contents.html).
In mathematics as in science, the standards are grouped into
grades K-4, 5-8 and 9-12.
With such a wide range of grades and math contend within
each of the three groups, you may want to check
with the teacher on their classes' specific knowledge and
math skills. For example, in K-4 the
standards discuss that all students should know how to multiply even
though that skill is generally not taught until the 3rd grade.
In high school, students following a college-bound curriculum may be
exposed to more advanced math concepts which have been noted.
For grades 9-12 you can expect students to know
or be learning the following:
Students use multiple mathematical solution techniques
from different math topics they have studied to solve problems.
Students may be introduced to mathematical arguments, logic, theorems, proofs
and the use of counterexamples.
Students advance their skills in algebra and are able to work with and
formulate equations, inequalities and matrices. They are able to use
tables and graphs to express algebraic solutions.
Students continue their study of 2 and 3D geometry. The concepts of similarity
and congruency are introduced. Students may be taught to draw
and understand 3D diagrams of objects. College-bound students
may be introduced to the concept of a vector.
Students study trigonometry including sine and cosine functions. College-bound
students may also study circular functions, polar coordinates and complex
numbers.