Conics---WE learned 4 sections to conics.
1. cirlce
2.ellipse
3.hyperbola
4.parabola
This is a conic: x^2 +/- y^2
General form of a conic is: Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0
A, B, C, D, E and F are elements of the set of reals. B cannot equal 0
Conics are ALWAYS squared
A circle happens when the A value and the C value are the same.

(x^2 + y^2) = 1 is a small circle
(x^2 + y^2) = 7 is a bigger circle...etc

Ex. Given the general form of the conic equation:
a) Identify the conic
b) State A, C, D, E, F
given... x^2 + y^2 - 8 = 0
a) So this is a circle because both co-efficients are 1.
b) A = 1, C = 1, D = 0, E = 0, F = -8

**An ellipse happens when A and C values are the same sign, but A cannot equal C. An ellipse is a squashed circle, an ellipse is also a subset of a circle.
**A hyperbola happens if A and C have opposite signs.
If the x is positive, than the hyperbola will open horizontally, but if the x is negat
ive the hyperbola will open vertically.
** You have a parabola if one of A or C is the vlaue of 0.
**A circle happens when the A value and the C value are the same.

Yesterdays class we leanred about binomial theom-to simplify/ evaluate binomials.
-Pascals Triangle is a triangle that is one big pattern full of numbers, you add the two numbers on top to make the botton number.
-Binomial expansions- some of the exponents is equal to the power of binomial, exponent of term 1 begins with some values as power and decreases by one in each term, exponent of term two appears in second term, increases by one until it matches binomials power, # of terms is one more than the power, coefficients are combinations of power number starts @ nC0 ends with nCn and have symmetry.

So the last few classes we have been learning about perms and coms.
Permulations- are the # of possible orderings of a set, provided that the order of set elements matters. Examples would be you phone digits..books on a shelf.locker combinations. Perms-BEST EXAMPLE EVER- put five blanks down on a sheet, then you put 26 (cause there is 26 letters in the alphabet)then 25 cause you used one then 24 then 23 then 22, and that equals: 7893 600 then the formula starts here: 26!/21!=n!/(n-r)!
n being the # of items to select from and r selecting items r at a time.
nPr=n!/(n-r)! "n things, permulated 5 at a time.
Coms- BEST EXAMPLE EVER: you have three different toppings for pizzas like turnips sardines and liver--> you have turnips + liver turnips+sardines sardines+liver, no matter what order you put them in its the same pizza ex) like turnips+liver, liver+turnips.
Perms: big #, order matters, nPr=n!/(n-r)!
Coms: small #, order does NOT MATTER, nCr=n!/(n-r)!
Another example: How many 3 digit #'s can be formed from digits 1,2,3,4,5,6,7
Provided they are both even+greater than 300? you then can make a ven diagram first circlwe having 3,5,7 middle circle having 4,6 then second circle having just 2. A=first # possible 3,4,5,6,7 B=even number ends in 2,4,6
Case 1= 5 time 5 times 1 = 25
Case 2= 4 times 5 times 1 =20
Case 3= 4 time 5 times 1 =20
All equal 65 3 digit even numbers greater then 300.

Another Example is Solve: nP2=30 n!/(n-2)! time (n-2)!/(n-2)!= three (and the (n-2) cancels out. n^2-n-30=0
(n+5)(9-6)=0 n=-5 n=6

Well...today was a productive day I tell ya. We had a substitute,and that meant we all got to do some catching up. I worked on my accelerated math, I'm doing a test right now. Whenever I did not know how to do a question, I just asked my handy dandy friend William, or Caity. They are tons of help.

Last class was on tuesday because we got wednesday off, due to Rememberance Day. Well anyway, we learnt "Approximating "e" and the natural logrithm(ln)"
What is e? e is approx. 2.71828... it is an irrational number. Our class learnt the new formula: f(n)=1+1/n;g(n)=(1+1/n)^n. For values n E II
A natural exponential function looks like a line facing upwards on a graph,(concave up)

Last class we learned more about logarithms."The Change of Base Therom" the last log law.
logb^n=loga^n/logab
ex) heres a little rule
log (x + 3) = IS ABSOLUTELY NOT- logx + log3
instead, it becomes:
log(2(3^x)) = log5
log2 + log3^x = log5
log2 + x * log3 = log5
x * log3 = log5 - log2
x = log5 - log2 / log3
x = .8340437671

Yesterdays class we learned logarithmic functions.
y=log6x if x=by(y as the exponent) y is the logarithm, b is the base and x is the argument.
Logarithms are exponents.
We did an example like, find log2(subscript)8=3 in exponential form. 2to the 3=8
2 to the ?= 16 9 to the ?=3
2 to the 4=16 9 to the x=3
log2(being the subscript)16=4 (3 to the 2)=3 therefore 2x=1 x=1/2
then: 2 to the ?=1/4 2x=4 to the exponent -1 2x=(2 to the exponent 2) -1(exponent) therefore x=-2 therefore log2(subscript)(1/4)= -2

Today in class we learned about expotential functions. We had learned lots of it in grade ten precalc. First we sketched out some simple graphs, and talked about them a bit, like what would happen if you changed the a or b value, ect..Then we did some observations , like D= all reals, graphs have no x intercept(no verticaln shifts). And then we did some examples, which were quite easy.

Yesterdays class was a catch up period, one of my favs. I worked on some accelerated math, and got 79%, wasn't bad, but I have to do some objectives over again which sucks. I was very happy we got a catch up block because I am somewhat behind in this class. And stressing over this math test comming up on thursday.

Today in class we did some more practice/considerations with identities. We learned about EXTRANEOUS roots.- "they are answers that look good on paper but practically don't make sense".
When we are doing our questions, all solutions must be checked for validity. In an equation you want to bring everything to one side, and when you have a question like cos(x)+1=sqare root thre sin(x), you always want to sqare both terms to get rid of the radical.

Today in class we learned how to simplify. Completely. And learned techniques to assist "proofing" idenities. There was eight different techniques. Such as reduce/simplify, work each side independently to some intermediate expression, DO the multiplication/subtraction of the rational expressions, Simplify GCF'S ALWAYS, FACTOR, try multiplyinf both numerators/ denominators by same expression, and lastly, if possible rewrite all trig. functions as sin(x) or cos(x); look for patterns.
And we learned to prove by LHS and RHS. I find it kind of complicating,but hopefully I will catch on.

Last class we got a CATCH UP CLASS! I especially love these days. Because I usually have a lot of catching up to do. I worked on exercise 12 that is due for monday. I unfortunatley did not finish, but I will finish it sometime this weekend.

Last class we wrote a math test. It was on trig stuff and transformations. I am not feeling too confident at all with it, hopefully I can do a re-write because i've got a feeling that I was not even close to a pass.

Last class we got our homework checked. I got a 100%, no big deal or anything. So while we got called one by one down, we had to work on exercise 11.

Last class we learned reciprocal functions. Reciprocal means fliped over. ex) a/b---->b/a. We learned that a reciprocal function is in which the numerator and denominator switch places. Then we learned how to graph it. The graph of a reciprocal function, compared to its orig. function, is curved and has one or more asymptotes along the x axis. The asymptote of the reciprocal function is found where the function crosses over the x axis. If the orig. function decreases, the reciprocal function will increase. We leanred this as: "GREATERING" and "LESSERING".

Last class and the class before we learned some more and more graphing, what joy! We used a table if values and what not to help us. We compared items like f(x)n to -f(x). We made a table of values and made a therefore that flip across x-axis when f(x) becomes negative f(x).
One to one functions- have inverses (passes the "horizontal line test". ex) only one point of intersection maximum with a horizontal. We then determined if the fxns are ODD, EVEN, or NEITHER.

Last class we learned all about transformations. We've learned the different graphs, and went on graphmatica and seen what they all looked like. Then moved on to translations. Def- every point in the relation moves some direction, same distance. Translations(slides)ONLY ever move the ref. function either left/right. We learned the general form: y=f(x-h)----->L/R. OR y=f(x)+k---> U/D, y=f(x-h)+k
h moves h units RIGHT. And k moves k units UP.

Yersterdays class was the test,but a few of us chose to write it a day later.This really helped me because i just looked at the practice test yesterday and today so i got alot of help. I think if I would have wrote it yesterday I wouldnt have been as prepared as I was today when I wrote it.

Graphing trig functions

So last class(three days ago) we were "tieing ends" on how to graph trig functions. Some definitions you might call them, are period- which is the smallest horizontal space within which repeats itself exactly once. A period of sin (sin curve, cosine curve) equals 2 pi/ b. Your domain is you x value, and your range is where it crosses the x axis. An exapmple question is f(x)=asin(b(x-c))+d. "a" tells us that it stands for the amplitude(which is the distance). "a" value tells you the amplitude.The period is how many times it makes a complete cycle in one cirlce. So the sine or cosine function- 2pi/b or 2pi/period=b. Tangent function = pi/b which also = period.(talking about how much horizontal space it takes up).
When written y=asin(b(x-c)+d c is A PHASE or HORIZONTAL SHIFT.

Yesterday in class we had a sub, so that meant we just worked on our assignments and mental math. I very much like catch up periods.

Today in class we learnt how to solve trig equations over the real number system. For this you really need to know your unit circle...its crucial. And I do have not memorized it yet so that is not good, but I will try my absolute hardest to know it inside and out.

Yesterday in class we just did example questions of solving trig equations with using the unit circle. This is very difficult for me. I somewhat get it when he is explaining how to do it, but when it comes right down to it. I would not know how to do it by myself.

Yesterday in class we had a little catch up period which was very nice, because I am fairly behind sched. I worked on my chart all class and am glad to say I am really understanding it. So, I got most of that done, but I still have all the exercises to do.

Yesterday in class, we went over the stuff we learnt on friday again, because lots of kids were gone that day for soccer, and football and what not. Going over it again helped me a bit. What we re learnt was how to solve some trig questions.Such as: if cot theta = -12/5, and sin theta < 0, find all the missing circular functions. You had to find: tan theta sin theta cos theta csc theta and sec theta.

Yesterday in class, thursday sept.17th, we were told to make a chart of the trig functions, due for monday. I did not get it at all, but then i asked for help and learnt that if you know the two triangles, ( this is the 30-60-90, and 45-45-90) you should be good to go. With just a little bit more help,from Mr.Max and students I think i will be alright with all these functions.

Today in class we learnt some trig functions. And we filled out our unit circle. There is a lot that is on there, and it got very messy, but i mostly understood it. I feel that i might have some troubles with this unit because there is just so much to know, but i just need to keep my ears open.

Reflection of class

We had a sub today, so that meant we just worked on the assignment that was assigned to us. I had to ask some classmates for help, then i understood, but that was for only questions one and two, the rest i did not understood too clearly.

Radian

What is a radian?
The measure of a central angle subtending an arc equal in length to the radius: equal to 57.2958°.(5.3)
3.14=180 degress

Goal pOsT

MY GOALS THAT I PLAN TO SET:
1) Get(at minimum) 70% as a final grade.
2) Complete my homework everyday
3)NeVeR get behind in any subject especially math
4) Try my hardest to achieve well!