Summary high School Mathematics in the USA I am a young postdoc at a large crowded university in the USA. Also, I am not from the USA, so my school experience has been very different from the high school experience of my students. 

Since I am teaching mathematics classes, I wonder whether there is a good and comprehensible summary the American students have seen in their high school mathematics classes. 

Given the fractured education system in the USA, good and comprehensible may be mutually exclusive, but the question is worth a try.
Every state has their own standards of what is covered in high school math classes. Many states (but not all) modeled their standards on the Common Core standards found in this link. http://www.corestandards.org/Math/

The topics covered are sorted into the categories of 1. Numbers 2. Algebra 3. Functions 4. Geometry and 5. Statistics and Probability. Each category gives more specific standards students are expected to master.

If you would like to see how topics covered by standards are presented good resources are EngageNY (https://www.engageny.org) which provides sample lessons/worksheets for the entire Curriculum. One note is most most teachers I knew who used EngageNY would modify/scaffold the material extensively for their students. Also to see sample exams JMAP has archives of New York's standardized tests by year/subject http://www.jmap.org/JMAP_REGENTS_EXAMS.htm and also with questions sorted by standard http://www.jmap.org/JMAP_REGENTS_BOOKS.htm

An important note is that Common Core standards go up through Algebra II but it is possible that some or even most of your students also took Pre-calculus and maybe even Calculus in High School as well. If you want to see what might be covered in a high school Calculus class one option is you can look at the course overviews for Advanced Placement calculus https://apcentral.collegeboard.org/pdf/ap-calculus-ab-course-overview.pdf?course=ap-calculus-ab and http://media.collegeboard.com/digitalServices/pdf/ap/ap-course-overviews/ap-calculus-bc-course-overview.pdf