Not a lot of people turned in answers last week, so keep the same problems for this week. Also, learn the sequence for pi. Awards will be given for Pi Day! March 3, 2009 is Square Root Day. 3 is the square root of 9, and 3 times 3 is 9.
1. February 2, 2004 was the last Square Root Day. When is the next Square Root Day?
2. Name two formulas that use square roots.
3. How many Square Root Days occur each century?
4. What is the sum of the first five squares? 9 is a square because 32 = 9.
5. Figure out my wife’s height using the following clues. Her height is x feet and y inches. (x + y)2 = 144. (x – y)2 = 4.
6. For the first time since 1997, the Dow Jones finished below 7000. It finished at 6,763. What is the closet square to 6,763?
7. I am thinking of a number. If I take the square root of my number, add two, square the number, and then divide by 5, the result is 45. What is my number?
8. A googol is a 1 followed by 100 zeros. What is the square root of a googol?
Monday, March 2, 2009
Tuesday, February 17, 2009
Problems of the Week--2/17/09
Answers due by Friday
1. What is the 20th term of the arithmetic sequence shown below?
13, 19, 25, 31, ...
2. What is the sum of A and B from the arithmetic sequence shown below?
7, 15, 23, A, 39, B, ...
3. What is the sum of A and B from the geometric sequence shown below?
32, A, 72, B, 162, 243...
4. The NBA All-Star Game was last weekend. The top vote-getter was Dwight Howard. Below is a breakdown of the voting for all Eastern Conference centers. Determine the percentage of these votes that Dwight Howard received.
Dwight Howard 3,150,181; Kendrick Perkins (Bos) 621,709; Rasheed Wallace (Det) 402,991; Samuel Dalembert (Phi) 396,119; Andrew Bogut (Mil) 357,997; Jermaine ONeal (Tor) 342,723; Al Horford (Atl) 323,302; Brendan Haywood (Wash) 291,490; Ben Wallace (Clev) 263,862; Zydrunas Ilgauskas (Cle) 219,697; Emeka Okafor (Char) 212,539
1. What is the 20th term of the arithmetic sequence shown below?
13, 19, 25, 31, ...
2. What is the sum of A and B from the arithmetic sequence shown below?
7, 15, 23, A, 39, B, ...
3. What is the sum of A and B from the geometric sequence shown below?
32, A, 72, B, 162, 243...
4. The NBA All-Star Game was last weekend. The top vote-getter was Dwight Howard. Below is a breakdown of the voting for all Eastern Conference centers. Determine the percentage of these votes that Dwight Howard received.
Dwight Howard 3,150,181; Kendrick Perkins (Bos) 621,709; Rasheed Wallace (Det) 402,991; Samuel Dalembert (Phi) 396,119; Andrew Bogut (Mil) 357,997; Jermaine ONeal (Tor) 342,723; Al Horford (Atl) 323,302; Brendan Haywood (Wash) 291,490; Ben Wallace (Clev) 263,862; Zydrunas Ilgauskas (Cle) 219,697; Emeka Okafor (Char) 212,539
Monday, February 9, 2009
Problems of the Week--1/9/09
MathCounts Inspired Problems
Double points week! Answers due Friday by noon.
1. February 2 was Groundhog Day. Every February 2, Punxsutawney Phil lumbers out of his home to predict the end of winter by looking for his shadow. If Phil sees his shadow, legend says that we will have 6 more weeks of winter. If the groundhog does NOT see his shadow we will have an early spring.
2. According to the “official” Groundhog Day website, Punxsutawney Phil is 123 years old. Normally, groundhogs live up to 6 years in the wild. If Phil is 123 years, by what percent has he exceeded the normal, unaided lifespan of his species?
3. A groundhog is also known as a woodchuck. Diana writes the letters w, o, o, d, c, h, u, c and k on separate pieces of paper and places the pieces of paper in a bag. If Diana randomly draws one piece of paper from the bag, what it the probability that the letter drawn is also contained in the word groundhog? Express your answer as a common fraction.
4. Groundhog Greg’s burrow has 5 holes he can enter or exit through. If he never exits through the same hole he entered through, how many entrance/exit combinations can Greg choose from? Note that entering through A and leaving through B is not the same as entering through B and leaving through A.
5. What is the 20th term of the arithmetic sequence shown below?
13, 19, 25, 31, ...
6. What is the sum of A and B from the arithmetic sequence shown below?
7, 15, 23, A, 39, B, ...
7. What is the sum of A and B from the geometric sequence shown below?
32, A, 72, B, 162, 243...
8. A worm has to climb a barrier 19 feet high. It climbs 8 feet every day and slips down 5 feet every night. Starting from the bottom of the barrier on Sunday morning, on which day of the week will the worm reach the top of the barrier?
9. How many fifteen-minute appointments can a doctor fit into her schedule if she works from 8:30 am to noon and from 1 pm to 4:30 pm?
10. On a $12.00 purchase, Michael was offered 3 successive discounts of 25%, 20% and 10% each in any order he wished. What is the difference in dollars between applying the discounts in order from greatest to least and in order from least to greatest?
Double points week! Answers due Friday by noon.
1. February 2 was Groundhog Day. Every February 2, Punxsutawney Phil lumbers out of his home to predict the end of winter by looking for his shadow. If Phil sees his shadow, legend says that we will have 6 more weeks of winter. If the groundhog does NOT see his shadow we will have an early spring.
2. According to the “official” Groundhog Day website, Punxsutawney Phil is 123 years old. Normally, groundhogs live up to 6 years in the wild. If Phil is 123 years, by what percent has he exceeded the normal, unaided lifespan of his species?
3. A groundhog is also known as a woodchuck. Diana writes the letters w, o, o, d, c, h, u, c and k on separate pieces of paper and places the pieces of paper in a bag. If Diana randomly draws one piece of paper from the bag, what it the probability that the letter drawn is also contained in the word groundhog? Express your answer as a common fraction.
4. Groundhog Greg’s burrow has 5 holes he can enter or exit through. If he never exits through the same hole he entered through, how many entrance/exit combinations can Greg choose from? Note that entering through A and leaving through B is not the same as entering through B and leaving through A.
5. What is the 20th term of the arithmetic sequence shown below?
13, 19, 25, 31, ...
6. What is the sum of A and B from the arithmetic sequence shown below?
7, 15, 23, A, 39, B, ...
7. What is the sum of A and B from the geometric sequence shown below?
32, A, 72, B, 162, 243...
8. A worm has to climb a barrier 19 feet high. It climbs 8 feet every day and slips down 5 feet every night. Starting from the bottom of the barrier on Sunday morning, on which day of the week will the worm reach the top of the barrier?
9. How many fifteen-minute appointments can a doctor fit into her schedule if she works from 8:30 am to noon and from 1 pm to 4:30 pm?
10. On a $12.00 purchase, Michael was offered 3 successive discounts of 25%, 20% and 10% each in any order he wished. What is the difference in dollars between applying the discounts in order from greatest to least and in order from least to greatest?
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!
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