Advertisement If you are interesting in participating in the American Regions Math League, let me know! See {\bf http://www.arml.com} for general information about ARML, and sign up to the Yahoo mailing list for local ARML teams at {\bf http://groups.yahoo.com/group/SFBA-ARML/} AIME perspective See the AMC web site for full statistics, but last year's mean score was about 2.85; the median was lower still -- and this is from a population of some 20,000 students who all qualified for the AIME in the first place!

Qualifying for USAMO: compute an index score: AMC + 10*AIME (whether 10 or 12). In 2007, theyll first take approx 330 students with highest indices FROM THE AMC 12 only.

Then: lowest AIME score for who qualified above gives a floor value. Approx 160 more students from 10th grade and below, no matter whether they took AMC 10 or AMC 12, will qualify based ONLY on the AIME floor. If there are too many students at this level, their index score will be used to break the tie. The ``floor'' last year was for the USAMO was 8 (with an index of 217.5), but this year it may be lower, as they are taking more students. It does depend on how hard the test is, which can vary a little from year to year. What you need to know This is just a partial list of concepts (and it wouldnt hurt to notice which ones we actually needed to do the problems today.) Between now and the AIME, you can't learn a LOT of new math, but you might want to review these lists and pick one or two new concepts to think about. A good, yet brief, overview is given in the introduction to ``The Mathematical Olympiad Handbook,'' written by Anthony Gardiner (Oxford Press, 1997). There is, of course, the ``Art of Problem Solving'' series available from artofproblemsolving.com, and you can find some nice online summaries of useful math facts by searching for ``Jim Sukha's Amazing ARML Handbook'' or ``The Noah Sheets'' of Noah Rosenberg.) Algebra Basic facts about polynomials, the quadratic formula, common factorizations (like the difference of two like powers), factors and roots and their relationships to the coefficients of a polynomial, the remainder theorem. The binomial theorem (see combinatorics, too). The rational root theorem. The formula for pythagorean triples. Arithmetic and Geometric series. Logarithms and exponential functions, Complex numbers. Geometry There are a {\em lot} of details and theorems to know here! Tom Davis has a nice summary of ``Contest Geometry'' at his website; http://www.geometer.org/mathcircles/geometry.pdf The aforementioned Noah Sheets include pretty much every theorem you need to know. The power of a point comes up a lot, so does the distance formula from a point to a line in Cartesian coordinates. Ptolemeys theorem has come up recently, and Stewarts theorem is often useful. The laws of sines and cosines are almost certain to be useful.

Basic Number Theory This should include the Euclidean algorithm, prime factorization of numbers, greatest common divisor and least common multiple, formulas for counting the number of divisors of a number as well as the sum of those divisors, modular arithmetic, the chinese remainder theorem, Fermat's little theorem. Euler's $\phi$ function. Combinatorics Pascal's triangle, permutations and combinations, binomial Theorem, principle of inclusion/exclusion. Ted Alper alper@epgy.stanford.edu