Final Reflection

We learned a lot of things this year in Advanced Math. I always think subjects are going to be hard at the beginning of the year, but it turned out not to be so bad. A few of the things we learned at the beginning of the year were easy, then it kept building up from there. I'm glad I got to know some of the concepts that we have learned, and I enjoyed doing other activities that helped me understand things better. The bridge project demonstrated good trigonometry usage and it was fun doing. Also, reading Flatland was also "fun", being that we kinda had a break from doing a lot of math. I actually might have learned a life lesson through this book though -.- but, overall, this class was pretty easy, sometimes, and sometimes it was difficult. But, I'll say one thing for sure, this year FLEW. Where'd the time go? Oh well. Well, I still don't understand limits completely, so I guess I'll have to study up some more, and hopefully pass this final exam Tuesday. At least it's multiple choice and has some easy beginning chapter material on it. Okay, I'm done now. HAPPY SUMMER.

final ONE!!

well we learned a lot of stuff this year, like 14 chapters of stuff to be exact. from having a formula for everything to reading a book about dimensions to having to memorizing the TRIG CHART!!. i think everyone had a successful year with everything we learned this year. some things were easier than others and some were really hard to get the concept. like logs and triangles were some easy things we learned this year. and a thing i never caught on to was the trig identies. overall i think everyone learned a lot that will be useful in college.

This year in advance math we learned a lot of stuff. One thing I found out in advance math is you have to learn your formula's and there are plenty of them to learn. If you dont know your formulas it is hard to even try to work a formula. Some of the easy things we did was logs. Codensing and working logs seemed to be easy. Also if you dont know your trig chart and unit circle you will probably lose a bunch of points and not know how to do everything in the trig part of the class. Everything revolves around the trig chart. Another thing that I thought was going to be really stupid was the book we had to read about the square in a flatland, but it had a lot of inside meaning and related to real life concepts. Overall it wasnt that bad of a class, but I needa make a good grade on my exam so I don't fail this last nine weeks.

FINAL REFLECTION!

So this year has been a long year and i thought advanced would be super hard (and it kind of was), but was not too bad, just took a lot of studying. But it also took a lot of memorizing and studying, we learned everything from factoring to trigonometry to the beginning of calculus. Well for this last blog i'll give examples of stuff i understood well throughout the year.

EXAMPLES:
Condensing.
1.)logm + log7 + 4logn
= log7mn^4
2.)5loga + logd + log6
= log6da^5
3.)logn - 3logh -logy
= n/yh^3
4.)4logt - logc
= t^4/c

Expanding.
1.)log5gh^2
= log5 + 2logh +logg
2.)m^3b^7/f
= 3logm + 7logb – logf

This is about trig review. I had to study hard but i guess i ended up doing decent with trig. This geometry type stuff just isn't my thing. I did understand a good bit though.
EXAMPLE:
C = 90 degrees
b = 7
c = 12
First i found angle A
cos A = 7/12
A = cos^-1(7/12)
= 54.315 degrees
Second i found angle B
sin B = 7/12
B = sin^-1(7/12)
= 35.685 degrees
Next i found length of a
tan 54.315 = a/7
(7) tan 54.315 = a/7 (7)
a = 7 tan 54.315
a = 9.747
Finally i found the area
A = 1/2 bh
= 1/2 (7) (9.747)
= 34.115

I'm gonna review something we learned at the very begining of trig, SOHCAHTOA.
sin=opposite leg/hypotenuse
cos=adjacent leg/hypotenuse
tan=opposite leg/adjacent leg
*You use SOCAHTOA for right triangles

We learned a lot of formulas we have to memorize like: sum and differences with sin and cos, half and double angles, and many more. I found the easiest formula to work with was tan alpha + tan beta/1-tan alpha tan beta. I also found the sin(alpha + beta) was easy.

We learned how to find the angle of inclination, which i found was really easy compared to some stuff we learn. We also learned about amplitudes, periods, vertical shifts, etc. There are some formulas we had to learn to be able to work these problems:
1.) For a line
m=tan alpha where m=slope and alpha=angle of inclination
2.) For a conic
tan 2 alpha=B/A-C
3.) For a conic if A=C then
a=pi/4

EXAMPLE:
Find the angle of inclination.
2x+5y=15
m=-2/5 tan alpha=-2/5 Checks are in the II and IV area and 21.801 degrees in I
alpha=tan^-1(-2/5)
180-21.801 alpha ~ 158.199 degrees, 338.199 degrees
158.199+180

I also understood how to do domain and range very well. The types of the domain and range problems i understood the most were the fractions and polynomials. (oo => stands for infiniti)
EXAMPLE: y=x^3+4x^2+12
For any type of polynomial the domain would be (-oo,oo) and for the range, odd:
(-oo,oo); quadratics: [vertex,oo] or [-oo,vertex].
The answer to this problem would be Domain: (-oo,oo) Range (-oo,oo)
EXAMPLE: 5x+4/x^2-4
First, set the bottom of the fraction equal to zero.
x^2-4=0
+4+4
x^2=4
x=+ or - 2
Your answer then comes to,
Domain: (-oo,-2)u(-2,2)u(2,oo)

I'll give an example of one of the problems from our Chapter 1 test:
13.)Solve for x by completing the square x^2 - 4x = 9
First you must dived b by 2, then square the answer of b divided by 2 then plug it in to the eqn.
-4/2 = (-2)^2 = 4 x^2-4x+4=9+4 Second you take the -2 from parenthesis and square it minus x, also must add 9+4 on the other side of equal sign. (x-2)^2=13 Third, you take the square root.
square root of (x-2)^2= square root of 13. Next you add 2 to each side giving you: x=2+ 0r - square root of 13. and Finally put the answer in point form: (2+squareroot of 13, 0) (2-squareroot of 13, 0).

The final thing we learned was stuff dealing with calculus.
Examples:
1. lim (4x^2+3) = 4(2)^2+3 = 19
x>2
2. lim x^2+5x-6/x-1 = (x+6)(x-1)/x-1 = (1+6) = 7
x>1

Basically i did decent in this class, and we started learning calculus so i hope do good in that next year, and this is our LAST BLOG :)

Final Reflection

Alrightttt, since I did my last reflection totally wrong I have to redo it. I really need to learn how to pay attention hah. Anyways, this year was a very hard year for me but I still some how managed to pull out with B's. At the beginning of the year I thought I'd never make it, but through out the year it got easier and easier as I started to catch on to how B-rob taught. I learned a lot this year, and actually for the first time still remember how to do a lot of it. I realized advance math is all about formulas, and if you don't study your formulas and notes you will never pass the class. I learned that each chapter builds off of the beginning chapters so it's smart to understand the beginning lessons before getting into the other chapters. One of the chapters you really had to pay attention on was identites, we pretty much used identies in everything for trig. One of the things I really remember how to do is logs and and finding if something is symetric (those are really random things to remember..I know). But I think I remember those the best because there the easiest. I also will never forget the trig chart after drilling it in my head, haha. Another thing that helped me was blogs, commenting on everyones blog helped me remember the lesson we learned in class that week, and reassured me if I was doing something wrong. That's pretty much all I have to say about this year, i'm not really sure what else to put. Overall, this year has been my hardest year yet in math..and I hope next year is easier.

FINAL REFLECTION!! :D

I'm soooo happy to say the time has finally come for our final reflection of the year! (: And I can honestly say I've learned a lot this year. Not only concepts that were new to me, but just that practicing and studying ALWAYS helps and makes a difference in this class. I remember in the beginning of the year I was complaining about how hard everything was and how the blogs were so hard and how everything was stressful. But now that I look back on the entire year, it really wasn't bad at all. Once I got used to how things were, I knew what to expect and I always made sure I asked my questions so I completely understood everything before I took a test. And I know that everytime we were assigned homework, I always thought it was too much, but I'm glad I did it because that deffinitely helped me understand things better. Commenting blogs during the week also was beneficial because if someone didn't know how to do something and I did, I was glad that I was catching on and understood what I was doing. Also, no matter how annoying the Chapter tests were (that we worked through about a hundred times for each chapter hah) that helped a lot, because everytime we had to retake the tests for a study guide, it helped me remember things better and I didn't have to look back at my notes that much. I can honestly say that I remember basically everything we learned this year, because the information was pretty much glued to my brain. Especiaaallllyyy the trig chart! I know that thing like I know my prayers haha. And identities is something that I thought was reaaaally easy this year. As long as you knew them, and knew how to apply them to a problem, you were good. OHH! And another thing you should be pround about Ms Robinson!! (: >> From all the things we went over this year I was able to help out my friends a lot in Algebra 2 with some things they were learning. I felt special because I thought it was extremely easy haha but anyway I was glad I could help them out. SOOOOO anyway, overall I don't think this year was really hard, but I can honestly say this is the most I've learned and can actually remember in a math class. All the other years I'd learn concepts, but by the time we went off for the holidays I'd forget so I had to relearn them. I don't think that's gonna happen this time. So I'm glad about that and I'm sooo ready for Calculus next yearrrr! (: ..not to sound like a nerd or anything ha

Final Reflection

So this is my last reflection of the year! I'm kind of excited about that, but i'm not too excited that i will be doing them next year. Yes, i am taking calculus, but i wasn't too happy about it. I'm starting to realize that it isn't going to be as bad as everyone is making it out to be. Its just math, what can be so hard about it? I mean we are learning pre-calc right now, and it is pretty simple. Well, if yo pay attention and do your homework, then you shouldn't have a problem with calculus. But we're going to have a total of like five people in that class next year. But anyway, i've learned A LOT of stuff in advanced math this year. In the beginning of the year, i was kind of nervous about the work and stuff, but i got used to it. I think that everyone in our class was so nervous because the advanced math class before us, was making it seem SUPER hard. But it really was not that bad. So i think that calculus is going to be easy next year. But i can definitley say that i have learned to factor. That is the one out of many things that i will take with me out of that class. I can also say that i, comfortably know the trig chart, and all of its meanings. I have also learned how to solve logs, how to apply formulas, and how to solve triangles. (and yes ashton i do know what a triangle is). Oh, and the bridge project! That was the funnest project ever, except for the fact that my group had to do it all in one night, because we don't pay attention to directions! Oh well, it was still fun because we had to pull an all nighterrr (: it was super duper fun! Not to mention the fact that we won still, our group's bridge still held the most weight, and the glue was still wet. But i have to say, that this year's math class, i have learned WAYYY more than i have ever learned in math. I will definitley take most, if not all, of the things that i've learned with me to college, and in everyday life. But guys, guess what?! We are almost out of school, soooo, FINISH STRONG (: we only have one week left. And everyoone should take the optional test on fridayyy, because it would be an extra grade. Plus this chapter is superrr easy!

Last Reflection

This is my last reflection of the year. And I was remembering one of the easy things we did which is logs. This will probally show up on the final exam.

Examples of some logs:

log 7 of 49 = 2 log x of 36 = 2
7^2 =49 x^2 = 36
x = 6

log 3 of 27 = 3 log x of 64 = 3
3^3 =27 x^3 = 64
x = 4

log 2 of 32 = 5 log x of 100 = 2
2^5 =32 x^2 = 100
x = 10

Logs should be easy if you just look over them.

Last Reflection

For my final reflection…
I’ve learned a lot this year in Advanced Math. We learned some stuff that just branched off of Algebra II at the beginning of the year, such as the rational root therom, domain and range, shapes of graphs, word problems, and reviewing basic factoring. But besides all of this, we learned a LOT of trig. (This also happens to be my least favorite part of this year.☺) First, the basic with SOHCAHTOA and the six trig functions. There were lots of triangles and angles, and most of it was very confusing (not to mention the bridge project *shudders*). Then there was the trig chart, one thing I actually know by heart! And now, as the year is ending, we begin Calculus. It’s surprisingly easy, but I am NOT looking forward to taking Calc AB next year. But anyway, all in all, I learned a lot this year.

School's almost out!!

5/16

This week went by uber fast!! The intro to calculus we learned was pretty easy. i actually understand it. Then we did worksheets, practice problems, and whatnot. hopefully, this calculus stuff is on the exam!! then maybe i'll do semi-good on it. but trig wise... mehhhh... i gotta go back and study for that stuff. and formulas. and the trig chart. i sure hope this week goes by as fast as last week did... so i can get this year over with and relax in the summertime

LAST ONE!!!!!!!!!!!!

Last Reflection

Formulas:Cos(α +/- β)=cos α cos β -/+ sin α sin βsin(α +/- β)=sin α cos β -/+ cos α sin βsin x + sin y= 2 sin x + y/2 cos x-y/2sin x - sin y= 2 cos x + y/2 sin x-y/2cos x + cos y= 2 cos x + y/2 cos x-y/2cos x - cos y= 2 sin x + y/2 sin x-y/2

tan (α + β)=tan α + tan β/1-tan α tan βtan (α - β)=tan α - tan β/1+tan α tan β

sin2α=2sin α cos αcos 2α=cos^2 α –sin^2 α = 1-2 sin^2 α= 2 cos^2 α -1tan 2α = 2tan α /1-tan^2 αsin α/2= +/- √1-cos α/2cos α/2= +/- √1+ cos α/2tan α/2= +/- √1-cos α or 1 + cos α=sin α/1+cos α=1-cos α/sin α

something that i understood the most was section 2 here's some examples:
tan α = 2 and tan β=1
find tan (α - β)
= tan α + tan β/1-tan α tan β
=2+1/1-(2)(6)
=3/-1
=-3

Find the exact value of: tan 15+tan 30/1-tan 15 tan 30
tan α = 2 and tan β=1
find tan (α - β)
= tan (15 + 30)
=tan (45)
=1

im gonna miss you guys, especially you b-rob!! im gonna miss failing every test this summer, but dont worry, i'll fail em all next year too

last blog

so we are now finished with the advanced math book, and now we're moving on to calculus which is surprisingly easy without a catch

Continuity, which means to draw a graph without picking up the pencil, is basically what chapter 1 is about

there are 4 types of discontinuity:

1. vertical asymptote (can't touch this)
2. removable (hole)
3. jump (enough said)
4. Osciallations (not dealing with it)

when you see f(#)it means youre only looking for the colored in y value

example:

limit as x -> 2^+ means: the limit as x approaches 2 from the right

by looking at a certain graph with several curves, lines, and points, you should be able to find the types of discontinuities

Finite Limits
y-values that the GRAPH is approaching
they do not exist if there are 2 different y values

functions are also used in calculus

f(x) = -x^2 + 4x

find lim f(x) x->3

-(3)^2 + 4(3)
-9 + 12 = 3

also used with trig functions

f(x) = sin x
lim f(x) x->pi/4

sin 45 = sqrt 2 /2

composite functions (f[g[x]]) are also used

Reflection 5/16

For my final reflection, I will talk about, well I forget the name of it, but the f(x) an g(x) thing....

ok

f(x)=x+4 and g(x)=x-2

what is f(4)
f(4)= (4) + 4= 8

what is g(3)
g(3)= (3) - 2 = 1

what is f(g(2))

g(2)=0, so f(0) = 4

see simple, you just have to break it down.

what is f(2g(5))

g(5)= 3, so multiply it by 2 because its 2g(5) and you get 6. So plug that into f....
f(6)= 10

See its simple. You just have to break it down one step at a time. Don't look at the problem as a whole or you will get confused. Jus look at it one step at a time. Like look at g(5) first...solve that, the 2g, then plug that answer into f(x) and you'll be fine. Just remember, ONE STEP AT A TIME!!!

Final Reflection

Just some stuff:

You use completing the square to solve a quadratic equation when factoring doesn’t work. This can only work when 1 is the coefficient of x².

For example:

x² + 6x - 2 = 0

x² + 6x = 2

x² + 6x + 9 = -2 + 9

(x + 3)² = 7

x + 3 = √7

x = -3 ± √7

(-3 + √7,0) (-3 -√7,0)

Final Reflection Stuff:

The most important thing we learned this year was probably learning the Trig Chart. Everything we did always came back to knowing the trig chart. An activity that help me this year was: All Seniors Take Calc to help determine were sin cos and tan are positive on a graph. All goes in the first quadrant, all of them are positive in quadrant one, Seniors goes in quad two because sin is positive there, Take goes in quad three because Tan is positive there, and Calc goes in quad four because thats where its positive.

REFLECTION 5/16

Timeeee for another bloggggg. OH BOYYY. Anyyyway, this week we started learning calculus, and it's pretty easy so far. I'd say the main thing we learned this week was limits (..but I don't have my notebook in front of me so I'm not sure haha) Well I'll give a few examples of finding limits without using the chart or calculator.

Ex. 1) lim x^2+2x+1/x^2-1
x>3
*when you're asked to find the limit, the first thing you want to do is plug in the number you're given for x into the equation. Start plugging in with the bottom of a fraction (if you have a fraction) because if you get zero as the denominator, then you have to use the chart.
*So for this problem, you get 8 as the denominator so you're okay.
*Also, to make things easier, you can factor the problem before you plug in.
*So you get (x+1)(x+1)/(x+1)(x-1)
*And you can cancel out the (x+1)'s and you get (x+1)/(x-1)
*Now you can plug in 3 for x. And you should get:
4/2...which equals 2

Ex. 2) lim 4x^3 + 6
x>1
*Since this problem isn't a fraction you don't have to worry about getting zero as a denominator. So you know you can just plug in
*So you get 4(1)^3 + 6
*And that equals 10

Ex. 3) f(x)=2x+3 g(x)=4x^2+1 *Find lim f(g(x))
x>2
*Alright this is just like a composite function except all you have to do is add a limit in
*So when you set it up you get: f(lim 4x^2+1)
x>2
*Now all you have to do is plug 2 into that equation
*And you get 4(2)^2+1
= 17
*So now you have f(17)
*So all you have to do with that is plug 17 into the "f" function you're given in the beginning of the problem
*So you get: 2(17)+3
*And that gives you 37

**Allrrigghtttyyy that's about all the examples I can show, because we also did alot of things with graphs so I can't show that on here.
(:

reflection may 16

This week went by pretty fast actually, i thought. The calculus that we learned at the beginning of the week is pretty easy. I really think i understand it:) Then we did worksheets, practice problems, and little quizes in class that i thought i did well on. So if we have a good bit of this new stuff on the exam, i think i will do pretttty good on itt. But other than this new stuff, i will have to study and look over the old stuff that we learned, like doman and range, ugh im so bad at those. And those problems where you have to memorize the formulas, yeah i suck at those too. Im very proud of myself with the trig chart though:), i studied that thing sooo much for the trig exam, all i will have to do is look over it a few times and i'll have it back again in my head. So, hopefully that this coming week will fly by so that we will only have exams left, which are half dayss! Then the summmerrr:)

Reflection.

Alright so we finished advance math and started calculus, which was suprisingly easy :) hopefully it just stays that way. I'll just explain some things that we need to know for the exam.

**Functions!
f(x) and f(g(x))

Okay, for functions you'll always get one, two, or more equations>>f(x)>> that you will use to solve individual problems like this for example:

Example 1

f(x)=x+4 g(x)=2x-3
(these are the two equations that you are given^)

a.) find (f + g) (x) >>By the plus sign, this notation tells you that you're going to add your two equations together like this:

x + 4 + 2x - 3
= 3x - 1

b.) f(g(x)) >>This is a composite function. What this function is telling you to do is plug in the "g" equation every time you see an x in the "f" equation. like this:

(2x-3) + 4
(*you always want to put what you plugged in in parenthesis in case you have to distribute a negative.)

then you get >> 2x-3+4
= 2x + 1


c.) find g(6) >> this notation has a number in parenthesis. Whenever you see a number in parenthesis you know that your answer should be a number.

So the function g(6) tells you to plug in the number 6 every time you see an x in the "g" equation.
so you would get >> 2(6) - 3 = 9

**Domain & Range!

There are four different ways you can find the domain and range depending on the equation.

The first one is domain & range of all polynomials.
The domain of all polynomials is (-00,00)
The range of all odds: (-00,00)
The range of quadratics: [vertex,00)/positive[-00,vertex]/negative

The second one is the domain and range of fractions.
To find the domain and range of fractions you just set the bottom=0. After doing that solve for y. Then set up your intervals. Which would be (-00,closest number to -00) (<--closest number to -00,closest numberto 00) (closest number to 00,00)

The third one is domain and range of absolute value.
Absolute value for domain is (-00,00)
Range if positive (shift,00)
Range if negative (00,shift)
*Shift is the number that's outside the absolute value.

The fourth one is the domain and range of square roots.
First you would set whats inside the square root equal to 0. Then set up a number line. Try values on either side, (to do this you plug in numbers that you find on the left andthe right of the number on your number line into the equation inside the square root)Eliminate anything negative. Then set upintervals.

Here are some things to remember:
**Notice all domain is (-00,00)
**When talking about vertex in polynomials you use vertex form.
**Domain is x values, Range is y.
**() means included - used for +/-infinity
**[] means not included - used on numbers