1. When a water tank is 30% full, it contains 27 gallons less than when it is 20% empty. How many gallons of water does the tank hold when it is full?
2. Stan drove 300 miles in 5 hours, 20 minutes. Next, he drove 360 miles in 6 hours, 40 minutes. What was Stan’s average speed in miles per hour for the total trip?
3. What is the difference between the 2000th term and the 2005th term of the arithmetic sequence −8, −2, 4, 10, ... ? An arithmetic sequence is found by adding the same amount over and over to find each term. For example, in the sequence 1, 3, 5, 7, 8… the amount being added is two. You can use this to find numbers in the sequence.
4. In the game “Cover It Up” two standard six-faced dice are rolled and their sum determined. The player can then cover that number on the game board or any two numbers that have that sum. For example, if you roll a 3 and 5, you can cover the 8, the 1 and 7, the 2 and 6, or the 3 and 5. What is the probability of being able to cover the 9 on the first roll of the two dice? Express your answer as a common fraction.
5. A teacher has made eight statements for a True-False test. Three statements are true and five are false. How many distinct answer keys could there be for the test?
Tuesday, May 12, 2009
Wednesday, April 8, 2009
Problem of the Month--April
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.
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.
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
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