Today we started second semester with new seats and new “textbooks.” We worked in groups on section 2.1.  It  focused on exponential functions and how different types of values compare.

I am going to show the first few values on the table for it took make more sense.

First differences (The differences between successive pairs of values) in exponential functions increase, but not at a constant rate.  If you compare linear, it is consistent, but exponential isn’t (see below picture).

The values verses the first differences is (value/first difference) and is constant.  This means the ratio is constant and it is PROPORTIONAL.

The Ratio between successive values (next value/current value) is a constant.  It has a constant growth rate.  All exponential functions had an add-multiply property. This is seen in the table below:

The 1.25 was explained.  We, in this case, wanted to increase by 25%.  We would take the value, we’ll say 200, and multiply it by .25 and add that to 200.  That leaves us at 200 + 200(.25).  This could be simplified to 200(1 +.25).  That’s how we get value times 1.25.

The next scribe is GEORGE!!!!!!!

Today we watched the film Hard Problems. The director of the film George Csicsery hopes that it will “inspire others to see mathematics as those in the film already do—the most challenging and the most rewarding of pursuits.”

I’d like you to react to what you saw. The following are some quotes from the film and some questions that may help you focus your reaction.

• “It takes a lot of stupid ideas to generate a good one”
• “Whenever I get something by my own effort is when things get really exciting”
• “[Math contests were] the first time I really discovered the subject of math rather than being taught random stuff”
• “Math is all about exploring. Trying new methods and techniques.”
• “I love not only getting the right answer but searching for the right way to get the right answer.”

What was your impression of what made the students in the film successful in mathematics?

What was your impression of how the students in the film viewed mathematics?

Here is a link to the problems that the students completed in the 2006 IMO.

Well, this is officially my second time writing this same post out. This would’ve been up sooner, but my computer crashed on me right when I had finally finished, so I had to rewrite the whole thing. But that’s besides the point.

After a slight delay, we began class with going over the properties for sine and cosine we went over yesterday.

1.) sin(A-B)= cosBsinA-cosAsinB
2.) since(A+B)= cosBsinA+cosAsinB
3.) sin2A= 2cosAsinA
4.) cos(A-B)= cosBcosA+sinBsinA
5.) cos(A+B)= cosBcoA-sinBsinA
6.) cos2A= cos^2A-sin^2A