jan. 9 2009's class..

On today's class we started the discussion talking about intercepts. We kinda went back to our last year's topic. Then Mr. K gave us a few graph that we could solve. The examples are on the slides. We started the workshop it went great. At first we don't really get it but when me and my group started talking about it I knew it wasn't that bad. Yaseen was pretty tired explaining what he did because he did it like three times. The most confusing part of the discussion was solving the pattern then you need to sketch it in the graph then define if its a function. Jess and Yaseen had a little debate about the equation. They were talking about what is the answer in the equation. It is confusing at first and but the longer we talked about it was ok. We kinda started the making a library or something. But it was something about library. We solved a few number pattern. It was easy. But I'm expecting that it would be hard the moment we came to the point where we should study harder or bigger numbers. Mr. K also told us to study for the exam.

And our assignment is ex. 58..

the next scribe will be AKEEM??

I'm not sure if Ana will be able to blog so in case she's cant, I will do it for the Friday's class.

On Friday, we only got through three slides. But aside from that, the class ended up pretty better than the other dry days; like what Captain Oh Captain had said.

In the beginning of the class, we had a hard time before getting to actual math because of the Blogging thing. Apparently, no one has blogged for the last few weeks meaning us students are actually losing easy marks just by not blogging.

Anyway, we also talked about groups. when Mr. K puts us into groups, he's telling us to work with each member of the group on solving the questions/equations. Or in other cases, sharing how we got to our answer because we cant learn just by watching someone else do it. Mr. K used basketball for example. If we just watched a basketball player shooting hoops, would we actually be able to do it? Of course not. Unless you do have the ability to have that kind of power. But anyway, the point is that we actually have to try it ourselves to get better at it. Mr. K also used a video game example. Most of us had played video games right? Well why don't we treat pre-cal and any other subject like a video game? When we play for the first time, do we actually get to 1st place? No. But it's not like we gave up that easily; WE KEPT TRYING.

Well I'll be talking about the work now. Today was pretty much just a review. As you can see on the slide below, there was this question that said " What is the domain and range of each relation?". For a) D : [ 0, 6] , R : [ 0, 6] The 6 was figured out because the center of the circle was 3. So it's like giving us a radius right there. 3 multiplied by 2 is equal to 6. And the 0 was figured out because it touched the x and y axis. Or well, from my point of view, I think that's how it worked. for b) , c) , and d) are still a little scrambled in my head so I apologize for not being able to explain it.

By the end of the class, we learned about Intercepts. Like when we want to find a y-intercept, we have to LET X = 0. And vice versa for the x-intercept.

HOMEWORK : EXERCISE 57.

NEXT SCRIBE : ANA??

PS: I hope I dont get in trouble by scribing -__-'

Reviewing Rational Exp & Eqns

Hello every one and Happy New Year!
I would like to say sorry for my late post. I will try my best to review what i have learned in class and what i knew about Ration Exp & Eqns.

Restrictions:
*We always have to know that restriction are found in the denominator of a rational exp & eqns.
*In some question we cannot find our restriction by not factoring it first.
*After finding the restriction of a question, our answer of that question will not be same or related to the restriction of that question (You may have to try again or the question is wrong).

Here are some examples:
This is what i would do first to find the restriction.
As i see this question one of the thing i would look at is that can i factor it first, my answer would be no.Then the second thing i would look is the denominator where we usually find our restrictions. I would take the denominator and make it as equal to zero.

x=0 Zero is the restriction
Click to practice

Additon/Subtraction of Rational Exp & Eqns:

1. Determine the LCD(Least common Denominator).
2. Rewrite each fraction as an equivalent fraction with the LCD.
3. Add or subtract the numerators while maintaining the LCD.
4. When possible, factor the remaining numerator and simplify the fraction.

The LCD is x(x+2)

I don't have time to explain subtraction of rational expression
but the difference is the Negative sign just be carefull with the sign.
Click to practice!

Next Scribe Post will be shawn !!!!!!!!

for any question or mistakes please make a comment!!

My Muddiest Point!!!

My muddiest point in this unit is the

word problem i don't seem to understand,

but i'm okay with the rational exp & eqns

Solving Rational Equations

Hi! Today we had two visitors who monitored us in class. Mr. Kuropatwa went over yesterday’s work and also gave us new questions to work on. During the workshop, we has to reach upto 15 slides but we only got to about 9 slides. I will TRY my best to explain everything so you can understand it:)

First, we should all know how to multiply binomials by this time.

For example:

And when its factored it looks like this:

This should all be familiar to us.

When factoring trinomials, you get the ones at the top and when you reverse it you get multiplying binomials. It is like undoing the expressions.

Now Mr. K introduced us an easier and faster way to multiply two digit numbers.

For example:

41 x 31 = ?

First you multiply the two 1st digits

4x3 which equals to 12 then multiply the second digits which are1x1=1

so, so far you have 12 and 1. .leave a blank in between 12__ 1

now to find out what the blank is, you need to do a rainbown multiplication

the rainbow multiplication would be 1x3=3 and 4x1=4 and 3+4 = 7

the middle number would be 7.

The Fast Multiplication relates to the first part because of how the procedures are done.

Heres a picture that might help you understand

Now the second part that we went over is balancing equations.

Ever since i have learned balancing equations form the past, I have

been transposing. .I guess it was the faster way of doing it and easier and I still get the right answer but today in class Mr. K. taught us something new. .

In this type of questions or any questions we DO NOT transpose because we don't just throw numbers from on side to another, we balance it.

to find the x. .

we make zero pairs so since there is x + 3 on the left side and 2 + 3x on the right side.

Add a negative x on the left side and add negative two on the right side.

Right now it isn't balanced so what we do on one side we do on the other

So we need to add -x and -2 on each side to balance the equation--there we go BALANCE EQUATIONS

The next question was. .

First of all find the greatest common factor or GCF. . not LCD because we are dividing to get rid of the denominator.

In this case the gcf is 4 because 4 can be devided by 2 and 4 evenly. When you have found the gcf, you have to multiply it by every term to balance it.

On the first term 4÷2=2 so 2 stays there since it cannot be reduced anymore. Now on the last term, you can reduce 4÷4=1 so it is reduced. REM

EMBER! "REDUCE" not cancell

Now since everything has been reduced you can multiply the rest

Finally. .

The gcf on this equation is x.

However . Make sure to state the restrictions after finding the gfc.

Now multiply x by every term to balance it. On the first term the x's are going to reduce so you're left with a four.

Just multiply every term by x and you will be left with 4= -4x.

To get the x by itself, divide both sides by -4.

JUST REMEMBER DO NOT FORGET TO STATE RESTRICTIONS OR ELSE YOU WILL LOSE A MARK !!!

Mr. K asked us if this was a rational equation, since it can be in fractions it is shown to be rational.

Please feel free to comment on this. Let me know if I have made any errors or if you want to share something and I'll add to it. If you still don't understand, talk to someone who knows best. Thanks and I hope you understand my scribe. .HAPPY HOLIDAYS!!!*

THE NEXT SCRIBE WILL BE ÿâssiÑⁿ♣ !!!!!!!!!!!

Simplifying Rational Expressions

First of all we played with the Google translator. Woohoo!

The class was kind of slow today, we just did some questions on simplifying rational expressions.

Some notes:

• We don't do subtraction in High school, we add a negative number.
• Give everybody a home

• Expressions are different from Equations:

In an expression, the denominator remains while in an equation,
the denominator is cleared out.

This is one of the expressions Mr. Kuropatwa asked us to do:



First, we factor it out.



Before we lose a mark, we should state the restrictions now.



Then we find the common denominators which is:



Now we should multiply each expressions with the number one, in another form, and it should give us the common denominator "because we built it that way".

,

Then we just add the numerators because we already have the common denominators.



This would be the final result.



But... in some expressions we could still further by factoring the numerator and reducing any common factors, but in this case we can't. Mr. K taught us a way to find out if we can still factor an expression, here's how:

We multiply the leading coefficient by the constant.


Then we look for the factor of that number that will add up to 9 which is the middle term.
In this case we can't and that makes it a PRIME number!

That's all I could say so see yah!

And Levi would be the next scribe...

Operations On Rational Expressions

On Today's class, we did workshop working on Rational Expressions. Mr. Kuropatwa gave us some examples that we need to work on in groups. After that, some of us in class explained how they got this answers.

Here are the examples that we worked on today...

a.)

So first you need to factor the numerator and then factor the denominator to get the binomial.
So it would be look like....

Then.. you need to state what the restriction is.
So the restriction would be look like...

And last, reduce the fraction you got with the binomial.

So the same numerator and denominator will be reduced.So it looks like..

That's your final answer.

b.)

This expression is just the same as above, so find the factors to get the binomials.

So it would be look like...

And then, find the restriction again..

So the restriction will be...

And Last.. Reduce it... So the answer will be...

c.)

This time, this expression is different.. So first you need to find the LCD(Least Common Denominator) So in this situation, the LCD is 15a³. So to find it you need to do this...

So it supposed to look like this...

And That's it.

d.)

The last question is different from the two expressions, but it is just the same from the third question because you need to factor the denominator to find the LCD.

You need to factor the denominator so it will look like like this....

You need to find the LCD of the the denominatorAfter you solve it, it would look like this...

And then after you solve this.. you will get this answer:

This expression can be simplified furthermore:

After simplified...

This expression could be simplifed furthermore..
It would look like this...

So that's your final answer i guess...

Well I think this is where I will end my blog.. So I Hope you guys will get it now..

And the next scribe will be..... Jesnicz!!,,

OPERATIONS ON RATIONAL EXPRESSIONS

In today's class Mr. K was not here and he had a sub to fill in for him. So we just continued working on Exercise 47 all question(DO NOT DO #9)

Here's an example:

1. You can't factor yet so you have to reciprocal.

2. Now factor out the variables.

3.Now just cross multiply; x and x = 1 and y and y = 1

4. now just reduce




The next scribe will be ...........................Akeem!!!