conics

here is another unit that I actually enjoy taking. connics is just a bunch of figures taken off of a cone section and put onto a flat 2 deminitonal surface. there isnt much to alk about here except for the fact that i remember most of this stufff and it is fairly easy for me to do this unit!

Responce to the "Busy Work" Article

Well...I really can’t give a definite, concrete answer to the question posed, "is homework a good or bad thing" but I can sure give my opinion from a few different standpoints. When I see this question AS a student FROM a student prospective my first instinct is that is bad, a total waste of my precious free time. Of course I am not speaking for everyone when I say this but I’m pretty sure a good chunk of the student population around the world could agree with me. Homework sucks. Cause really, what would you rather be doing. Going for a nice dirt bike ride down the Cowan trail with a few friends on a beautiful fall day, or sitting down in the basement in a little room at a desk studying Romeo and Juliet. The choice is pretty clear. Now to the other side of the argument, homework is really a good thing. How can it possibly be a good thing you may ask? Well, from a teacher perspective homework is essential to a students success in developing good study habits that will be beneficial in years to come, and esp. in university's. The plan is to start giving them bits of "homework" early off in grades 1 and 2 and slowly progress to the point where it is a lecture in class and the actually bookwork is left up to the student to do on his own time. I can see where this last line can make sense, but really, how is Romeo and Juliet going to be in any way useful to me in pursuing my future goals in becoming a mechanical engineer? This is where the issue of is homework a good thing or a bad, unless way of just getting students off teachers back must taken into perspective. I believe that homework is not too bad of a thing, but it must be given out in decent amounts and the teacher must filter out the repetitive stuff and just give the important stuff. For example. I took an English class with a teacher when I was in grade 9, and it was a class that consisted of a ton of tedious assignments that usually consisted of drawing posters and coloring pictures and that sort of stuff. It would have been alright except for the fact that almost 75% of the work was done off campus, and at home. Now this kind of work would definitely be considered "busy work" and I am completely opposed to this kind of homework. If I take an English class, I expect to do english related material, not art class. At this point I look back at all the homework I have done over the years and ask myself if it was all really necessary. After much consideration and thinking, I was actually quite surprised to find that the answer to this question is YES. Homework has been a pretty large part of my life all through the years, sure I missed a few days or forgot my stuff at school but for the most part I got all my school work done, and Homework has kept me from getting lazy. So to sum it up, homework is an excellent tool and it teaches students time management, helps them to develop study skills, and lets teachers to put a little more effort into their lesson plans. If there wasn't any homework, our classes would be much harder and for the time a student is at school he/she is working their butts off. So I think that after considering this article and what i wrote down i have come to the conclusion that, for the most part, homework should live on in out schools today!

stevalknieval

Everything About Logs (last 2 weeks)

this unit, like i said before, is pretty easy and strait forward for me, therefor i never really kept up with my posts cause i never really learn't anything that new. I like the logs section because of how strait forward and concrete it is. I get it cause it is so formula based and just a set of rules. Logs are exponents, therefore exponent rules apply, and i do believe that this is another unit that is faily simple!

Log's and Identities

More rules and identities that need to be followed in order to do some more complicated log problems. we were given all the identity formulas and put them use in a couple of example problems. to me this is pretty simple stuff and it is good to just strengthen my knowledge of logs. so far in this course i think i am doing 100 time better than the first time around, but I'm still a little confused when it comes to functions being even, odd, inverse functions, horizontal line test, etc.... so i think i am getting my studying cut out for me.

Basic Logarithinms

today we were introduced to general simple functions, and observing their graphs. Mr. Max was putting up examples on the board and then putting them into graphamtica and seeing how they behave. I personally love this unit because it make the most since to me and i find it to be mostly algebra. i am pretty confident in this part of the unit and remember alot of what happened last year, so i am hoping to do quite well in next weeks test. from her on into this unit i will refresh myself, and continue to learn the things i didntcatch the first time.

Monday, October 26

Homework day. All I did today was start into my acceleratd math and plugged my way through the identities section. not much help need there but alot of work is needed. the day before. which was thursday (no friday due to SAG day) i had to post for the class, so i had no post for the day.

Identities-3

today we took a more back door approach to concept of identities, we solved a few problem, but rather than using formulas we used our knowledge of previous units over the years. We also did some work with extraneous solutions and squareroots and powers. the thing to remember with a root problem is that there is going to be a plus andminus solution. this happpens cause in a square problem there two negatives will equal to what two positives equal. *sigh* now there a mouthful. anyways when you get you answere you will have to check all over them, cause some wont work, but seem to work.

Identities-2

Posted below are the rules, I will try hard to memorize these as this is the section that I dislike most in this course. the trick is to do anything that will eventually lead to the question getting simpler, which in turn will become equal to the other side. It doesn't have to be anything that confusing but even the smallest changes can do alot in the end.

Identities

I believe that an identity are two different problems, related to trig, that in the end they will be equal to each other. The questions on either side of the equals sign may not look similar but are same sames, just different versions. Identities work for any value of any value. they will always work no matter what the inputs are.

DEF. an equality (trigonometric) that evaluates as true for any value of input, that is both sides of the trig. equations are true for ALL possible variables.

*note...trig equations that are not identities are conditional equations....*

trig identities are much like a logic sequence that we learned about many many years ago. ex, if a=b and b=c, then a must = c. it is a simple concept until you start applying it to trigonometric sequences. the harder part of this it trying to understand is that the sequence and everything in the question has a numerical value.

Absolute Values (graphing)

Piece-Wise Function - different rules or outputs depending on relative domain values

absolute values can be understood as piece wise functions.

absolute values on a graph look much like a bouncing ball. But instead of a ball bouncing on the ground, it is a function bouncing along the x-axis. absolute values are actually quite simple, but more complex questions can get quite confusing. The trick to remember here is to take the question one part at a time. and end up at the answer rather than start there. first work with parent function, then add in all the negatives and brackets, inverses and reciprocals, then finally find the absolute values of everything you have got so far.

Reciprocal Functions

Recripocal functions can be defined as;

a/b --------> b/a

In today's class we learned the basics of a reciprocal function. We were refreshed using some grade 11 examples, taught that a reciprocal function is one in which the numerator and denominator switch places, and learned algebraically how to do this. The tricky part come when we put this thing onto a graph!! The graph of a Reciprocal function, compared to it's initial function is curved and has one or more asymptotes along the x axis. first, The asymptote of the reciprocal function is found where the initial function crosses over the x axis (the x intercepts). Near each asymptote the reciprocal function behaves in a manor opposite to the initial function. If the initial function increases as it approaches the asymptote, the reciprocal function will curve off and get smaller and approach the asymptote. Similarly if the initial function decreases, the reciprocal function will increase. The terminology given to was GREATERING and LESSERING. the most important part to remember when deciding whether each function greaters or lessers it to read in the same direction to or from the asymptote. If you read it differently and switch directions at any time, none of the graph will be correct.

Flips, and Symmetry (Even, Odd)

function=vertical line test

inverse function= horizontal line test.

Now this is where it gets difficult, i am going to take some of the screenshots from the lesson today just as a reminder for the next test and so i can view them at home at a later time. This is just basic algebra, but in the end we have to apply it to some set rules that we learned today (ref to screen shots), in all honesty i haven't really caught on to any of this stuff last semester, and it is still confusing at this point. I think the only way to do well on this part of the unit is to memorize the rules and keep going over them even after the class is over. Here is what i got out of today's class:

. -f(x) is different from f(-x)
. The difference is how it is reflected (over x axis and y axis respectively)
. a inverse function is reflected over the line y=x
. EVEN function have symmetry over the y axis (flip symmetry)
. ODD functions have symmetry about the orgin (rotational symmetry)

I still am not to sure how to do the algebra parts and the comparing but i shall research that tonight and refer back to the notes tomorrow!

transformation

Horizontal Compression/Vertical stretch:

a)y=3abs(x) - 3 times as vertically stretched
b)y=1/2abs(x) - 1/2 as vertically compressed

*the "A" value is what is affecting the vertical compression and stretching*


c)y=abs(3x) - 3 times as horizontally compressed
d)y=abs(1/2x) - 1/2 as horizontally stretched

*the "B" value (inside brackets) affects the horizontal compression and stretching*

Summary:
The hardest part to remember is whether it is horizontal or vertical, and today I learned which terminology to use in that certain circumstance. the absolute value refers to the value inside the brackets always being a positive value. This class was mostly a refresher, and it was useful to learn the terminology.

Unit 2 "Transformations"

Terminology:

Translation-"Every point in the relation moves same direction, same distance in a plane." y=f(x-h) - left and right, y=f(x)+k - up and down. it is moved either up down, left right, or a combination of the two.(which can be viewed/seen as a diagonal shift)

So we had our first unit test yesterday, therefore I had no post. In my opinion I found it to still be on the more difficult side, but this time i had the skills to look a little deeper that just the question itself. I could see the unit circle much more clearly this time around, and it help in more ways than I would have though possible. So I am hoping for the best on this one, and hopefully my class is of to a good start!!

graphing trig functions

GENERAL EQUATION

F(x)=a*sin(b(x-c))+d

KEY

a=amplitude (is a distance)
b=period (amount of occurrence in a given space)
c=Phase or horizontal shift
d=Plane or vertical shift

*note: a x-1 shifts 1 unit to the right, just as a x+1 shifts one unit to the Left, a positive x it just the -(-x), which make it a positive*

This is some fairly straight forward and basic stuff. The hardest part for me is remembering that -1 shifts right and +1 shifts left. Also i have to remember how to calculate the period of a function. That is the one thing that I have never really known how to do at all last year, and am finally learning it now for the first time.

I dont have a post for monday due to the fact that I put all my time into the class bolg. It can be viewed there!!

Solving Generally Over the Reals

Sometimes when solving trig equations, we will not be given a domain on which to solve this question, therefore there will be multiple answers from negative infinity to positive infinity. In a situation like this you have to coincide that any answer will occur every 2pi rotations (which is 360 degrees) with this in mind, we will have to make this known in out final answer. To do this we add on to the end of the answer 2kpi or kpi,(depending on how often it occurs). what this says is that for every K (which is an integer) rotations, this answer will occur to infinity.

Another Lesson Learned

Today we went over alot of examples similar to the questions found on exercise 4. I learned that when you factor a binomial expression (Ex x2+2x+1=0) there is the possibility that you could end up with an answer that looks like costheta=3 or anything that will cause a calculation error. In an situation like that you will completely ignore that part of the question, therefor the complete answer will solely come from the other half of the question. this concept in my head is similar to non-permissible values; answers that fit the description and seem to work out, but only cause you grief and despair!

Work Period

today we were given the oppurtunity to catch up on excercises, finish up our creations (the chart and unit circle) and were given a new blog assignment. I chose to work on my assigntments and got actually a substantial amount finished, For me lesson 4 was a lot of review, and I had to brush up on alot of my old algebra skills learned on the past. It is amazing how and what person will remember, even if you think that you dont know what you are doing!

Examples

We worked away at some accelerated math questions. Today I learned that angles that are over 2pi are actually very simple to solve. first you have to find the nearest degree in radians that you are familiar with that is closely related to the angle, i find that pi or 2 pi is the easiest. Next, all you have to do is add up the rest of the angles from that and eventually you will find an angle that you are familiar with that is within the 0 < theta < 360, from there it is just another simple trig problem that we have been doing since the start of the course.

Solving Trig Equations

today we started into the ever so loved trig equations. Although I seemed to understand most everything that Mr. Max was talking about, Alot of people didn't and therefore this class was a good refresher for me. All the Repetition and going over things made it so that the information presented was drilled into my head. We also learned how a trigonometric function can be put onto a graph. this is the basic function that will be always appearing throughout this course. I learned a bit more on how exactly to solve where each asymotope is and also more importantly how to solve a question that involves several answers cause the question has a set limit. I found this class very useful because asside from this i also got 1/2 of my chart finished!

Exact Values

Thursday, September 17, 2009

Exact values is just a really technical term for a value at a specific, given location. The trick to these is to first evaluate where on the unit circle the angle is. We can do this by just remembering what we learned about the unit circle in previous lesson, and just expand our thinking just a bit. for example: 17pi/4 looks impossible, but if you think that pi can be didided into 4 and a inverse fraction is possible because we are more than only one pi. Once i can grasp that principal i had no problems when working my way through lesson 3. An exact value, if refering to a unit circle, is just a coordinate on a plane, and depeinding if you are asked to find the Sin Cos or Tan, the coordinates will always follow a type of pattern (as i found from working on the chart we were asked to make).

Creation of the Unit Circle

- Extremely logical
- If you know fractions you should be able to solve this Unit Circle

Six trig ratios:

Sin=y/1 Cosecant=1/y
Cos=x/1 Secant=1/x
Tan=y/x Cotangent=x/y

*memorization of inverse terms is important*


The second time around in this class allows you to catch all the tiny bits of information that slipped by the first time. What I learned this class is that I need to think less about the question and focus more on the principals that I already know, cause everything that Mr. Max teaches us can be applied in some way to the questions we will encounter in the future on tests and the Final exam. The trick is to go outside our traditional thinking areas and try to come up with something new that we havenet really thought of before.

Work Period

Because of our lack of computers in the cafeteria, Iwas not able to make a post, so I am doing it today. Well yesterday we had a substitute teacher, therefore it was a period where we could "catch up" with out old work and also start into out accelerated math packages. Basically I just finished up my exercises 1 and 2, but need to get some accelerated math so I can get that done. Helping others will also, even though you may not know it at the time, help yourself as well. Now that is the main thing i have learned today!!

Circular Functions (unit circle)

- Co-terminal angles will always end up at the same place (exact same terminal angle), only one runs cw and the other ccw
-S=Theta(r)--------(S=arc length, Theta=inside angle, r=radius)
- Unit Circle implies the radius at any point along that circle is 1 unit long
- sides x and y on the unit circle are easily calculated using simple grade 11 trig or Pythagorean theorem
- cos=x, sin=y (x,y)
- The hardest part is just understanding that the circle isn't just something to be memorized, it is actually to the contrary very logical and can be be thought of as just fractions

Radians

-3 and a little bit radians (3.14) is equal to 180 degrees
-Pi radians=180 degrees
-2 Pi radians=360 degrees
-one radian=57.3 degrees

My Goal

well to begin this is my second kick at the can for math, but this time my goal is very simple, a 90%+ average so i can eliminate my first year university and go straight into it. I will definitely be able to concentrate alot more on my math now as i only have one class in school this semester. If it means that i will have to stay after school some days or even come in on the weekend for tutoring, well than so be it. This class will be my to priority for this part of the year and hopefully all goes smoothly.