What does learning high school math in america/(insert your european

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At my school you could choose between Economics, Greek, Latin, "Modern Languages", Sciences or Math.

At most you could get 8 hours math a week which included Calculus I and Linear algebra. Though not all that advanced.
I think the lowest you could get was 2 hours which probably only coveed the stuff you said in OP.

>Romanian hs
Off the top of my head, in 9th and 10th grade you have trig, vectors, complex numbers, logs, counting. 11th grade has differential calc, series, linear algebra. 12th grade has integral calc and abstract algebra

>>9123020
>At my school you could choose between Economics, Greek, Latin, "Modern Languages", Sciences or Math.
Well, here we couldn't choose anything, we had like 250 minutes every week for each subject (the last important ones we had 50/100 minutes). You had to take math, physics, biology, history geography, chemistry, arts, portuguese and english.

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File related is the exam I took back in 2010. You won't get all of the questions I guess, but you can get the gist of it.

>>9123084
That's pretty good. What kind of exam is that?

>>9123095
The "Maths B, vwo level"
Dutch high school education, broadly speaking, is divided into three levels
>VMBO, low tier, 4 years
>HAVO, middle tier, 5 years
>VWO, high tier, 6 years
Then, at least in HAVO/VWO, you choose your subjects once you hit the second half (year 3 for Havo, 4 for VWO). Generally speaking, the "paths" are economics one way science the other. We split maths into 4 forms, depending on what you'll do you get something. Maths A is "simpler", more statistics and used by the econ lads mainly, Maths B is the more science math, maths C is a weird thing for science/econ hybrid or something, I don't know. And Maths D is an extra class you could take if you had Maths B, which is basically what Maths B didn't cover from maths A and some more advanced stuff.

>>9122990
>Burger land

Before Common Core

>Preschool
Counting
>1st Grade
Basic addition
>2nd Grade
Basic subtraction
>3rd Grade
Negative numbers, zero, big numbers
>4th grade
Times tables/fractions, inequalities
>5th Grade
Division, powers, decimals
>6th Grade
Roots, primes, factors (no Euclid's algorithm)
>7th Grade
Pre-algebra (coordinate geometry)
>8th Grade
Algebra I (single variable linear equations)
>9th Grade
"Geometry" aka Pythagorean theorem, similar triangles, and a few basic geometric definitions
>10th Grade
Algebra II: Quadratics, conics, matrices (no applications, not even solving systems of equations), polynomials (no solving cubics or quartics)
>11th Grade (10th if honors)
Trigonometry: definition of (co)sin, (co)tan, (co)sec, sin^2+cos^2=1 (no other trig identities), (1+x/n)^n definition of exp(x), logarithms
>12th Grade (11th if honors, 12th is the same but AP)
Calculus up to disk and shell methods

After Common Core

>Preschool
Counting
>1st Grade
Basic arithmetic
>2nd Grade
Basic arithmetic
>3rd Grade
Basic arithmetic and geometry
>4th grade
Basic arithmetic and geometry
>5th Grade
Basic arithmetic, algebra and geometry
>6th Grade
Basic arithmetic, algebra and geometry
>7th Grade
Basic arithmetic, algebra and geometry
>8th Grade
Basic arithmetic, algebra and geometry
>9th Grade
Basic arithmetic, algebra and geometry
>10th Grade
Algebra I (single variable linear equations) [last required math class growingly becoming optional in most schools because algebra is useless for most people]
>11th Grade
"Geometry" aka Pythagorean theorem, similar triangles, and a few basic geometric definitions
>12th Grade
Trigonometry: definition of (co)sin, (co)tan, (co)sec, sin^2+cos^2=1 (no other trig identities), (1+x/n)^n definition of exp(x), logarithms

>>9123423
That before common core is pretty spot on. I was in accelerated for 4-8 and got a bit deeper/maybe a year earlier with a lot of that stuff and had APs. Also a lot of people would have a 1 year delay to most of how you spelled out. What you listed would be a "good" student's course history. I think that may have influenced common core to be standard.

>>9122990
>I often hear that brazilian's math education is somewhat "harder" than most countries.

it's only "hard" if you're trying to get into the likes of ITA and IME. And even in that case, just normal hard, not harder top schools than elsewhere.

>>9122990
I'll only tell you what i remember so bear with me here:

Year 9: Solving quadratic functions, factoring, simple trigonometry like definitions of the main 3 ratios.
Year 10: Powers, surds, percentage formulae, recurring decimal conversions, histograms, volume of cones, spheres and pyramids, probability
Year 11: Proportion, congruence, pythagoras' theorem, estimation, simultaneous equations, cosine and sine rules, vectors, graphs of trig ratios, set notation, inverse and composite functions and differentiation.
Year 12: Completing the square, arithmetic and geometric series, integration and area under/between curves, differentiation and minima and maxima, radian measure, binomial expansion, trig identities (sin^2 + cos^2 = 1 and tan=sin/cos) and logarithms.
Year 13: Graphs of modulus, inverse trig and trig reciprocals, differentiation and integration techniques, vectors, partial fractions, more trig identities (double angle, etc), exponential function, volume of revolution.

You could also do further maths in yr12 and 13 which was:

Year 12: Complex numbers (argument, solving cubics and quartics), matrices (multiplication and inverses) and parabolae.
Year 13: More complex numbers (de moivres rule, z=re^ix, etc), more matrices, second and first order differential equations, arc length and surface area of revolution, hyperbolic trig functions, derivatives and integrals of inverse trig and hyperbolic trig functions

Uk btw

UK here, probably a bad representative since I took several exams early but here's the few bits from my memory

Format: Year(UK)-Grade(US): Maths
2-1: (Not sure if sub. was already done) But we did times tables up to 6(?) long multiplication, shapes & their properties (incl symmetries)
3-2 I remember right angles, long division and cartesian co-ords. Times tables up to 13 (not 12 for some reason)

5/6 - 4/5 Quadratic eqn, circle theorems (still the bane of my life). SOH CAH TOA

8 - 7 surds, e^x &logs
9/10 - 10/11 partial fractions, double angle matrices basic diff eqs (i.e. set up n solve using sep of var) and calc using trig but not hyp subs

>>9123503
NB i remember learning a lot of things early then doing fuck all in maths for like 3/4 consecutive years - to the point that id done the 2/3 to 3/4 of the A level syllabus before going to 6th form

It depends where you are in the U.S., how smart you are, etc.

Typical highschool kids usually take up to stats/pre calculus
If you're reasonably smart you'll probably take calc 1 senior year
If you're actually intelligent you can get through linear algebra and differential equations without even taking summer classes

>>9123423
In my high school (about 4 years ago) our 11th grade math was first half algebra 2/ second half trig with grade 12 being precalc.

>>9122990
New Zealand math education varies extremely from school to school
Some high schools only teach basic statistics and no calculus whatsoever in final year, some teach calculus, complex numbers, etc in final year

>>9122990

Italian here, before I start I have to explain how the education system here works.

You have 5 years of elementary school and then 3 years of middle school. These are the same for everyone.

After these, you can choose two main branches:

- Professional school. It's three years long, and is geared towards low level professions like plumbing, generic factory machine operators, etc. Usually features hands-on experience in real factories and such.

- Liceo classico/scientifico. 5 years long, but it's essentially useless on its own. You learn greek, latin, maths etc. It's only useful if you're sure you want to go on to university.

- ITIS/ITCS/ITES/etc. I went to an ITIS (State Institute for Technological Instruction). All ITIS courses share the first two years, then the oter 3 years are specialized. I'm not sure the first two years are shared with ITES and ITCS too, I don't think so.

Anyway, this means that the first two years are the same wether you're studying chemistry, computer science, electronics, mechatronics, etc, so the math is pretty mundane.
I went to a computer science school, and the math really picks up after the 3rd year.

My very first lesson in 3rd year was trigonometry. By the end of it we'd done limits, derivatives. By the 5th year we were up to 2nd order differential equations and differential equations with more than one independent variable.
Also we did some statistical analysys (combinatorics, probability distributions etc), though it was considered a different course.

HS here is 3 years, and only about 50% of kids go to HS instead of vocational school, in HS kids choose between 'short' and 'long' mathematics, short being absolute brainlet tier. Long has 10 courses:
Functions and equations
Polynomial functions and equations
Geometry
Vectors
Analytic geometry
Derivative (intro to differential kinda)
Trigonometric functions
Root- and logarithmic functions
Integrals (calculus)
Probability and statistics

>>9124198
Norway?

>>9124200
Close, Finland

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International Baccalaureate HL mathematics syllabus pictured. Further Mathematics means you take all the options, if I recall correctly.

There is a more detailed syllabus that covers the sub-topics (there's proof by induction and complex number stuff etc.) but that's too lengthy to fit into one image.

>>9124229
Although if anyone is interested in knowing a more detailed list of topics covered they're pages 17 onwards in the following PDF:

sdgj.cdhuaying.com/ckfinder/userfiles/files/3cc65c478e92085f8c4d5448ba9a7cd3.pdf

>>9122990
>Basically quadratic equations, logarithm, functions
>last high school year
Anon, I...

>>9124257

Yeah, that's second year level and we have 5 years of HS.
I'm not sure but I think quadratic equations might have even been in the first year.

>>9122990
Coming from America, depends how smart you are, and if you want to take math. You're only required to understand up to algebra 2. For example I'm on senior year and I don't even have math, instead I'm doing a web dev class at a technical college, along with programming 2 and a separate web dev class for college credit. The school let programming 1 count as a math elective so I literally only did math sophomore year.

>>9123423
Same for me with the "before" column, except I did systems of equations in algebra 2 and precalculus was its own class - after trig and before calculus.

>>9123423
>That After column
I don't believe you.

In fact, I find it hard to imagine how anyone could learn math without the algebra->geometry->algebra 2->trig->calculus progression. I honestly believed every class was setting me up for the next one. Except for geometry; I don't remember a goddamn thing about that class.

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>>9122990
>I often hear that brazilian's math education is somewhat "harder" than most countries.
Lel no way.
Richard P. Feynman said
>"It is true that Latin Americans with the same degrees in science or engineering as their foreign counterparts seem to be very much less able.
>This (as I shall explain) is because they have not really been taught any science.
>Material is memorized in Latin America completely without understanding.
>Lectures are dictated so slowly that students can copy them word for word into their notebooks – and sentences are even repeated so they can check them back.
>When asked what Brewster's Law is All I receive are blank stares. No one knows.
>This shows something is completely wrong. There is no knowledge whatsoever of nature.
>This, along with the fact that salaries are absurdly low, shows a lack of interest by the Brazilian government, people, and industry, in the development of science in this country. "
Source:http://calteches.library.caltech.edu/46/2/LatinAmerica.htm

>>9122990
The problem with high school "maths" all around the globe is that you dont learn proofs and definitions.
Even hs physics is closer to maths than maths.

former IB student here (international baccalaureate). It's unfair to compare the IB's maths to the one u showed because the three levels in the IB are so far from each other. Math Studies (lowest) comprises of mainly statistics and probability, only going as far as being able to operate a graphing calculator (they're allowed in the exams). I took standard level, which looks like your study book but maybe slightly more in-depth in respect to quadratic functions and includes simple integration and differentiation with all the "prior knowledge" maths (trig, logs, etc). The higher level goes way deeper than your book, adding complex numbers and proofs to the curriculum. I've heard that american maths are ridiculously easy, though, so i'm sure this level is more than enough to prepare you.

In Russia we have two years of HS instead of 3(4 years to get Bachelor's). In schools with phys/maths profile one may even have improper integrals and diff. eqs(second year HS, everyone). However, in most schools there is only basic integration and differentiation are the most advanced stuff . I'd say such calculus oriented curriculum sucks hard, I would wish to learn more Algebra in my High School, that is, groups, rings, modules. Hell, we weren't even introduced to Categories which is the basis of modern mathematics.
TL:DR; Math education sucks in russian schools

>>9124257
That's because the 3rd year I took was "integrated", it's basically a revision of 1+2 and then 3. You don't really learn these things, just revise.

>>9124389
He is right tho. Classes are hard because teachers often just throw content on you, most people don't even remember what was taught after taking the tests, maybe just the basics.

>>9124544
There is a total of 8 books I think, but I just found those 3(?). The last books probably includes more deep things, since I remember taking complex numbers, integrals, reverse sqrt, differential equations and some other shit.

>>9124544
The higher level just throws you a bunch of shit without proper motivation or formality and expects you to do some bullshit test that is just hard considering the ridiculous amount of time you have. It's only useful if you want to enter some top institutions, but I had to relearn most of the shit after I entered university. What an advanced curriculum should have is a more axiomatic/rigorous geometry to properly formulate trig, some expansion on algebra concepts and a good intro to calculus.

>>9124544
It's not exactly easy, but people who have trained themselves to do well on tests without really thinking about what they're studying are right at home here. It's difficult in terms of how fast you need to work in order to do well in class. Proofs are lamentably absent the majority of the time.

>>9122990
I literally learned nothing in school, my third world south american shitty ass study system is that shit.
I give my thanks to all math phys and chem olympiads I was in all the knowledge I have,and I'm so happy I could run away from that country and get a full ride on a university here in a first world country.

Denmark here. High school is kinda different as we have obligatory public ed up to grade 9? (15 years old) and then secondary ed for three years if you want to go to university which I guess is kinda equivalent to high school in the US.

>3 years, C/B/A-level (translated so some terms might be a bit off)
>C-level = 1 year
>solving equations and quadratic equations
>functions: linear, exponential, power and logarithmic
>trigonometry
>geometry

>B-level = 2 years, C+B
>solving polynomials
>expanded trig (more fleshed out)
>lines and circles in coordinate systems: relation to each other, equation of circle and meeting points
>derivatives, tangent lines and optimasation
>statistics: basic stat, descriptive stat, normal and binomial distribution, chi^2
>vectors in 2D

>A-level = 3 years, C+B+A
>vectors in 3D
>integrals
>differential equations

Don't know if we're brainlets but there's a lot of focus on actually gaining an understanding on what's going on instead of just memorising what to do. There are a lot of oral exams were you have to explain what's actually going and how it relates to other branches of math and the real world.

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hodor

>>9125150
>What an advanced curriculum should have is a more axiomatic/rigorous geometry to properly formulate trig, some expansion on algebra concepts and a good intro to calculus.
This, although its rigor would probably be too much for students new to the notion of proofs and formality