<p>I just read my school news that my friend scored 99.9% nationally on AMC 10 and he scored the highest score in state(southern). Does it mean my friend made almost perfect score on it? Or just 99.9 out of 150? But it doesn't say he qualified for AIME.
Also, does taking AMC/AIME/USAMO guarantee getting accepted to MIT, Havard or other top universities? </p>
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<p>No.</p>
<p>wait, do they matter… i had to miss my amc 12 this year because i took my driving test… ugh didn’t know</p>
<p>*99.9 out of 150 is impossible.</p>
<p>*99.9% is very likely near a perfect score (or around 144+).</p>
<p>*Making USA(J)MO does not guarantee admission. I scored 13 on USAMO and was rejected by Caltech.</p>
<p>I am planning to take AMC 12 and at least qualify for AIME. What I am concerning is that this is my first time taking AMC 12. I did not even know AMC has been existing until I came College Confidential.</p>
<p>When I tried to solve past AMC 12 problems, honestly, I could not solve any. I am trying to start from very very basic from now on. So can you guys advise me what to do? Whats the best book for beginner? Also, share how to study effectively!</p>
<p>Thank you sir in advance 
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<p>Try the “Art of Problem Solving” books. I think they also have a website. If you have taken through algebra 2 and geometry, traditional education alone you should be able to be on the cusp of qualifying 90-100 if you have aced your classes.</p>
<p>hmmm, I read somewhere that only a small fraction of the population actually has the talent to be competitive in the international olympiad for math. Don’t beat yourself up if you can’t solve a single problem. </p>
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<p>^That goes without saying. </p>
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<p>To expand on my post, AMC12 is the first exam, so it is the easiest. Something like 8000 people in the country get over 100 out of 150, which qualifies them for the next stage (the qualifying point went down to 90 I heard). To qualify, at a minimum you have to have a rock-solid mastery of algebra through algebra II and geometry–you should be getting A+s in your math classes, and fairly easily. One of the high schools was a good school and we usually had like 1 qualifier per 500 students, and usually not freshmen.</p>
<p>The people who are best at these contests are ones that can find a creative solution to a new problem. For instance, when you do a new unit in math, you should try to solve the example problems before you are given a method for solving it. </p>
<p>Although the best students can find solutions on their own, I think Art of Problem Solving presents them with challenging problems that are just out of their current level of mastery, then they solve that problem or attempt to, and then they are a little more sophisticated. I think there are some themes of problem solving that you learn as well. Finally, there is some memorization of algorithms that helps as well.</p>
<p>A classic math team type problem is solving for the sum of the first 100 numbers. The BEST way to do this is to start to write down numbers of this sum in different ways and then notice patterns. Then you notice that the first and last number sum to 101, the second and the second-to-last number sum to 101, and so on. From there, you can generate a formula (Sum of first n numbers = (n+1)n/2.) Even great students (myself included) fail to do this, though I’m convinced you get better at it by trying even with failure. Gauss famously derived this solution when he was in 1st grade.</p>
<p>However, through training a student will encounter that problem and then know how to do it. So a bit artificially, the talented students do get better and will get that problem right on one of these exams. Chess is like that too; at some point you do memorize responses to different positions, though intuition is still crucial. Some advance problems on the AMC12 that were number theory-ish were like “find the number of prime numbers in 1997” or that sort of thing. Some more training in specific fields helps on these tests. Number theory tricks (factorization, prime numbers, multiples), combanitorics (probabilities), in addition to hard algebra and geometry problems (the gimmes) are staples of this test.</p>
<p>Hopefully, next time they also learned something about <em>how</em> it was solved and not just the algorithm. For instance, I didn’t fully appreciate that writing a series of numbers down in different ways could help you see a pattern; typically, I thought you should be able to do it from intuition, algebraic manipulation, or by visualizing it alone. </p>
<p>At the highest level of these contests, you have to be very creative. </p>
<p>Just wanted to throw in the observation that E. T. Bell, in Men of Mathematics, wrote that Gauss was 10 when he came up with the summation method spontaneously (rather than 6 or 7, which you might expect for a first-grader). </p>
<p>Sigma Xi has a site with multiple tellings of this tale, over the years: <a href=“404”>Error;
<p>The excerpt from work by A. Galle in 1916 stated that Gauss was 9 at the time. Ludwig Haenselmann in 1878, asserted that Gauss was “in his ninth year,” which I take to mean 8 + some months. If I had to bet, I’d go with Haenselmann. Spotting the summation trick at 8 or even 10 is still plenty of an illustration of genius, especially in Gauss’s era.</p>
<p>Still, it is worth noting that while Gauss had not been shown this particular method, he was not completely untutored in mathematics beforehand. I have read that his uncle set mathematical puzzles for Gauss when Gauss was a young boy (of preschool age).</p>
<p>I am firmly of the belief that anyone can increase his/her mathematical problem-solving skill by working at it. If you try to approach your study by just learning algorithms, it will most likely give you a few extra points in the math contests, but not take you very far. If you approach your study by trying to really understand things, I think you will find that your creativity blossoms, too.</p>
<p>In a related vein, when I listened to seminars or read scientific papers or books back in college, I would generate a few questions, but they weren’t all that great–mostly pretty detail-oriented. Now, after many years, I am all about questions. Every scientific issue I encounter inspires large numbers of questions. </p>
<p>Also, it looks to me as though a perfect score (150) on the AMC 10A would put a student at the 99.93 %ile. Unless my arithmetic is wrong. Which does happen from time to time. A perfect score on the AMC 10A is really great!</p>
<p>It’s probably worth mentioning again that excellence in the AMC and related math competitions is neither necessary nor sufficient for MIT admission. (I will not beat the dead CC horse of whether it should be.)</p>
<p>I’m not sure how much the AMC 10 is weighted compared to other math competitions. Personally if someone scored very well on the AMC 10 but not on harder math competitions (AMC 12, AIME, USAMO) I would not be impressed.</p>
<p>@kdajfpasfiu AoPS introduction/intermediate books are good resources, ranging from MATHCOUNTS and middle-school level problems to more advanced AMC/AIME problems. The first 5-10 problems on the AMC are usually fairly introductory, similar to ones you’ve seen in school. #20-25 can be quite challenging (even for me) and are comparable in level to early-mid AIME problems.</p>
<p>I am not really familiar with the AMC10. It didn’t exist when I went to school. What’s the difference between AMC10 and AMC12?</p>
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<li><p>You can take AMC12 in 12th grade and below, AMC10 in 10th grade and below.</p></li>
<li><p>AMC10 does not test pre-calculus (i.e. no problems require topics such as trig or logarithms).</p></li>
<li><p>This one is fairly recent, but you can only qualify for USAMO through AMC12 and USAJMO through AMC10. USAJMO is also new (started in 2010), it’s basically an easier olympiad.</p></li>
<li><p>AMC10A and AMC12A are offered on the same day, as well as AMC10B/AMC12B (so you can take two AMC’s officially in a year). The A tests and the B tests each have about 10-15 questions in common.</p></li>
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<p>If you’re familiar with AHSME, the AMC12 is basically a newer AHSME.</p>
<p>Some additions @kdajfpasfiu, to the excellent posts made here:</p>
<p>Log on to USAMTS.org. The first round problem set was posted last week. These problems will give you a flavor of the AMC. And, yes, much like chess or crossword puzzles, there is a culture and rhythm to the questions, and some inculcation is needed. AoPS is an excellent resource. USAMTS is also a qualifier into this USAMO track.</p>
<p>While AMC is based on being clever quickly (not everyone who is clever is fast, and not everyone who is fast is clever); AIME supposedly takes a deviation and asks that you have some background/practice in proofs.</p>