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Category Archives: Contest Math
Conceptual Solution to 2008 AIME I, Problem 14
Here’s a solution to problem 14 on the 2008 AIME I contest that attempts to avoid computation as much as possible. Sometimes, it’s an amusing exercise to try to solve a contest problem entirely in your head. Doing so often forces … Continue reading
Posted in Contest Math, math
Tagged AIME, circles, ellipse, geometry, optimization, tangent
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Do you believe this?
Here’s a triangle: I’ll use the vertex labels to also denote the corresponding angle measures. Take the sines of all 3 angles in the triangle: , , and . Would you believe it if I told you that these three … Continue reading
Posted in Contest Math, math
Tagged law of cosines, Ptolemy's theorem, similarity, sine, triangles, trigonometry
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2013 AIME 2 Problem 10
I’ve been asked about the following problem from the 2013 AIME 2 a few times, so I decided to blog a couple of solutions for it: Given a circle of radius , let A be a point at a distance from … Continue reading
2012 Math Prize for Girls: #1620
Here are comments and solutions to (some of) the problems on the 2012 Math Prize for Girls contest that took place at MIT on September 22.
Use Your Mind to Save Yourself Time
I’m looking forward to Games Night at the Math Prize for Girls coming up this weekend. I’ve been working with the author of “Mess or Math?” to create a really fun math activity and I hope many of you who … Continue reading
Posted in Contest Math, math, Math Education
Tagged AMC 12, circles, circumference, geometry, similarity, tangent circles
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2011 Math Prize for Girls: #15
Here are comments and solutions to problems 15 on the 2011 Math Prize for Girls contest that took place at MIT on September 17, 2011. Earlier I blogged comments and solutions for problems 610, problems 1115, and problems 1620.
2011 Math Prize for Girls: #610
Here are comments and solutions to problems 610 on the 2011 Math Prize for Girls contest that took place at MIT on September 17, 2011. Earlier I blogged comments and solutions for problems 1115 and problems 1620.
2012 AIME 1 Problem #12
I was checking out Mess or Math?’s cool blog and her latest post wonders whether problem 12 on the 2012 AIME 1 has a simple solution. Simple is a subjective term. The problem’s setup certainly suggests invoking things like the … Continue reading
2011 Math Prize for Girls: #1115
Here are comments and solutions to problems 1115 on the 2011 Math Prize for Girls contest that took place at MIT on September 17, 2011. Click here for comments and solutions for problems 15. Click here for comments and solutions for … Continue reading
Back to Basics: Arctangent
Recently, a student asked me about problem #8 on the 2008 AIME 1 competition, which is reproduced here for your convenience: Find the positive integer such that . She was able to solve this using the sum of arctangents identity … Continue reading