Wikipedia:Reference desk/Archives/Mathematics/2010 August 25

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August 25

Help on ACT/SAT math

Hey guys. I'm taking the ACT and SAT in the near future. The concepts tested in the math section are pretty elementary, in my opinion (but I take AP calc :|). BUT! I still get one or two wrong in easy places when doing practice tests due to arithmetic errors. SAT math is ~25 questions per section and ACT math is 60 questions, and I generally have 5-10 minutes left at the end. I don't usually get the "hard" one wrong because to me they're not really hard to me. So does anyone have tips on how to reduce these, and how to check over my work? I'm most interested in the latter; I can't go over all of the questions in the time left over, but I also can't really identify problems I might have done wrong because of an arithmetic error. 76.230.231.191 (talk) 00:11, 25 August 2010 (UTC)

The most important point is that if you are scoring above 700 (for the mathematics section of the SAT), and there are still a few weeks to go before the test, then you are doing fine. What score are you achieving on an average? Unfortunately, the mathematics section of the SAT is all too easy these days and so if you make just one mistake in the whole test, you might get 720. I know you probably do not want to be hearing this, but I think that these points are important to keep in mind. (And for some universities such as Caltech, they might reject your application if you have scored below 760 on the mathematics section without even bothering to read the rest of your application - this is also unfortunate.)

As for your question, the best advice I can give you is to write all your computations without ommitting a single detail - not one. It does not matter if you are moving from $(5+4)-(2+3)$ to $4$ or something more complex - expand the brackets carefully in at least 3 steps! I know this sounds boring, but it is the only way I know to avoid silly errors. There is ample space to work out your questions so you should use this as much as you can. And once you have worked out a question in many steps, it is very likely that you will not make a mistake. However, always double check at the end of the test.

Also confirm that you are bubbling everything correctly - double, no triple check this! One mark is "gold" on the higher end of the scale and so you should not be losing marks because of incorrect bubbling.

You are probably thinking that if you do all these things, then you will run out of time. I think that taking tests at home is the key here. Try different strategies, decide how to manage your time on the questions, and you should be fine. The first 15 questions should take 5 minutes at the most especially if you have done AP calculus. The last 10 questions should take 10 minutes at the most. And this should give you ample time to check. But I strongly believe that you should try to do everything carefully the first time around - then, there will be no need to check! (But still check!) In particular, while this strategy is possible, you should also try other strategies that enable you to spend more time on the easier questions. If you have 10 minutes left over, then you are doing the test too fast. Try to divide that extra 10 minutes among the easier questions. Hope that helps! (Disclaimer: I am no expert on these matters.) PST 02:37, 25 August 2010 (UTC)

Caltech is not going to throw out an application just because of one or two missed questions on the SAT math section. SAT scores are not a particularly good predictor of how good a student will be, so the admissions committee cares far more about the rest of the application.

My advice to the OP is to just stay calm at the test and be SURE to get enough sleep the night before. The others have good advice, too. But don't worry if you miss a few questions. Eric. 82.139.80.104 (talk) 16:27, 29 August 2010 (UTC)

When you check an answer, it's useful to try to solve the question in a different way. If you have an error you will be less likely to repeat it. -- Meni Rosenfeld (talk) 09:01, 25 August 2010 (UTC)

I have one possibly weird piece of advice. A lot of the multiple-choice questions on those tests are of the form "what number x satisfies [some condition]". These can be further split into two types. It's usually obvious at a glance what type a question is:

• "Which number gives 15 if you double it and then add 3?" (type 1)
• "Which number is 2 less than the square of a prime number?" (type 2)

Type 1 means you can set up an equation with a unique solution (2x+3=15 in the example), then solve for x, then look at the multiple choices and find the one equal to x and fill in the bubble. Type 2 doesn't have a unique answer so you have to examine the 5 choices and see which one satisfies the condition. Type 1 is more common than type 2, or at least it was on the SAT that I took, back in the day.

With a type 1 question, it's usually faster and less error-prone to solve the equation first and look at the choices afterwards. It's faster because you do just one calculation instead of trying out several guesses, and less error-prone because if you make a mistake, you'll probably get an x that doesn't match any of the choices, so you know something is wrong and can go back and fix it. With type 2, you just check the choices one by one.

It is possible to hit a type 2 question that looks like it could be a type 1 question, causing you to burn a lot of time if you're trying to stick to the above strategy rigorously (I did that and probably lost a few points because of it). Just remember that all the questions are basically easy, so if you're spending more than a few moments figuring out a type 1 approach, it's possible that there isn't one or that you're missing it somehow, so just switch to type 2 and get on with it. 67.117.146.38 (talk) 07:34, 26 August 2010 (UTC)

here's the non-answer, what is the question?

Resolved

There is a certain unsolved problem in combinatorics (Ramsey theory I guess) that seeks to determine the value of a certain number n. The situation is something like this: just about everyone believes n=6. It's obvious that n>4, and it can be proven with a little work that n>5. There is a ton of experimental evidence pointing to n=6, though it might not come as a complete shock if it turns out that n=7 or even n=8.

However, the best lower upper bound anyone has been able to rigorously prove on n is something like n = the 10 millionth Ackermann number.

Anyone know what I'm referring to? Thanks.

67.117.146.38 (talk) 21:48, 25 August 2010 (UTC)

You're thinking of Graham's problem. The upper bound you're thinking of is probably Graham's number (which article also states the problem), though that's not the best bound known. Even the best known upper bound is absurdly large, however: much bigger than the 10 millionth Ackermann number. For a long time the solution to the problem was believed to be 6, but it is now known to be at least 11. Algebraist 22:09, 25 August 2010 (UTC)

Thanks! I guess the deal with the number is less clear than I thought. I remembered there was a general belief that the actual value of the number was quite small, not that it was somewhere unknown within a vast interval. 67.117.146.38 (talk) 22:34, 25 August 2010 (UTC)

Line integrals

Hey guys. We're studying line integrals in class, and I've got three homework assignments about them. The trouble is we don't have our books yet and I left my notes on campus :( The problems are pretty basic (two involve linear bottom function things--forgot the word, sorry!--and the third is an ellipse). Since it would be simple to solve these with basic calculus or even geometry, we're getting graded on the work more so than the answer. So i guess what I'm asking is, can someone demonstrate how you would do the line integral (being sure not to skip steps please), with any function you think is best or just a circle centered at the origin and with radius 1 (That's not one of the problems, I just want to see how it's done)? thanks. 68.249.1.8 (talk) 23:39, 25 August 2010 (UTC)

All right, let's do the easy thing and integrate $f(x,y)=1$ along the unit circle, using the natural parametrization ($x=\cos t,y=\sin t$). By the first definition in Line integral, we then have:

$\int _{C}1\,ds=\int _{0}^{2\pi }1\,|(-\sin t,\cos t)|\,dt=\int _{0}^{2\pi }{\sqrt {(-\sin t)^{2}+(\cos t)^{2}}}\,dt=\int _{0}^{2\pi }{\sqrt {1}}\,dt=\int _{0}^{2\pi }dt=2\pi .$ 85.226.206.72 (talk) 06:29, 26 August 2010 (UTC)

The crucial step was deciding the best parameterization for a circle. In the case of a circle, it is easy to map two-dimensions (x,y) to a single parameter (t) (distance along the circle). From basic geometry/trigonometry, we know that the relationship {x=sin(r), y=cos(r)} is a suitable description of a circle. In general, you need to find the "simplest" parameterized representation of your line path - preferably as a one-dimensional function in the form of easily-integrable parts. Nimur (talk) 21:46, 26 August 2010 (UTC)