MathCounts Competition

On Saturday, February 7th, nine Calvert students spend the morning and afternoon competing with other schools in the MathCounts Chapter Competition. For the second year in a row, Calvert School placed as a team with the state qualifiers. Last year we placed 5th, and this year we placed 4th. Before last year, we never had a team place in the chapter competition.

In addition, Joshua Khuvis placed 4th in the region out of around 200 participants. Robby Vint, Paul Berman, Bert Schmickel and Joseph White placed in the top 16 students. Tess Kamauff also placed in the top 36 students. All six of these students have qualified for the State Competition in March.

The other students that participated in the competition are Peter Cooke, Ashley Mitchell, and Dale Waters. These students also did very well, but their scores were not quite high enough to qualify for the state competition.

Stay tuned for the results from the State Competition next month!

Problems of the Week—January 27, 2009

Bowling Buddies
Anita, Cheri, Miguel, and Jake went bowling one night. For fun, they decided to pit the girls against the boys, with the highest total score for each team winning.

Anita scored 18 less than Miguel. Cheri's score was 16 less than twice Anita's. Cheri outscored Jake by 21.

If the total scored by all four kids was 529, what was the final score of the match?


Dimensions
A rectangle has an area of 147 ft2. The length is three times longer than the width. What are the length and the width of the rectangle?


Who likes which snack?
-Cindy does not like sweet treats.
-Carl loves fruit.
-Catherine does not like cantaloupe or cinnamon rolls.
-Chuck likes cake.
-Carrie likes icing.
-Someone likes cookies, and another likes cereal.


Say What?!?
The sum of a certain number of consecutive integers, starting with -22, is 72. What is the largest number in the group of integers?

Problems of the Week--Inauguration Day

Submit the answers by 8:15 am on Monday morning. I forgot to post these. I wrote them over Winter Break...

1. The 2009 inauguration is expected to see record levels of attendance. Lyndon B Johnson’s inauguration currently holds the record for attendance at 1.2 million people. Originally, attendance for the 2009 inauguration was projected to be as high as 5 million. Now, based on more accurate data, the projected attendance is around 2 million. What is the positive difference between the originally estimated percent increase over the current record attendance and the newly estimated percent increase over the current record attendance? Round your answer to the nearest whole number.


2. The National Mall is 300 acres. It stretches 1.9 miles from the Capitol building to the Lincoln Memorial. This will be the first time in history that the entire mall will be open for an inauguration. If attendance is the estimated 2 million people and all of the people spread out evenly over the mall, how many square feet will each person get? Note that 1 acre is equal to 43,560 square feet. Express your answer as a decimal to the nearest tenth.

Problems of the Week

Sorry for the delay. I will accept the answers by midnight on Friday, January 16th.

Football – The Problems
January 12, 2009

The minimum starting annual salary for rookies in the NFL is $295,000. The minimum annual salary is $370,000 for second year players and $445,000 for third year players. For a player earning the minimum salary for their experience, what is the positive difference between the percent increase the $75,000 represents from the first to second year and the percent increase the $75,000 represents from the second to third year? Round your answer to the nearest tenth.

There are 32 teams in the NFL. Sixteen of the teams are in the American Football Conference (AFC) and the other 16 teams are in the National Football Conference (NFC). At the beginning of the season, Julia tried to predict the teams that would be in each conference's championship by randomly drawing 4 teams (2 AFC teams and 2 NFC teams) from a hat. What is the probability that the 4 teams she selected are the same four teams that will be in the conferences' championships? Express your answer as a common fraction.

In football, teams can score 6 points with a touchdown, 3 points with a field goal or 2 points with a safety. Additionally, after a touchdown, teams can score 1 bonus point with a field goal kick or 2 bonus points with a 2-point conversion. The final score of a particular football game was 23 to 11. If every touchdown is followed with a successful bonus point attempt (1 or 2 points), how many different scoring combinations could have resulted in the losing team's 11 points?

Using the remaining teams, I have created a formula for determining the Super Bowl Champion. Based on their ranking in each category, a team is awarded points. The highest ranked team receives a 1, and second ranked team receives a 2, and so on. In the case of a tie, give both teams the lower score. For example, if two teams are tied for second in a category, give both teams 2 points. The lowest total score is the team that should win the Super Bowl. Using this formula, which team should win?