Please review the solutions to the previous week's set. Then, move onto this one. In the meantime, be looking at the marathon problems.
1. Laws in certain states require a 60% approval rate from voters before issues are “passed”. If 1,140 people voted in favor of the law, and this represents 57% of the total number of voters, how many voters were there in this election?
2. Two congruent cones with radius 12cm and height 12cm are enclosed within a cylinder. The base of each cone is a base of the cylinder, and the height of the cylinder is 24cm. What is the number of cubic centimeters in the volume of the cylinder not occupied by the cones? Express your answer in terms of π.
3. The sum of three different prime numbers is 40. Find the product of the largest two of the primes.
4. Shauna did a number trick with Zach. She told him to pick an even number, double it, add 48, divide by 4, subtract 7, multiply by 2, and subtract his original number. She then told him the result he should have attained. What was it?
5. A positive three digit integer is divided by a positive two digit integer, yielding an integer quotient and zero remainder. What is the smallest possible integer quotient?
Have fun, guys!
Sunday, February 6, 2011
Friday, January 28, 2011
Problems of the Week 1/31
Please review the solutions to the previous week's problems. Then, move on to this set. Meanwhile, be looking at the marathon problems and providing solutions to some of them.
1. Isabella can paint a house in just 2 hours. Amy can paint a house in 200 hours (because she takes breaks to read and sip lemonade :-)). Working together, how long will it take them to paint 2 houses?
2. Amy is playing with her choo-choo train. Every 5 seconds, she giggles, and every 8 seconds, she claps her hands with glee. After what percent of a minute does Amy clap her hands and giggle at the same time?
3. Amy received a little conductor doll for her choo-choo train. She placed it on top of the train and then watched excitedly as it fell off the train and got squished under the wheels. Suddenly, it hit her that her conductor was dead, and she began to cry with pure anguish. Isabella, famous detective, was called in to investigate the cause of the conductor's death. The conductor was a flat rectangle and Isabella drew a chalk rectangle that exactly matched up with the conductor's plastic body. If the perimeter of the rectangle was 14 centimeters, and the product of the length and width is 10, what is the length and width?
4. Isabella came over to Amy’s house to play with her choo-choo train set. Unfortunately, Amy slipped on an ice cube and broke the set. They then divided up the work into two halves: Amy would find the pieces and Isabella would put them back together. It takes 3 hours for Amy to find a piece and 4.5 hours for Isabella to put it in its right spot. If the train set has 5000 pieces, how long will they be working?
HAPPY PROBLEM SOLVING!
1. Isabella can paint a house in just 2 hours. Amy can paint a house in 200 hours (because she takes breaks to read and sip lemonade :-)). Working together, how long will it take them to paint 2 houses?
2. Amy is playing with her choo-choo train. Every 5 seconds, she giggles, and every 8 seconds, she claps her hands with glee. After what percent of a minute does Amy clap her hands and giggle at the same time?
3. Amy received a little conductor doll for her choo-choo train. She placed it on top of the train and then watched excitedly as it fell off the train and got squished under the wheels. Suddenly, it hit her that her conductor was dead, and she began to cry with pure anguish. Isabella, famous detective, was called in to investigate the cause of the conductor's death. The conductor was a flat rectangle and Isabella drew a chalk rectangle that exactly matched up with the conductor's plastic body. If the perimeter of the rectangle was 14 centimeters, and the product of the length and width is 10, what is the length and width?
4. Isabella came over to Amy’s house to play with her choo-choo train set. Unfortunately, Amy slipped on an ice cube and broke the set. They then divided up the work into two halves: Amy would find the pieces and Isabella would put them back together. It takes 3 hours for Amy to find a piece and 4.5 hours for Isabella to put it in its right spot. If the train set has 5000 pieces, how long will they be working?
HAPPY PROBLEM SOLVING!
Sunday, January 23, 2011
MATHCOUNTS School Round Prep!
Please review the solutions to the previous week's problems. Then, move on to this set.
1. Sally is thinking of a number. The product of the digits is one half of the number. What is the smallest positive, two-digit integer she could be thinking of?
2. Find the hypotenuse of a triangle with legs of length 20 and 21.
3. If the hypotenuse of a right triangle is 25, then what is the smallest possible leg, if the two legs must be whole-integer lengths?
4. If you take Isabella’s age, double it, and add 1, you'll get the 9th prime number. How old is Isabella?
5. Bob the panda eats at a rate of 1 bamboo stick per minute. His friend Alice the panda eats at a rate of 2 bamboo sticks a minute. How long, in hours, would it take for them to finish a pile of 3000 bamboo sticks?
1. Sally is thinking of a number. The product of the digits is one half of the number. What is the smallest positive, two-digit integer she could be thinking of?
2. Find the hypotenuse of a triangle with legs of length 20 and 21.
3. If the hypotenuse of a right triangle is 25, then what is the smallest possible leg, if the two legs must be whole-integer lengths?
4. If you take Isabella’s age, double it, and add 1, you'll get the 9th prime number. How old is Isabella?
5. Bob the panda eats at a rate of 1 bamboo stick per minute. His friend Alice the panda eats at a rate of 2 bamboo sticks a minute. How long, in hours, would it take for them to finish a pile of 3000 bamboo sticks?
Monday, January 17, 2011
NMS Math Team Marathon!
Hi everyone,
Just thought that the marathon chain was getting a little too long, so I decided to continue it on this post.
Rules:
1. Look at the posted problem. If you know how to do it, solve it and post your solution, not just your answer.
2. After getting a confirmation that your solution is correct, you will be able to post your own problem for others to solve. (Only the first person with the correct solution will be eligible to post another problem.)
3. At any given time, only 1 problem should be "active".
4. The problem you post should be of your own challenge level.
5. Mention the problem number when you post a problem.
6. The marathon will run in this chain.
Enjoy!!!
Just thought that the marathon chain was getting a little too long, so I decided to continue it on this post.
Rules:
1. Look at the posted problem. If you know how to do it, solve it and post your solution, not just your answer.
2. After getting a confirmation that your solution is correct, you will be able to post your own problem for others to solve. (Only the first person with the correct solution will be eligible to post another problem.)
3. At any given time, only 1 problem should be "active".
4. The problem you post should be of your own challenge level.
5. Mention the problem number when you post a problem.
6. The marathon will run in this chain.
Enjoy!!!
Problems of the Week 1/16
Please review the solutions to Snow Day Problems - Set 3. Then, move on to this set. Be sure to look at the marathon problems and their solutions as well. HAPPY PROBLEM SOLVING!
1. Nidhi buys a chair for $60. She tries to sell it for double the price, but when no one would buy it, she reduced that doubled price by 60%. However, sales tax is 7%. Including tax, what was the final price of the chair?
2. The product of two numbers is 30 and their sum is 16. Express their difference in simplest radical form. (You may use the √ sign in your answer. Copy and paste the sign from here.)
3. If 3 zoogs are worth 5 moogs, and 7 joogs have the same value as 3 moogs, how many joogs would you expect to get in a fair trade for 36 zoogs?
4. Maya is a pilot who regularly flies her small private jet from New York to Chicago. Flying with a 25mph tailwind, the flight takes 3 hours. Flying with a 25mph headwind, the flight takes 4 hours. How far is New York from Chicago?
5. What integer n could be included in the set of integers {6, 11, 13, 7, 14} so that the mean is equal to n + 1?
Don't worry about the names; it's just for encouragement :)
1. Nidhi buys a chair for $60. She tries to sell it for double the price, but when no one would buy it, she reduced that doubled price by 60%. However, sales tax is 7%. Including tax, what was the final price of the chair?
2. The product of two numbers is 30 and their sum is 16. Express their difference in simplest radical form. (You may use the √ sign in your answer. Copy and paste the sign from here.)
3. If 3 zoogs are worth 5 moogs, and 7 joogs have the same value as 3 moogs, how many joogs would you expect to get in a fair trade for 36 zoogs?
4. Maya is a pilot who regularly flies her small private jet from New York to Chicago. Flying with a 25mph tailwind, the flight takes 3 hours. Flying with a 25mph headwind, the flight takes 4 hours. How far is New York from Chicago?
5. What integer n could be included in the set of integers {6, 11, 13, 7, 14} so that the mean is equal to n + 1?
Don't worry about the names; it's just for encouragement :)
Friday, January 14, 2011
Snow Day Problems - Set 3
Please review the solutions to the previous set. Then, start working on this set.
1. Vishal had walked half way from home to school when he realized he was late. He ran the rest of the way to school. He ran 3 times as fast as he walked. Vishal took 6 minutes to walk half way to school. How many minutes did it take Vishal to get from home to school?
2. Three darts are thrown at a standard dartboard containing the numbers 1 through 20. Assuming that an equal probability exists of hitting any of the numbers, and assuming that each of the three darts land on one of the numbers on the dartboard, find the probability that the sum of the numbers hit by the three darts is greater than 57. Express your answer as a common fraction.
3. The perimeter of triangle ABC is 62 feet. The lengths of its sides are AB = 4x + 6, BC = 2x – 3, and AC = 3x + 5 feet. Which angle is the triangle’s largest interior angle, angle A, B, or C?
4. Grace and Simran play a game involving a circle whose circumference is divided by 12 equally-spaced points. The points are numbered clockwise, from 1 to 12. Both start on point 12. Grace moves clockwise and Simran, counterclockwise. In a turn of the game, Grace moves 5 points clockwise and Simran moves 9 points counterclockwise. The game ends when they stop on the same point. How many turns will this take?
5. Neha rolled two fair six-sided dice. What is the probability that the product of the two numbers is a composite number? Express your answer as a common fraction.
1. Vishal had walked half way from home to school when he realized he was late. He ran the rest of the way to school. He ran 3 times as fast as he walked. Vishal took 6 minutes to walk half way to school. How many minutes did it take Vishal to get from home to school?
2. Three darts are thrown at a standard dartboard containing the numbers 1 through 20. Assuming that an equal probability exists of hitting any of the numbers, and assuming that each of the three darts land on one of the numbers on the dartboard, find the probability that the sum of the numbers hit by the three darts is greater than 57. Express your answer as a common fraction.
3. The perimeter of triangle ABC is 62 feet. The lengths of its sides are AB = 4x + 6, BC = 2x – 3, and AC = 3x + 5 feet. Which angle is the triangle’s largest interior angle, angle A, B, or C?
4. Grace and Simran play a game involving a circle whose circumference is divided by 12 equally-spaced points. The points are numbered clockwise, from 1 to 12. Both start on point 12. Grace moves clockwise and Simran, counterclockwise. In a turn of the game, Grace moves 5 points clockwise and Simran moves 9 points counterclockwise. The game ends when they stop on the same point. How many turns will this take?
5. Neha rolled two fair six-sided dice. What is the probability that the product of the two numbers is a composite number? Express your answer as a common fraction.
Wednesday, January 12, 2011
Snow Day Problems
Hi guys! Enjoying the snow days? Below is a set of math problems to do during the break!
1. Vishal purchased 15 plants at a nursery, some at $3 and the rest at $5. The total cost was $55. How many $5 plants did he buy?
2. Given that x < 5, rewrite 5x - l x – 5 l without using absolute value signs.
3. Northwestern Middle School sells graphing calculators to raise funds. The school pays $90 for each calculator and sells them for $100 apiece. They hope to earn enough money to purchase an additional set of 30 calculators. How many calculators must they sell to reach their goal?
4. Simran defined a clever integer as an even integer that is greater than 20, less than 120, and such that the sum of its digits is 9. What fraction of all clever integers is divisible by 27? Express your answer as a common fraction.
5. If a 12 pandas can eat 5 shoots of bamboo in 7 days, how long would it take a group of 7 pandas to eat 37 shoots of bamboo? Express your answer as a common fraction.
Participants with the most correct answers/best efforts will have their name printed in a problem!
HAPPY PROBLEM SOLVING!
1. Vishal purchased 15 plants at a nursery, some at $3 and the rest at $5. The total cost was $55. How many $5 plants did he buy?
2. Given that x < 5, rewrite 5x - l x – 5 l without using absolute value signs.
3. Northwestern Middle School sells graphing calculators to raise funds. The school pays $90 for each calculator and sells them for $100 apiece. They hope to earn enough money to purchase an additional set of 30 calculators. How many calculators must they sell to reach their goal?
4. Simran defined a clever integer as an even integer that is greater than 20, less than 120, and such that the sum of its digits is 9. What fraction of all clever integers is divisible by 27? Express your answer as a common fraction.
5. If a 12 pandas can eat 5 shoots of bamboo in 7 days, how long would it take a group of 7 pandas to eat 37 shoots of bamboo? Express your answer as a common fraction.
Participants with the most correct answers/best efforts will have their name printed in a problem!
HAPPY PROBLEM SOLVING!
Sunday, January 9, 2011
Happy New Year 2011!
This week's problems are below. Please complete them and also continue running the marathon. It will help you build better math skills.
Problems:
1. If 8 cars are worth 5 planes, and 4 planes are worth 9 boats, how many cars are worth 90 boats?
2. Two legs of a right triangle are 12 and 5. What is the length of the hypotenuse?
3. Alice and Bob live 22 miles apart along the only route between their houses. Alice begins riding her bicycle towards Bob's house, while Bob does the same after a while. Alice bicycled at 3/5 the rate Bob bicycled at. When the two met, Alice had been travelling twice as long as Bob had been. How far from Alice's house did they meet up?
4. To train for a marathon, Mei runs an 18-mile course at a constant speed. If she doubles her usual speed, she can complete the course in an hour and a half less than her usual time. What is Mei's usual speed and her usual time to complete the course?
5. Is 2011 a prime number? What numbers did you divide by before reaching to your conclusion?
Problems:
1. If 8 cars are worth 5 planes, and 4 planes are worth 9 boats, how many cars are worth 90 boats?
2. Two legs of a right triangle are 12 and 5. What is the length of the hypotenuse?
3. Alice and Bob live 22 miles apart along the only route between their houses. Alice begins riding her bicycle towards Bob's house, while Bob does the same after a while. Alice bicycled at 3/5 the rate Bob bicycled at. When the two met, Alice had been travelling twice as long as Bob had been. How far from Alice's house did they meet up?
4. To train for a marathon, Mei runs an 18-mile course at a constant speed. If she doubles her usual speed, she can complete the course in an hour and a half less than her usual time. What is Mei's usual speed and her usual time to complete the course?
5. Is 2011 a prime number? What numbers did you divide by before reaching to your conclusion?
Sunday, December 19, 2010
NMS Math Team Marathon!
Hi everyone!
I know that some of you would love an opportunity to post math problems on this blog for others to solve. So, I have come up with an idea to run a marathon game.
Rules:
1. Look at the posted problem. If you know how to do it, solve it and post your solution, not just your answer.
I know that some of you would love an opportunity to post math problems on this blog for others to solve. So, I have come up with an idea to run a marathon game.
Rules:
1. Look at the posted problem. If you know how to do it, solve it and post your solution, not just your answer.
2. After getting a confirmation that your solution is correct, you will be able to post your own problem for others to solve. (Only the first person with the correct solution will be eligible to post another problem.)
3. At any given time, only 1 problem should be "active".
4. The problem you post should be of your own challenge level.
5. The marathon will run in this chain.
Enjoy!!! This marathon may run for a couple of weeks.
3. At any given time, only 1 problem should be "active".
4. The problem you post should be of your own challenge level.
5. The marathon will run in this chain.
Enjoy!!! This marathon may run for a couple of weeks.
Let's start with an easy problem:
Kareena and a friend order one pizza that is half-pepperoni and half-vegetarian. Kareena eats 1/3 of the pepperoni part and 1/4 of the vegetarian part. What fraction of the pizza did Kareena eat? Express your answer as a common fraction.
HAPPY PROBLEM SOLVING!
Sunday, December 12, 2010
Problems of the Week - 12/13
Hi everyone,
I'm quite impressed with your work! Continue to put forth your best efforts and work on this week's problems.
Vishal, Nidhi, Maya, and Simran earned a treat for last week. Congrats!
Agni
I'm quite impressed with your work! Continue to put forth your best efforts and work on this week's problems.
Vishal, Nidhi, Maya, and Simran earned a treat for last week. Congrats!
Agni
Monday, December 6, 2010
Problems of the Week - 12/6
Hello everyone,
Enjoy this week's problems! I hope we have another hearty discussion on the blog.
Agni
Enjoy this week's problems! I hope we have another hearty discussion on the blog.
Agni
Sunday, November 28, 2010
Mixed Problems of the Week
Hi everyone,
All participants who post their answers and/0r approaches to this week's problems will receive a treat from Mr. Pearson.
Have fun!!
Captain Agni
All participants who post their answers and/0r approaches to this week's problems will receive a treat from Mr. Pearson.
Have fun!!
Captain Agni
Monday, November 22, 2010
Happy Thanksgiving!
Hello everyone,
I am posting problems for you to do over Thanksgiving break. I urge you to do the problems for your own benefit. You'll always miss the shot you never take!
If you have any difficulties, let me know. I will give you hints so that you can proceed further. Meanwhile, also be looking at the solutions to the previous week's problems.
Remember to post your answers. Have a Happy Thanksgiving!
Captain Agni
Monday, November 8, 2010
Welcome!
Hello everyone,
Mr. Pearson has nominated me as the NMS math club captain. You will recieve competitive homework problems and tutoring from me every Monday morning at the math club meeting. If you have any questions or concerns, feel free to post them on the blog:
pearsonalgebra.blogspot.com
If you wish to go farther into the competitive and challenging math world, be sure to try all the weekly assigned problems posted on the blog! (I will be glad to help you with any of the problems.)
We have already been registered for the MATHCOUNTS competition. The Chapter Round will be held sometime in January at GA Tech. 5 of you will be chosen to represent our school in the competition. So, please be active and do your best!!!
Thanks,
Captain Agni
Mr. Pearson has nominated me as the NMS math club captain. You will recieve competitive homework problems and tutoring from me every Monday morning at the math club meeting. If you have any questions or concerns, feel free to post them on the blog:
pearsonalgebra.blogspot.com
If you wish to go farther into the competitive and challenging math world, be sure to try all the weekly assigned problems posted on the blog! (I will be glad to help you with any of the problems.)
We have already been registered for the MATHCOUNTS competition. The Chapter Round will be held sometime in January at GA Tech. 5 of you will be chosen to represent our school in the competition. So, please be active and do your best!!!
Thanks,
Captain Agni
Thursday, October 14, 2010
New Pass
I added a page tab that has a team pass to come to my room any morning we have a meeting or if you just need to see me for help with something
Wednesday, October 6, 2010
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