Responses have dwindled each week since these questions do not count for Black and Gold points, but there are a few dedicated students that still have been waiting for the problems of the week. Instead, there will be a set of problems for the month of April and the month of May. The prize list is still up for grabs for 4th quarter. Good luck!
Problems of the Month
1. If b is positive, what is the value of b in the geometric sequence 9, a, 4, b? Express your answer as a common fraction. A geometric sequence is found by multiplying by a common factor. For example, in the sequence 1, 2, 4, 8... the common factor is 2. Find the common factor, and then use it to solve.
2. Noel earns $25 each week mowing lawns. Each week he spends two-fifths of his earnings on himself and has the rest of his earnings placed directly into a savings account. Every third week he withdraws $20 from his savings account to take his girlfriend to the movies. If he continues this same spending pattern, how many weeks will it take Noel to first exceed $125 in his savings account? Express your answer as a whole number.
3. Two complementary angles A and B have measures in the ratio of 13 to 17. What is the ratio of the measure of the supplement of angle A to the supplement of angle B? Express your answer as a common fraction.
4. Amy and Belinda each roll a sheet of 6-inch by 8-inch paper to form a cylindrical tube. Amy tapes the two 8-inch sides together without overlap. Belinda tapes the two 6-inch sides together without overlap. What is the difference of the volumes of the two tubes?
5. The scale of a certain map is 0.8 inch = 16 miles. A square park is represented on this map by a square with side length 0.625 inch. What is the actual area of this park? Express your answer as a decimal to the nearest hundredth.
Wednesday, April 8, 2009
Monday, March 2, 2009
Problems of the Week
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?
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?
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?
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