HS math is elementary algebra, trig and precalc for most, and calc for some toward the end. Depending on where you are, you have some input on what you actually take. About halfway through high school, I stopped trying to be 'cool' and just realized that I had an aptitude for math and so I should probably actually study calc ASAP. I requested to take calc during senior year but I was told that because I hadn't taken enough math in sequence, this would not be possible. Later I ended up taking a (here) standard university calculus sequence and completing a bachelor's with a math major. Some of the last things I was exposed to in HS math were De Moivre's theorem and the "rational root test" (which I've since forgotten but been meaning to re-learn).
HS Physics is not calc based, but the graphical notion of a derivative was introduced (in my case) as it relates to physics inquiries. Vectors and SI units are introduced, and there are simple "design things" projects and spring-loaded newton-measurements. I actually read almost all of my HS physics textbook cover-to-cover in my free time. My personal trouble was that most students had a personal dislike of the teacher (myself included), but again I figured I ought to know these things. Later there's basic terminology of electricity derived SI units, and even a little particle physics exposure (I once begged off a different class to listen to a researcher who had spent time at the neutrino lab at the south pole). I have never taken a university level physics course.
>>7846584 In American high schools you can take a particular level of class called Advanced Placement (AP) where it's essentially the equivalent of a university level course.
So at the end of the year you take exams for your AP classes and if you score high enough (and if your university allows it) then you can get credit for the equivalent college level course.
In that earlier poster's example, AP Physics C is a class you can take in high school that's the equivalent of calc-based mechanics and E&M that you'd take as intro college courses. If he scores well enough on his exams at the end of the year then hopefully he can get credit for intro mechanics and E&M in college.
Also in America calculus is split up into three courses. Calc I is differential calculus, calc II is integral calculus, calc III is multivariable and vector calculus. Most high schools offer AP Calculus AB and BC which are the equivalent of Calc I and II at the college level. If you go to a very science and math intensive high school like mine was then chances are they will offer calc III and differential equations that you can take for college credit as well.
There really isn't a "standard" curriculum for math and science in the US. It all depends on how far you want to go. When I was in high school I took through calc III and differential equations and three other AP science classes but I never took AP physics.
I just wanna round this out with what I remember of HS bio and chemistry.
At that point in my life, I was more interested in chemistry, and I took everything I could get short of AP. Again you actually play with chemicals at the heavy lab desks, the teacher showed us where the eyewash was, and we learned significant figures, nomenclature, orbital theory/why the table is the way it is, and just the littlest bit about quantum stuff, and the names around these. When I did take a uni-level first-year chem sequence, it was basically re-hashing what I already knew from HS, (just slightly harder exams) so I found it fairly easy.
I found HS bio to be a bit confusing (understanding processes, something about RNA and similar that didn't stick with me), but the names part was easy. during HS bio classes I dissected a fetal pig, and we went to a cadaver lab at a university and were allowed to see and handle a male and female cadaver. I held an RL human brain in my hands before I was 18 years old. However, I also have never taken a university-level biology course.
Naive set theory (NZQRC), Complex numbers (I mentioned De Moivre's theorem which implies them) and polar coordinates were introduced in HS, and sequences and series (sigma notation) were also introduced. I should also say that they just scratched the surface of what a limit was, but I didn't know what it actually was until I went to uni (in my first few weeks of calc I didn't get that a limit may differ from a function's value/lack of value, but of course one has to learn that quickly) so integrals were not ready, but HS teachers had calc books in their rooms and I realized I wanted to know what the symbols meant. Those things looked so intimidating to me as a kid!
The average student probably completes pre-cal his senior year. I took the easiest math classes I could and remember doing something vaguely pre-cal. My teacher gave up on teaching the "hard" parts because we were lazy seniors and I suspect many others do the same.
But I know plenty of kids who took AP exams which basically amounted to college cal.
At my high school: algebra I, algebra II and trig, geometry l, advanced algebra, precalc, math history, calc, multivariate, linear algebra, diff Q's, statistics, advanced euclidean geometry, math applied to financial markets, discrete math, actuarial math, logic, math research, programming, other cs related.
There was probably a stats course available, but I didn't take one in HS (or college for that matter!). Some word problems and combinations/permutations relating to probability were sprinkled throughout, but never as a devoted treatment.
Geometry was "introduced" very early on, just past elementary algebra and the quadratic theorem. This was my (and therefore the rest of the class') first lifetime exposure to how mathematical proofs actually work. A large portion of our early geometry work was given over to proving that such-and-such (usually triangles) are congruent, or not. We would organize our arguments into two columns, making observations in the left, with their supporting statements or theorems "reasons" at right: "SAS, SSS, AAA..." Later, I anticipated that both the right-isosceles triangle and the "30-60-90" triangle were special, which set me up very nicely to learn trig.
On my own, I derived formulas for the area of such-and-such a regular polygon in terms of its sides, and sitting in german class, I started playing with the fibonacci sequence and I realized that the ratios of its successive terms tend toward Φ, le ebin golden ratio xD. That was a big deal to me at the time.
>>7846614 Thanks; I think I get the American schooling system now. Where I'm from, we tend to do 3 Advanced Levels (or 4/5 if we're really smart) spread across 2 years. A levels seem a lot more comprehensive though, but I'm guessing that many more than 3 APs are taken or that they're taken alongside other qualifications. E.g. one can take an A level in Mathematics with Statistics, which covers all 3 forms of calculus you mentioned, coordinate geometry, surds, trig, etc., with multiple areas being combined (such as integration of a disguised quadratic trig function).
>>7846726 >HS Physics is not calc based, but the graphical notion of a derivative was introduced (in my case) as it relates to physics inquiries. Vectors and SI units are introduced, and there are simple "design things" projects and spring-loaded newton-measurements. That doesn't sound like a complete physic programm ^^
>>7846702 Coming from a guy who studied internationally (US born), European studies are much more rigorous and theory based, and Asian studies are calculation intensive.
US high school rigor seems to focus on application and fundamentals, but theory is becoming more important as classes adopt to teach as universities do. The rigor is also very sporadic and can very greatly even in neighboring public schools
standing waves vs traveling waves. EM spectrum. Visible light, UV, IR, gamma/ radio, etc. Newton's three laws. Kepler's laws (astronomy). The notion of entropy, and laws of thermodynamics (which escape me atm) Derived SI units for electricity, and the simple laws relating them Volts, Ohms, etc. I always found it odd that the Ampere was fundamental, while the Coulomb was derived. Right-hand rules. Quantum stuff was just talked about in a general way, much moreso in Chemistry for obvious reasons. There you had things like the black body experiment, spin, pauli exclusion principle, maybe a De Broglie wavelength (I forget). Moles, but I'm digressing back into chemistry.
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