<p>I already started a thread for Basic and Intermediate SAT Math Strategies here: <a href="http://talk.collegeconfidential.com/sat-preparation/1475829-sat-math-strategies.html%5B/url%5D">http://talk.collegeconfidential.com/sat-preparation/1475829-sat-math-strategies.html</a></p>
<p>In this thread I would like to focus on more advanced strategies. I want to emphasize immediately that most of these strategies are not necessary. It is actually possible to get an 800 in math without learning any of them. However if you want to give yourself an edge and increase your chances of getting an 800, you may want to learn some or all of them.</p>
<p>If you are not scoring over a 600 on College Board practice SATs, then I wouldn't bother with these right now. Focus on the more basic and intermediate strategies mentioned above instead.</p>
<p>Please feel free to ask questions, discuss, agree, disagree, comment on, etc. with each strategy that I bring up. </p>
<p>I think it would be nice to discuss one strategy at a time, so I would prefer if you don't jump in with lists of your favorite advanced strategies all at once. Instead try to add your input to any of the techniques that have already been mentioned. </p>
<p>I will post the first strategy soon.</p>
<p>Awaiting the first strategy! :)</p>
<p>Let’s start this thread off with a classic: Xiggi’s formula</p>
<p>Description: Xiggi’s formula can be used to find an average rate when two individual rates for the same distance are known. The formula is:</p>
<p>Average speed = 2(rate 1)(rate 2)/(rate 1 + rate 2)</p>
<p>Comments: (1) Some people refer to Xiggi’s Formula as the Harmonic Mean Formula, but I think here on CC we all agree that Xiggi’s Formula is the better name.</p>
<p>(2) Be careful - Xiggi’s Formula only works when the two distances are the same.</p>
<p>(3) Even though the distance is often given in these types of problems, note that the formula does not use the distance - only the two rates.</p>
<p>Here is an example of a problem where Xiggi’s formula is the best way to go.</p>
<p>An anteater traveled 7 miles at an average rate of 4 miles per hour and then traveled the next 7 miles at an average rate of 1 mile per hour. What was the average speed, in miles per hour, of the anteater for the 14 miles? </p>
<p>Try to solve this problem in 2 ways - with and without Xiggi’s formula.</p>
<p>Hi DrSteve. This is quite helpful. Can you post more ? :]</p>
<p>Nobody actually needs most of these formulas. All of the SAT math question only require for you to know simple mathematical concepts, but they disguise the questions in a way that only those who really know what they’re doing get it right. </p>
<p>Remember, the SAT is a STANDARDIZED test. Not everybody has covered all of the topics another student may have, which would put a lot of students at a disadvantage - the SAT would have no purpose for colleges then. </p>
<p>Sure, these formulas may help you get the answer a little quicker compared to a student who’s using a different methods, but remember: every SAT question can be done in about 30 seconds by only using the formulas the CB gives in the beginning of every SAT math section. You don’t NEED any of these complicated formulas, in which you can easily make a mistake recalling, BTW.</p>
<p>@UnfetteredDreams</p>
<p>I have already stated in the first post from this thread that it is possible to get an 800 in SAT math without knowing any of the advanced strategies I will be putting in this thread. However, from firsthand experience I can tell you that most students going for an 800 will find the strategies, formulas, and techniques that I discuss here extremely valuable.</p>
<p>For example, the question I gave above is very similar to an actual SAT problem, and Xiggi’s formula is the quickest way to solve that problem. So if you know Xiggi’s formula and you happen to get a question where it can be applied directly, you will probably save at least 30 seconds which can be used on another problem. Time is a precious commodity on the SAT.</p>
<p>Whether an individual student chooses to memorize Xiggi’s formula is up to them. I have no strong feelings either way. </p>
<p>@relativelysmart</p>
<p>That’s how you do it.</p>
<p>For everyone else - I suggest you make sure you know how to solve the above problem with and without Xiggi’s formula. </p>
<p>In fact, let’s make our next strategy: Solving rate problems using a “d=rt chart.”</p>
<p>Before we discuss this more formally, would someone like to solve the problem above using this method?</p>
<p>Ok, so the 1st 7 miles at 4mph took him 1.75hrs and the next 7 miles at 7mph took him 7 hours, so with d=rt that equals 14(total distance)=r*8.75(time) solving for R leads to 8/5</p>
<p>Didn’t really understand the chart thingy hehe</p>
<p>The d=rt chart would look something like this (sorry it looks a bit messy, but CC doesn’t allow for very good formatting - most of the underscores should just be spaces).</p>
<p><strong><em>Distance</em></strong><strong><em>Rate</em></strong><strong><em>Time
1st part of trip</em></strong><strong><em>7</em></strong><strong><em>4</em></strong><strong><em>7/4
2nd part of trip</em></strong><strong><em>7</em></strong><strong><em>1</em></strong><strong><em>7/1 = 7
total</em></strong>______<strong><em>14</em></strong>_______________________________8.75</p>
<p>DrSteve, thanks for this! Keep it coming it really helps</p>
<p>Can you go over permutations/combinations and general probability? Im pretty sure many students(including me) have trouble with that.</p>
<p>I’m with MedicalBoy. I too have problems with those.</p>
<p>Gruber’s has SAT Math Strategies as well. That could be useful if you are looking for additional strategies.</p>
<p>Ok - let’s start with Permutations</p>
<p>The factorial of a positive integer n, written n!, is the product of all positive integers less than or equal to n.</p>
<p>n!=1∙2∙3⋯n
0! is defined to be 1 So n! is defined for all nonnegative integers n.</p>
<p>A permutation is an arrangement. The number of permutations of n things taken r at a time is nPr = n!/(n-r)!. For example, the number of permutations of {1, 2, 3} taken 2 at a time is 3P2=3!/1!=6. </p>
<p>These permutations are 12, 21, 13, 31, 23, and 32. </p>
<p>On the SAT you do not need to know the permutation formula! Just use your calculator.</p>
<p>To compute 3P2, type 3 into your calculator, then in the MATH menu scroll over to Prb and select nPr (or press 2). Then type 2 and press Enter. You will get an answer of 6.</p>
<p>And now Combinations</p>
<p>A combination is a subset of a particular set containing a specific number of elements. The number of combinations of n things taken r at a time is nCr=n!/[r!(n-r)!]. For example, the number of combinations of {1, 2, 3} taken 2 at a time is 3C2=3!/[2!1!]=3. These combinations are 12, 13, and 23.</p>
<p>On the SAT you do not need to know the combination formula. Just use your calculator.</p>
<p>To compute 3C2, type 3 into your calculator, then in the Math menu scroll over to Prb and select nCr (or press 3). Then type 2 and press Enter. You will get an answer of 3.</p>
<p>@UnfetteredDreamz</p>
<p>I agree with you, these formulas are too narrow and only end up cluttering one’s brains. The SAT writers are going to tweak the questions in a way that requires one to thoroughly understand the general concept of average speed and its application to varied situations. </p>
<p>Here is what I would actually want students scoring at the 800 level to be prepared for:
- When the length of the return route is twice as long as the initial route.
- A problem where the distance is divided in to three sections that are traveled at different speeds. </p>
<p>Here is a good example from AMC 10 that could show up on the SAT and something I am pretty certain all 800 scorers would be able to do:</p>
<p>A triathlete competes in a triathlon in which the swimming, biking, and running segments are all of the same length. The triathlete swims at a rate of 3 kilometers per hour, bikes at a rate of 20 kilometers per hour, and runs at a rate of 10 kilometers per hour. Which of the following is closest to the triathlete’s average speed, in kilometers per hour, for the entire race?
(A) 3 (B) 4 (C) 5 (D) 6 (E) 7</p>
<p>Yes, one could extend the harmonic mean formula for this case as well. But what is the point of complicating life? I would not recommend anyone to memorize the formula. Instead, understand the underlying concepts and be prepared to apply it to new situations.</p>
<p>I have never seen a rate problem of that level on the SAT. It is about 2 levels harder than any SAT question I have seen, and it lies outside the scope of this thread. </p>
<p>But in any case, for those interested in how to solve it, the second strategy I mentioned takes care of it pretty quickly. Just set up a “d=rt chart” with one more row. </p>
<p>Furthermore, again for those interested, I believe the generalization of Xiggi’s formula here would be average rate = 2(r1)(r2)(r3)/(r1<em>r2+r1</em>r3+r2*r3). This can be derived directly from the “d=rt chart.”</p>
<p>Again, I believe this problem to be well outside the range of problems tested on the SAT in its current form. So think about this problem only if you are interested in the problem itself, not in preparation for the SAT.</p>
<p>If someone has an actual SAT problem of this level of difficulty, please post it. I have yet to see such a problem. But if one exists, I will adjust my philosophy on these types of problems accordingly.</p>
<p>As long as we’re back on the subject of rate problems, let me just throw out another practice problem (a problem like the one that follows can definitely appear on an SAT).</p>
<p>Joseph drove from home to work at an average speed of 30 miles per hour and returned home along the same route at an average speed of 45 miles per hour. If his total driving time for the trip was 3 hours, how many minutes did it take Joseph to drive from work to home?</p>
<p>(A) 135
(B) 72
(C) 60
(D) 50
(E) 30</p>
<p>Try to solve this problem 4 different ways:</p>
<p>(1) With a “d=rt chart”
(2) Using Xiggi’s formula
(3) By starting with choice (C) (See this thread for more info:<a href=“http://talk.collegeconfidential.com/sat-preparation/1475829-sat-math-strategies.html[/url]”>http://talk.collegeconfidential.com/sat-preparation/1475829-sat-math-strategies.html</a>)
(4) By estimation</p>
<p>Which method do you like best? Note that methods (3) and (4) would not work if this were a grid-in question.</p>
<p>Don’t worry - we’ll get back to Permutations and Combinations shortly…</p>
<p>Let me add another way: by thinking about numbers and ratios. It’s good to develop methods that transfer to other settings. I encourage my strongest students to be able to quickly break any pile of stuff into any require ratio…</p>