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Math League

West Math League

The Mankato West Math League competes in the Minnesota Valley Conference against eight other teams. There are five meets throughout the year. At these meets, each of the students take two of the four available tests. On each test there are four questions, the first being worth 1 point and the last three all worth 2 points. 8 students from each team are chosen to count towards their team total. With each of these students taking two of the tests, the sixteen scores counted for team totals must be divided so that four are from each event (A, B, C, and D). Then the same 8 students, as a group, take a team test composed of 6 questions worth 4 points apiece.

The West Math League Team has done very well in the past and has usually been one of the top three teams to finish in total points each year. They have even made some state tournament appearances in the past and have placed well. During the 2001-2002 season one student had tied for the highest individual points scored during the season and was able to compete in the state tournament as an individual.

Steven Jones
 

Minnesota Math League

 

Important Information

Meet Procedures

Math League Meets begin at 3:45 and last until about 5:45. During this time all of the different teams are in a cafeteria or other large room and the students wait at tables for their events to take place. While waiting, the students from Mankato West usually snack on food, chat with each other, and play different card games to pass the time.

First the Event A students are called, and they all file into certain rooms in the school and sit at an open desk. They are given 12 minutes to work on four Event A questions. Each correctly answered question is worth 2 points except the first question which is only worth 1 point because it is easier than the other three. After the twelve minutes are up, a supervisor collects the tests and brings them to the test scorers. After Event A is finished, the Event B students are called. Then the Event C students are called, followed by the Event D students. Last, the 8 Team Event members from each school gather into their own room and are given 20 minutes to work on six Team Event problems as a group. Each of these questions is worth 4 points if correctly answered.

After each event has finished testing, the answers for that test are posted in the halls for participants to look at to see how well they did. Also, after all of the tests for a particular event have been graded, the totals for that event of the students who count towards their team score are posted on a team leader board. This lets the teams know how many points ahead or behind they are of other teams after each event. The team with the highest total of points for a certain meet have the privilege to take home the leader board for that meet, and the team with the highest total points accumulated over all of the five meets, earns the right to go to the state competition.

Practice Procedures

Practices occur about three times a week. One practice is for the Event A and Event B participants, one practice is for the Event C and Event D participants, and the last practice is for the Team Event participants.

Practices last from 3:15 until 4:00. For the Event A/B and Event C/D practices, the coach hands out tests from previous math league meets, and the students work on the problems for 12 minutes just like they would in an actual meet. After that they go over the answers and discuss the difficult questions. The same happens for the Team Event practice, except the students get into groups and work on the problems together for 20 minutes.

The coach also provides a bowl of candy to the students during practices to help fuel their minds for thinking.

Sample Problems

These are some sample Math League problems that came from some of past year's actual questions.

1. Solve ax + b2 = bx + a2 in terms of a and b, given that a does not equal b. 

2. A car can go r miles on s gallons of gasoline. How many gallons of gasoline would it take for a journey of t miles?

3. Our newest scanner can grade 25,000 exams per hour, a great improvement over the three hours it took our previous machine to do the same job. We still have two older machines available, one of which took five hours, and the oldest that took seven hours to grade 25,000 exams. How long (to the nearest minute) would it take all four machines working together to grade 75,000 exams ?

4. Two runners start running laps at the same time from the same starting point (in the same direction). One runner takes 90 seconds to run a lap; the other takes 65 seconds to run a lap. When will the runners next be even to each other (in minutes and seconds)?

5. Express sin4x = cos4x as a function of sin 2x. 

6. ABCD is a square and both triangle BAF and triangle CBE are equilateral. What is the measure of angle FEB? 

7. The inner regular hexagon in the figure is formed by joining the midpoints of the sides of the outer regular hexagon. What is the ratio of the area of the larger hexagon to the smaller? 

Click here for the answers