<p>Does anyone know any shortcuts/formulas for certain math problems?<br>
For example, for distance/rate problems, where the question of the total mileage in a round trip is asked, I use the formula (2<em>rate1</em>rate2)/(rate1+rate2). Any have any good ones? They'd be much appreciated! :D</p>
<p>bump it up</p>
<p>Don't use formulas!!!!</p>
<p>I can bet you that of all the people with an 800 on the SAT Math, 75%+ did not even study for it. And many people will pass that information off as "Well they're geniuses" but no one ever considers what MAKES them "genius". I'll tell you why you shouldn't use formulas: If you memorize them, and then forget, or if you memorize them incorrectly, then you are SCREWED. Very few people who are accomplished in math memorize anything anymore. It's all about the ability to use what you know already (simple + - x /) and some rules, like distributive property and fractional methods, to derive and arrive at anything you will ever need. It takes a certain open and flexible mind, and one that is very goal oriented. For example, let me show you how I would approach a problem like this (I also got 800m and SAT2 800m2, AP BC 5, etc)</p>
<p>Bob drives to SATville, 100 miles away. He drives 50 miles per hour there, and 25 miles per hour back. What is his average driving speed?</p>
<p>Ok, you could apply the formula if you wanted, but then you have to memorize it, and you have to memorize ALL the formulas for ALL sat math problems, and then what are you going to do when you see problems after the SAT? Like, for example, in college? No! You have to be able to figure it out. Ok, so here, you just think, what is average speed? Which means, Total Distance over Total Time. Total distance is 200 miles. Total time is 2 hours there, 4 hours back. So his average speed is 200/6 mph. But I didn't MEMORIZE a formula, I just figured it out. That's what you need to practice, the ability to figure things out, and then, you win. Do this by thinking "what am I looking for" and "How am I going to get there". Good luck.</p>
<p>*This really applies mostly to the last 3-4 problems of a section, the ones prior to this usually are really easy if you consider the answers with the problem.</p>
<p>By the way, other 800 scorers tell me if you agree or disagree.</p>
<p>"what is average speed? Which means, Total Distance over Total Time. Total distance is 200 miles. Total time is 2 hours there, 4 hours back. So his average speed is 200/6 mph. But I didn't MEMORIZE a formula, I just figured it out."</p>
<p>Without even mentioning that the average rate problems are usually presented quite differently, I hope you do realize that "Total Distance over Total Time equals average speed." is a FORMULA. </p>
<p>While you're correct that one does not need to memorize formulas, the reality is that what is needed is to KNOW them, which is not the same thing, as I believe your pre-calculus teacher should have told you. Figuring out formulas DURING the test is simply not appropriate, and is one the traps in which ETS expects unprepared students to fall.</p>
<p>Sorry Xiggi, I know you are well respected on the collegeconfidential boards, but I must beg to differ.</p>
<p>What I said was not to MEMORIZE formulas. I did not say "Don't figure formulas out", as that was clearly the opposite of what I'm saying. Figure things out, but become good at it, and fast, so that no math problem, SAT or not, posses a challenge. But memorizing things such as (2<em>rate1</em>rate2)/(rate1+rate2) beforehand, or the definition of the derivative for a test, or anything, is extremely backwards and is representative of the poor rote teaching manner that happens in a lot of American schools. </p>
<p>Look, the SAT is a test that is to get into college, and although it tests how well you take the SAT more than how much math you know, if you are teaching someone methods EXPLICITLY and ONLY for the SAT, they will arrive in a good college completely unable to complete the math that they are expected to be able to do. If, on the other hand, one teaches a student how to do math, how to confront and complete math problems efficiently and accurately, the SAT will be like eating cake, as it was for me and my other mathematically oriented friends. </p>
<p>My thoughts for doing well on the math section:</p>
<ol>
<li><p>Know your algebra and trigonometry backwards and forwards, upside down and twisted. Be able to convert and find x's in difficult equations quickly and effortlessly. This comes by practice with complicated problems. Also, be able to VISUALIZE math, and the relationship between geometrical shapes. That will help a ton. </p></li>
<li><p>Be extremely careful. If you are good at math, and fail to get 800, a lot of it is just misreading the problems. Spend a good solid minute on problems in the middle section, and more on the hard section. It'll help you that way. </p></li>
<li><p>Know your calculator. Be able to use the "calculate" section in the graphing part of it, it can be very useful for checking answers.</p></li>
</ol>
<p>There's more, I'll add as they come.</p>
<p>Final note: Here's the difference between memorizing and figuring something out:</p>
<p>A cylinder's volume is pi<em>r^2</em>h - memorized. </p>
<p>Figuring it out: </p>
<p>A circle is pi*r^2 (you can memorize these elementary things). When you move it 3d for a certain direction, you'll get a cylinder. That direction is H. Memorized!</p>
<p>A triangle's area is bh/2 - memorized</p>
<p>Figuring it out:</p>
<p>A rectangle is bh. A triangle is always half a rectangle (whether scalene, acute, or obtuse. Try it). So bh/2</p>
<p>These are simple equations, but this manner of thinking applies just as easily to far more difficult and convoluted problems.</p>
<p>Risingsun, you are mixing apples in oranges, and seemingly mixing up the tests as well. The SAT is a test of reasoning, not a test requiring deep knowledge of algebra nor trig. The Subject Level II might be a test where you need to know your calculator well, but for the SAT it is best to leave under the desk for most of the questions, if not all of them. </p>
<p>All the things you mention have to be KNOWN. They have to be encrusted in your brain and subject to immediate recall. Knowing the surface, perimeter, number of diagonals of simple geometric figures without hesitation are a must. The same thing for simple ratios of inscribed figures (a circle in a square, or the opposite.) The best way to develop those reflexes is by practicing. </p>
<p>Oh well, there are many paths to reach the top of the mountain. To each its own!</p>
<p>if you practice, youll probably end up getting to the hard questions with lots of time to spare, so make use of it</p>
<p>its good to have at least 5 minutes to check over everything, but still take your time to relax and figure things out calmly</p>
<p>so with hard geometry, it helps me to draw in lines that can be assumed or presumed based on rules of like, a right triangle will form a rectangle opposite it, and</p>
<p>with exponents, it usually helps to reduce everything to simplest form, especially when it tells you to give "8 to the xth in terms of 2 to the yth"</p>
<p>it helps me to relax, because usually they are very obvious, there will be a few that are just tedious, but most are just like puzzles, you need to relax, not think of it as a schoolwork problem, but think of all the things you could apply, not just the obvious application, because once you see what little trick they put in to "get you," or how they changed something, or how the given information fits together, you're as good as done</p>
<p>the doing is not harder usually (for me), it's more just seeing the path to the solution</p>
<p>if you really, really need some help with problem solving, try "How to Solve It" by George Poyla, but most of that is unnecessary for the sat</p>
<p>it's a good book, but only if you have the will to read it</p>
<p>good luck everybody, hope this helps</p>
<p>I definitely agree with RisingSun. </p>
<p>First off, the math section isn't very hard if you think about it. It's really the time issue that makes math harder than it actually is.</p>
<p>Finish the easiest problems the quickest, and leave the hardest to the end. This will enable you to have more time, which gives you more time to answer the hard questions, which in turn generally leads to a correct answer. Like I said, the hard questions really aren't all that hard; it's the time constraints.</p>
<p>Xiggi's formula on average distance problems is very useful.</p>
<p>I thank him for that.</p>
<p>Well I semi agree and disagree. It's helpful to remember some formulas but the formulas that truly stick are ones you use all the time and not gained through memorization.</p>
<p>It's a useful formula, I'm not denying it.</p>
<p>But Xiggi isn't the first person to figure this problem out, or define it (no offense intended, I'm just stating the facts). In all honesty though, how frequently does this type of problem come up? I've only seen it once, and I've taken like 7 practices tests. </p>
<p>The SAT is full of problems at the end of the test that are so minute in frequency that you probably will never see it again. It is luck.</p>
<p>just do more practice. the more you see it, the better and quicker you'd get. After practicing around 40 sections of SAT math, I've raised my math score by at least 100 points. If you practice alot, you'd gradually find short cuts and strategies to do certain kinds of questions in the easiest fashion. Oh, and make sure you take the time analyse correct and incorrect answers, and those "not-so-sure" questions (even though you guessed them correctly) just to fill up the gap.</p>