Calculus Comparison

Pre-College Issues High School Life
1

<p>How are you guys so good at math that you can do calc your freshman or sophomore years (I'm not being accusatory or anything, just trying to figure it out)? With my schedule I had (beginning in the 8th grade and progressing each year until calc my senior year) algebra 1, geometry, algebra II, Pre-calc, calc...that's typical right? Do you guys take more than one math class/ school year? Have you guys already done all those classes by your sophomore year?
It's hard for me to understand...my class is really smart from what I can tell (most got national merit commended or higher, we dominate academic meets, and our average SAT is well into the 2100s, plus we own our AP tests in other subjects...we haven't taken any math ones) but we do terrible in calc as seniors (the class I mean). I was happy to get a 50 on our last quiz, beating most people in the class (and that's normal for our grades in calc). Does anyone have any ideas as to why there's such a difference...wait, I'll post some problems from our last quiz. Are these pretty easy? I tried to write them clearly.</p>

<p>1) find the average value of the function y= 12 over ((36-16x^2)^(1/2)) on the interval from x=0 to x=3/4</p>

<p>2) ln(cos(lnx))...find the derivative</p>

<p>3) solve the initial value problem: dy/dx = 2 over (1+x^2), y(0)=3</p>

<p>4)find the derivative. y= sinxlog(subscript5)x</p>

<p>5) locate and identify the absolute extreme values of y=ln(sinx) on [pi/6, 3pi/4]</p>

<p>6)find the derivative of y with respectt ot the independent variable: y=2^((cos)(pi)(theta))</p>

<p>7) Find dy/dx: lny=(e^y)(cos4x)</p>

<p>8)find the equation for thel ine through the origin and tangent to y=ln5x</p>

<p>9)find the derivative of y with respect to x: y=(sin^-1)(e^(4t))</p>

<p>10) The amount of alcohol in the bloodstream, A, declines at a rate proportional to the amount, that is, dA/dt = -kA. If k = 0.5 for a particular person, how long will it take for his alcohol concentration to decrease from 0.10% to 0.05%? Give your answer to the nearest tenth of an hour.</p>

2

<p>i'm a junior and i guess from the looks of it we're a bit ahead of you</p>

<p>anyway, as far as frosh and sophs taking calc, all that usually means is that they started alg 1 earlier, and i guess some do math over the summer</p>

<p>it's more about having the alg/geo/precalc background than about being old enough to be able to learn calc</p>

3

<p>Hey, I know a couple of 14 years olds who learned calculus who aren't that intelligent. And guess what? They only had IB HL Math by their 12th grade year and never got into Ivy. One of them only managed to get 2060 on the new SAT</p>

<p>The problem is the school district and the assumptions therein. It assumes that everyone will learn Algebra I or Algebra II at the same pace, which is obviously not true. More of us could have learned calculus at age 14, like those two 14-year olds, if only we had the opportunity to do so - though keep in mind that those two are graduating at ~ 17.</p>

<p>Meanwhile, **~50% of Caltech students<a href="source,%20Ben%20Golub">/b</a> never have anything beyond Calculus BC.</p>

<p>Someone at CC (back in 2004-2005) went all the way up to real analysis and only managed a 95 on the AMC-12.</p>

4

<p>
[quote]
How are you guys so good at math that you can do calc your freshman or sophomore years

[/quote]
</p>

<p>Some people try very hard to "get ahead" in the math track, even to the point where they're willing to take math courses at a university over the summer or via independent study programs such as EPGY. (I wouldn't necessarily recommend this)</p>

<p>Or they just go to very selective high schools where such "odd" courseloads are typical.</p>

<p>(And just because people are ahead in math doesn't mean they're any good at it. If you go too fast you often end up not knowing the subject as well as people who go slower. The juniors in our French 3 class often seem to get better grades than the sophomores.)</p>

<p>
[quote]
we do terrible in calc as seniors

[/quote]
</p>

<p>a) Often seniors care a lot less about their courseload than other people. I distinctly recall people sleeping and throwing airplanes during the AP Bio exam.
b) Your calc problems seem like the type of stuff we'd do in our local math competitions (in which an 70-80% would be enough to get you in the top 10% or so of the competing pool). Most people who go to said competitions from our school get much less than 50% of the questions right.
c) Maybe your teacher just doesn't teach well.</p>

5

<p>My D was always a math whiz---and was in a group of 6 kids who took Algebra I in 6th grade, Geometry in 7th, and Alg II/Trig in 8th grade. I'd never suggest anyone pushing themselves (or their kids) too quickly in math, but with her, she would have been extremely bored otherwise. Starting that early, she was able to take AP Calculus AB (and then also took and got a '5' on the BC portion) in her sophomore year. Was mostly "out" of math courses to take this year as a senior...is doing Calculus III as an independent study class with a few other math geeks.</p>

6

<p>Hm, I wish I could go back and edit my post. Bolding characters makes me look really condescending...lol... even though if I want to emphasize a point, it's one of the only ways to do it. =P</p>

<p>Anyways, this thread is nice:
<a href="http://talk.collegeconfidential.com/showthread.php?t=320343%5B/url%5D"&gt;http://talk.collegeconfidential.com/showthread.php?t=320343&lt;/a&gt;&lt;/p>

<p>==</p>

<p>I actually was in the equivalent of Algebra I in 8th grade, and managed to get a 5 on the Calculus BC in 10th grade. In fact, the time gap between my 5 on the BC Calc exam and the time I first learned the quadratic equation was less than 2 years.</p>

<p>^Wow, that statement makes me wish I took math more seriously after I took the Calc BC, so that I could be an inspiration to some other poor 8th graders. ^_^ Ah, if not for that bout of existential angst.</p>

7

<p>I'm currently a freshmen and I'm taking Calculus AB as a sophomore. The reason I'm doing this is because of my high school magnet. It requires the freshmen to be in precalculus as a freshmen. I took algebra 1 7th grade, geometry 8th grade, took algebra 2 over the summer (and the teacher who taught me at summer school ended up being my real teacher in precalculus), and then precalculus. Since there are so many people who never took algebra 2 in middle school, they set up summer school at another High school. Two of which worked at my high school. You had to maintain AT LEAST a B average and a lot of kids had to drop out of the magnet because of a C and wasted their summer. Any way, that's how my school gets people in precalculus freshmen year and calc sophomore year</p>

8

<p>there are several different tracks of math at my high school.</p>

<p>failed math placement exam:
9-pre-algebra
10-alg 1
11-geometry
12-alg 2</p>

<p>average students:
9-alg 1
10-geo
11-alg 2
12-pre-cal</p>

<p>above average students:
9-geo
10-alg 2.honors alg 2(get an A both semesters in hon., skip precal)
11-pre-cal/11-ap cal ab
12-ap cal ab/12-ap cal bc</p>

<p>advanced (5-6 students in this):
7-alg 1
8-geo
9-honors alg 2
10-ap cal ab
11- ap cal bc
12-differential equations and multivariable calculus</p>

<p>some also opt out of the calc track and take ap stats. min req for ap stats=alg 2 with a B. also, you must pass a placement exam with a minumum of 70 for each level you plan to test out of at my high school. its private, so can't measure the level of the 30 different 8th grade algebra 1 programs that end up at the school. alot pass the alg 1 exam and that's it.</p>

<p>with that said. i took the advanced track and i am now in ap calc ab.</p>

<p>with regards to your quiz, it looks like a standard ap calc quiz. nothing seems all too difficult and its standard problems.</p>

9

<p>I agree. That looked quite easy compared to what my class gets sometimes. I took the "advanced" path. I had to take math analysis in tenth grade though ( precalc \ trig) and there is no way around that, so I'll end up with calc BC for my senior year. The problem for me though, is that I don't have the time for the class this year. I really do need more practice, but even just getting my homework done pushes me until about 2am - 3am.</p>

10

<p>At my school, people spam Summer/Online classes to get ahead especially in math.</p>

11

<p>As a freshman in calc AB, here's what I did:</p>

<p>In middle school, all of the incoming 6th graders were placed in 3 dif versions of pre-algebra. Accelerated, normal, and "slow" (forgot the name). When I looked at the textbook, I already knew everything. So I went to talk to the head of the math department, and he allowed me to take the honors Algebra 1 class as a 6th grader. Meaning I was with a bunch of big and scary 8th graders (they actually turned out nice). Anyway, after that, I went to H geom. For 8th grade, they didn't offer alg2/trig at my middle school, so I took it at a local community college during the schoolyear. That also meant I had 1 less period of normal public school. And now I'm a freshman in Calc AB.</p>

12

<p>Some schools are very lenient with their classes. Like going from Algebra 2 to AP Calc. Wow.</p>

13

<p>I go to the same school as gar_spartan, and in reality, our H Alg 2 class covers everything you would learn in PreCalc. They just squish everything into one year. 3rd quarter is entirely trig, and we touch on functions and limits in the last quarter (although the first bit of Calc covers that again anyway).</p>

14

<p>I took geometry as a freshman. Then I switched HS and bypassed enough math to enter calc as a sophomore (I knew alg II and pre-calc from my participation in math contests).</p>

<p>Btw, the questions are easy.</p>

15

<p>Some people are just smart [and then there are the rest of us].</p>

<p>I know this one seventh grader who was in my geometry class last year. Assuming that he doesn't skip any more years, he'd be taking Calculus BC as a sophomore. That may not seem all that amazing, but the thing is, he was only nine years old...</p>

16

<p>haha 9 years old taking BC is kinda scary :P</p>

<p>I just had enough of a math background in 6th grade (due to interest in elem school, cd-roms, dad, and cty logic course) to skip into Alg I.
My school's math sequence is like this:</p>

<p>Failed Exam:
9: Pre-Al
10: Alg I
11: Geom
12: Alg II</p>

<p>Average:
9:Alg I
10:Geom
11:Alg II
12: Math Analysis</p>

<p>Above Average
9: Geom
10: Alg II
11: Math Analysis
12: Calculus or AP Calculus AB or AP Calculus BC or AP Stat or AP Comp Sci</p>

<p>Accelerated
9: Alg II
10: Math Analysis
11-12: the rest of the classes</p>

<p>The Cool Kids.
9: Math Analysis
10-12: the rest of the classes</p>

17

<p>

Oh no, don't get me wrong. He was nine last year when he was taking geometry as a 7th grader. He'll be 12 when BC rolls around. :p</p>

<p>I can't imagine a nine year old in BC. That's like 3rd/4th grade... damn...</p>

18

<p>Here's how I got accelerated:
In 5th grade, I started going to a private elementary/middle school. For math, there was a placement test, and I placed into math 8 H in 5th grade, the highest offered. I continued on this track:</p>

<p>5th: Math 8H
6th: Math A (I)
7th: Math AB (II)
8th: Math B (III)
9th: Pre-calc
10th: skipped
11th (this year): Calc BC
12th: Multivariable</p>

19

<p>Pwnage Sequence:</p>

<p>9th: BC Calculus -> Linear Algebra or Multivariable Calculus, Intermediate Trigonometry\Complex Numbers [Competition Mathematics], Number Theory
10th: Complex Analysis, Differential Equations, Abstract Algebra, Some Random Courses
11th: Point-Set Topology, Partial Differential Equations, Graph Theory, Some Random Courses</p>

<p>:cool:</p>

<p>
[quote]
I know this one seventh grader who was in my geometry class last year. Assuming that he doesn't skip any more years, he'd be taking Calculus BC as a sophomore. That may not seem all that amazing, but the thing is, he was only nine years old...

[/quote]
</p>

<p>Nevermind. O_o"</p>