This Week's Work : Week 46 - for Inquisitive Young Mathletes

Finally, this year's Mathcounts state problems are clear for discussions.

Check that out here !! We'll talk about those harder problems this week at our group lessons.

Please let me know how you did/what scores you got if you have followed this blog.
So far, there were a few states' top 10, 20, etc.. and two students I met online will go to the Nationals.

Some e-mails make my day and definitely make me more productive.

Thanks a lot in advance.

For this week's work :

If you haven't watched this video, do so this week.

Joint Proportion : In the video, three methods are discussed and as you can see, the last method is much, much
faster so try that to see if you fully understand the relationship now and can implement it on new, seemingly hard
problems.

We'll continue working on some rate, proportion questions (the harder ones) at our lessons besides reviewing and
practicing speed to solve other harder, counting/probability and geometry questions.

New Mathcounts Mini : Recognizing Squares and Solving a Simpler Problem

From TED Talk : The Magic of Fibonacci Numbers presented by Arthur Benjamin

This Week's Work : Week 45 - for Inquisitive Young Mathletes

From Mathcounts Mini : More Constructive Counting

See if you can use "sticks and stones" to solve the following questions (it requires a little twist).

Tossing 3 dice, what is the probability that the sum is 10 ? 

Tossing 4 dice, what is the probability that the sum is 10 ?

Tossing 4 dice, what is the probability that the sum is 18 ? 

If you want to try harder problems, check out this year's AIME II, 1, 3 and 4. (related to what we've learned recently)

This week's new links, working together, direct and inverse proportion, rate, time distance. 

• Section 7.1: Direct Proportion
• Section 7.2: Inverse Proportion
• Section 7.3: Joint Proportion
• Section 7.4: Speed Part 1*
• Section 7.4: Speed Part 2*
• Section 7.4: Rates Part 1*
• Section 7.4: Rates Part 2 - Work Problems*
• Section 7.4: Speed Problem Solving
• 
  

Take care and happy problem solving. 

Cheers, Mrs. Lin 

Mathcounts Prep -- Number Sense

Check out Mathcounts: the best competition math program up to the national level.

Problems: (Solutions below)

#1: 2005 Chapter Team-- A standard deck of playing cards with 26 red cards and 26 black cards is split into two piles, each having at least one card. In pile A there are six times as many black cards as red cards. In pile B, the number of red cards is a multiple of the number of black cards. How many red cards are in pile B?

#2:  2000 State sprint #30. Joe bought a pumpkin that cost cents more per pound than his sister's. Together, the two pumpkins weighed pounds, but Joe's pumpkin was heavier. Joe paid dollars and his sister paid cents. How many pounds did Joe's pumpkin weigh?











 

Solutions :

#1: You know the total cards in pile A is a multiple of 7 because there are six times as many black cards as the red cards. (given)

6 Black, 1 Red on pile A gives you 20 Black and 25 Red cards on pile B. (doesn't work)

12 Black and 2 Red cards on pile A gives you 14 Black and 24 Red cards on pile B. (doesn't work)

18 Black and 3 Red cards on pile A gives you 8 Black and 23 Red cards on pile B. (doesn't work)

24 Black and 4 Red cards on pile A gives you 2 Black and 22 Red cards on pile B. Yes!!

The answer is 22 Red cards.

#2: 

Solution I : 

Let x dollars be the cost per pound for Joe's sister's pumpkin and x + .1 dollars are the cost per pound for Joe's pumpkin. Since the pounds of each pumpkin is the cost cost per pound, we have

. Solving, . Cost per pumpkin for Joe is , so

Solution II:  Make a list:

Joe's sister        Joe

1 lb.                 19 lb.       (doesn't work since 19 x 58 cents are too much)

2 lbs.                18 lbs      (doesn't work)

3 lbs.                17 lbs      (No)17 x (48/3 + 10) = 442 (still too much)

4 lbs                 16 lbs      16 x (48/4 + 10)= 352 (yes)

The answer is 16 pounds.

This Week's Work : Week 44 - for Inquisitive Young Mathletes

From Mathcounts Mini : More Constructive Counting

Also try the warm-up, retry the problems in the video on your own and spend some time
pondering on those follow-up, harder problems.

#7 and 9 are more challenging.

Review 2014 harder school round problems, especially the "Harvey" method.

Try the first 8 2012 AMC-10 B questions again and see if you have the speed.

Have fun problem solving !! Mrs. Lin

This Week's Work : Week 43 - for Inquisitive Young Mathletes

From Mathcounts Mini : Using Similarity to Solve Geometry Problems

Also try the warm-up, retry the problems in the video on your own and spend some time
pondering on those follow-up, harder problems.

#4, 5, 6 are state level problems. #7 is challenging.

From Mathcounts Mini : Tangent Segments and Similar Triangles

#8 is state/national level.

Have fun problem solving !! Mrs. Lin