TFS Math Corner: Earn EXTRA CREDIT for YOUR Math Class

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Thank you to all those who participated in the first edition of The Forest Scout problems from the 2nd period Advanced Math Problem Solving class! We were pleased to see that our problems were viewed over 300 times!!!!

We had 3 winners: Anna Bazell, Robert Hammond, and William Shen          

Congratulations to all winners!

Remember, there is extra credit available from your math teacher for those who win!

This week’s problem set

“Easy” problem:

TFS Math Corner: Earn EXTRA CREDIT for YOUR Math Class

“Moderate” problem:

Write the following function as a product of linear factors:

TFS Math Corner: Earn EXTRA CREDIT for YOUR Math Class 1

“Hard” problem:

Find the ideal height of a cone with a slant height of 6” for the maximum volume.

 

Please note, we’ll be dropping the Weekly problem due to the low number of submissions.

To submit answers: https://goo.gl/forms/oIZ8xYw5da0HVkLs1

Answers for these problems will be released 10/20/2017. Happy Mathing, and happy Friday!

 

TFS Math Corner: Earn EXTRA CREDIT for YOUR Math Class 2

TFS Math Corner: Earn EXTRA CREDIT for YOUR Math Class 3

TFS Math Corner: Earn EXTRA CREDIT for YOUR Math Class 4

TFS Math Corner: Earn EXTRA CREDIT for YOUR Math Class 5

 

 

 

 

 

 

 

 

 

 

 

 

“Moderate” Problem

Imagine a circular pizza. One person cuts it in half, then cuts the half piece in half and so on. Each time he cuts the piece in half, he labels it with the letters of the alphabet, the first being labeled as A, the next half cut as B, etc. If the radius of the pizza is 6.383 inches, what is the sum of the areas of pieces H and K.

Solution:

1st slice (A): ,       2nd slide (B): or ,     3rd slice (C):

 

Since H is the 8th letter of the English alphabet, and K is the 11th letter of the alphabet,

 

We need the sum of all these values to find the total area of the pizza we have.

 

(Use a calculator to get that if you prefer).

 

We need of the area of the pizza. Total area of pizza:

in2.

 

 

 

“Hard” Problem

a, b, c, d, and e are distinct integers. If

 

Find the product of the integers.

 

Solution:

Prime factorization:

 

Let , ,     and   ,

But we can’t repeat numbers. So, let’s make some negative numbers.

 

, . But now our product is negative. So we need to make it positive.

 

must equal . , .

And since must have a value, we can multiply our overall number by 1, so ,

.

, , , , and .

Product of ae: 3,465