### Happy Holidays!!

I would just like to wish everyone HAPPY HOLIDAYS!!! Hope everyone is having a great time off school! And HAPPY NEW YEAR!!

An interactive log for students and parents in my Pre-Cal 20S class. This ongoing dialogue is as rich as YOU make it. Visit often and post your comments freely.

I would just like to wish everyone HAPPY HOLIDAYS!!! Hope everyone is having a great time off school! And HAPPY NEW YEAR!!

The time has come, a new unit gone by so fast, and a test in no time. What i think about this unit is that it was ok, we did not learn anything much but when we came to something that was hard that i did not understand, it slowly came to me! What i thought was cool was when this unit introduced that everything was bundled together and i did not have much problems. This unit is like pretty good, did not learn much because it was already introduced in earlier units. Also what i thought was cool was that f(x)=3x+1 is that it is the same as y=3x+1 but you get to find an ordered pair with the 1st one. GL HF on your test!

Hello every body

Tomorrow we have the unite test about function and Relation. This unit was easier then I thought it would be, like everything was something we know befor. In today’s pretest our group did very well except for one question. I don’t have much to say about it. *~*

Just good luck and marry Christmas (*_*)

this unit talks about function and relations

during the past day we've learned about the basics of functions and relations because it's the first time for some of us in the class to study it. i've learned that functions are more easy to use because it's more explicit it tells you what are the values of x and y just by looking at the functions. i think that this is easier than the past lesson i hope i get better marks this time.........merry christmas to all of you........

We went through this unit very fast knowing that winter break is coming up and we only have a couple more units to go before we finish math. When I look back at all the new things we learned, there are a lot. But I noticed that most of the new things we learned are linked to things we've learned in the past.

There were many things that I liked and didn't like about this unit. Usually I enjoy and like what we're doing only if I understand it well. I hate it when I don't understand what we're doing in class, I get this funny feeling in my stomach and I want to cry. But I'm a big girl, so I keep it in. I liked the Domain and Range stuff we did in class. I also like the functions and equations we do.

When I found out that we were going to be graphing again, I freaked. Graphing isn't one of my strengths in math. But I did start to understand things I didn't get before. I still am a bit sketchy in some areas, especially perpendicular stuff, but I am going to study like crazy on the break. I fear the exam!

Overall, all I got to say is that this unit went by quickly (faster than any pace I've went in math) and that I enjoyed it. I understood some stuff and others were challenging. That's what I like about math, the challenge of it. I hope this test isn't very difficult and I hope that everyone does well. Good luck tomorrow!

-SAMUS

Another month, another unit, another test. What a way to start our Christmas Break by having a test.

For the past few weeks, we've been looking into the unit of functions. How an input will determine the output. If you look at the equation y=2x+2, it just means what ever x is, you double it and add 2. Another way to look at it is f(x)=2x+2. It means the exact same thing but here f is a function if x. Another part of this unit is domain and range. Domain being numbers on the x-axis and range being numbers on the y-axis. When writing domain and range be sure to use correct brackets.

I don't know what else to say so I'm going back to watch Scarface. Goodluck to everyone on the test.

Welll another unit has been completed.

This unit was on functions and relations I found this unit was fun.

The unit started off eazy as a ll the others until it reaches the last part of the unit.

I think that this unit went a little bit to fast since there wasn't alot of new material to learn.

I think that the last part of this unit was confusing but I started to understand it when we did more exerises on it. Well good luck to everyone on the test tomorrow.

Aaaannnnnddddd happy holidays Merry Christmas to all and to all a good night

Have a happy new year everyone see ya :)

Well it's time for another test, and with another test is another reflective blog. Well this unit was functions and I'm apprehensive to say that it wasn't to bad. I don't want to regret saying that tomorrow. When you first look at it and it's very intimidating, but really the closer you look you can see that it's really a linear equation. Just instead of having a y you have f(x). Then it was time to substitute the numbers in for x which also wasn't too bad. Being taught the domain and range was a little tricky because first you have to remember which is which (domain=x, range=y). Also the concept of it going on forever or infinity. Once you understand the basics everything else comes more easily. I hope that the confidence I feel now is reflected on the test. I wish everyone goodluck tomorrow and study hard!!!=)

FUNction and RELAtion.

This the a not bad until, it give me another chance to learn about graphing because in my science class right now, I am also going graph so this really helps me. In the begainning of this unit it was confusing because the the teacher explan to us saying a *function is a rule that turns "an in put" into "an out put" * A rule that turns one thing into another *a rule that turns a number into another number. when he tell us to write it down in our dictionary, i just go "Huh" "Eh" "what" "where" when" "how. because iam just going like INPUT? OUTPUT? what on earth are those. Later on when i see more examples and think about it, it really mean that to find out if a graph is a function or not then to check if you can see 2 dots of y-int. and only one of x-int. then the graph is not a function, but if you see one dot in the y-int. 1 dot in x-int then is a function.

This the a not bad until, it give me another chance to learn about graphing because in my science class right now, I am also going graph so this really helps me. In the begainning of this unit it was confusing because the the teacher explan to us saying a *function is a rule that turns "an in put" into "an out put" * A rule that turns one thing into another *a rule that turns a number into another number. when he tell us to write it down in our dictionary, i just go "Huh" "Eh" "what" "where" when" "how. because iam just going like INPUT? OUTPUT? what on earth are those. Later on when i see more examples and think about it, it really mean that to find out if a graph is a function or not then to check if you can see 2 dots of y-int. and only one of x-int. then the graph is not a function, but if you see one dot in the y-int. 1 dot in x-int then is a function.

yess one more day of school then winter break.

last test for this year, wow semester is almost over. =/

Well this unit was really hard for me. i'm not doing to well in this class. I told my friends that and they showed me this textbook thingy, its helping me out alot. Umm i hope everyone does good on the test. Todays pre test was okay, i mostly got the sketch of the graph wrong. I like the questions asking us to put things in an equation.

I really have nothing else to say so good luck to everyone!

in this unit we learned about functions and relations. domains and ranges.

one thing that i learned about relations on a graph or how to check if it is a relation or not, is to do the vetical line test. and how to do that is to put your pencil or whatever you have if its a ruler or whatever just as long as its a straight object. you put it on the graph vertically and move it along the page and if you see two points on the line then thats a relation. if there is only one point on the line then it is a function. this unit was pretty hard for me, I think. well thats all i can say about this unit, that it was a hard one.

and to everyone have a merry christmas, a happy new year and a happy birthday to me!!! hahaha

and happy holidays

hi everybody. its the time of day where we HAVE TO BLOG.. FOR THAT ONE MARK =). anywayz. what i think of this unit is very confusing, frustrating, and hard. i really didn't understand much about this unit. i had difficulties and felt as if i should give up BUT, i will not give up. i will be studing soon and hope that it'll do me some good. tomorrow is also the last day, BEST WISHES FOR EVERY ONE ON THE TEST. MAKE THE LUCK BE ON YOUR SIDE... HAPPPYY HOLLIDAYYY EVERYONE =).

Tomorrow is the last test of the year 2005 for pre-cal, wow the year went by so quickly. This unit is about functions and relations. I've learned lots of things in this unit such as functions, relations, domain, range and writing a new equation(example: f(x)=2x-2). I also learned how to write the range and the domain, for example the given range is (0,14). This means that the lowest point on the graph in the y-axis is zero and the highest is 14.Most of the things I've pretty much learned. Like the graph, table of content and an equation can tell you the all the same thing. Well good luck on the test tomorrow and may all of you people have a happy holiday=)

Hi Guys,

Well this is my blogging post. I think this unit was the easiest unit so far. I think i got pretty much everything. But I could be eatting my words later. Almost everything in this unit was material we previously done.

I think I should've done the editors thing, but I couldn't find anything. I've got to try way harder... I need these marks.

I personally think the test should've been after the break. It would've beeen more time to study, but I know where you guys are coming from.

Anyways it's time to study. Hope we all do very very very well!

HAPPY HOLIDAYS! Have fun!

Sincerly,

stePhANIE

This unit about functions isn't so bad at all. The only that's confusing is questions about finding the domain and range of this kind of question:

{x,y|y=2x-1}

The only thing I know about this kind of problem is to find its domain. The range is I think y is greater than or equal to -1. But then again, I don't really know. Function of x is the really topic I had fun with, as it only involved substitutions of variables.

Other than that, I wish everyone luck for tomorrow's test, and Merry Christmas and a Happy New Year!

Hello to all... I'm today's Scribe!

Note:

Friday, January 27 -AM English -PM Geography

Monday, January 30 -AM Science -PM

Now, back to today's lesson...

We began the class with going over some of yesterday's homework (exercise 55.)

Then, of course, we had our Pre-Test. Examples of questions were:

If f(6) then evaluate: f(x) =2x^2-x+4 Answer...70

Other things we were asked were things like the

From the people I talked to, most found the Pre-Test pretty straight-forward, but I still know we'll be studying away tonight. We have NO HOMEWORK, but like I said, we should be studying. Remember everyone our test is tomorrow and good luck!

Scribe for the first day back from the holidays will be...neecole.

To everyone I wish a Merry Christmas, Happy Hanukkah, Crazy Kwanzaa, or just a great holiday season!

Hello everyone, well jeez has this semester gone fast, just two more days till Christmas Break (yes!!!) and were already half way through one of the days. Well this unit was umm okay but definitely not one of my best, some things Mr K was talking about I was just like BLAH... But after some work I pretty much got it. The input, output thing was easy for me I caught on right away because it's just a new name for substituting then solving for x or whatever the variable is. That was probably my favorite thing in the unit because we've done it tons of times before. The domain and range was confusing to me at first, I understand it sort of now but it's alright. Well good luck on the test everyone.

Have a good winter break

Merry Christmas:)

-Brittany

I pretty much liked this unit this time around. I think it's because I got a pretty good mark on my rational expressions test, and it gave me that little push that I needed to keep me going, you know what I mean? I really like working with functions, when I know what I'm doing. I know I had problems with the analytical geometry unit, but working on this unit is also helping with my graphing and linear equation skills, which is always nice, because the exams are sneaking up on us. I think and hope that I do well on this test. It would be such a nice christmas present!

Happy holidays! Good luck to everyone for the test!

In todays class we basically focused on two problems. The first one was as follows: The are of a trapezoid is given by: A=1/2(B+b)h. A trapezoid is bounded by the lines y=1/2x+4, x=4, x=10, and the x-axis. Find it's area.

The first thing we should do is draw a graph with these lines on it. We know what the x axis is, so that is already on the graph. We know that x=4 is a vertical line where the y coordinate, or "output" is 4. The same thing for x=10: it's a vertical line where the output is 10. To figure out the last line(y=1/2x+4) we know that the y-intercept is 4, so we plot a point on the graph where y=4. Then we also know that that slope is 1/2, so we RISE one, and RUN two. Now we have our trapeziod.

To figure out the area of the trapezoid, we need to know the lengths of h, B, and b. The trapeziod that is drawn is a right triangle, but is tipped on it's side. The height(h) is the x axis. To figure this out, we take the x coordinate of ten from one point, and subtract 4 , which is the x coordinate of the other point, which gives us 6. So we now know that the height is six.

To figure out b, which we know is at coordinates (4, x). We don't know the y coordinate, or the "output". But because we have the input of 4, we substitute that into the equation y=1/2x+4, which will give us the y coordinate of 6. SO, between coordinates (4, 0) and (4,6) there is six points. So b=6.

We now need to figure out B. We do the same procedure for this that we did for b. So we substitute as the input in the equation, whic gives us 9 as the output or y coordinate. Between (10, 0) and (10,9) there is nine points so B=9.

Now we know all the information we need to do the formula. So, substituting all our values in the right places would result in: A=1/2(9+6)(6), which gives us 45 units^2!

The second question that was given was as follows: A cellophone contract costs(C) $20/month plus 10 cents/minute(t). Monthly changes are calculated using the formula: C(t)=0.10x+20.

We we first told to draw a graph. A helpful way to do this is to do a table of graphs, using incriments of 10, instead of one. So, use 0, 10, 20, 30....etc as inputs and see what you get as outputs. Then you plot the points and connect the dots.

Then we were told to find how much it would cost if we were to talk on the phone for 320 minutes. To do this, we simply substitute 320 for x, (C(t)=0.10(320)+20 which would result in the answer of $52.

Then, the next part of the question was if there was no teim used on the phone, would there still be a cost? In other words, if the input is zero, is the output also zero? If you plug in zero for x, for find that the output is 20. In other words, even if you were not to talk on the phone for that month, you would have to still pay $20.

We were then asked what the slope is, and what it means. The slope is 0.10, but even though decimals are delightful, fractions are our friends, so the slope is 1/10. The slope represents cost per minute, or rate of change of the cost.

The domain of this function is [0, 44640] because there are 24 hours in a day, 31 days in December, and 60 minutes in an hour. (24)(31)(60)=44640. This is the MOST amount of time that could be used in one month.

The range of this function is [20, 4484} because when the input is 0, the output is still twenty, and we CANNOT HAVE NEGATIVE TIME. There are 60 minutes in an hour, and 24 hours in a day, and (60)(24)=4484.

Thats about it folks. Homework for tonight is Exercise 55. FUN WITH FUNCTIONS! yay.

The scribe for tomorrow is..kimc!!!! good luck!

Oh wait...we have a pre test tomorrow eh? well then I guess she's scribe um....when we get back! happy holidays everyone!

This unit was pretty much all new stuff and the ones that we already knew about.

It covered start to functions and relations and explaining what is Domain and what does it do, which is find the x-coordinate and Range is the y-coordinate. Mr. K also told us what is a relation and give us examples about the differences between a function and a relation.

We then studied about function notation

I hope you guys get a good mark ;)

see you!

p.a

Wow, what can I say? Six weeks have gone by, and within those six weeks we've done three units, our third one to be rapped up tomorrow. Meaning every two weeks we've been getting a unit test. : Insane difference than that of last year, ain't it? (to those who went to jr. high)

I was pretty interested in this unit, functions and relations. It seems as though I can understand the things being asked, not 100%, but close enough. I think I really come to like this unit. Everytime we are soon to finish a unit, I try to think of what kind of questions would be asked, which mainly consists of those being asked in class, and I feel confidence that I can do it.

Just some prepping, and reminders to keep me from making unseen mistakes, and I'm up for it! In addition to my confidence level, I got an extra bonus mark! -- at least... that's what I think. Too bad E.I takes too much time. I could soo use those extra bonus marks.***Quick re-cap of a function;**

- A function is a relation(usually an equation) in which no two ordered pairs have the same x-coordinate when graphed. One way to tell if a graph is a function is the vertical line test, which says if it is possible for a vertical line to meet a graph more than once, the graph is not a function, therefore making it a relation.

Best wishes everyone!, and I know it may be a day or two early, but happy holidays/winter break as well :)

Wow, just one more unit. I can't believe how fast the semester passed. This unit was probably the easiest, since it was a combination of the previous unit.

I think most of you thought it was easy too. The only problem for me during this unit was interpreting the graphs. But its not so much no more. I developed a new way to study on test. (just encase anyone wants to know.) Well, basically I finish my homework then study and read through my notes. So that I don't forget. Because my old way was the opposite, and I would forget what I read. Well I hope everyone has a good test. *And John D. way to go on your last test!*

Well, this unit goes by fast.. (this line is getting real old). Functions.. In the beginning, it was quite hard to understand and get it into my head but now.. it still is.. but not really :)? Well like always, it gets better near the end.

Domain, Range, Functions, Relations are all terms in this unit. The part that was most hard for me to understand in this unit was the difference between functions and relations but that part is long gone. I understand it all now thanks to the idea of using my head and ears ;).

I strongly believe that I'll do good on this test and so will everyone else because most of the stuff within this unit is very relative to what we already learned such as the equation of a line and solving for an unknown variable. It's quite straight forward but Goodluck to everyone anyway.

Our unit on functions is coming to a close, so fast time goes by...

This unit did in fact go by very fast and although most of the things we learned were "review," reviewing can still be a challenge. Some aspects of this unit I thought were really simple, like how to tell the difference between a relation and a function, especially on a graph. Sometimes, there were things I didn't completely understand, like what zeros were...and how exactly to find the area of a trapezoid on a graph (today's lesson.*) Luckily, Mr. K. is always there to answer my questions and I know he never wants us to leave his class with a foggy mind.

In general, I think I have a good understanding of the things in this unit and I hope that's reflected in my test mark. Of course, I will study hard and try to understand the concepts but all-around, I think this could be a unit that we all do very well in. Good luck to all, but obviously don't depend solely on luck. Study hard and think you can.

<---relation,

Hello everyone. Today in class we got our Rational Expressions tests back. Then Mr.K went over a few questions that people had trouble with. Afterwards Mr.K put up some questions on the board to review on function notation are two of the questions that we were given.

f(x)=3x2-6x+5

B)f(2x)substitute in a 2x to replace the X

3(2x)2-6(2x)+5=

3(4x2)-12x+5=

12x2-12x+5

Then we had a question where we were asked to graph the points heres one of them:

y=2x; xEbrace0,1,2,3,4,5,6close brace

Mr.K said that it would be easier if we made a table of values even though were not asked too.

X Y

0 0

1 1

2 2

3 3

4 4

5 5

6 6

from the table we found the Domain and Range

the Domain is from(-∞,∞) R=(-∞,∞)

We also learned that we can write from negative infinite to positive infinite two different ways

1)(-∞,∞)the we usually write it and

2)(-∞

The last thing that we did was vote when our unit test would and it will be this Thursday the last day before the break.

The homework for tonight is Ex.54 the whole thing

And tomorrow's scribe is

see ya:)

Here's the new set of acrostics for you.

Your task is to create an acrostic "poem" that demonstrates an understanding of functions related to any one of these concepts:

FUNCTION

RELATION

DOMAIN

RANGE

MAPPING

NOTATION

As an extra challenge (worth an additional bonus mark) try to make a Double Acrostic, that is, each line should begin and end with a letter of the word you are working with.

Remember, this is a bit of a race. Your answers have to be posted to the blog in the comments to this post. If someone has already used a word or phrase in their acrostic you cannot use the same word or phrase. i.e. It gets harder to do the longer you wait. ;-)

Here is an example of an acrostic that Mrs. Armstrong wrote:

A triple header this weekend.

Mr. Zhong Kui will make you laugh. I think his "problems" are the easiest ones to solve.

Rat is another "escape" puzzle. Every time you do something wrong he squeaks.

No. 5 is a set of three puzzle/adventures to get a little boy out of trouble.

As you all know, we do not have homework this weekend - OH YEAH!!!! :) Unless you didn't finish the exercise in class today that is ...

In today's class we had a substitute, Ms. Alexiuk. Our tests weren't ready yet so we didn't get them back, and will on Monday. She told us what we were going to do for the whole class, which was to go over any questions from exercise 49 (which there wasn't any of..) and then to work on

I think everyone pretty much got the questions... I think number 5 was function of a function type of question, as me and Kim had discussed :P and the rest were pretty easy after you gave some thought into it. I'll go over some questions from the exercise if some of you didn't get it.

Question 5)

a. f(g(2)) [at first glance this question could make you go, "wah!??! o_O" but really it's a function within a function type of question, so first thing you need to do is solve the inner function first.]

g(2) = 2

= 4 [now that you have the inner function, you just simply substitute it within the outer function, giving you f(4).]

f(4) = 2x+1

= 2(4)+1

= 9

Question 6)

b. f(k+1) = 4x+3

= 4(k+1)+3

= 4k + 4 + 3

= 4k + 7

Question 8) This noted that tha function is called a constant function, therefore all answers equal 3.

a. f(4) = 3 b. f(1) = 3 c. f(k) = 3

3k - 6 = 60

3k = 66 (moved the 6 to other side of equal sign changing it to a positive, therefore making 60+6)

k = 22 (66 divided by 3)

And there you have it! See, I may have had an easy scribe post today and all I could've posted was three lines but ... I didn't. :) I announce once again that we DO NOT, yeah that's right - DO NOT have homework this weekend :) and that scribe for Monday is --

BTW Mr. Kuropatwa; hope you knocked them off their chairs with your presentation thingy-ma-jiggy ^_^

Bye now :D Have a good weekend everyone!

Today's class we wrote in our dictionary. Here are the notes just incase anyone wasn't in class:

Any function of x can be expressed by using the variable

Example:

This allows us to generate a table of values for any function

Example: x-2-1 0 12

y-7-5-3-11

We can determine a specific output for any input.

Example: Find y when x is 7

y=2(7) - 3

y=11

-->There is a point on the graph of this function(7,11)

Using the function notation,

Example: Find f(7)

f(7) = 2(7) - 3

= 14 - 3

= 11

-->We also know there is a point on the graph at(7,11), but it is expressed much more explicitly.

All the following are essentially the same.

an equation y=2x - 3

a function f(x)=2x - 3

a mapping f:x-->2x - 3

Function notation, f(x), is used exclusively for functions. You cannot use function notation for Relations.

Relations are expressed either as equations or mapping.

Functions can be expressed in all three ways.

-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*

If you need help on how to solve functions and relations problems check

Homework exercise, exercise 49. Tommorow's scribe will be ---------------------------------------------------------------->

Hello

I am the scribe again, Lucky me!

Today we start the class by doing some exercise on:

1. IDENTIFY EACH GRAPH:

As a FUNCTION or RELATION:

The answer was

Function: a, b, c, d

Relation: e, f

(a, b, c, d,)are Functions because each input number exactly one out put number.

(e, f) are Relation because it turn one input into one or more different outputs.

2. Which of the following are Functions? Why?

a. {(1,3),(-1,4),(1,0),(0,4)}

b. {(3,2),(0,4),(1,3),(4,3)}

Answer:

(a) is an Relation, because it have tow same input (output is the y)

(b) is an Function because, the input are different (input is the x)

( If the input (x-coordinate) repeats more than once then it may be a relation. Check to see if it has two different outputs, if it does then it's a relation, not a function.)

3. In which of the followings is:

i) x A Function of y

ii) y A Function of x

y=3x-2

y is Function of x

y=x^2-3x+2

y is Function of x

x=y^2-4y-3

x is Function of y

x^2+y^2=9

y is not Function of x

x is not Function of y(because it’s not written as Function)

Functioning its just word, and how the word have written

4. Look at the graph in #1 fore each one wrote the Domain and arange.

a. Domain (-∞,∞)

Range (-∞,∞)

d. Domain

Range [0,∞) {∞ This is called a Lemniscate}

Range: The range is the set of all possible output values (usually y), which result from using the function formula. Keep in mind that domain = INPUT and y = OUTPUT. So, we can say, in terms of the xy-plane that the point (x,y) = (domain, range). In other words, INPUT = domain, which is x and range = OUTPUT, which is y.

The home work is ex#48 omit #13, and the scribe for tomorrow is rus-L [*.*]

Today we started a new unit, It is called function's and relations. We learned the definitions of these 2 new word's or what ever you would like to call them.

This new unit may be a little confusing because function is a rule that turns "An input" to "An Output" or a thing that turns one thing into another.

Relation on the other hand means a role that turns a single number into one or more different numbers.

We also learned that Domain means the set of all possible inputs for a given function.

There is also Range which means the set of all possible outputs for a given relation.

We learned that we can write functions and Relations in three different ways (Mapping, Pairs, Graphing, and the graph of a circle (for Relations only)).

We put all of this into our Math Dictionary.

The next scribe shall be A.Z.

'The goal of the puzzle is to switch the the pegs on the left with the pegs on the right by moving one peg at a time.

Move pegs by clicking and dragging them to open slots. A peg may only be moved to an open slot directly in front of it or by jumping over a peg to an open slot on the other side of it. You may not move backwards. The game ends when you win or get stuck.'

Play the game here. Can you win the 8 peg game? ;-)

(

It's that time again, another test another unit over. All I can say is that our first unit was a great pre requisite for this unit. This unit for me was so-so in that I sometimes could not really follow along well and did not understand at first but after awhile of looking at it, I have sort of figured most things out and glad that I figured most of it or some of it before the test it feels like I'm king of the world ! This is all i have to say for this unit. GL, HF.

This unit was hard and easy in same time. But if you follow the step you should be ok. Because it’s easy to get lost in the question step. (Especially the signs.)

I think I might do well in the test. The practice links was very help full. The first like was easier than the second one. But with magic triangle and the chart it’s easier to understand the question that asked. that's all i have to say.

Good luck every body!

I've nothing really much to say about this unit. This unit is neither easy nor hard. We just had to apply what we have learnt from earlier units like simplifying fractions, factoring and stuff and use it to simplify rational expressions. I think I've did this unit before when I was still back in the Philippines when I was taking 1st year High School. It was complicated at first, but after lots of practices, it got a bit easier. The experience really helped me here.

I've really got nothing to say anymore, so I'll end here. I wish luck to everyone for the test tomorrow.

This unit was really hard to follow. I got help from an other teacher because Mr. K was busy, and I kind of understand it better now. I hope I do good enough for the test. Most of the exercise questions were hard, same with the pre test, but I happen to get some right, and I got pretty close for some other questions. I enjoyed the questions that were adding and subtracting, those are easy, but it can get confusing at times. Then there’s multiplying and dividing which is okay…and again it gets hard sometimes. Well that’s all I have to say about this unit, I notice the blogs are getting shorter and shorter.

OK folks, as promised, I've got two excellent little review quizzes you can take to practice your skills. If you have trouble with any of the questions, copy it down and post it to the blog so you can work on it together as a class.

Here are the quizzes:

- Rational Expressions (15 questions)
- Rational Equation Word Problems (15 questions)

Don't forget the links in the del.icio.us box!

This unit I think is not very hard but not easy also. Not hard because as Mr. K said there's nothing new in here. It's not very easy because there are many things involve here like division multiplication subtraction restrictions complex trinomials and many more. Many of us are having trouble with the Distance Rate and Time word problems. I hope we'll do good for the test tomorrow. This is my blog before the test.

Here we go again, blogin for the unit test. Alot of the things thats on this unit is basically all the information that was covered earlier in the year; adding/subtracting fractions and multiplication. The new materials were dividing(multiplying by the resiprocal and the restrictions(the non-permissible numbers). Complex trinomial that needs facting is still kind of confusing I still get it. Hope everyone gets pass this one of the last test... I think. GOOD LUCK:D

this is one of the days where we have to study hard and get nervous for the unit test tomorrow. i hope everyone in my class is ready for the test tomorrow. study hard fellow class mates =). what i think about this unit is that i liked it more than "SLOPES" :) ... doesn't anyone agree with me!? i think "t-sa" agree's with me!! =) i liked learning about adding, subtracting, multipling, and dividing rational expressions because step 0: was to factor everything to the simpliest as we could and no doubt about it that i was excellent and loved factoring.. (most times) and it was great that i learned how to use some of my past learning to combine with rational expressions =). at one point i didn't know what in the world mr. k. was teaching the class, but the next day i caught up very fast, came in for help at lunch and now i think im about ready to do the test.

GOOD LUCK FELLOW CLASS MATES ON THE TEST TOMOROW. =)

Every mark counts! This unit was just okay. Like usual, I still have problems with it. I absolutely HATE stating restrictions, I find it pointless. I had fun in class during this unit! Even though I'm not the best in math, I enjoy being in the class. (: I hope Mr. Kuropatwa's mouth gets better! So, I guess dentists can still scare me. ._. Okay, good luck to everyone on the test tomorrow! Happy Studying!

I like this unit the best! I felt like I understood most of this unit because it mostly consisted of material we already learned previously. For example, Factoring, adding & subtracting fractions, multiplying and dividing fractions.

The only new things were restrictions and factoring out a negative, and I dont' thing thats't complicated.

I still have some troubles but they're not too bad.

Now I think, I think I get it when Mr.k says "fractions are our friends."

anyways...

Hope you all studied. I hope everyone does well on the test tomorrow! GOOD LUCK GUYS! =)

Today we put alot of thing's in our Math Dictionaries. We put Adding and Subtracting, Multiplying, and Dividing rationale expressions. We also put some examples of expression's which is very good because now I or We can just look in our Math Dictionaries instead of having to go through our notes and waste good time looking through the note's. We also put specific step's to simplifying rationale expression's (Factor everything, Restrict variable, and Reduce as much as possible). We also put a nifty little trick in our dictionaries, it is factoring out a negative one out of an expression, and now if we "wish" that a particular expression had opposite signs we can just use this little technique. An example

We put the "Magic triangle" in our Math Dictionaries too which helps with Rate, Time, and Distance questions.

We will have our test tomorrow so good luck everyone and don't forget to study and make a blog for your blog mark and dont foreget your lucky charm but not a rael lucky charm because that's cruel :)

The new scribe is IAN.

The test is tomorrow and who isn't ready for it? I thought it was today so I studied all night just to write in our dictionarys , but oh well. We basically are using the same rules and patterns in our first unit of factoring and putting them to use on different types of rational questions.

In this unit we learned how to add, subtract, multiply and divide rational expressions. Mr. K said that before you do anything, step 0 is to factor. Then step 1 is to state the restrictions. For example 3+8x/x-2 x here can not be +2 because if x was +2 in the demoniator then this question has no solution. We must always state the restrictions unless we are told not too. Thats basically it. Good luck to everyone on the test which is tomorrow not today if you read this post earlier.

Well I was glad that this unit didn't really have any new matarial. Because I always liked fractoring so I think that I'll do ok. For me this unit was pretty good because I only had to learn how to solve fraction within fraction questions. The only part that I'm a little shakee on is the word problems and fraction within fraction questions. Other than that I'm good I hope that there's only one word problem on the test *cross fingers*

well this is all that I have to say about this unit

so good luck to everyone on friday.

Alas the time has come when we must post our pre test weblog. This unit like all the units we've went through has sure come and gone by fairly quickly. It seemed like we learned a lot of new things in this unit but clarified by Mr. K, he says that we are only utilizing old lessons to solve more complicated equations.

This unit is solving rational equations. I must admit that I had some misunderstandings in the beginning of this unit. I had problems with multiplying a set of number by one to convert them into numbers with common denominators. Of course I did the right thing to do and went to Mr. K with my concerns immediately and cleared up a tangled mess.

Another thing that I am having quite some trouble with is probably the latest thing we learned in the unit? (the stuff where we find missing values given distance, time or rate of travel etc). I guess that all we can do is practice, look over notes and hopefully overcome our obstacles.

With our lucky day off in the middle of the week, I do hope that you guys go through those practice quizzes in hopes of doing great of the unit test on Friday. That's all folks!

when the first time I encounter this unit I thought I couldn't do it. When mr. k told us that "mathematics is the science of patterns", I remember the lessons that my teachers in the past years thought me. And I apply it on the problems that mr. k gave to us, then my answers were correct. As the day goes by I've learn a lot of things about this unit. And now, let's study for our test on friday. Don't forget the ALWAYS and NO because if you forget that you will be in a big trouble. Until here, see you next time. STUDY HARD and GOD BLESS everyone for the test on friday.

Before we start our pre-test

Our teacher Mr. k remind us about the steps

In simplifying rational expressions, the zero step is factoring

Then stating the restrictions

After working on our pre-test individually

We were put into seven groups

Duscussing and comparing our answers

We were able to decide whose paper are we going to hand it in

Mr. k told and discuss the answers

And for friday, be ready for the test

Finally, the next scribe will be DIYAA

this unit there wasn't really much that was new. it was good kind of. well i'm reflecting on how the unit was and i think i did good. multiplying and dividing fractions are hard but i get most of it. on the pre-test we had today i did petty good. I think if i study over the time we have i should get it and hopefully this time I can pass my test. i don't really know what else to say so yes. and that is my reflective blog for this unit. until next time everyone. GOOD LUCK!

Oh boy, looks like only after two weeks we've come up to yet another unit test. Can' t do anything but get used to it, huh? I am not looking forward to this upcoming test. Nope nada nidoran ....... : (nidoran - pokemon? HAH) *cough..right. anyways ....

At the beginning of the unit I was doing pretty well.. and then all these more complicated questions came up in my face and I can't really get down the steps needed in order to solve the question correctly. I mean, we learn how to do some of them, but then when I go home and do homework, the questions are really different and you have to find another way and there's added steps to correctly solve it.

Pattern of math ..... could possibly be the most hated pattern in

Algebraic fractions unit, or whatever it's called, has been like any other unit except the previous one. Previous unit (geometry) was pretty sweet, because I got a good mark on the test :) Which made me happy. I'm not so sure about this one though ..... *getting sad*. D`ahh well. Wish the best of luck to you guys and let knowledge be on your brain o_o

Hi everyone!

I am posting again because of the test that is coming up this Thursday!

This unit was almost a review of the other stuff (mostly factoring) that we learned before.

(don't forget to review your dictionaries for the factoring and the signs)

In this unit we learned how to simplify rational expressions, multiply, divide, finding the restrictions,

solving for X, factoring again, and in the end some word problems that I think most people {I

did} had trouble doing it on the Pre-test.

In general, nothing was new in this unit, and it was basically what we already knew from before,

except the restrictions.

That is all I have to say!

Good luck everyone and see you all Thursday. :)

Wow, another test ! I can't believe it. We move faster and faster as time goes on, it's crazy! I'm really worried, because I know that I don't have a very high mark in the class, and I failed the last two tests. I must admit, it's really hard not to get discouraged, because, yikes. I am. I would go and ask for help, but unfortunately, I really don't ever have time. I need to stay focused. I want to keep studying and studying, but I also learned not to overwork myself. Yikes, I'm really lost. I mean, at the beginning of the unit, I liked what we were doing, but now, I'm not so sure. And every time I do a test, I feel good coming out of it, only to find out that I failed. I think I need to think up some new strategies. Any ideas?

I definetly have had a lot of muddiest points, and I really don't know which one is my muddiest. I think I'm gonna try a study group, and then maybe I dont' know, some late night studying or something. I'll do anything it takes. I just gotta remember Sisyphus! *sigh* Well, the test is coming up, I hope I do well! If anyone is having trouble too, I know how you are feeling, because I am stuck at the moment. I almost want to use the "S" word, and say I'm stupid, but I know how much Mr. K doesn't like that. I just know how some of you are feeling, because I'm feeling it too. Well, I just gotta keep at it, I guess. I have to think, "I THINK I CAN I THINK I CAN I KNOW I CAN!".

I like balancing equations though. And suprisingly, I don't mind factoring as much anymore like I did at the beginning of the year, which is a positive thing. And hopefully in the next few days, a light will go on, and I will be able to do all the different kinds of expressions. I think I might need just a little bit of help....

Here are a number of quizzes you can work through to help get ready for the test on Thursday.

- Simplifying Rational Expressions (5 questions)
- Multiplying Rational Expressions (5 questions)
- Dividing Rational Expressions (5 questions)
- Rational Expressions with Like Denominators (5 questions)
- Rational Expressions with Unlike Denominators (5 questions)
- Mixed Expressions and Complex Fractions (5 questions)
- Solving Rational Equations (5 questions)

When you finish each quiz you can refresh the page to get another one. ;-)

today’s class was very interesting( like always) and in the same time nothing was new.

we start the class by Mr. k, saying that tomorrow is the

and that we have sub teacher.

So here is what was going on in the class. We did some questions for solving for X.

-solve for x:

1) (9)/(x+2)=(5)/(7) {don't forget the instruction} X≠ -2, -7

7x=5(x+2)

7x=5x+10

7x-5x=10

2x=10

x=5 (always check your answer before moving to another question because it will help to you sure that your answer is right and it will also help you to remember the restrictions( Because it might remind you if you forgotthe restriction or write it wrong so you can fix it.)

2) (4)/(x)+(3)/(2x)=(11)/(4) X≠ 0

{Find the less common denominator that will divide the other denominator evenly.}

(16)/(6)=(11x)

(22)=(11x)

2=x check your answer

3) (x-1)/(x+1)+(3)/(x-1)=1 X≠ + or - 1

the common denominator is (x-1)(x+1)

(x-1)(x-1)+3(x+1)=(x-1)(x+1)

(X^2)-(2x)+(1)+(3x)+(3)=(X^2)-(1) balancing the equation (both have x^2 both side, so they reduce.)

X+4=-1

X=-5 Check your answer

Mr. K gave as some helping steps we could use:

1. Always see if you could factor any thing.

2. Write the restrictions.

3. Check your answer.

4) (7)/(3x-12)+(1)/(4 -x)=(2)/(3) X≠ 4

(7)/3(x-7)+(1)/(4 -x)=(2)/(3)

(7)/3(x-4)+(1)/-(x-4)=(2)(3) the common denominator is 3(x-4)

The negative sign could move from between -(x-4) and change the + sign to -.it’s like having.

(7)/3(x-4)-(1)/(x-4)=(2)(3) {t he common denominator will reduce.}

7-3=2x-8

12=2x

6=x

Mr. K finish by saying: "math is science of patters. Nothing is new in this unit accept the factoring and divide and the restrictions."

And then we start some word problem.

Recall: Distance= (RATE)(TIME)

Nicole and Jaindrive in opposite directions. After 3 hours they are 360KM apart. If Nicole’s rate is 10KM/K faster than Jian’s rate, how far did Jain travel?

Nicole___________________& _____________ Jian

10KM/K -----------------------------360--------------------

Jians’s Rate =x (if you don’t know something, then it isX)

Nicole’s Rate= x+10

We used the Magical triangle Distance

Rate_________Time

3x+3(x+10)=360 (3 is the hours)

3x+3x+30=360

6x=330

x=55

The second question was:

Natasha can mow a lawn by herself in 1.5 hours. Steve can mow the same lawn is 2 hours. If they work together mow how long will it take to mow the lawn?

If Steve work 1 lawn in 2 hours then:

(1 lawn)/(2 hours)= (x lawn )/(1 hours)

1=2X

½ =x

Natasha: (same thing but different number)

(1 lawn)/(3/2 hour)=(x lawn )/(1 hours)

1=3/2 x

2/3=X

Finally our home work is Exercise number 53, and omit 11,12,14

The scrib for tomorrow is K.M.

I know that posting reflective blogs isn't the only option anymore, but I still like reflecting on our units so this is my rational expressions post...

If you ever had any doubts about why we needed to learn something in previous grades, you shouldn't have those doubts anymore. This unit was all about using techniques we had previously learned and applying them to some new things like a binomial. The only new things we really learned were things like restricting the variable.

At first I didn't really like this unit, even though it covered things we'd already learned. Slowly I started to get more comfortable with it as old techniques started to come back to me but it's easy to make a small error. Overall, this unit was pretty good since we didn't have to worry about learning any formulas or anything too new. Still, remember to do all your homework and although you can't really "study" math, make sure to practice, practice, practice until you feel comfortable with it.

A muddy point of mine was deciding when to cross multiply. Maybe, we could put a rule for when to cross multiplication. Just today, we when over when to use cross multiplication. **ONLY** use the cross multiplying rule when solve an equivalent fraction equation.

I thought the weekend homework, Exercise 52 was tough. I when to talk to Mr. K. After, a long while of conferencing, I learned when and how to cross multiply properly. After, the meeting I had a better feeling. I felt better, but still a little worried.

Today, Mr. K told my a funny story of how the "Pythagorean theorem." On exercise 52, question 12, it says "John is building a house 20-m by 10-m but he lost his carpenter square. How can he make sure his house found is at right angles without buying another square?" A carpenter square is a triangles that is 3 by 4 by 5. Which is 3² by 4² by 5². Which equals to 9 + 16 = 25. The conclusion is that home builder's use the "Pythagorean theorem" in real life.I thought the weekend homework, Exercise 52 was tough. I when to talk to Mr. K. After, a long while of conferencing, I learned when and how to cross multiply properly. After, the meeting I had a better feeling. I felt better, but still a little worried.

We've been studying rational expressions. Use the comments of this post to:

» share your personal"Muddiest Point"about what we've studied

» make suggestions about what kind of new information we've learned would be helpful to include in yourmath dictionaries

» any other questions, concerns, complaints, confusions, uncertainties, anxieties or other inquiries you may have.

You can use your name or leave your comment anonymously, but, whatever you do, share your troubles here. Remember, you can help each other too! Leave tips and advice in the comments for your classmates. And don't forget, you can form an online study group and "meet" in the chatbox of our blog! Unlike Sysiphus, you're being set up to succeed! Take advantage of

The objective of Cubeoban is to push/pull all the blocks to their corresponding lights. Do this by clicking on the blocks and drag them in the direction you want to push them. Play it here.

Level 1 was so easy that even I could do it. Level 2 (the image), started my thinking.

December 01 (Thursday’s class):

In Thursday’s class we learned how to multiply and divide Rational Expressions.

First, Mr. Kuropatwa gave us four questions to solve, which were:

x²+5x+6 ⁄ x²-6x+5 · x²+x-30 / x²+9x+18 and the solution was:

{we ALWAYS factor and write the restrictions first}

(x+2)(x+3) / (x-5)(x-1) · (x+6)(x-5) / (x+6)(x+3)

and the restrictions are

=(x+2) (x+6) / (x+6) (x-1)

=(x+2) / (x-1)

the other questions was:

a²-3a-4 / a²+5a ÷ a²-7a+12 / a²+2a-15

we factor it:

(a-4)(a+1) / a(a+5) ÷ (a-4)(a-3) / (a+5)(a-3)

X≠ 0, -5, 3, 4

because it is dividing, we write down the first one and than in the second one we change

the numerator to the denominator and the denominator to the numerator. And change the

dividing sign to multiplying sign.

(a-4) (a+1) / a(a+5) · (a+5) (a-3) / (a-4) (a-3)

for finding the restrictions we should look at the first denominator: a(a+5) and both numerator and denominator of the second one: (a+5)(a-3) all over (a-4)(a-3)

(a+1) (a-3) / a(a-3)

= a+1 / a _ _ Notice that here comes the big NO!

And also two other dividing questions, which I am going to write it and you, can try and solve them by your self (if you weren’t at the class)

3n+6 / 2n+2 ÷ n+2/ n²-1

and: 6x²-37x+6 / x²-9x+18 ÷ 12x²+16x-3 / 5x²-12x-9

{if you do this one, you have learned everything about it}

after this we did some Qs about solving for x: for example:

3 / x+1 = 5 / 3x-1

we cross multiply:

3(3x-1) = 5(x+1)

9x-3=5x+5

4x=8

x=2

x ≠ 1, 1,1/3

Homework is exercise. 52 omit Q.11.

Scribe for Monday is: