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 02-29-2008, 04:24 PM #1 Junior Member   Join Date: Sep 2007 Posts: 187 important math formulas what r some formulas that r helpful for the sat other than the ones that are provided already in the math section ? Reply
 02-29-2008, 07:27 PM #2 Senior Member   Join Date: May 2007 Location: Swarthmore Posts: 3,227 There are none. The SAT is mathematical reasoning. You don't need to know any formulas that aren't given at the front of the section. Reply
 03-01-2008, 07:12 AM #3 New Member   Join Date: Aug 2007 Posts: 11 if you have a graphing calculator - like TI 89 its good to know calculator input functions - especially "solve" saves a lot of time Reply
 03-01-2008, 07:33 AM #4 Senior Member   Join Date: Jan 2007 Location: VWG '14 (and married to Quasi) Posts: 9,571 2xy/(x+y) for the distance/speed/time questions. Reply
 03-01-2008, 11:52 PM #5 Junior Member   Join Date: Sep 2007 Posts: 147 Know your Pythagorean triples (3-4-5, 5-12-13, 8-15-17, etc.). They've helped me multiple times. And another for distance/whatever - "dirt" (d=rt, distance=rate*time). Reply
 03-02-2008, 06:28 PM #6 Member   Join Date: Dec 2005 Posts: 906 dchow is right--you should be able to solve everything from scratch. Some tricks and shortcuts do save you time, though. What tetrisfan mentioned (it's called the harmonic mean) is a really nice one, but you have to have enough practice with it to recognize when to use it. Reply
 04-03-2008, 06:10 PM #7 Senior Member   Join Date: Mar 2008 Location: NJ Posts: 1,313 I think you need to know only a few formulas, but lots of facts (admittedly, these two words overlap a bit). Most of the needed formulas are given, although there are some others, perhaps too "obvious" for many people here, such as: x^-n = 1/x^n ("^" means "to the power of"), average=sum/N, the difference of squares a^2-b^2=(a+b)(a-b), the distance formula (though this just comes from the pythagorean theorem), and so on. By "facts" I mean things like: two lines intersecting make two angles that add to 180 degrees, an equilateral triangle has three angles of 60 degrees, the slope of a line is rise/run, etc. etc. I've collected a pile of these facts along with the few formulas into short pdf files (free and non-commercial) on my web site; if people are interested, I'll post the link... Reply
 04-03-2008, 06:40 PM #8 Junior Member   Join Date: Feb 2008 Posts: 94 Average rate = [2*Speed1*Speed2] / [Speed1 + Speed2] Of course, these problems can also be solved using a bit of common sense, like any math problem on the SAT..... Reply
 04-03-2008, 10:08 PM #9 Senior Member   Join Date: May 2007 Location: Swarthmore Posts: 3,227 I give no formulas, because I'm afraid that people use them out of context. They become what I call "zombies," mindlessly using equations and getting themselves all the wrong answers. For example, in that equation for distance/time: 2xy/(x+y), some people will say to themselves, "Perfect! That's all I need to know." Let's look at a rather simple problem: A car goes 25 miles per hour for 10 km, then goes 50 miles per hour for another 10 km (technically this is impossible, the car would have to accelerate from 25 to 50, but whatever). What's the average speed of the car? Now, by using the equation above, you get 33.3, while the answer is clearly 37.5 miles per hour. I think a lot of people feel a sense of security when given an equation, because they think that that's all there is to it, when it requires thinking. Also a way lots of high school students approach math class--remember this formula, remember that equation, without any understanding of how basic equations arise and how they can be used. Reply
 04-05-2008, 03:21 PM #10 Senior Member   Join Date: Jan 2008 Location: West Coast ---> MIT '14 Posts: 2,318 dchow didn't you mean 25 mph for 10 miles? Although the formulae are given at the beginning of the math section, you should have stuff like the distance formula or the volumes/surface areas of various 3D figures memorized. Time spent flipping to the front of the booklet is time not spent on doing the problem. Don't use something like 2xy/(x+y). As my English teacher says, "Let common sense be your guide." Reply
 04-05-2008, 05:23 PM #11 Junior Member   Join Date: Jan 2008 Posts: 86 what he means is that often people use formulas to plug and chug answers without really understanding the reasoning behind the solution. the answer to the aforementioned question is 37.5 miles/hour, translate kilometers into miles...1 mile=1.6 km...Memorizing formulas is fine...but if u don't know how to correctly apply/manipulate them...it's moot point... Reply
 04-05-2008, 05:28 PM #12 Junior Member   Join Date: Feb 2008 Posts: 94 Well, of course, knowing when and how to apply formulas is key. OP asked for "formulas that r helpful for the sat other than the ones that are provided already in the math section" - the formula for average rate happens to be one that I used on the March SAT. Did it take "common sense" to know when/how to apply it? Yes. Did it help to know the formula & its usage beforehand, given that the SAT is a timed test? Again, yes. Reply
 04-05-2008, 05:58 PM #13 Senior Member   Join Date: Mar 2008 Location: NJ Posts: 1,313 That's well said, jamesford. I tend to suggest that people memorize the formulas that are given in the booklet, especially the first three figures along with the pythag. theorem (6th figure). You will either waste a lot of time flipping back and forth, or (worse) you won't realize that the formula is even available in the first place. For example, you are given a 30-60-90 triangle along with its hypotenuse and you need to find the side across from the 60 deg. angle. First, you have to know that the 30-60-90 triangle is a given formula to get the question; it is even better to know it from memory. Most of the remaining math you need to know is more factual (i.e., what an isosceles triangle is, slope-intercept line form, etc.) than formula-based. I have to admit, I would never suggest that people memorize "2xy/(x+y)". This formula is very specific to one type of question that appears only occasionally. Even stronger students looking to save a little time would probably be better off knowing/learning the underlying concepts in that type of problem rather than that formula. Reply
 04-05-2008, 10:42 PM #14 Senior Member   Join Date: May 2007 Location: Swarthmore Posts: 3,227 jamesford: I meant it to be 10 km. Of course some people will actually convert kilometers to miles, as if that will change anything! If you go the same distance for both speeds, that's all that matters. I could have given it in feet and inches and leap years if I wanted to. Reply
 04-05-2008, 10:43 PM #15 Member   Join Date: Mar 2008 Location: --->Pton '13 Posts: 564 the pythagorean formula should be your tool. And what I have noticed that it is great to understand how to check your answer QUICKLY, since eliminating 1 careless mistake can give you up to 30 points Reply

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