In my country "politics" is a synonym of "corruption". As in people who take money under the table to do things around the law.
Btw, another American thing I've never understood - the concept of college. I mean, is it some kind of middle stage between high school and higher education? In my country, for as long as I can remember and even before I was born, the concept has always been that: 1st through 12th grade (which includes high school; starts at age 6-7), then you graduate from that at the age of 18-19 (12th grade), and after that comes the university (the higher education) which (usually) lasts 4 years, or longer, if you go for the "doctor of whatever" or "master of whatever" titles. There's an American college in my country but many of us, myself included, still don't understand how the college fits in all that.
Also, at what ages do you start and finish school in USA? There was this... I guess you could call it a "hearsay" some time ago that what we learn in 6th grade, Americans learn in 9th or 10th grade. Like, in 6th grade we learn about equations of the type "ax + b = 0" and raising to power. And the hearsay was that Americans learn these things much later than 6th grade.
I'll be honest, almost everything you said about America here is incorrect.
While corruption exists in American politics, it's not synonymous like you're describing. There are certainly corrupt politicians, but it's not the majority, and the widespread bribery you're describing just isn't part of American culture.
College is just another word for University, both of which are the "higher education" you're talking about. While there are community colleges, which are kind of like an extra step between high school and university (higher education as you're calling it), that's still part of the university track. Someone might go to community college for 2 years, then finish out their university degree for another 2 years (4 years total for the standard higher education bachelor's degree). It's not a rule written in stone, though; some people take 5-6 years for a bachelor's because they're doing it part-time, some people cram and finish in 3 years. There's also post-graduate education, which is Masters and PhD programs, both of which are what Americans would call 'higher education' - effectively, these are the training to become a Professor.
Standard ages vary for Americans in schooling, and some places have the break points slightly different, but the usual process I recall is:
Pre-school (optional) - 3-5 years old
Kindergarten - 5-6 years old
Elementary School (a.k.a. primary school or grade school) - 6-12 years old, 1st through 6th grade
Middle School (a.k.a. junior high school) - 12-14 years old, 7th and 8th grade
High School (a.k.a. secondary school) - 14-18 years old, 9th through 12th grade
College OR University - can start at 17-18 (depending on age when finishing high school; some really smart kids can and have also skipped 12th grade to go straight into university) and lasts as long as a person wants to and can afford to keep attending, with the 4-year bachelor's degree I mentioned above being the most common.
As for education topics, there's no universal nationwide curriculum order all US schools are expected to follow (nor are there even standards most schools follow; there are a few trends, and that's about it). However, basic algebraic equations, which is the type of math you're describing, are generally part of "pre-algebra", and often show up in 7th or 8th grade, depending on the school (not 9th; that is most often full-on algebra). Exponents, which is the other type of math you're describing, are usually taught during pre-algebra or a year earlier in 6th or 7th grade. Other factors that may alter the order in which subjects are learned include the district curriculum system, specific teachers, and even the individual student. For instance, I took pre-algebra in 6th grade, and was learning full-on algebra in 7th grade as an advanced student. That said, since there is no universal curriculum, and since different subjects' education progress likely varies from country to country, that doesn't tell you anything about any other subject.