<p>@collegealum: LOL. This is true (even in a such an easy question though, one can probably bet they’ll give two options for where X lies, or something else to get people to make mistakes). How much one can check one’s work winds up depending more or less on how many no-brainer questions relative to that individual there are.</p>
<p>@QuantMech: interesting, I guess maybe it’s less useful than the people at Collegeboard suggest, and that I’m confusing the two since I took the AP exams around the same time. I do recall the practice tests being a lot more formula/trick intensive than the actual exam. One thing though is that SAT II math is a lot less “cohesive” than AP Calculus, in the sense it smashes together miscellaneous math topics, so it may be that one can just fake one’s way through questions that are otherwise unfamiliar by using a calculator.</p>
<p>Tentatively, what I’m going to say is that a student who has worked with all the ingredients of the SAT II pretty extensively might be very comfortable answering the questions without a calculator. Perhaps my memory is different, because I studied calculus without ever taking precalculus, and thus never really messed very much with inverse trig functions, polar coordinates, etc at that stage of my life.</p>
<p>For your average student taking it, perhaps it’s a bit murkier a question whether a calculator helps or not. Could be a useful crutch.</p>
<p>I though the example about the 4th degree polynomial is a good one. Not essential, yet it gets it out of the way quickly. One can use basic calculus to find where polynomials attain zeroes, but that still sounds slow.</p>
<p>Why would they even ask the question about a non-factorable 4th degree polynomial? With a calculator it’s trivial. Without a calculator, it could be difficult.</p>
<p>I just took a look at some of the sample questions on the CB web site, and I see that one would want a calculator for some of those questions (a change from the “olden days”). It looks as though you need to be able to set up a linear least-square regression with a calculator.</p>
<p>Not sure that I see questions that require tricks or memorized formulas, though.</p>
<p>@QuantMech: your question in no. 203 can be rephrased, perhaps: why write an exam where you claim 55-60 percent of the questions are designed to be such that a calculator can be useful? One could just as well write an exam without calculator-use. I haven’t used a calculator for years and years, so clearly it’s not necessary for one’s future education.</p>
<p>Sometimes there are little tricks with polynomials, like a 5th degree polynomial whose derivative is always positive, and this can tell you an easy-ish way to determine the number of zeroes without factoring. But in other cases, not so much.</p>
<p>That said, I think there’s some general consensus that students in this era should be calculator-trained, and so it’s made to play a role on standardized exams.</p>
<p>I think some memorization is probably necessary for the average high schooler – there’s a lot of random material in SAT II math coming from general algebra and elementary function knowledge that I think I had to basically memorize, since I didn’t have it taught to me in any class. I know that if I didn’t read a prep book, and answered the SAT II math questions without anything but my knowledge from AP Calculus, it wouldn’t have been nearly as much of a no-brainer.</p>
<p>To give an example, I think some manipulations with matrices and vectors are somewhat unnatural to students who haven’t had to really use these in any setting, yet worth just learning to do for SAT II purposes, unless I’m making up that this is on the exam. I understood matrices better and better the more I took mathematics courses, and vectors after some physics and vector calculus. But as a frosh/sophomore in high school, not so much.</p>
<p>I can understand writing questions that require a calculator for 4-function arithmetic, in order to simplify the numerical work in a question where the thought goes in elsewhere. I heard once that old chemistry texts had a lot of questions about CaCO3, not because it was such a key chemical, but because of its atomic weight! Now they can use any species in the problems.</p>
<p>The example of the 4th-order polynomial doesn’t seem to fit with that, though–the question seems pointlessly trivial for someone with a graphing calculator. </p>
<p>I agree that it’s useful to have worked with matrices before taking the SAT Math II. On the other hand, I can’t think of any reason that someone needs to take it as a freshman or sophomore, if one hadn’t had matrices already.</p>
<p>I guess it depends what one’s coursework prior to calculus did. I took the test after having taken calculus, and still found I had to review things in the book on my own. It was straightforward after that review, but I’d guess not so much so before, because it did test actual knowledge, rather than just basic tricks as the SAT I did.</p>
<p>Also, while that question is trivial with a calculator, I think that’s part of the deal – to do well on that test, it’s good to practice what you should and shouldn’t use a calculator for. If I saw a polynomial like that, I’d try to analyze it using calculus, and it wouldn’t even occur to me to try to use a calculator. Yet it seems they want you to try graphing things with a graphing calculator when possible to speed things up.</p>
<p>Why would you assume that? Students who understand the concept of a 4th degree polynomial and its solutions would find this problem incredibly easy. On the other hand, a student that can only churn out answers following an algorithm wouldn’t have a clue to the simplicity of the problem given a calculator. </p>
<p>Not all Students find math interesting or enjoyable. There are other things in life that interest them.</p>
<p>Re #221: No, it does appear on the exams (or at least it did–I think that CB might have removed the section in which it used to appear). The correct answer was that it is not possible to tell from the information given.</p>
<p>There was an entire section on comparing the entry in column A with the entry in column B. Choices were: A larger, B larger, A and B equal, or can’t tell.</p>
<p>or if x is negative, then x^2 will be bigger.</p>
<p>As Quantmech said, “you cannot tell from the info” is one of the choices. </p>
<p>For people who are good at math, the cases you listed jump out at you and it doesn’t take any time to solve the problem. People who don’t have good intuition get tripped up by questions like those, however.</p>
<p>And oh, if there’s a “can’t tell” option, then alright. That makes more sense. I still don’t like the question, but what can you do? Just glad those tests are behind me.</p>
<p>Most students don’t get a full holistic review. For the vast majority that don’t have the grades or the SAT or have’nt taken the required course load then they will get a fail-safe review. A quick glance by a human to ensure that someone like a Hollywood star or Olympic athlete isn’t so quickly rejected. But barring that, I’d guess that 36000-90% of the applications get quickly sent to the rejection pile with little more than a couple of minutes of consideration. (Not really holistic in my opinion)</p>
<p>However I do tend to believe the best 4000-10% will probably receive a thorough Holistic review with the admissions trying to arrange the best possible freshman class.</p>
<p>My point is that 90% probably doesn’t get one, but the top 10% probably does.</p>
<p>I personally know somehow who went from a 2200–approx. 770 M, 690 W and 740 CR (and 221 on the PSAT) to a 2400 over a period of six months, without any sort of studying (or so he says). It just seems frustrating to me that this apparently random fluctuation could give him an edge in admissions, while others who have a clearer sense of where their passions lie and have pursued activities which show initiative and interest in those passions must fight with thousands of other applications to earn approval. </p>
At least as far as MIT goes, this is completely false – the admissions officers have written extensively about the admissions process on the blogs. </p>
Only a very small number of clearly non-competitive applications are removed before general reading, and no more are removed before selection. The number of applications that aren’t fully read is, to my understanding based on conversations with the admissions officers, significantly less than ten percent. The remaining applications are read by several readers, then discussed in selection committee until a decision is reached.</p>
<p>In terms of time, each application is read multiple times, at around half an hour per read ([First</a> read | MIT Admissions](<a href=“http://mitadmissions.org/blogs/entry/first_read]First”>First read | MIT Admissions)). Selection lasts full-time for about two weeks or so (including weekends), which is about another 10-15 minutes of discussion. Of course, MIT doesn’t get 40,000 applications – it gets less than half that, and they are divided into more manageable chunks (EA, RD domestic, RD international). </p>
<p>
This is also a misconception, incidentally – the grades and SAT scores of applicants fall in a very narrow band. Very few grossly unqualified people bother to apply.</p>