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Preparing for math competitions


brownie
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For those of you who have done this, what would you say is an efficient way to prepare for math competitions? I am working through Competition Math for Middle school with my 5th grader now, and I am fairly pleased with it.  I have AOPS' Olympiad Problems which has been way too easy for a couple of years now (I emailed Richard about it - he said the contests have gotten progressively harder so the old problems are easier).  Is there a particular source of practice problems you would recommend as more worthwhile than others?

 

I should mention as far as level that he is finished with pre-algebra and we are just biding our time now until fall, hitting some gaps, doing some competition math and AOPS pre-algebra problems, Khan academy mission Algebra, etc...

 

Brownie

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My 8th grade daughter competed in and did well in our State Mathcounts and the AMC's 8 and 10 this school year.  Her best preparation so far I think has been having a strong understanding of the basic topics from using more challenging math throughout her elementary years.  From the time she was in 2nd grade we'd do a problem solving day once or twice a week.  For this she used Singapore Math CWP and IP books, Russian Math 6.  When in 6th grade, she moved to AoPS texts from Introduction to Algebra onward which included daily problem solving. 

 

Depending on which competition your son is taking, for practice problems you may want to get some previous exams from more recent years.  I think the difficultly levels will be more comparable to what may show up on a future exam.  You may also want to time him so that he gets used to the pace of an exam.

 

I also like the book, Art of Problem Solving Volume 1, The Basics.  Some of these problems can get very indepth with proofs and geometry, so you may want to wait until after he's completed Algebra and had a little Geometry to begin.  Also,  AoPS Counting and Probability and Number Theory books also cover some of the math that may show up that would not be found in most regular math texts. 

 

Good luck!  :)

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My oldest won scholarships through mathcounts. We think the best thing is to solidify the foundation of math and take it as deep as possible. AoPS is great for this.

Old tests are helpful, but there is only so much LEARNING that comes from these. Mathcount mini's are fantastic for learning the math around a specific area. They take a problem from previous chapter or state tests and make a video showing how to solve the problem. There is a worksheet that starts with problems easier than the video problem, then you watch the video and then you do more problems using those new concepts.

Alcumus is also great.

I would recommend all the Intro to books by AoPS before vol. 1 and 2.

I took a couple of kids to state mathcounts this year and they are working to do better for next year.

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Dd's story: We began homeschooling during her fifth grade year, floundered around with math that year, started AoPS with pre-algebra in sixth ("Mom, what do these letters mean after the problems?" "Math competitions? I want to do that!"), and have continued through the AoPS progression (pre, algebra, C&P, geometry, NT, Intermediate Algebra). She will use AoPS books/ take classes until they run out.

She has a very good grounding in math to this point.

She has been focusing on the various AMC competitions (no MathCounts team for homeschoolers here and no time left for me to start one). When she first started, she'd do just a few AMC 8 problems at a time. As it got closer to her first time for competition, we moved to timed complete tests (I printed them off from somewhere). This year I was able to find a place for her to take the AMC 10. I purchased a CD from MAA with years and years of all their exams---8, 10, 12, AIME, USAJMO, and USAMO---and she began systematically working her way through the AMC 10s.

I am going to get the two Problem Solving books for dd to have for additional practice. I haven't seen them yet.

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Besides what's already been mentioned, a few other resources:

 

MathCounts. If your child participates, he might qualify for college scholarships later. I believe homeschoolers can compete individually if they don't have a team and then at the contest, form a team with other individuals (there are three tests: individual, team, and team -- IIRC). One year in Illinois at the state meet, a group that formed a team like this placed high. Imagine if they had worked together the whole year!

 

http://www.artofproblemsolving.com/Store/contests.php?contest=mathcounts

 

The Mandelbrot Competition is sort of like the AMCs. Offers a range of problems.

 

http://www.artofproblemsolving.com/Store/contests.php?contest=mandelbrot

http://www.mandelbrot.org/resources/samples.html

 

:)

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I was wondering about the AOPS Problem Solving Basics book and its level.  So you think that is higher level than their counting and number theory books?  Brownie

I think of the AoPS Volume 1 Problem Solving Basics text as a summary of many elementary math topics with helpful tips geared towards math competitions.  It would be helpful (but not necessary) to have covered topics like Number Theory or Counting and Probability first.  I think it really depends on the background of the child.

 

In my daughter's case she did AoPS Volume 1 during the same semester when she was doing the second half of the AoPS Geometry, and it went well for her.  For her it wasn't necessary to have finished the Geometry textbook first.

 

I think several of these books (AoPS Number Theory, Counting and Probability, Volume 1:The Basics) could be done simultaneously.  The prerequisite would probably be the first half of the AoPS Algebra book or some other Algebra I course for a less frustrating experience.

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