Information submitted by Foothill High School's Math Team—
On June 4th and 5th, Foothill High School's Math Team brought Pleasanton students together for a battle of wits - the Foothill Math Tournament (FMT).
Foothill's Math Team officers Akshay Ravikumar, Yujin Kim, Nathan Zhang, and Roland Huang, under the supervision of Mr. Scott Gorsuch, organized FMT to expose competition math to students in an enjoyable format. An impressive 150 students participated, representing all of Pleasanton's middle and high schools.
On the first day was a "guts round," in which teams of three students tried to solve as many problems as possible in a short period of time. The results from this contest were used to create brackets for a tournament round the next day.
The top eight teams were awarded with over $1000 worth of prizes, generously donated by Ross Stores, EMC, Texas Instruments, Jane Street Capital, Art of Problem Solving, and Wolfram Research.
Math competition problems are unlike anything seen in a standard math class: though solvable with precalculus methods, these problems require intuition and insight to solve.
Here are a few examples of FMT problems:
- Three students were supposed to graph a line with negative slope; however, the students were pretty careless. Wyatt accidentally switched the slope and the constant term, and Bryce accidentally switched the x and y intercepts - each of these produced an incorrect graph. However, Akshay graphed it correctly. When they put their three graphs on top of each other, they all intersected at exactly one point. What is this point of intersection? Express your answer as an ordered pair.
- Circle w intersects a larger circle with center O at points A and B. BC is the diameter of w. If OC is perpendicular to AC, BC = 7, and AB = 2, find the area of circle O. Justin breaks a 12-inch ruler into three parts and makes isosceles triangle ABC with AB = BC. If he took AC and cut off a piece of length x, he could make an equilateral triangle. Instead, if he took AB and cut off a piece of length x, he could make a right triangle. Find the value of x.
Foothill and Amador's Math Teams work together to promote an interest in math and participate in competitions. While having competed in locations like Boston, Los Vegas, Pasadena, and New York, these students have founded several endeavors in Pleasanton. These include the Pleasanton Math Circle (pleasantonmathcircle.com) and the Pleasanton Geometry Bee. For more information, please contact email@example.com.