Yet Another Eventless Scribe Day...

Once again, I am forced to scribe on another eventless day as Mr. Maksymchuk has to supervise the students taking the Applied Math Pilot-Exam. As such, today's period is a free one; however, Maksymchuk strongly encourages you employ this period to learn about geometric sequences from the Math 40SP website and/or work on subject material you have a poor grasp of.

It would probably also be prudent to practice for the Final Exam.

Oh yes, and one last thing: badgers!

-I.B.

Comb. + Conics Test

First off, I apologize for not getting this post up sooner; the Sun computers were having some trouble with "Java enabled cookies" or something along those lines and I was consequently unable to log onto Blogspot.

At any rate, it should not matter as all that happened during my scribe day was the Comb. + Conics test, which I hope everyone performed well on.

Remember to get your Accelerated Math Objectives done on time (50 by next friday last time I checked).

-I.B.

April 23 Screen Shots

Sorry, Icky et al...I didn't export the files to the coursework drive as I normally do....here they are below:

C&P Test Tomorrow

Today's class was spent going over perm&comb questions before tommorrow's big test. (I can't figure out how to post the images from pdf onto Blogspot so if you want to see what Maksymchuk did just go to My Computer>Rsfiles on 'Svrss 2' (J:)>Coursework>Math>2nd Semester Pre-Calculus Grade 12 and then scroll down to find pc40april2308moreperms&combs.)

For more practice, feel free to do the math40s.com Permutations and Combinations exam (with solutions here).

Sincerely,

IB

Not Much...

Very little (read: nothing) happened in the way of instruction on my scribe day so unfortunately I have very little to write about for my blog post...

At any rate, here are a few interesting links:

http://www.math10.com/en/math-games/3D-logic.html

This is simply a 3d logic game - just connect the squares. I thought it would be pertinent to our math glass since logic skills and mental three-dimensional rotation skills are closely related to mathematical aptitude.

Also for the more verbally inclined:

http://www.freerice.com/index.php

Just a simple vocabulary test, only with a little extra feature: for every word you get correct, the site will donate 20 grains of rice though the UN World Food Bank to help end world hunger.

Also for the budding autodidacts among us:

http://en.wikipedia.org/wiki/Natural_logarithms
http://en.wikipedia.org/wiki/E_(mathematical_constant)

Enjoy!!!

Pi Day!!!

HAPPY PI DAY EVERYONE!!!

picture via the Hope University math newsletter Off on a Tangent

In case you weren't aware, it is also Albert Einstein's birthday. Also, a proper Pi Day celbration should not begin until it is 1:59:26 on March 14 (π = 3.1415926... = 3rd month, 14th day on 1:59:26).

Today's lecture was short as Mr. Maksymchuk decided that we should use the period to work on the pre-test and catch up with accelerated math. Employing the sum and difference identities that were taught to us yesterday, Maksymchuk showed us how to derive sleek-and-sexy numerical values for trigonmetric functions with"strange" angles, among other things:

Here he derived an equivalent expression for sec(θ-π/4):

Continuing with the sleek-and-sexy values:

And finally we were given our assignment:

Mr. Maksymchuk finished this around 12:30 p.m., giving us about 40 minutes to work on our pre-test and finish up our accelerated math.

Anyway, since this post was so short I think I will provide my fellow classmates with a puzzle they may or may not choose to figure out:

You have 9 balls - all of which are indistinguishable by sight - and a balance scale. Eight of the balls weigh exactly the same while the last one is either heavier or lighter than the other eight. This differential in weight is so small that you can not tell by holding the "odd" ball in your hand whether or not it weighs any differently than the other eight; that is, you will have to employ the balance scale to figure this out. What is the smallest amount of weighings that you can do to find the odd-ball-out? How did you carry these weighings out?

Feel free to post your solutions.

-IB

Trigonometric Sum and Difference Example Post

1). Find sin (60º-45º)

Employing sin(a-b) = sin(a)cos(b) - sin(b)cos(a)

sin(60º-45º) = sin(60º)cos(45º) - sin(45º)cos(60º)

=(√(3)/2)(√(2)/2) - (√(2)/2)(1/2)

=(√6 - √2)/4

2). Find cos(-x)

Employing cos(2π-x) = cos(-x) and cos(a-b) = cos(a)cos(b) - sin(a)sin(b) we have:

cos(-x) = cos(2π-x)

= cos(2π)cos(x) - sin(2π)sin(x)

= (1)cos(x) - (0)sin(x)

= cos(x)

Voilà!

Functions: EVEN/ODD Functions and Transformations

First things first: these Sun computers are annoying, awful, awfully annoying, annoying awful, and just bloody slow.

Having gotten that out of the way, I would like to begin my blog post: Mr. Maksymchuk spent almost the entire class lecturing about functions and their transformations. First, he explained to us what a one-to-one function is:

Basically, a function cannot have an inverse if more than two elements in the domain map onto a single element in the range; if it does have an inverse, it is consequently called a one-to-one function since it must therefore have its domain mapped onto its range via a one-to-one mapping.

Mr. Maksymchuk then showed us how to employ this fact to simply determine whether a function has an inverse. We use the "horizontal line test" to do this:

Pretty self-explanatory.

Anyway, we then got to the main part of the lecture explaining what odd and even functions are:

Succinctly put, an even function has the property that f(-x)=f(x) and an odd function has f(-x)=-f(x). On a graph, even functions are symmetrical about the y-axis whereas odd functions are symmetric about the origin - i.e., an odd graph remains unchanged if you rotate it 180° about the origin.

We then applied our knowledge by doing some sample questions:





At the end, Maksymchuk talked about graphing reciprocals:




Mr. Maksymchuk then asked us to prove that 1/f(x) can never be zero. As far as I can tell, this can not be the case since we would have 0=1/f(x), 0*f(x)=1 or 0=1. What do you think?

IB

Goal Setting by IB

Greeting ladies and gentlemen, and welcome to my first posting.


Font Test


My goal in this class is to obtain a final grade of 90% or higher. I am very confident that I will get very close to 100%.


Here is a picture of me:

I'm so awesome! =)

At any rate, here is a resource I found on the internet:

http://www.artofproblemsolving.com/

It is for high school math students looking for a challenge and/or to practice for math competitions.

Good luck with the course.

IB