Most of our math contest preparation consists of working lots and lots of old test problems. Occasionally, however, I put together a tip sheet summarizing a topic that my students have trouble remembering.
Here are a couple of tip sheets I will be adding to my Handouts page:
Things to know about triangles (pdf 64KB)
We started with some basic observations about the relationship between angles and sides in a triangle, then moved to equilateral triangles and the 30-60-90. Unfortunately, I didn’t have much space for the Pythagorean Theorem — I really need to make a new tip sheet on that! Page 2 covers some basics about hexagons, especially as they appear in MathCounts problems.
Counting and Probability Basics (pdf 57KB)
Permutations, combinations, probability, odds — what’s the difference? This tip sheet gives you just the facts, with an absolute minimum of factorial notation. Mix with plenty of problems to solve, stir well, and discuss.
And here is one more source of practice problems, from my Resources page:
Preparation Drills for MATHCOUNTS
You can choose the type of problem (such as geometry, counting, or probability), whether you want multiple-choice or fill-in-the-blank questions, and anywhere from 5-30 problems on a page. Fun!
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