Functions
Ah... the joy of blogging... it's such a wonderful feeling. Well anyways... today we started a brand new unit called " Functions ".
For starters, what is a function? Well... A function is a relation between two variables (x,y) where each x-value has only on corresponding y-value.
Examples of functions are y=x+3, f(x), g(x), t(x), s(x), e(x), etc.
NOTE: Some teachers what want to mess with your little minds and put in different letters. It's the same thing, x and y are just the most common ones.
To see if it's a function, use the vertical line test.
If the vertical line touches only one y-value on the parabola, it is a function.
If the vertical line touches more than one y-value on the parabola, it's just a relation.
Terms you should know by now:
Domain:
- x values
- input
Range:
- y values- output- - - - - - - - - - - - - - - - - - - - - - - - - - -
"Things To Do"
You done? Not yet? Okay... Take your time. Done now? Kay good! Well here are the answers.
- - - - - - - - - - - - - - - - - - - - - - - - - - -
Composition of Functions
Now for the final part, composition of functions.
Composition of functions looks something like this: (f ○ g)(x) or f(g(x))
In these equations, 'g' replaces 'x' in the f(x). Confused? Thought so. Well here's some examples.
Try these questions.
Given: f(x) = 3x + 2 and g(x) = x²
a) f (g (x))
b) f (f (x))
c) g (f (x))
Take you time, no rush. Done? Good! Here are the answers.
a) f (g (x)) → f (x) = 3x + 2
............................ = 3x² + 2
b) f (f (x)) = f (3x + 2)
............... = 3 (3x + 2) + 2
............... = 9x + 6 + 2
............... = 9x + 8
c) g (f (x)) = (3x + 2)²
................ = 9x² + 12x + 11
Lastly, we have Exercise 51, Questions 1 - 7 for homework. Have fun! =D
That's it for me. Finally done. Sorry it's kinda of late. Well anywho... it's time fo the best part of this whole, who shall be the next scribe! Well, since this person didn't do it before and sits across the room, I chose Chrycel! WAIT! Can I chose Mrs. Ingram as the next scribe?! If I can, I chose her! If not then... I guess it's Chrycel once again.
Pre-Test Blog
wewt, I'm pretty much the last blogger, again...
Anyways, circles. Like richard said they started out pretty easy, and gradually increased in difficulty but hows that different from any other unit? They weren't ridiculously hard for me, but I kept forgetting stuff, so there was always that one easy question that I could't do, because I forgot the tangent thing, or the inscribed angle thing. Most of the time it was simple logic thatsolved the questions (with the help of alittle existential knowledge on the subject.)
Yeah so Circles, = 7 out of 10 on the ridiculously hard scale.
Good luck on thetest everyone, I know I'll need it -_-;
Test day
Sorry I wasn't there today. I wasn't feeling very well.
For all those who blogged,
yes you will still get the mark even though it wasn't asked for on the test.
I hope the test went well for all, I'll have them marked in a couple days.
Tomorrow we start functions
Ms. Ingram
Pre Test Blog
Circles.. I found this unit very
difficult. it started out easy and when it started to get into the unit it became harder and harder maybe it was because i have miss so many classes in this unit or maybe it is because this unit hates me.
Your fellow student Richard
Pre-Test Blog: Geometry
What can I say about this unit... hmmmm? I'd say that it was the easiest unit yet.
Even easier than the parabola unit because all you have to do is memorize the silly rules like the inscribed angle is half of the central angle. I'm glad we didn't have to do a dictionary on it too.
Anyways, nothing outrageously tricky, just like I said before, memorizing those rules.
Yes now I get my one mark! Victory Fanfare plays in the background*
nyuk nyuk nyuk nyuk nyuk
Pre-Blog ; Circles
I'm really not in the mood. But whatever. It's one mark. My day hasn't been so great. I'm sleepy its 1 in the morning and I haven't had time to do homework. I've just realized while doing that homework that I had to blog. Well here it is. HMM circles. Not fun. Mrs. Ingram made it LOOK understandable and simple and it probably is but I'm probably just thinking too hard. Wasn't a fun unit but in any case, which isnt? To the point. It was an alright unit and I understood most of it, but my siblings warned me about circles, and how NOT fun they are. Correct they were. I found the inscribed angle was alright and all but having to prove an angle or arc was very hard because you'd have to put it into words. I THOUGHT THIS WAS MATH?! It's really simple if you study it. I studied but in actuality, I probably won't remember much because I'll have been so sleep deprived from this night. Well it was an alright unit all in all So yeah. My hands are starting to cramp up. I need water. So I say good day for now. Tired I am
--Mr.Lawrence ~ Out
Unit Blog: Geometry OR Circles + Triangle
Circles… and triangle... It seemed like you people didn’t enjoy this unit very much. As for me, I thought this unit was so much fun. I enjoyed this unit out of all the ones we did so far. I thought some parts were confusing, but then later on we did a whole bunch of questions and I got the hang of it. To tell you the truth, I wrote down almost everything she wrote down just so I would have something to put in the math dictionary. I had everything planned out and all, then all of a sudden… I was informed that there was no math dictionary… I was devastated! Well… maybe not… but this math dictionary (if there was one) I would have rather done instead of all the other ones… sigh…Well anyways… that’s it. I will be back on this very soon, so don’t miss me too much. By the way… Thanks Xuan for somewhat reminding me to do this and... any time Nelsa! =D- Jasmin
Unit Blog: Geometry
Ohmygosh! I almost forgot about this! Hahah.Uhhm, weell, this unit didn't have a lot to it, not really. Just a lot of round things, circles I believe they are called. So uhm, well, I thought the whole.. concept of circles was easy.. Weell, at least the whole inscribed/central angle thing is understandable. But once you have a bunch of lines and the question asks you to look for angles.. yeah, that got a little confusing. ^^;; I guess you just have to do more questions like that, just to get you used to the idea. That's how I got used to it anyways, seeing it over and over like that, made it easier for me.So, that's my little.. blog, there's not much to say.. Hahah, good luck on the test you guys. And thanks for reminding me to blog Jasmeen. XD
Geometry Unit Blog
This unit was ehhh, I mean okay.. at least we didn't have to do a math dictionary ^_^ It was easy at first then it got challenging. I hated solving for different angles with all the lines through the circles, it got confusing. But once I figured out one angle to the question, it made sense after. Sooo, yeah. Study hard everyone and good luck !
Pre-Test Blog for Geometry
Well.. this unit was quick and simple. It was mostly about knowing the rules about the circles. As long as you knew a little information on the cirle, its easy to figure out everything else. Well, here I am saying that it's all easy, and tomorrow, I might even fail the test ! Aw man. I'll go study now .. (maybe) haha.
CIRICLES -_-
well i'd like to say.. this is one of the units i hate! at first it was easy, then later it just got difficult.. i didnt know a circle could be so complicated. i mean i learned about circles in nursery! and it seemed so simple then. anyways.. after a few more lessons and the teaching from mr elven hansana.. it got to be more simpler for me. except when he would yell at me -_- i guess one of the hardest parts is finding so many angles in one circle with a bunch of lines. it scares me.. literally. i look at it and i'm like whoaa.. haha kay well anyways.. hopefully the test wont be so bad tmr.. goodluck to everyone and especially mooiii (:
Geometry Unit Blog
Since I'm feeling cheap today, I'm just going to use Paul's outline..hehe.
* How do you feel about the unit?
I hated it..it gave me a headache. :(
* Was there something you felt was difficult?
Alot, I'd rather not get into anymore detail than that.
*Do you think this unit was easy?
No..and I am so going to fail the test. >__>
Test Blogging
Double post Sorry about that
This was by far, the fishiest unit ever.
* How do you feel about the unit?
I loved how short and uncomplicated everything was.
If only all math was like this ):
* Was there something you felt was difficult?
I did get confused briefly with inscribed tangential angles... but everything is fine now.
*Do you think this unit was easy?
Yes!
FEELING DOWN IN LIFE? DIDNT GET THAT PROMOTION?
SMELLING A BIT LIKE FISH CAN HELP! FIND OUT ABOUT HOW GREAT YOUR LIFE CAN BE!
(I couldnt help it)
Test Blogging
Well to for me this unit was...i dont know complicated. I'll jus say that tomorrow I will most likely fail the test. Is that enough? Well let me try to drag this out longer if not.
everything bothered me...well not everything but most of the concepts just went though one ear and out the other and i'm an auditory learner...
I really dont know what else to say... I really have to study hard for this test. T_T
Ok, i'm done well happy studying to you all
For the circle units
i guess i am the first one to start blogging before this so-complicated circle test_
i heard somewhere that geometry is for guys_ -_-;
i know it sounds sexist_ but its definitely not for me_ +_+
there wasnt any hardest or easiest
the whole thing was all blended in one question
i think thats why i got confused so much
i have to think all of the things i learned during the unit_
o_ yeah the easiest was that getting sum of the inside angles of polygons_
o well, anyway_ i hope i dont get confused tomorrow_
Introduction to Polygons and Circle/Polygon Properties (According to my Excercise book)
ATTENTION!:This blog has been
EDITED. Look for RED TEXT, indicated edited material.------------------------------------------------------------------------------
Volume 1:
"Introduction to Polygons"
The following Volume describes three different properties of a Polygon and how to find thier values.
Property 1: Number of Sides
Like the title says, one property of a Polygon is how many sides it has.
Property 2: Number of TrianglesVolume 1:
This property determines how many triangles the polygon can be divided into. So if you have a nice polygon like this:
You can divide it into many triangles like so:
And there is usually more than one way to make the triangles. If you're bored, try to find all the combinations for a polygon!
Property 3: Sum of the Angles
This property determines the total (sum) of each and every angle.
So how do all these properties relate to eachother?
They are related because each property can be used to find another. Meaning:
If you have the number of sides:
You can determine the amount of triangles with the following formula:
# of triangles = (n - 2)
Where "n" is the amount of sides.
You'll notice the above polygons follow this rule.
And, building upon that, you can determine the sum of the angles.
Sum of angles = 180t Where "t" is the amount of triangles.
Solving for questions where you are given a different property just requires you rearrange your work a bit.
Ex. Find the amount of sides if the sum of the angles of a polygon is 1440 degrees.
->1440 = 180t
--> 1440 = 180(n - 2)
---> 1440 = 180n - 360
----> (1440 + 360)/180 = n
-----> 1800/180 = n
This is too tiring, you figure out the answer for yourself.
Anyway that pretty much wraps up this Volume.
Important details summary:
- Number of triangles = (number of sides - 2) or (sum of angles/180)
- Sum of angles = 180(number of sides - 2) or 180(number of triangles)
- Number of sides = (number of triangles + 2) or (sum of angles/180)+
Volume 2:
"Inscribed angles with Tangents"
I just made up that name, because none of the "circle lessons" have had a title, and I felt this adequately described the lesson.
Anyway, lets get on with it.
We have a circle, chord tangents and two points like this:
Now lets connect these lines and create this nice litte mess here.
Now here's the part where we would normally measure the angles of GWU and GLU aswell as JGU and NGU. But since Windows doesnt have a protractor accessory (that would be cool), I'll just explain what should happen.
GWU + GLU = 180 just as JGU + NGU = 180 (its a straight line, makes sense). GWU = JGU and GLU = NGU. This is because they share an arc of GU.
[edit]
Even I am having trouble understanding what I just wrote, so if you don't understand it, ignore it. The main point is that the LEFT GU arc will be equal to twice the value of angle NGU and the RIGHT GU arc will equal twice the value of angle JGU. JGU is inscribed in the RIGHT GU arc, and NGU is inscribed in the LEFT GU arc. Very useful information, especially if you're stuck on question 2 of the Pretest.
[/edit]
And such ends this Volume and blog. Onward to picking the next scribe.
....eenie, meenie.... blah blah,
Jasmin.
Almost two whole months without doing one!
Warning to bloggers: NEVER USE POINTY BRACKETS. EVER.
They are detected as HTML tags, and when I used them in my blog the lines using them got deleted. D:
Also, does anybody even add labels to thier posts?
And now I'm going to bed.
Labels: (n-2), arc, circle, polygon, properties
TANGENT
Hello so here’s the blog for today...
Steps
1. Find the centre of your circle like usual, erase construction lines and label centre O
2. Pick a point outside the circle and label it P
3. Draw a tangent line from point P to the circle label it point A
4. Draw another tangent line from point P to the circle label it point B *Tangent- a line touching at a single point a circle/curve.
5. Measure distance of point PA and PB *you should be able to get the same distance
6. Draw line from point A to O
7. Draw line from point B to O
8. Measure angle PAO and PBO
* should be able to get 90 degree angle on both
Now on the same circle
1. Pick another point outside the circle and label it J
2. Draw a tangent line from point J to the circle label it point U
3. Draw another tangent line from point J to the circle label it point G
* And again Tangent- a line touching at a single point a circle/curve.
4. Measure distance of point JU and JG *you should be able to get the same distance
5. Draw line from point U to O
6. Draw line from point G to O
7. Measure angle JUO and JGO
* should be able to get 90 degree angle on both
Summary
1) IF TWO TANGENTS ARE DRAWN FROM A COMMON POINT EXTERIOR TO A CIRCLE THEN….
“THE DISTANCE FROM THE EXTIRIOR TO THE POINT OF THE TANGENTS WILL BE CONGRUENT”.
2) IF THE RADIUS INTERSECTS A TANGENT LINE THEN…
“THE POINT OF TANGENCY WILL FORM A 90 degree ANGLE”
WELL THATS ALL FOLKS...
IF I MADE ANY MISTAKE PLEASE FELL FREE TO CORRECT ME
AND AND FOR THE NEXT BLOGGER I PICK MY DEAR FRIEND CHRYCEL hihihi...
OH YEA n FOR HOMEWORK
EX.34 NUMBERS 1-6
Monday quiz
Good news for all. My photocopying came in so we can have a quiz on Monday.
Enjoy the weekend.
Ms. Ingram
Parallel Angle
this is Michelle NOT Paulette.
STEP 1: FIND THE CENTER OF THE CIRCLE, LABEL ‘O’
STEP 2: MAKE TWO CHORDS WITHIN THE CIRCLE, LABEL AB, CD
STEP 3: CREATE A PARALLEL LINE TO AB, LABEL LM
STEP 4: CONSTRUCT
STEP 5: CREATE A PARALLEL LINE TO CD, LABEL RF
STEP 6: CONSTRUCT <ROC, <FOD ; MEASURE
‘O’ the CENTRAL ANGLE ..
- gives the arc measurement
- the parallel lines and the arc measurement is the same,
so the central angel will be the same
EX.) AB is parallel to LM, so when ‘O’ connects ‘A’ to ‘L‘, and
‘B’ to ‘M’ they will have the same angle because they share
the same central angel ‘O’
the next blogger is Paulette.
hehe thanks lette for letting me use your account (:
In class, Ms. Igram told us to find the center of the circle on the sheet she gave us (learned in previous classes).
After that, she wrote down steps to follow on the board, they were:
1) Place 3 points on the circumfrence of the circle (randomly placed) and label the points, A, B, and C.
2) Make angles ABC and AOC and measure.
3) Plot another point somewhere on the circumfrence, and label it M. Make angles BOM, and BCM, then measure.
Angle ABC ---> Inscribed (1/2 of central angle)
Angle AOC ---> Central angle (twice of inscribed angle)
288/2 = 144 degrees
144 x 2 = 288 degrees
4) Add a point anywhere on the circumfrence between AB or AC, and label it F. Make angle AFC, measure. Add another point anywhere on the circumfrence between AB or AC (whichever one you haven't plotted point F) and label it G. Make angle AGC, measure.
Angles that are all inscribed in the same arc, will all have the same value.
Angles ABC, AFC, and AGC all have the same value (in this case, it's 144 degrees).
And that's the end of it. Now, it's the really really fun part, choosing the next scribe ... HAHA yaaay ! hmmm.. shall I choose my budddy, and my desk neighbour? Or .. send it across the room like she told me to? haha.. hard choice. But oh well, since I'm such a GRRRRREAT friend, I throw it to the other side of the room. Sorry, but I choose, Chricel.
Central and Inscribed Angles
Alrighty, well roxee picked me to do the blog for today, so that would explain why I'm posting. Anyways for those of you who might not have been in class today (the 9th of May) we did some more work with circles and chords, specifically finding out about Central angles, and Inscribed angles. So, without further adeu, on with the blog!
Inscribed and Central AnglesA few quick definitions and points about Inscribed angles, Central angles, and the word subtended. (*Note* These make up the majority of todays lesson, so it would be good to read this if you weren't present.)
Central Angle - The vertex the central angle is at the center of the circle, and is equivalent to twice the inscribed angle.
Inscribed Angle - The vertex of an inscribed angle is located on the circumference of the circle.
- If the endpoints of two inscribed angles are the same, the measurement of those angles is also the same.
- Inscribed angles that are subtended by the same arc have the same measure.
- Inscribed angles are half of the central angle.
Subtended - The point at which an arc 'cuts' an angle, ending the angles. Example. Arc AB subtends Angle ADB at points A and B (because the lines making up angle ADB technically go on forever, they are considered "subtended" by arc AB, as they do not continue past the arc.)
Now, with those three points out of the way we have our nifty little diagram that I threw together. Now it isn't perfectly drawn up, so the center may not be at the exact center, and the angles may not be exactly 90 degrees, but for the sake of my sanity, we will assume they are, as they would be if everything was done perfectly.
So, on the graph you'll notice a line, that is the diameter of the circle. This line is labeled AB. There are also, two angles, ADB, and ACB, both of which are designated as 90 degree angles. Both of these angles are inscribed angles, and were made by picking some point on the circumference of the circle, and joining it to the endpoints of the diameter of the circle (A and B).
Now you may be wondering the use of this, and the answer is simple. Since you are constructing right angled triangles that happen to have the diameter of your circle as one of their sides, you can use these inscribed angles to find various thing out about your circle. These things include, obviously, the diamter, the radius, and many things I'm sure we will learn about tomorrow in class ;p
So for those of you who missed it. The homework for today is Exercise 30, questions 9, 10, 12, and 14. AND Exercise 31, questions 1 to 3. :)
Anyways I'm pretty sure that that sums up todays lesson. Nothing too huge, as we always expect to see at the beginning of a unit. If I missed anything, or didn't explain something well feel free to scold me and say your right and I'm not :P I'll be sure to change it asap.
So! Now comes the best part of the blog. Picking the next blogger!! >D I think I'mma go with my projectmate, the lovely Xuan. Have fun! ;)
Now it's off to work for me -_-;
oOoOo CIRCLES (:
Unfortunately, i will have to blog today -_- i'm so sad *tear. kay anyways, today's topic started off with our new unit with CIRCLES. boooo just kidding lol
First, we were given a circle, with the center already marked.
Then, we had to make one chord (a straight line in a circle with its end points on the circle). First chord is labelled as AB. Then draw a perpendicular line from the center to the chord AB, labelled as OM.
Then, we measured AM and MB which are 3.6 and 4.5.
After, we drew another chord and labelled it as CD. Then we drew another perpendicular line from the center to the chord CD, labelled as OF.
Then, we measured CF and FD which are 4.7 and 4.9.
The line splitting the chord in half is called the, perpendicular bisector.
Perpendicular bisector -> is the diameter
-> will go through the center of the circle
-> cut chord in half
After, we were given another circle but this time we had to find the center of the circle. To do this, first draw two chords, just like the first circle. After, draw the two perpendicular bisector on each chord. This will give you two diameters and where they meet is the center of the circle. Example...
FINALLY, done (: woot woot but anyways.. note/comment/edit/watever if there are any mistakes, knowing me there must be mistakes or things that i didn't mention but was suppose to. -_- lol and HOMEWORK FOR TONIGHT: excercise 30 # 2-7 yup yup (:
NOW THE FUN PART, TIME TO CHOOSE THE NEXT POKEMON OR DIGIMON or whatever they're called (: lol I CHOOSE YOU JUSTUSMON LOL
AND NOW FOR THE JOKE OF THE DAY LOL
What does a farmer use to count his cattle?
A COWculator! hahahahahahahaha funny right lol
Monday's class
Don't forget!!!!
You need to have a ruler, protractor, pencil etc for Monday's class. The new unit will require the use of these tools.
See you Monday.
Pre test blog
Well I yet again forgot to do this before yesterday lol.
Anyways this unit was alright, not really tooo complicated. the hardest part of it was remembering everything since it was like 3498675498 units in one. Besides that though I didn't have much trouble with it. Anyways good luck to everyone, see you at the test :P
Test Blog
I found this unit to be quite harder than the others. It took me awhile before I understood what was the equation of a circle and the distance formula. The three variable equations were the worse. They took up a page of work and then your answer was still would not have 100% of correction. All in all, after a deep review of the unit, I believe I understand everything.
Pre test blog: Analytic Geometry
uhmmm.. this unit is quite hard because there were so much this to do especially that 3 variable system, maann in that thing i coould spend all night just doing one or two questions. haha. uhm there were a lot of parts I had a hard time I think I had a hard time on all of it. Most of it confused me. Yeah so i think this unit is quite harder than the past units. Uhmm I think that's all i could say. Well thats all what i have in my mind as of now. Just gud luck with the test later and i hope i past. hehe bye
Unit Blog: Analytic Geometry
o My Gosssss__ its 12;33 a.m. i just remembered to blog before the test_
someone shouldve told everyone_
well its still before the test so it counts right? -_-;
This unit was the hardest unit i think
especially inequalities were challenging yeah yeah
and I HATE the 3 variable thing_
i think its so much of waste of time_ o well, its pre cal _ i know it
one thing i liked about this unit was getting perpendicular
distance between one line and one point on other line
It was something totally NEW_ o well,
i m dying to go to sleep _ so everyone _ c u to mo rro w_
z_z ;;;;;
Unit Blog: Analytic Geometry
ALRIGHTY... I'll take a break from doing my dictionary to do this. Okay... the unit. Well I thought it was confusing at first with all that circle stuff, (maybe it was because i couldn't really see the board) but then the other things became more understandable. All you guys said that you didn't really enjoy doing the three variable equations... WHY NOT?! I thought that was the best part! ( two variable equations as well) The worst part for me was doing the whole finding the inequalites with the number line and seeing if it was positive of negative and what not. That's about it. I just hope that tomorrow I won't make stupid mistakes like adding instead of multiplying... again. Back the the dictionary!- Jasmin
Analytic Geometry Blog
Shoot. Everyone's doing it... guess i'll use this format too!
* How do you feel about the unit?
This unit was oookay, little too long. There should be a condensed version.
* Was there something you felt was difficult?
Gosh, anything i thought i did good on, or thought was easy, was the exact opposite on a test or something, but im going to risk it. everything was preeetty straight forward, it was all just following a bunch of steps
*Do you think this unit was easy?
Heaven's no. Since when was math easy!? Even in elementary! That darn multiplication table...
- Joseph
Pre-Test Blog ; Calm Before the Storm
COPY AND PASTE FTW!!!!!!11!!
How do you feel about the unit?Well for the most part, it cause me to cramp my brain which eventually leveled out to low blood sugar -_-".
* Was there something you felt was difficult?Since when was Pre-Cal easy? Tell me really... *mumble* Three variable *mumble mumble* Waste of time *mumble mumble* kills trees *mumble mumble* kill... BTW it wasnt actually hard, it was just really time consuming.
*Do you think this unit was easy?..Uh, is this practically the same question just refraised? ANYWAYS, in terms of solving yes, in terms of quickness... NO.. unless you're youna.
¬_¬'btw, I'm still getting this blog pages in korean other than the actual blog. -__-" So the only thing appearing english is what i type. Lame.. My two cents.
I SAY GOOD DAY ~ Mr.Lawrence
Pre-Test Blog: Analytic Geometry
This unit seemed longer than the previous ones and I have to admit it was not easy. Most arduous part was 3 Variable Systems. I wasted so much paper on them... (Poor Mr. Samuels). I don't understand why I always end up with a fraction...
Even though we can't graph it on our calculators I did enjoy learning about the Z Axis. My favourite part of this unit was sign diagram especially because Ms. Ingram let us use interval notation because set notation is icky.
Yay! Now I get one mark on the test. That should make a difference...
Well it's time to go back to my math dictionary.
BYE BYE
Analytic Geometry
.. yeaaa i'm sick and i almost forgot to blog -_- luckily i remembered! even though it's really late.. but anyways this unit was easier than i thought it was but at the same time it still requirred a lot of thinking espeically the 3 variable equations. ooo so evil. ha always made me mad when i was so close to finding the answer, and it turned out to be a decimal! omg almost made me crazy but anyways, i'll probably be back tomorrrow to write the test. *crossing fingers* lol ANND good luck fellow peers.. lol
Analytic Geometry
.. yeaaa i'm sick and i almost forgot to blog -_- luckily i remembered! even though it's really late.. but anyways this unit was easier than i thought it was but at the same time it still requirred a lot of thinking espeically the 3 variable equations. ooo so evil. ha always made me mad when i was so close to finding the answer, and it turned out to be a decimal! omg almost made me crazy but anyways, i'll probably be back tomorrrow to write the test. *crossing fingers* lol ANND good luck fellow peers.. lol
Unit Blog: Analytic Geometry
Overall, this unit was ugly.. just kidding I mean it was challenging, I didn't like the 3-variable equations because it had so many steps. I enjoyed doing the 2-variable equations and finding where two lines intersected. So yeaah, good luck on the test kiddos. Bye.
Pre-Test Blog for Algebra Geometry
Hey everyone! Well, I thought this unit was medium speed, packed with a lot of teachings that hopefully I'll remember for tomorrow's test! Uh Oh, haha. Well, the only thing that I got confused on with the inequalities, because I didn't know when to put a square bracket or not, but now I do. So it's all good. Well, I'm off to finish up the dictionary! And study a bit. Goodbye.
Elven's Pre-Blog thingymajig.
Hehe I jacked Paul's questions. COPY AND PASTE BABY!
* How do you feel about the unit?
I feel hungry. Really though the unit was abit complicating.
* Was there something you felt was difficult?
YEAH MAN. Jees, 3 variable questions take like a gajebebalfqhjgtioengienBILLION years. Not only that, but number lines and circle equations! ETC..
*Do you think this unit was easy?
.. NO. I would say this was the hardest unit. It was like 5827582 units together you know?! Circle equations to 3 variable equations.. THEN SOMETHING LIKE INEQUALITIES. AHH. Not that its hard seperately. But put together, they make a killer team -.-'
mmk, I'm done! Later days.
- elven!
BLOG WARS V: RETURN OF THE TEST BLOG
* How do you feel about the unit?
It was alright, but hardly the easiest to understand.
* Was there something you felt was difficult?
Some parts took me a while to understand. Nothing specific, but overall it was a little blurry to me.
*Do you think this unit was easy?
No, not really, no.
I still say we shoud've have gotten the weekend to do the dictionary >:(
Test Blog
Okay...lets see. I thought that this unit was long! I mean I dont even remember learning the circle equations. Some of the concepts were a bit troublsome. Three variable systems...i made really lame...mistakes [Like not changing signs, doing one operatoin when i should have been doing another, etc] Once I made one of those mistakes i went through
ALOT of trouble finding the mistake and correcting it. Inequalites were confusing at first and after a bit of questioning they arent so bad. Circle equations...yeah didnt even remember learning those. Distance equations...the only thing that gave me the slightest if trouble was the perpenducular equation thingy, but it really wasnt that difficult.
On the birght side, i picked up 2 veriable systems without much trouble. But i bet everyone else did too. XD
Well I'm going to go finish my dictionary plus a few other assignments. Happy Studying ^_^
Unit Blog: Analytic Geometry
Ookaay, at first I was like, "Woah.. where is everyone? Is this that one unit that we don't blog for? That makes no sense!"
Hmm, soo analytic, I thought this unit was fuun. I think my.. I guess "favourite" thing about this unit was the two equation thing we did, yeah, I had fun with that. What I didn't like, was missing a whole chunk because of the Music Trip. That was uncool. I went on the blog though, and I was all confused at first.Not fun you guys, not fun. Don't even miss math!
Pre Test Blog
K, I'm not really sure if we were supposed to do this or not, but Nelsa said so! So if we weren't..give me bonus marks plox..
Anyways, I thought this unit was a bit confusing at first since I hated working with those circle things and that weird distance formula thing with the A's and B's is hard to remember and gets confusing. Once we got to the 2 system linear equations and the one with 3 equations though, I found it to be really fun..surprisingly. Those were probably the only things I really liked out of the whole unit, although they took waaay too much room on my paper..seriously..more than half the page..c'mon! As for the inequality parts, I found it so-so...
Yep, that's it. I hope I won't be the only one doing this *glares at you ppl*..k..got to go not study for the test..wahoo!
Yesterday and Todays blog!
Man I still don't see why I gotta blog twice. -_-'
" RATIONAL INEQUALITIES "
STEPS TO SOLVING THESE ..
x - 1
--------- <>
(x-2)(x+3)
Because the expression is LESS THAN 0 then you are looking for a negative solution(s).
STEP 1:
FACTOR NUMERATOR + DENOMINATOR..
(In this question Mrs.Ingram kindly provided you with, it is already factored)
OMG WHY IS THIS COMPUTER BEING SO SLOW.
STEP 2:
Determine the CRITICAL NUMBERS .. WOW THIS COMPUTER. !@#%@$^ What are critical numbers? Same as restricted values. What will make the denominator zero.
But now including the numerator.
SO THE CRITICAL NUMBERS ARE ..
(2, -3, 1)
STEP 3:
Place the critical numbers on a number line.
OKAY.. SO NOT ONLY THE COMPUTER IS SUCKING. BUT SO ARE MY QUALITIES OF PICTURES. whatever.
I know its beautiful, because it was made in 5 hours.
p.s. don't even try reading the little jibberish. dont even look like english haha. but if you somehow manage and tell me what it says, amazing, i'll give ya a cookie.
REMEMBER that <> are OPEN CIRCLES. and LESS THAN + UNDERSCORE ( <_>_ ) .. (Greater than or equal to, less than or equal to) are CLOSED CIRCLES.
Step 4:
Test each interval. Doing this by taking ANY number ( yes even gajabebebillion ) EXCEPT the open circled numbers. So taken from the crusty image I provided you, anything from -oo to -4 .. Then taking those numbers and plugging them into the expression ..
x - 1
------
(x-2)(x+3)
so lets choose -11, because everyone loves it and its beautiful and its special and its cool and the best kk.
SO .. (-11) - 1 = -12
(-11-2)(-11+3) = -13(-8) is something something.. BUT THE ANSWER IS POSITIVE and thats all that matters.
because now it would be NEGATIVE / POSITIVE .. which is NEGATIVE.. Still with me?
Now knowing that the WHOLE region from -oo to -3 IS NEGATIVE, we still have to find the other regions, using the same steps of choosing and subsituting.
Because I'm nice and lazy, I'm just going to tell you signs of each region.
(-oo, -3) = NEGATIVE
(-3, 1) = POSITIVE
(1, 2) = NEGATIVE
(2, oo) = POSITIVE
Now because we know what solution(s) we are looking for, we pretty much choose which region is the correct one.
Therefore the solution is ..
(-oo, -3) AND (1, 2)
WOOHOO..
NEXT! .. This one had no title. But I'm going to guess it is ..
" ABSOLUTE VALUE INEQUALITIES " (on the calcul
ator it says "ABS(" LOLOL .. uh lots of laughter )
Okay yet another crappy image. But you gotta hand it to me, its still beautiful. Anyways the text on the left shows ..
" Y = x " .. and the right says..
"Okay this is your basic everyday " Y = X " graph. Have you ever wondered what would happen if the equation was
"Y = x" ? .. Yeah me neither ha. But if it was, the VALUE of X would always be positive, thus forming a V..
Alright now .. solving absolute inequalities are as easy as wrestling a great white shark.
GIVEN THIS EQUATION MRS.INGRAM, AGAIN, KINDLY PROVIDES.
X - 2 <= 5
Two ways of solving ABSOLUTE VALUES.
FIRST WAY)
TREAT IT WAS AN EQUATION. so ..
1) X - 2 <= 5
2) x <= 7
SECOND WAY)
ADD A NEGATIVE TO THE SIDE WITH X
1) -(X - 2) <= 5
2) -X+2 <= 5
3) -X <= 3
4) X >= -3
Now using the number line, plugging the values 7 and -3 in. Remember, closed circles.
because X <= 7 and X >= -3, then region is in the middle!
The interval would be ..
-3 <= x <= 7 ( Justice says its ugly so .. )
[-3, 7] CLOSED BRACKETS. OR SQUARE WHATEVER YOU CALL IT.
If you are given a question such as..
X/2 + 1 <>
YES EXACT ..
" ha ha, you can't do that, nice try. you can't mess me up like that. oh come on. I know better than that. Now go give Elven some cookies "
... AND CUUT!
yes.. 2 blogs. pretty deadly = .. NOW FOR MY FAVOURITE PART. THE CHOOSING THE NEXT BLOGGER THINGYMAJIG
mmm. its of course.. the one and obvious
ROXXANE .. YUMANG ..
* DUN DUN DUNN
hA! i hope she doesn't see this so that she misses her blog and has to do 2 or 3 and suffer like i did.
yea anyways. this is brought to you by Elven. Please edit if you see mistakes. Thanks!
mm im hungry
