Tuesday, March 24, 2015

Some Articles to Read and Ponder after Mathcounts state competition

For those students who really love problem solving, who care and are inquisitive but are disappointed at their chapter's/state's performance, I want to let you know that it's an honor meeting you online and learning from/along with you.

I know no matter how sincere I write here, it won't help much, so I'll just shut up.

However, I'm also disappointed at some students who said they need to take a break for the foreseeable future.

Well, if you love ___ (fill in the blank), you won't stop if you don't get to the chapter/state/nationals.
So there...

Here are some articles that after your taking a break from problem solving (I hope it's not too long), hope to see you come back and read them. Best of luck !!  Keep me posted !!

Pros and Cons of Math Competitions

Dealing with Hard Problems

What is Problem Solving?

Life After Mathcounts

Great Mathematicians on Math Competitions and "Genius"

Math Contests Kind of Suck from Mathbabe

TEDxCaltech -Jordan Theriot- The Pleasure of Finding Things Out

Why Physics? Skateboarding Physicist and Educator Dr. Yung Tae Kim

Richard Feyman --The Pleasure of Finding Things Out

Hope it helps !! 


Monday, March 16, 2015

2015 Mathcounts State Prep: Simon's Favorite Factoring Trick

Check out Mathcounts here, the best competition math program for middle school students.
Download this year's Mathcounts handbook here.

The most common cases of Simon's Favorite Factoring Trick are:

I:  \(xy+x+y+1=\left( x+1\right) \left( y+1\right)\)

II:  \(xy-x-y+1=\left( x-1\right) \left( y-1\right)\)

It's easy to learn. Here is the best tutorial online, by none other than Richard Rusczyk.
The method Rusczyk uses at the second half is very nifty. Thanks!!

Questions to ponder:(answer key below)
#1: Both x and y are positive integers and \(x>y\). Find all positive integer(s) that \(xy+x+y=13\) 
#2: Both x and y are positive integers and \(x>y\). Find all positive integer(s) that \(2xy+2x-3y=18\)
#3: Find the length and the width of a rectangle whose area is equal to its perimeter.
#4: Twice the area of a non-square rectangle equals triple it's perimeter, what is the area of the rectangle? 













Answer key:
#1:  x = 6 and y = 1
#2: ( x, y ) = (4, 2) 
#3: Don't forget square is a kind of rectangle (but not the other way around) so there are two answers: 
4 by 4 and 3 by 6 units. 
#4: One side is 4 units and the other 12 units so the answer is 4 x 12 or 48 square units. 
There is another one, 6 by 6 that would fit if the question doesn't specify non-square rectangle.