<p>Hey guys, I want to try out for my schools math league team next year and try AMC. I am not to familiar with how to prepare. Math is nowhere near my best subject, but I believe I have the intelectual capacity to improve. I am a freshman. I am not to experienced so I will not start with the beginner basics. The team is very hard to make at my school. Most kids pass AMC and get to AIME and a few even get to USAMO. Not only our A team, but also our B and C teams are heads and shoulders above any other team in the state. I want to make the team. I have heard Art of Problem Solving is good, but I have no clue which ones to get. Could someone recommend which to start with or any other good series. Thanks</p>
<p>If you’re already familiar with Algebra II, Geometry, and Trig, try Art of Problem Solving Volume 2. If not, then start first with volume 1 and move to volume 2. IMO, volumes 1 and 2, as well as plenty of AMC/AIME practice tests, should be enough to reach USAMO level.</p>
<p>Yea, you should be going on artofproblemsolving.com and not this website if you want to learn stuff about math. I wouldn’t recommend reading the textbooks, I haven’t found them particularly helpful in improving at contests, although they are interesting. </p>
<p>What you should do is take AMC 12s until you are able to consistently do almost every question (try and do them in 75 minutes, but a lot of people who just work slow get 110 on AMC 12 and 12 on AIME). When the AMC 12s no longer challenge you, move on to AIMEs. USAMO is a different beast entirely, and if you think you have the capability to solve questions on USAMO, by all means practice. But keep in mind that the majority of people who make USAMO (which are the top ~300 math students in the entire country) will get a zero or a one.</p>
<p>First, you should have a solid command of algebra, geometry, trigonometry, pre-calculus, and counting/combinatorics. Competition math (especially at the AIME/USAMO/IMO level) requires knowledge of many theorems not often covered in high school math, including Vieta’s formulas, AM-GM and Cauchy-Schwarz inequalities, Muirhead’s inequality, Ceva’s theorem, Jensen’s inequality, Brahmagupta’s formula, and so on.</p>
<p>Don’t worry if you don’t know all of these theorems/techniques right now. You’ll learn them eventually. </p>
<p>Try some of the easier AMC10/AMC12 problems first (you can look on AoPS for past years). After some practice, try some of the mid-range AMC problems. Over time, you’ll find yourself solving these problems faster and more quickly than before.</p>
<p>The last five or so AMC problems are tricky, especially in the past few years. Those are comparable in level to mid-AIME level problems. AIME problems range from fairly simple, two step problems to very difficult problems with a very clever but hard-to-find solution.</p>
<p>If you manage to make it to USAMO, it’s usually better to already know how to write proofs, so if you think you can make USAMO, start practicing (you don’t want to make it to USAMO and score 0). I only made USAMO once (10th grade) but scored a 13/42.</p>
<p>If you make it to MOP, you have my respects forever. Most MOP students I know are extremely sharp and have started training since 6th grade. However I do know someone who got a gold medal at IMO even though he didn’t start until ~10th grade.</p>
<p>Since you’re in 9th grade, you may want to start with AMC10 and work your way to USAJMO. However, you’ll have to know topics covered in pre-calculus when you take AIME.</p>
<p>Thanks for the help guys. I am in no way going crazy hard on math. I have not really liked math as a school subject, but problem solving has started to appeal to me. I will probably take pre-calc next year, so that might hold me behind. Other competitions I participate in are of higher importance to me. I just want to be on the school team and qualify for AIME sometime in high school. Not even gonna ever think about USAMO. This year, 5 freshman got to AIME and 1 is at USAJMO. They are very impressive. I can’t even think about being on the same level as them. I would just like to study this for self-improvement and self-satisfaction. I have found the problems very cool. It would be cool if I could learn to solve them and make the Math League team.</p>
<p>Yeah, qualifying for AIME definitely helps on college applications. A score of 8-10 will likely qualify you to USAMO/USAJMO (although I got 8 last year and missed the cutoff). But even if you don’t make USAMO, you’ll still gain the problem-solving edge and it will be advantageous when you take more difficult classes in college.</p>
<p>The nice thing about AMC/AIME/USAMO is that they don’t go past pre-calculus level but they are much harder and more complex (and more fun) than math problems you see in high school.</p>
<p>What do you think of buying just one of the AoPS books? Should I buy the first one, or the second one, or would you really recommend buying both? I’m a junior with a strong (Chinese) mathematics background. I’d like to start preparing now, over the summer. I only got 89 this year without preparation, but I’d like to at least qualify for AIME next year.</p>