How far does high school math go?

For the discussion of math. Duh.

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starn
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How far does high school math go?

Postby starn » Thu Feb 21, 2008 9:50 pm UTC

I'm in my last year of secondary school (high school) in Ireland. I'm pretty interested in maths and I find that the course we take is pretty substantial and challenging, and it covers a lot of topics. So I was wondering how it is in comparison to America.

Here's the higher level exams that you take at the end of high school; see what you think:
http://examinations.ie/archive/exampape ... P100EV.pdf
http://examinations.ie/archive/exampape ... P200EV.pdf

As a reference, about half of my year do higher maths.

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Re: How far does high school math go?

Postby CodeLabMaster » Thu Feb 21, 2008 10:17 pm UTC

In comparison to my school at least, you would be able to teach any of our math courses in high school if you were an A student after your second year over there. My school doesn't teach discrete mathematics (groups, probability, etc.) and only teaches calculus in a senior course (4th year) that only a handful of math students end up taking. I would say that your school is much better than the one I attend in terms of math, because our seniors (4th years) couldn't beat your sophomores (2nd years).

EDIT: Btw, only about 50 or so students of our 800 end up taking the higher maths (which would be slightly rigorous trigonometry and 2 dimensional coordinate systems followed by a simple calculus course in junior and senior years).
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Re: How far does high school math go?

Postby Micron » Thu Feb 21, 2008 10:19 pm UTC

It is not really possible to compare anything with all of the US. For one thing there are no national standards or high school exit exams. Since 2001 each state has been required to develop some set of standards and assessments for their students but these can still vary a great deal between states and usually reflect the minimum expectation for any graduating student (ie someone in the lowest level courses available).

A better comparison might be to look at the advanced placement ("AP") calculus tests some high schools offer. These are a set of nation wide(but not government controlled) tests that are intended to be college level courses available in some high schools. Most US colleges will award college credits or allow students to skip entry level courses if they perform well on AP tests.

Based on my personal experience the tests you linked are close to the high level math courses available I was offered, probably on par with the lower level ("AB") AP calculus test but below the higher level ("BC") calc course. It is a bit hard to compare since you linked general assessment tests which cover a broad range of math subjects while I usually only saw tests targeting a single semester's material. My final exams contained more calculus problems because they were not intended to assess my skill with algebra, trigonometry, geometry, probability, or other areas.

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Re: How far does high school math go?

Postby scarletmanuka » Fri Feb 22, 2008 2:56 am UTC

No idea about US standards (or lack thereof), but most of these questions would have been appropriate for the year 12 (last year of highschool) exams here in Australia - I'm assuming we're talking about the more advanced maths courses on offer, rather than the easier ones. The main exception is the group theory stuff. Some topics (complex numbers, elementary linear algebra) were not in the high school syllabus when I went through but have since been moved into it, as a result primarily of the move to graphical calculators and the attendant reduction or removal (I don't know which) of certain topics.

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Re: How far does high school math go?

Postby Charlie! » Fri Feb 22, 2008 3:13 am UTC

It seemed about the same for "standard" advanced math in the US. Not sure about the sum of the series or the integral of the arc tangent, but other than that it all seemed like stuff that I know is covered in the average Michigan calculus path.

Of course, there are always going to be nonstandard groups who are wondering why it's so easy, but that'll happen in every country.


The other thing, though, is that this would be beyond the abilities of the "substandard" math course, which I put in quotes because it's probably the standard, really. Of course, this is also probably the same everywhere.
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Re: How far does high school math go?

Postby Ieatsoap6 » Fri Feb 22, 2008 4:04 am UTC

Apart from the AP Calc students and maybe some non-AP-Calc students, I doubt many students at my high school could do well on that exam. The math generally consisted of basic algebra and geometry and then either more algebra with or without trig and some calc. No discrete stuff and very limited complex stuff. The matrix stuff was mostly determinants.

This high school is in Georgia, so it's not exactly top-tier. Actually, apart from one teacher, the math department sucked.

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Re: How far does high school math go?

Postby Sir_Elderberry » Fri Feb 22, 2008 4:13 am UTC

Here's how the average math student, I think, would progress through my high school, in rural Oklahoma:

Freshman year: Algebra I
Soph/Junior Year: Geometry/Algebra II (order is up to you)
Senior Year: Trig

Of course, this is the bare minimum. Thirty of them will walk in having had Algebra I. I walked in having Algebras I and II, took Geometry my Freshman year, skipped trig, and am in AP Calc BC this year. There are lots of opportunities if you look for them.
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Re: How far does high school math go?

Postby stormgren » Sat Feb 23, 2008 7:40 pm UTC

As a senior at a college prep school in the US, I can work every problem on that exam (at a glance). I'm on the honors math track here. So I would say you're about even with us. That being said, I agree that it is difficult to compare to the "US school system" since there isn't really one standard. There are standard exams, but they have a very low ceiling. My entire school easily got perfect on the Ohio Graduation Tests, and so did a nearby public school. Many of my friends in public schools would not take the same level math. Then again, some of them will.

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Re: How far does high school math go?

Postby TheAmazingRando » Sat Feb 23, 2008 9:17 pm UTC

I would say it's about the same as the math I took in my senior year, but plenty of people graduate high school without ever taking calculus.

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Re: How far does high school math go?

Postby skeptical scientist » Sun Feb 24, 2008 4:41 am UTC

I would say that seeing group theory in high school is pretty rare in the US. Apart from that, it seems similar to what someone who did calculus in high school sees. Of course, there are many people who graduate high school without having taken any calc.
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Re: How far does high school math go?

Postby RedWolf » Sun Feb 24, 2008 5:44 am UTC

Math courses offered at my high school:

Algebra I and II
Geometry
Precalc and AP Calculus
Consumer Math (basic math)
Statistics/Probability
Discrete Mathematics

Although the last two aren't being taught this year and haven't been for a few years due to the lack of students signing up for them.

EDIT: Let me add that if a student has particular trouble in math, Algebra I can be split into two years. And my school only requres 3 credits of math to graduate. So many students don't even make it to Algebra II...

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Re: How far does high school math go?

Postby McDutchy » Sun Feb 24, 2008 9:33 am UTC

I think that there are a reasonable number of people at my school who would be able to work that exam at a glance. The math courses offered at my high school are:

Algebra I (can be 2 years if a student needs it)
Geometry (accelerated, regular)
Algebra II (accelerated, regular)
Trig/Function Analysis
Precalculus
IB Math Studies
IB Calculus (SL, HL)
AP Statistics (not core curriculum)

Note that Trig/Function Analysis is meant to be taken in place of Precalculus, and similarly with IB Math Studies and IB Calculus.

Our school only requires Algebra II to graduate, so there are people who get to that and quit. However, a reasonably large number of people at my school are pretty smart and attending college level math courses in addition or in place of the above. I, as a junior, have taken Linear Algebra, Number theory, Calculus 3, and some Discrete math at the city college, and I know there are others who have done somewhat similar things.

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Re: How far does high school math go?

Postby musicmunky » Sun Feb 24, 2008 5:05 pm UTC

Hmmm...well, I can't really answer this question very well. I failed algebra in 7th grade, because I sat in the back and read a book all year. So I got up to geometry later, then was expelled, then taught myself trig, then didn't touch math for 10 years, then took calculus as a freshman in college and did pretty well (got an A). From what I remember about my high school, most of the kids would have cried if this had been their final exam, however I know of at least a few students who would have done well enough to pass.
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Re: How far does high school math go?

Postby yeyui » Mon Feb 25, 2008 2:19 am UTC

I think that someone from Ohio has already responded, but I thought I'd chime in anyway.

My high school math track (the honors track) was:
Algebra II
Geometry
Pre-calculus w/ Trigonometry
AP Calculus AB/BC (equivalent to Calculus 1 and 2 at most US colleges)

This was 5 credits of math. I'm gonna guess that 6-8% of students took calculus, and in most years, few to no students took the BC Calculus. My year was exceptional and had about half of the clac students took (and passed) the AP Calculus BC exam.

Normal math track at my HS was:
Algebra I
Algebra II
Geometry
Trigonometry

Only 3 credits of math are required, so many student's did take the Trig.

Minimum was
Algebra A
Algebra B
Algebra II

I hear the minimum will be increased for the class of 2012 to require 4 credits instead of just 3.

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Re: How far does high school math go?

Postby NOT Steve » Mon Mar 03, 2008 2:17 am UTC

In my school in southern California, the basic order is this:

Algebra I (H/CP)
Geometry (H/CP)
Algebra II (H/CP)
Math Analysis (H/CP)
Calculus AP
Statistics AP

AP=Advanced Placement
H=Honors
CP=College Preparatory

Only 3 credits are required, so some just take the first three courses. Algebra I is usually in 8th or 9th grade, with students progressing from there, and those who took it in 8th grade can take maths through senior year, choosing between Calculus or Statistics. However, one classful of the most advanced students in each year can skip the 7th grade math class, taking Algebra I in 7th grade. These students can then take both Calculus and Statistics.

I myself am currently at the Math Analysis H level, and I could do maybe half of those listed, so I assume students that did well in the Calculus class wouldn't have too much trouble passing the exam.
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Re: How far does high school math go?

Postby Nigy » Mon Mar 03, 2008 6:35 am UTC

My highschool offers both AP Calculus AB and AP Calculus BC (second year calculus), as well as AP Statistics. But I dont think most highschools go as far as second year calculus; mine is (supposedly) a poster-child from west coast education. =\ Sure if you're a jazz/drama star its the best but... uhh </tangent>

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Re: How far does high school math go?

Postby leigao84 » Mon Mar 03, 2008 9:51 pm UTC

In my school at least, 80% of the school will eventually takes AP Calculus AB and 30% takes AP Calculus BC. Of course a few will even take Linear and Multivar in their senior year from the local university. But I guess that's what happens when the school pays for your AP exams...

Oh back on topic, yeah I'd say that's pretty much on par with AP Calculus AB students. We did study a bit of group theory in Pre-Cal (Trig), so it'd be fine.

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Re: How far does high school math go?

Postby niteice » Tue Mar 04, 2008 1:20 am UTC

My school (and probably many in the state) works as follows:
Algebra I (honors, regular)
Geometry (honors, regular)
Algebra II (honors, regular)
Pre-calc/trig (semester each) (regular)
Calculus (university co-op, regular)

If you're lucky, you take algebra in eighth grade, so you jump right into geometry in HS, get a year ahead of 85% of your class, and get to take calculus as a senior. Occasionally people who get placed in algebra I are put there by accident (usually due to spending 8th grade in a school other than the public middle school) and get to double up on geometry and alg II as sophomores.
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Re: How far does high school math go?

Postby PanicButton » Wed Mar 05, 2008 2:40 am UTC

My school has math from Algebra I to Linear Algebra.

I am currently a sophomore in Calculus BC, and I have no idea what some of the methods or theorems are in the tests the OP linked (eg, Newton-Raphson method and De Moivre's Theorem). Otherwise, I would be about to do all the problems.

Also, the tests shown are over a variety of topics, so some reviewing may be required beforehand to recall the geometry, matrices, etc., that are from previous math classes.

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Re: How far does high school math go?

Postby Yakk » Wed Mar 05, 2008 6:13 pm UTC

I didn't solve the problems, so it is possible that there are some tricks that would be hard.

But glancing at them, I'd think that the most "advanced" problems would be: 6b, 8b, 10 -- all from the second test you linked.

10, simply because teaching group theory isn't that common.
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Re: How far does high school math go?

Postby SPsnow02 » Wed Mar 05, 2008 6:19 pm UTC

My High School has two paths

Algebra 1 - Geometry - Algebra 2 - Analysis

Geometry Ac - Algebra 2 Ac - Analysis Ac - Calc Ac/Bc

And if you have a free hour you can trow AP stats in somewhere
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Re: How far does high school math go?

Postby leigao84 » Wed Mar 05, 2008 6:44 pm UTC

PanicButton wrote:My school has math from Algebra I to Linear Algebra.

I am currently a sophomore in Calculus BC, and I have no idea what some of the methods or theorems are in the tests the OP linked (eg, Newton-Raphson method and De Moivre's Theorem). Otherwise, I would be about to do all the problems.

Also, the tests shown are over a variety of topics, so some reviewing may be required beforehand to recall the geometry, matrices, etc., that are from previous math classes.


How can you be Calculus and never heard of Newton's method? O_o

It's called Newton-Raphson method because apparently Raphson discovered it independently of Newton as well.
But De Moivre's Theorem should have been covered in Trig, although probably not proven.

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Re: How far does high school math go?

Postby BirdLauncher » Wed Mar 05, 2008 10:51 pm UTC

My curriculum from a public school in Massachusetts (in a generally strong school district):
1st year - Geometry, normal or honors
2nd year - Algebra II, normal or honors
3rd year - Trig/Precalc, normal or honors
4th year - Calc, AP Calc AB or BC, AP Stats, or discrete math (but not at a particularly high level, it wasn't an honors course)
There were 5-10 students most years who had skipped a year of math in middle school and did everything a year earlier, but there wasn't any math for us to take past BC Calculus senior year, so most either took statistics or didn't take math senior year, which was unfortunate.

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Re: How far does high school math go?

Postby PanicButton » Thu Mar 06, 2008 12:33 am UTC

leigao84 wrote:How can you be Calculus and never heard of Newton's method? O_o

It's called Newton-Raphson method because apparently Raphson discovered it independently of Newton as well.
But De Moivre's Theorem should have been covered in Trig, although probably not proven.

Oh, I've heard of Newton's method, but I didn't recognize Newton-Raphson.

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Re: How far does high school math go?

Postby the tree » Thu Mar 06, 2008 1:46 pm UTC

Bear in mind that in the UK basically noone takes maths above the age of 16, so there is a hell of a lot more compulsory maths in the US. Also, hardly any geometry gets taught over here.

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Re: How far does high school math go?

Postby MostlyHarmless » Fri Mar 07, 2008 4:45 am UTC

I think I went to a pretty exceptional high school in the US (Maine, to be specific), but I took algebra, geometry, trigonometry, multivariate calculus, ODEs and linear algebra. They also offered abstract algebra, and some sort of real analysis course on a rotating basis (as in one of the two every year), but I didn't take those. At college I managed to skip all the standard freshman and sophomore classes. As I said though, I don't think that's normal for a high school.

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Re: How far does high school math go?

Postby sesetamhet » Fri Mar 07, 2008 5:39 am UTC

Well, I'm not sure what's really standard, but at my high school, a lot of people get to BC calculus by sophmore year. I'm a junior, and just finished Differential Equations and Linear Algebra. The high school doesn't offer these, so most people just go to the local University (University of Utah). It's public school, so I don't think it's that high above the norm...

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Re: How far does high school math go?

Postby pkuky » Sat Mar 08, 2008 9:03 pm UTC

standart over here is calculus, trig, algebra(no matrices), along with geometry (for mid-high level) and vectors/logs/analytic geometry and complex numbers (for high level). my school has an option for discrete maths and some elementary nuimber theory as well, but that's exeptional and only about 10-20 per year take it.
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Re: How far does high school math go?

Postby Quixotess » Mon Mar 10, 2008 7:23 am UTC

I have no problem taking this time to complain about my (US) high school's idiotic system of math classes.

We don't have any of your "algebra" or "geometry" or "trig." That would be too normal. We have "Integrated" 1, 2, 3. Average students will take Integrated I freshman year. If you get a D or F in one of these, they send you off to 1.5 or 2.5 and you're stuck in the portables with the subdefectives.

After you've gotten through the integrateds, which are not separated into honors/normie, you take Math Analysis if you're a senior and Pre-calc if you're a junior or below. Math Analysis sounds like it would be interestingly challenging, but instead it's the same book as pre-calc, except they skip the harder units and do the more interesting ones on combinatorics and whatnot. If you make it through pre-calc, you can take AP Calc or AP Stats if you actually hate math but were only doing it for the colleges.

I'm in the middle of AP Calc right now.

I only know how to do half of those problems off the top of my head, but that's probably because I'm not in a math mode right now; I think if I were preparing for your test I would have no problem.
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Re: How far does high school math go?

Postby Rouge Rogue » Thu Mar 13, 2008 11:57 pm UTC

At my East Coast school, our program goes up to a Linear Algebra/Vector Calculus course. Beyond that, they provide Seminars with more advanced topics. Of course, it's a very good school.

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Re: How far does high school math go?

Postby Rorgg » Wed Mar 19, 2008 4:24 pm UTC

We're going back a bit (1989) but I went to a pretty typical public high school in the US, and that's about what you could expect a student who went through senior Calculus to do, which is one year accelerated from the baseline path.

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Re: How far does high school math go?

Postby J Spade » Wed Mar 19, 2008 9:14 pm UTC

For my high school, Calculus III.

I'm not going to take it, because AP Calculus AB/BC should be good enough. I don't want to hate math.

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Re: How far does high school math go?

Postby archgoon » Thu Mar 20, 2008 3:10 am UTC

You are using more set notation then I remember from 6 years ago. Also, proofs were largely unheard of, outside of Geometry's two-column proofs.
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Re: How far does high school math go?

Postby NathanielJ » Thu Mar 20, 2008 3:09 pm UTC

What am I missing about Question 8 b) ii) on the second test that you linked to? It says to show that the MacLauren Series converges for -1 < x < 1, but the series is finite since (1 + x)^m is a polynomial and thus the series converges everywhere.
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Re: How far does high school math go?

Postby You, sir, name? » Thu Mar 20, 2008 6:03 pm UTC

In Sweden, you can pretty much choose how much maths you want to take. I think A and B are obligatory for everyone.

A -- Basic algebra, geometry
B -- More algebra
C -- Calculus (differentiation), trigonometry
D -- More calculus (integration), exponential functions?
E -- Basic differential equations, complex numbers
Discrete -- Eponymous.

Trig may have been in D and exponential functions in C. I'm not 100% how they're ordered...
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Re: How far does high school math go?

Postby hobbesmaster » Mon Mar 24, 2008 1:41 am UTC

leigao84 wrote:
PanicButton wrote:My school has math from Algebra I to Linear Algebra.

I am currently a sophomore in Calculus BC, and I have no idea what some of the methods or theorems are in the tests the OP linked (eg, Newton-Raphson method and De Moivre's Theorem). Otherwise, I would be about to do all the problems.

Also, the tests shown are over a variety of topics, so some reviewing may be required beforehand to recall the geometry, matrices, etc., that are from previous math classes.


How can you be Calculus and never heard of Newton's method? O_o

It's called Newton-Raphson method because apparently Raphson discovered it independently of Newton as well.
But De Moivre's Theorem should have been covered in Trig, although probably not proven.


I hadn't heard "Newton-Raphson" until studying power flow in a graduate level EE class. This after taking AP calc, calc 2-4, numerical methods, discrete math and a stats class. Half of numerical methods was solving linear equations!

Also, no idea what De Moivre's theorem was until I looked it up. Turns out I've been giving Euler far too much credit for few years. :lol:

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Re: How far does high school math go?

Postby hypersoar » Mon Mar 24, 2008 7:28 am UTC

My school only goes up to calculus I. They also offer stats for people who aren't tough enough for calc.
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Re: How far does high school math go?

Postby Zak » Mon Mar 24, 2008 8:25 am UTC

My school has some crazy maths goin' down:

Intro to Algebra
Math Support/Basic Math
Algebra I
Alg I P (year-long)
Discrete Math
Geometry
Geometry H
Algebra II
Algebra II/Trig. H
Pre-Calculus
Pre-Calculus H
AP Calculus AB
AP Calculus BC
Calculus D
Linear Algebra
Statistics
AP Statistics
Business Math
Advanced Topics

I'm taking stat in my junior year, some people i know will be taking AP Calc BC

(And for the record, each of these classes (unless otherwise specified) are completed in a semester))
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Re: How far does high school math go?

Postby Luthen » Mon Mar 24, 2008 10:18 am UTC

I have enough trouble knowing what the different maths courses available in my state cover. I did IB HL Maths (not called IB Calculus here though) which covered everything on your tests but some of the group stuff (its an optional extra, along with discrete mathematics and Taylor/McLaurin Expansions).
The VCE (Victorian Certificate of Education or Very Cr*p Education) offers very poor (Studies) to average (Methods) to advanced pure (Specialist) and applied (Further) maths (the brackets are the courses' names). However judging what we're doing in maths at Uni, the VCE lives up to its nickname. We just did matrices (which they hadn't done) and are going to do proof by induction - which is also supposed to be new.
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Re: How far does high school math go?

Postby snails » Tue Mar 25, 2008 11:21 pm UTC

Colorado here: Calc III/Differential Equations is the highest level in quite a few schools. My school also has Linear Algebra, but it probably won't be offered next year because there won't be enough people taking it.

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