Why Two Answers?

We've been learning how to solve trigonometric equations. I've tried to emphasize that when we are given an equation like sin(x) = (1/2) we are trying to work backwards from the vertical length that sine represents to the angle from which it came. (i.e. we are finding the inverse sine A.K.A. the arcsine)

Check out this applet. The red line repersents the sine of an angle. The blue and green lines represent the two angles associated with a single value of the sine function. Click on the lines and play with it -- you'll see what I mean. Make sure the [degrees] button is seleted in the top right corner of the applet window. You can also look at the cosine and tangent functions by clicking on the buttons you'll find there. We wont really be studying the tangent function until Pre-Cal 40S but there's nothing wrong with getting a head start. You can also see what happens when you click the [radians] button. ;-)

Heather can draw the pictures ... can you? ;-)

Sticks and Shadows

Follow this link to answer the question: "What is Trigonometry?" You'll also find out what sticks and shadows have to do with trigonometry.

Read through the site pages starting with Sticks and Shadows (Part 1) through to sine and cosine Do "the Wave". Each page has a really cool java applet to help you visualize and understand what we were talking about in class today. You can go farther if you like as we'll be covering that material eventually; if not in this class then in Pre-Cal 40S. ;-)

Have fun with it!

Our Readership

I thought you might be interested to know about our readership. Our blog is being read by people all over the world. The graphic below shows where the last 82 visitors to our site have come from. Of course, this is constantly changing as more and more different people pop in to see what we're doing. While some of them visit only once a number of them do keep coming back. (The "unlisted" reader is from Brazil.) People are interested in what you have to say and what you are learning.

Ladies and gentlemen, you have an audience. It's worth your while to make a good impression by making sure your spelling and grammar are correct when you post. ;-)

Thought You'd Like To Know ....

Miss Nicholson, a student teacher from U. of Winnipeg, dropped into our blog tonight and left Rosel a comment here. I thought you might like to know what she wrote ....

---

Hi!

This is Miss Nicholson, the student-teacher who sat in on your class today. Hopefully you're all in bed already since it's beneficial to get a good night's sleep before a test, but I just wanted to say that I enjoyed observing the ways in which you worked together in class today and am really impressed with how you are using this blog. I'm getting a lot of great ideas to use when I will be a teacher.

On that note I wanted to encourage you all in your studies by telling you what my experience has been like being back in high school observing courses that I took several years ago. When topics come up that I struggled through in school, even though it's years later, I start feeling a little anxious too. Then I watch the teacher work through the problem or I work it through myself which is when I immediately realize that I really did learn it and it's actually not as difficult as I always imagined it to be. It's pretty exciting!

So, even though the math seems to be getting harder and harder, you're all acquiring more and more skills and tools to get that boulder up the hill (ahh, sisyphus). Just keep on using them, and by the time your exam rolls around, you'll wonder how you ever struggled through such simple questions. :)

Good luck!

myy blog =)

Today's pre-test was weiiirrrddd..... it's just I totally blanked out for the first 5 minutes then for the rest i was rushing, I thought I was the only who didn't understand it =(... But I wasn't! And in my group we all helped each other out and Mr. K explained everything and I'm starting to get it. When someone told me pre-cal30s was hard I didn't believe it until now! But you guys are making it easier, Mr. K wasn't kidding these blogs are preeeettttyyyyyyyyyyyyyy gooooodd and a HUGE help to everyone, especially me! SO THANK YOU!

Test tomorrow hope everyone is studying and is ready. My tip is relax... we've gone over every single bit of detail in class... so don't worry your ready!! Oh and before I forget... though we're trying to remember all those equations and parabolas don't forget about checking over the simple stuff like multiplying and adding/subtracting.

OH WAIT! lol.... don't forget to check over your test in the end. TRUST ME! So many times in the past i didn't check over my test and i lost a mark because of something... alright that's all =) good luck everyone....

blogging before the test...

Okay, um.. i just finished reading some posts and i agree with some of them... pre-cal this year is harder than last year. but just remember sisyphus. just like what Rannell said in her post. =)

hmmm,

So far, i think the class is going
great! It's like.. WOW. im surrounded with super bright people. Just by reading their blogs you can already tell how bright they are. *thumbs up*

hmm... what else to write in here.. oh!a reminder again that....











In a problem solving context...the left side of the graph does not exists. But mathematically it does.

for instance:

if a ball was thrown from a top of a building and then lands. If you graph it in a distance-time graph it should look something like the graph shown above.

if you're wondering why the left side of the graph does not exists in that graph, its because we cant have negative time, we can't go back in time.

okay, thats it for now.

Test tomorrow... GOOD LUCK !

-kat ^_^

BLOGGERS 'R 'US

For you guys who really need help Blogging or Posting or Just doing Whatever around here. Here's some help.

Part 0: Getting On Blogger

For most of us who already made an Account. You already know. For the rest of us... Sigh/// You had to ask... No I asked. Hahaha. We'll first go here. Blogger Home If you didn't sign up. Then sign up. Hahaha. If you already did... Then look for the Sign in Box and sign in with the account you made.

Part 1: Editing Your Profile.

There are two ways to find the link to edit your profile. #1 is at the Dashboard. There's a link that says Edit your profile on the Right Side. #2 is if your viewing your profile. There's a link to edit your profile on the Left Side. Remember you can only edit your profile if your signed in. Duh. Hahaha. Well When you Click on those links you end up in the Edit Profile Page. You can change allot of stuff. Including your screen name for you guys who still need to edit your screen name. Esp. the Pre Cal 20S Guys. Once your done. Look for the Save Profile button and save.

Part 2: Making a Blog.

If you really wanna make a blog. I mean really... Like if your CRAZY ABOUT BLOGGING!!! Go to the Dashboard. Click on Create a blog. Make a title. Make an address. Write the silly little letters. Choose a template and I think your done. Blog made.

Part 3: Posting on a Blog.

Everyone needs help on this one right. Ya I know. A blog by my definition is a series of collective thoughts in your mind that you just wanna get out in the world weather it's funny, sad, happy or mad or something else that doesn't fit on any of those categories. Or. For everyone else out there. Something You do when you got nothing to do. But I like the first Definition better. Don't you. Well... To post on Blogger. Go to The Dashboard. It always starts with the Dashboard. Then go to. New Post. You should automatically be on the create a post page. Then you type a title. YES TITLES are IMPORTANT!!! They Define the Blog. Weather it's a SCRIBE Post or Just a Random thing that you wanna post. Titles are important. Because it makes things allot easier. Now the content. In the Big Rectangle with the white space is where you write your blog. I already stated that it can be funny, sad... I am not gonna go through that again.... Well anyways... After you write whatever. Click on Publish Post. And you don't like what you wrote. Go click on Save as draft. Which means you can still edit the post whenever you like but it will not be shown on the blog. Did I cover everything... Um Ya.

Part 4: Editing a Post.

Now this is fun. Hahaha. Thought I was finished eh? Of course not. Muhahaha. Too bad. Well to Edit a post that you posted. YES YOU cause only you can prevent... I mean. Edit your own posts. Cause Only you can sign in to your blogger account. Does that make sense... Whatever. So you click on Edit Posts. Find your post. And then. Click on Edit. Easy as that. Then you edit your post and click on Publish Post again. But you don't want that post to go back up you can again go to Save as Draft.

Part 5: Deleting a Post.

Quick and Simple. Your Work. Your Post. Only You can Delete your posts. Dashboard... Arg... Ok. Just find edit posts and look for the delete thing and that's that. Ok that was weak.

Part 6: Leaving a comment.

Comments are cool. Of course they are. They provide insight to everything we do on a blog. That's why I try to leave a comment in every post that comes up. They help writers become better writers. Etc. It's really a complicated process. Don't just write Good Job or Cool Post like I've been doing. I'm really getting lazy. Provide comments that leave a Blogger something to think about or improve. They could even edit their post just because of one comment. So remember this. Comment's are good.

Part 7. Yes. Other Stuff...

This stuff is practically random. Or just some stuff to do while editing a post. But it deserves it's own mention. Um. To add an image click on the add image button on the post. To add a link click on the add a link button on the post. To edit your HTML code click on the edit HTML tag. It's really useful for all of your HTML users out there. You can change the colours of your text on the colour text button. Also. You can also chang the size of the text. The Font. Bold, Italic. Did I miss anything? Oh ya. To change where your post is on the blog. Yes this is important. Change the time and date. It really works. Really.

Hey. Person reading my blog. Yes you. Am I missing anything? Well Leave a comment then. Hahaha. Well that's the end of that. If you need extra help. Call my cell. Hahahahahahahaha. Later.

Test Update - More Practice!

Our test day has been moved to Friday due to the time we lost to picture taking today.

Here are some more online quizzes you can do to get ready for Friday:

• Standard Form (5 questions)


• Factored Form (5 questions)


• Finding Roots (5 questions)


• Complete The Square (5 questions)


• General Review (explanations and solved examples)

Don't forget to get your post up before test day as described in my post Blogging on Blogging. Your "scribe" post doesn't count for this mark.

Also, if you haven't read this yet, make certain that you do before getting your post up. ;-)

Robert's Scribe

Robert is having computer problems. He emailed me his "scribe" report. Here it is:

---

Hello people this is Robert. Well we started off the class by doing two review questions on finding the roots. These were the examples given:

^ ----> means "to the power of"

f(x) = x^2 + 2x - 4 f(x) = x^2 + 2x + 1 - 1 - 4 y = (x + 1)^2 - 5 0 = (x + 1)^2 - 5 5 = (x + 1)^2 +/- sqr root of 5 = x + 1 -1 +/- sqr root of 5 = x

f(x) = -x^2 + 4 x - 7 y = -(x^2 - 4x + 4 - 4) - 7 y = -[(x - 2)^2 - 4] - 7 y = -(x - 2)^2 + 4 - 7 y = -(x - 2)^2 - 3 0 = -(x - 2)^2 - 3 No Roots

Then after those question we then did two problems in class. The first type of problem dealt with a farmer or someone that needed to make a rectangular area with a certain amount of fencing using one side of something like a barn for example. We then had to find the dimensions that would yield the maximum area. One thing that Mr. Kuropatwa really made clear was that when finding the answer in these problems always write the original equation. For example Area = ( Length ) ( width ). The second problem had us use a equation to find the vertex and x-intercepts.

Following all of the questions and problems Mr. Kuropatwa gave us a review and told us that if we did the review and got it all right we would ace the test. Finally he told us that tomorrow we would have a pre-test followed by a test the next day. Tomorrows scribe is...Craig K.

Getting Ready for the Test

Here is a good review of the material we've covered so far. Everything is clearly explained with several examples all of which have detailed solutions. About a third of the way down the page you'll find an applet that you can play with and see the effect it has on the equation of the parabola. The last example includes a carefully explained solution to the area problem we were discussing in class today.

Here are some online quizzes you can also try to get ready for Thursday:

• Graphs and Equations (5 questions)


• More Graphs & Equations (5 questions)


• Graphs and Equatins Again (5 questions)


• All About Parabolas (5 questions)


• More About Parabolas (5 questions)

Those last two you can take over and over again. The questions will keep changing!

Tomorrow we'll talk more about problem solving and try to get a pre-test in. ;-)

Quadratics at the Movies!

Here is another video that covers some of the material we've been studying:

• Sketching the graph of a quadratic function using transformations
    (10 min. 59 sec.)

If you have trouble understanding anything: "Pause ... Rewind ... Repeat ..." until it makes sense. ;-)

I`m not very good at this but ill try my best.
uhm,okay ...
So we started class by talking about the on-going project. It`s about making that class character or something that will have a problem and we have to use math to solve it. OR picking any topic that we've learned and make a video about it.

And we learned more about "Completing the Squares". If a is > than one then you can factor it out first. For example:

y=2x²-12x+13
=2(x²-6x+9-9)+13
=2[(x-3)²-9]+13
=2(x-3)²-18+13
=2(x-3)²-5

the 2 is outside the bracket because it is more than 1. and if you`re wondering how we got what's inside the round bracket... this is how,first you take half of the middle term then you square it. (x²-6x+9) = (x-3)². After that we distibute 2 to whatevers inside the square bracket and thats how we got y=2(x-3)²-18 then bring down the +13 and the answer will be y=2(x-3)²-5.

look at the example that i just made... is that how you did your work? is that how you wrote it? if that's how you wrote it then you just lost some marks. why? because the "y" or "0" is not written before the equal sign. Remember what Mr. K said... DO NOT FORGET TO WRITE DOWN THE "Y" OR ZERO. so it should look like this...

y=2x²-12x+13
y=2(x²-6x+9-9)+13
y=2[(x-3)²-9]+13
y=2(x-3)²-18+13
y=2(x-3)²-5

We also learned how to find the roots.
But first, how do you know if it has roots?

f(x)=a(x-h)²+k

we only need to look at the a & k.
if the a > 0, the parabola opens up and if the k > 0 then it wouldnt have roots because it is above the x and it opens up. but if a is greater than (<)0 and k > 0 it has roots because the parabola opens down and the k is above the x.

finding the roots or x-intercepts.

how do we find the roots of y=(x+3)²-16?
first we just balance the equation.

0 =(x+3)²-16
let y= 0
16=(x+3)²
move the 16 to the other side of the equal sign
-3+4= x OR -3-4=x
take the square root of both sides
-3+4=1 and -3-4=-7
so therefore: x=1,-7
*note: dont forget to write the "x=".

okay so that was easy... but what if its not a perfect square?
it doesnt matter if it is or not... it still has roots.
example:


-let y=0
-then move 5 to the other side of the equal sign
-then take the square root of both sides.
- move the 3 to the other side. (it becomes negative)

^^ and you can leave the answer like that.




important things to remember:
-DO NOT DROP ONE SIDE OF THE EQUATION or FORGET TO WRITE THE "Y"/ZERO because if you do, you`ll end up losing marks.
-always write "x=" when writing the roots/x-intercepts.
-some equations are prime but still has roots.
-when drawing a graph don`t forget to label them.. it`ll also cost you a mark.

*i know these things were said million times already but ya... just a reminder ;) * hehe

well... thats all i could remember for now. til next time! ^_^

AND TOMORROWS SCRIBE IS... Robert.

Chatting and Study Groups

I noticed a lot of chatting going on in another blog so I installed a little chat window, it's called a Shoutbox. Give yourself a screen name and anyone can talk anytime you're here!

You may recall I talked about you all getting together in groups of 3 or 4 to create study groups. Meet once a week, say Wednesday's at lunch in the library or whatever works for you. Well, with the Chatbox you can set a time anytime when you call all meet online, chat and get whatever help you need with your homework in the Chatbox.

I think this will be a powerfull learning opportunity for all of you. It depends entirely on each of you individually. It's up to you whether or not you choose to get involved.

You'll find the Pre-Cal 30S Chatbox window down there at the bottom of the right hand sidebar.

Please leave me feedback in the comments to this post. Is this a good idea? Are you getting anything out of it? Should we keep it or delete the Chatbox? Leave your vote here. ;-)

Cheers,
Mr. K.

Completeing the Square!

Class time seems to just fly by! Sometimes we get hung up on a difficult problem and time seems to  d r a g  and sometimes we cover so much material in such a short time that it just seems to fly by.

I know some of us are still struggling with completeing the square. Well, help is here. I've got a brief video taped lecture you can watch to help you with this material over the weekend if you need it. The movie is of an instructor from the University of Idaho.

In order to watch the video you need to download the free realaudio player from here. (It's a little more than 11 Mb so if you have a slow internet connection this isn't a very good option for you.) After that, just click on the link below for help with completeing the square!

• Solving Quadratic Equations by completing the square
  (9 min. 58 sec.)

Let me know what you thought of the video in the comments to this post. Did it help you learn? Is it clear and easy to follow? Should I post more of these? ;-)

Have a great weekend!

Parabolas [click here to start]

We've learned about all sorts of things you can do to the graph and equation of a parabola. We've also spent some time learning how to read the equation of a parabola. This is a good little review of what we've learned.

Scroll down a little bit and you'll see a button marked [click here to start]. It will open a new window that will allow you to see, instantly, how changing the values of a, h and k effect the graph of a parabola. Play with all three sliders. The section of notes that begins with a red B covers material we will talk about tomorrow. Read it tonight if you want to get ahead of the game. ;-)

The Scribe List

This is The Scribe List. Every possible scribe in our class is listed here. This list will be updated every day. If you see someone's name crossed off on this list then you CANNOT choose them as the scribe for the next class.

This post is can be quickly accesed from the [Links] list over there on the right hand sidebar. Check here before you choose a scribe for tomorrow's class when it is your turn to do so.

Cycle 4
Larisap elizabethh Richard C. AichelleS. JessiccaI RoselS GraemeW	Jacky S. Craig K abriel_S KAT L. pamela_l Rannell d. Kasiaw	Jamilyn G. jennie_s Abdi JonathonJ. Robert aldridge robinna

How Many Parabolas Do You See?

As promised, tomorrow we will be putting some notes about how to transform the equation of a parabola to shift it up, down, right and left into our math dictionaries. We'll also look some more at stretching and reflecting.

You can read a review of what we talked about here. Scroll down towards the bottom of the page to see some neat animations of what we've been learning.

BTW, how many parabolas do you see? ;-)

Students Made This!

Blogging is a very public activity. Anything that gets posted on the internet stays there. Forever. Deleting a post simply removes it from the blog it was posted to. Copies of the post may exist scattered all over the internet. I have come across posts from my students on blogs as far away as Sweden! That is why we are being so careful to respect your privacy and using first names only. We do not use pictures of ourselves. If you really want a graphic image associated with your posting use an avatar -- a picture of something that represents you but IS NOT of you.

Two teachers in the U.S.A. worked with their classes last year to come up with a list of guidelines for student bloggers.

One of them, Bud The Teacher, has these suggestions, among others:

1. Students using blogs are expected to treat blogspaces as classroom spaces. Speech that is inappropriate for class is not appropriate for our blog. While we encourage you to engage in debate and conversation with other bloggers, we also expect that you will conduct yourself in a manner reflective of a representative of this school.



2. Never EVER EVER give out or record personal information on our blog. Our blog exists as a public space on the Internet. Don’t share anything that you don’t want the world to know. For your safety, be careful what you say, too. Don’t give out your phone number or home address. This is particularly important to remember if you have a personal online journal or blog elsewhere.



3. Again, your blog is a public space. And if you put it on the Internet, odds are really good that it will stay on the Internet. Always. That means ten years from now when you are looking for a job, it might be possible for an employer to discover some really hateful and immature things you said when you were younger and more prone to foolish things. Be sure that anything you write you are proud of. It can come back to haunt you if you don’t.



4. Never link to something you haven’t read. While it isn’t your job to police the Internet, when you link to something, you should make sure it is something that you really want to be associated with. If a link contains material that might be creepy or make some people uncomfortable, you should probably try a different source.

Another teacher, Steve, developed a set of guidelines in consultation with his students. You can read them here.

Look over the guidelines and add the ones you like in the comments section below this post; either from one of Steve's students or one of your own. I think Bud's suggestions are excellent. We'll be using the one's I highlighted above as a basis for how we will use our blog.

Cheers,
Mr. K.

Scribes Subscribe

Hahaha. So… I don’t know what to say… *Reads last post… Oh so that’s how you do it. Hahaha. So today in math we talked about Quadratic Functions. And how it’s important in Math. The first thing we talked about Foil. And guess what. No more Foil anymore. Ok. Just great. We now must all depend on the distributive property. Because Foil will Foil you. Hahahaha. Then we figured out how to use different perspectives to figure out an equation like X²+5X+6=0. Finally we got to get open our Graphing Calculators. So big… Err… Confusing… Just great. At least were learning how to use a Graphing Calculator like this instead of reading that big instruction book. By the way. No more Division… :’( Only Multiplication... My life has just got more complicated… Great. The last thing we did was some definitions for our Math Dictionary. Bell Rings. Homework. Next Class. What fun…

The Next Scribe is... ELIZABETH

Blogging On Blogging

A good class today folks! You gave good verbal feedback over the course of the lesson. Thank you. There's still a little more room for growth here though.

Today was our first extensive use of the graphing calculator. I know it can be a little confusing at first; it's hard to remember exactly where the various commands are hidden on the keypad. Don't worry about it too much. In a few more classes you'll feel like you've been using it your whole life. ;-) I know some of you are still trying to get your hands on a graphing calculator, if you have any trouble with it see me and we'll work it out together. One of the things I emphasized was the three different ways to represent a function; symbollically, numerically and graphically. This will become more important when you begin your study of calculus. It's also kind of neat to learn the meaning behind all that algrebra you had to grind out in Pre-Cal 20S. ;-)

We were talking about exactly what sort of post you're supposed to make to get that mark on your test. The kind of post I'd like you to make should have one or more of these characteristics:

• A reflection on a particular class (like the first two paragraphs above).


• A reflective comment on your progress in the course.


• A comment on something that you've learned that you thought was "cool".


• A comment about something that you found very hard to understand but now you get it! Describe what sparked that "moment of clarity" and what it felt like.


• Have you come across something we discussed in class out there in the "real world" or another class? Describe the connection you made.


• Respond to a Blogging Prompt I posted. (see below)

Your posts do not have to be long. I'm far more interested in the quality of what you write rather than the quantity.

Blogging Prompt
To help us along our blogging journey I've decided that I will also occasionally post a Blogging Prompt. It will be easy to find because I'll always put it under a heading like the one above this paragraph. Feel free to create your own Blogging Prompt for the rest of us if you like. If it's a really good one (i.e. has rich possibilities for blogging) we'll count it as your post. ;-) Here's my first one:

Use your graphing calculator (or an online tool; x² is written as x^2 and do not include the "y=".) to graph these three functions (y is the height and x represents time):

• The height of an arrow is given by: y = -16x² + 112x + 0


• The height of a baseball is given by: y = -16x² + 64x + 0


• The height of a football is given by: y = -16x² + 64x + 75

Blog a brief paragraph identifying ways in which these three functions are similar. Blog a second paragraph outlining the ways in which they are different and what causes these differences.

This sort of compare and contrast exercise can be made easier to do using Venn Diagrams. Draw three large overlapping circles. List the similarities in the appropriate overlapping sections and the differences in the non-overlapping sections. If you like, you can use this web tool to do it online. If you do blog about this prompt and want to post your diagram we'll talk about how to post pictures sometime in class. ;-)

Happy Blogging!

You're Here! Let's begin ....

Hi There! You found our blog! This is the place to talk about what's happening in class; to ask a question you didn't get a chance to ask in class; to get copies of a handout you didn't get in class (here's the course outline); for parents to find out "How Was School Today;" to share your knowledge with other students;.... Most importantly it's a place to reflect on what we're learning.

Remember what I said about the Forgetting Curve? Well a big part of Learning and Remembering involves working with and discussing new ideas with other people -- THIS is the place to do just that. Use the comment feature below each post, or make your own post, or make your own blog and link it to this one, or....the sky's the limit...let your imagination soar and lets get down to some serious blogging!

Here's your first online assignment:

Do you see the Links list in the side bar over there on the right? Follow the Study Skills Resources link. Browse through the sites until you find one that you think has excellent suggestions on how to study math; then, on a piece of loose leaf paper (or this worksheet) to be handed in on Monday:

1. Write the address and name of the site you most liked.


2. Rate the site out of 100; i.e. give it a grade!


3. Write a brief description (no more than 4 or 5 sentences) of the site.


4. Include a comment on what it was about this site that made it stand out for you (no more than 1 or 2 sentences).

Repeat this exercise for the second link that deals with Test Taking, i.e. how to write a test.

If you take this assignment seriously now and invest some real time and energy into it, you'll probably do real well in my class this semester...who knows, it might even help you in your other classes too! ;-)

Have Fun!