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).
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.
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...
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.
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."
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...
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.
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.
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.
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
Um, it's not 37.5. A common misconception, but the car spends more time (b/c it's going slower) at 35 mph. In total, it spends .6 hours driving, and it goes 20 miles. So 33.3 is correct.
Replies to: important math formulas
its good to know calculator input functions - especially "solve"
saves a lot of time
And another for distance/whatever - "dirt" (d=rt, distance=rate*time).
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...
Of course, these problems can also be solved using a bit of common sense, like any math problem on the SAT.....
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.
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.
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.