Math Symbols

Here is a great website for inserting math symbols into your blog posts:
http://www.freemathhelp.com/finding-roots.html 
Scroll to the bottom and you can create the symbol you need.  Then copy and paste into your document or blog post.  Let me know if you encounter problems.

8-7

Hey Everyone, I will keep the short because I know from personal experience that I do not like to read long blogs.

Here is what we learned today:

= positive or negative (if exponent is positive then output will be positive. If exponent is negative then the output will be negative)

= Undefined (no matter what your calculator says, and it will say many things….)

= Imaginary.

= Negative

= Undefined

Have Fun doing the homework. I know I will.

Review for ch8 quiz

Today we went over the homework, assignment 8.6, pretty solid assignment not to bad. But reviewing the homework was different because we used the reverse color thing on the elmo! Then we got a review that we went over quickly, just the pointers from each section that we should know for tomorrow. We had the rest of the class to do the review worksheet, the usual work with a partner/ listen to your ipod. So basically just the typical review day.

Some quick reminders for tomorrow's quiz:

- when u have a square root in the denominator of a fraction you want to move it to the top. So multiply the square root on the bottom to each numerator and denominator of the fraction. Also remember that simplifying first may be easier than doing at the end.

-If you are having trouble with the cube root or the forth root stuff remember to just write it out then group them.

-Don't forget the geometric mean! Multiply each number then depending on how many numbers there are in the set use that number root then the number all the numbers multiplied up to.

If you have any more questions you could:

-email Mr. cope ( bcope@glenbrook225.org)

-review the note key on moodle (http://GBS-Moodle.glenbrook225.org/moodle/course/view.php?id=1304)

-get the answers from review sheet (http://gbs-moodle.glenbrook225.org/moodle/file.php/1304/8.4-8.6_Review_Key.pdf)

Hope this helped! Good luck tomorrow and Happy St. Patty's day :)

March 15, 2011 Lesson 8.5

Homework: Assignment 805

Today we skipped homework checking and went straight to the lesson, so it's probably best to use Mr. Cope's moodle key to check your homework before the homework quiz, whenever it may be.

We then began to simplify radicals to tie together past lessons with yesterday's lesson, all to today's lesson. Mr. Copes goal: for us to be able to simplify ⁵√64x¹¹y²⁷z⁵³ to 2x²y⁵z¹⁰ ⁵√2xy²z³ .

Mr. Cope skipped the formal definitions, for a more practical approach, by using one of his colleagues explanations of factoring, The Jailbreak Method. To use the Jailbreak method one needs a pair of the same number to "break out" of the radical, while the unpaired numbers remain under the radical.

He then linked this to todays lesson by explaining that when you factor out various types of radicals like ∛ ∜, instead of just looking for a pair, you look for the number thats written. In these cases, groups of 3's or 4's.

To simplify radicals, you must factor out the radicals, then look for the groups, indicated by the number before the radical. The number(s) that can complete the number needed "break out" of the radical, while the rest must remain under.

Ex: ∛80

/ \

2 40

/ \

2 20

/ \

2 10

/ \

2 5

While the purple 2's form a group of three, the red 2 & 5 don't, the the answer would then be:

2∛10

To multiply radicals you need like terms, i.e. ∛2∗∛6 then you multiply, and simplify if necessary. In this case:

∛2 ∗ ∛6

∛12

another example from the notes is:

∜3⁶w⁷ ∗ ∜3²w²

∜3⁸w⁹

3∗3∗w∗w∗∜w

9w²∜w

***Note*** to simplify radicals with variable, if it helps you can

write them out, and box the groups of variables.

Ex: ∜16n¹²

/ \ nnnn nnnn nnnn

2 8

/ \

2 4

/ \

2 2

The answer is 2n³ because the 2's form a group of 4, and the there are 3 groups of n's able to be formed.

Hope this helps, if not you can always look back to the moodle notes or ask Mr. Cope for help.

Today we got the results back from our 8.1-8.3 quiz. Overall, the class did pretty well; the average was and 80%. We went over a few problems but there was little confusion so we moved on.

Next, since we didn't have any homework, we skipped right to the lesson, 8.4. To begin lesson 8.4, Radical Notation for nth Roots, we reviewed some of the ideas from previous sections that are critical in understanding this one. The two most important are probably: an

x^1/2 = √x

ⁿ√x^m = x^m/n

A useful example (from the notes) is:

Suppose x ≥ 0. Simplify ³√x¹².

What you should do is take (x¹²) and raise it to the 1/3 power.

(x¹²)^1/3 = x⁴

In lesson 8.4, however, it gets a little more complex. I hope I can help you understand it. Instead of being formatted like the example above, problems in this section look a little more like this:

Suppose x ≥ 0. Rewrite √(√(√x))). It’s pretty tough to write that on word, but it’s basically the square root, of the square root, of the square root of x. You would write it using radical exponents, like so:

((x^½) ^½) ^½ or, since you multiply ½ by ½ by ½, its x^1/8.

So, if you suppose x ≥ 0, can you solve ⁶√y⁴ ?

Here is how you would: (y⁴)^1/6 = y^4/6 = y^2/3

The homework for tomorrow is As. 804. I hope this was helpful! If you have any questions, the notes are on moodle: http://gbs-moodle.glenbrook225.org/moodle/login/index.php

-Meg Karnig

8.1-8.3 Quiz

Hello clase,

I will summarize the extent of our days activities on Friday the 11th.

We took a quiz.

Ok, so the quiz was on sections 1-3 of chapter 8. As for how the quiz went, i thought that i did good, and i thought that i knew the material really well, though as i recently found out, i didn't seem to do very well on it...

You will remember that on this quiz we were not allowed to use our beloved ti inspire calculators, and instead we were forced to use the old school calculators that Mr. Cope said he used in High school, which then put him in a solemn state of mind, in which perhaps he pondered for a minute, flowing through wonderful memories of his high school career. He then made it clear to us that real life was much better, and we became confused because we assumed that we were in real life. I think we all left class that day shaken...

Anyway, as for the quiz material, you could obviously read all the posts below which go into far greater detail about each section, though ill give you an overview of all three sections.

Pause: I just realized i forgot my math folder somewhere.. or i lost it. So give me a couple seconds to look up the notes on moodle, which you can get to by going to http://gbs-moodle.glenbrook225.org/moodle/. What a great example of what you can find on moodle. You should view me as an example of a common mishap that you can learn from.

Perhaps you forgot your folder, and you have algebra homework due the next day...

WHOA

Ok, once you've recovered from the shock, you may proceed to http://gbs-moodle.glenbrook225.org/moodle/

where you can find not only every notes sheet from every section so far, but also the answers to the homework from the previous night. Not only that but you can even access the online book, with a code and a link that is posted on the algebra moodle page.

So as another example, Say you did your homework, and in class you checked each one of them with the answers Mr. Cope puts on the board. When you get home you realize: i accidentally forgot to correct one of the questions on my homework.

OK, OK

You now wont be freaking out, because of this vital information i have just given you. Instead you will immediately remember the Wisdom of Téo. Go to moodle. here is the link once again:

http://gbs-moodle.glenbrook225.org/moodle/

Also the link to go to the book is http://www.ucsmpmath.com/

and the access code for the book is: 1CED23F3

So now that i found that excellent connection in which to point you to moodle for all your needs and desires, let me get back to explaining the quiz material.

8.1

-Composition of functions

http://gbs-moodle.glenbrook225.org/moodle/file.php/1304/Chapter_8_Notes/8.1_Notes_Key_2011.pdf

if you remember, this is when we simply put one function inside of another. From previous lessons we have learned that when we see f(x) notation, whatever is in ( ) gets plugged in place of x. This same concept applies here. though instead of placing a simple value such as 5 inside the parentheses, we insert a whole other function. Sometimes, if theres variables we insert the entire other function into the ( ) though for some we simply simplify one function and insert its value into the other, which we then solve.

example:

theres no good way of showing this here but...

If we define 2 functions, g(x)=x^2 and f(x)=3/4X-10

and we want to evaluate f(g(2))

we know to solve g(2) first because it is the furthest to the right, and like Mr. Cope analogied to us the other day, its like reading Arabic.

So we would first solve g(2)

g(2)=2^2=4. We plug in 2 to the function g and we get 4.

Next we insert the 4 into the function f, because as you can see f(g(2)), we plug in the result of g(2) into f.

f(4)=3/4(4)-10=-7. We get -7 when we plug in the result of g into f. So -7 is the answer.

I hope that you can somewhat understand what im saying here.

8.2

-Inverses of Relations

As stated in the notes which are found at: http://gbs-moodle.glenbrook225.org/moodle/file.php/1304/Chapter_8_Notes/8.2_Notes_Key_2010.pdf

there are three rules for inverses.

1) a rule for g can be found by switching x + y and solving for y

What this means is that if we have the equation y=2X+5, then we simply make the y an x, and we make the x a y, like so..

X=2Y+5

2) A graph of g is found by reflecting f over the line y=x

this may sound confusing, as i didn't exactly understand it myself at first, but no matter what, the inverse is reflected literally over the equation y=x. Simple as that

3)the domain of g is the range of f. the range of g is the domain of f

This is pretty straightforward, though ill explain it anyway. the domain of g is the range of f and the range of g is the domain of f. ok theres no other way to say it. um...

8.3

-Properties of Inverse Functions

http://gbs-moodle.glenbrook225.org/moodle/file.php/1304/Chapter_8_Notes/8.3_Notes_Key_2010.pdf

The term thing used to reference the inverse of a function is f^-1

For points on a graph, the inverse of a point is found by switching x and y, much like in 8.2 above. So for the point (a,b), the inverse is (b,a).

We learned in this section how to determine whether or not the inverse of a function is a function, by applying the horizontal line test. Its just like the vertical line test but horizontal.

The above image, assuming it shows up, illustrates how to use the horizontal line test. We know from this graph that the inverse is not a function because each horizontal line intersects the graph at 2 places.

This image now illustrates when the horizontal line test would pass. Here, each horizontal line intersects the graph at only one point, which tells us that the inverse is a function.

Now once again, this is acting simply as a broad summary of all the sections that were on the quiz but if you would like to see the more in depth ones for each section, you can find them below this post. Also ill post the link to each:

8.3: http://advalg1011p2.blogspot.com/2011/03/8-3-properties-of-inverse-functions.html

8.2: http://advalg1011p2.blogspot.com/2011/03/tuesday-march-8th-2011-lesson-82.html

8.1: I could not find for some reason, the 8.1 blog post on the period 2 site so ill post the link to the one that i found on the period 1 site, which should be better anyway since period 1 is so much better than us haha, just kidding. http://advalg1011p1.blogspot.com/2011/03/chapter-81.html

If you made it this far to read this, thank you and i hope that i was able to somewhat give you an overview of our day and our quiz on Friday.

8.1-8.3 QUIZ TOMORROW

We started today's class by checking our homework. We made sure that we understood all of the questions and got all the right answers. Then Mr.Cope handed out a review packet for quiz 8.1-8.3 quiz. The quiz is tomorrow. REMEMBER WE ARE NOT ABLE TO USE OUR CAS CALCUL ATOR ON THE QUIZ!!

Here are some resources:
-You can look on Moodle for
1. Chapter 8 homework answers
2. Chapter 8 notes
3. 8.1-8.3 review key
4. You are also able to access the online textbook

-In the textbook
1.Page 516- Page 536 is lesson 8.1-8.3
2.Page 574- Page 577 is the review section.

Sorry...This is not one of my best sections. I'm still reviewing. Next post will be better!!

Remember non CAS Calculator

Remember to bring a non-CAS calculator to class tomorrow for our quiz.  A TI-83 or 84 is fine or a simple 4-function calculator.  I am available before school if you need help with the concepts.

8-3 Properties of Inverse Functions

At the start of class we of course reviewed the previous day's homework, which was section 8.2. After our homework review we wet over Mikaela's last post on section 8.2. This took up a good chunk of time. Mr. Cope also talked about how he takes things personally when he doesnt need to. Like when a student falls asleep in his class, it's not his fault. The student definetly should have went to sleep earlier and possibly slept in the previous class so that it didn't happen in Mr. Cope's. We then talked about how Mr. Cope and how he hasn't caught anyone texting during class in a while.


Section 8.3 is about the properties of inverse functions. Here's the basic objective you need to know before you start computing anything:

1. We denote the inverse of a function as f^-1. (f^-1 means the inverse of a function)
2. For every point (a,b) on the graph of f, the point (b,a) is on the inverse graph. (the point (a,b)'s inverse is (b,a))
3. To determine whether the inverse is a function or not without graphing, we apply the horizontal line test. (use the h.l.t. to see if the inverse will be a function without graphing)


Given the general equations y=x, y=x^2, and y=x^3, we know that y=x is a function using h.l.t., y=x^2 is not a function because it doesn't pass h.l.t., and y=x^3 is a function because it passes h.l.t.

The three steps to finding an inverse are...
1. Replacing f(x) with y
2. Switching x and y
3. Solve for y

When combining any two functions the inverse "undo" eachother. For example when we plugged g(f(x)) and f(g(x)) into the calculator both outcomes equaled x.

On a test Mr. Cope may say are these two functions inverses? To solve this you would simply plug the functions into eachother [g(f(x)) and f(g(x))].

The inverse function theorem states that two functions if and only if f(g(x))=x and g(f(x))=x.

The tricky part was power functionsand inverses.
f(x)=x^6's inverse wouldn't be a function because it's a parabola. Parabolas never ever pass h.l.t. It causes a problem when you attempt to plug negative numbers into the inverse function. X can't be negative in an inverse. So to take care of that you can restrict the domain to X is greater than or equal to 0.
f(x)=x^an odd number passes h.l.t., and is much simpler than an even power function.

Next blogger is... Emma B!

A couple days ago we took the chapter 7 test. This test consisted of two parts: a no calc. section but we were able to use our "green cards" and then a calculator section.

In preparation for this test we had a review sheet the day before. This review sheet first discussed what would be on the no calc. part: it went over power functions, geometric sequences with recursive,explicit formula and domain and range. Also on the review sheet Mr. Cope gave us practice problems that required us to use properties of powers with negative and fractional exponents. On the back of the sheet it discussed the calculator part of the test: topics it covered were compound interest,word problems, and using properties of powers with numbers not on the "green card".
If you had trouble with any of these topics or problems remember you can always refer to moodle or your notes from class.

Something I recommend when we are reviewing before the test that you(Mr.cope) actually discuss and go over it with us in class rather than us just doing it ourselves and making us go on moodle if we want to check our answers because im a sure most of us forget and just wing it on the test not even knowing if we did the problems correctly.

And as far as the test goes I don't think there should be a no calc. part because the majority of the quiz's you gave us for this chapter were no calc. and us as students tend to not do as well on them, therefore bringing down our scores. but overall the test was ok, I just wish I had more review and better assistance from the teacher.

mikaela allmon

Tuesday, March 8th, 2011 Lesson 8.2

Today in class we went over the homework we had over the weekend which was 801, then viewed the blog. Mr. Cope gave us the rubric on how we would be graded for the blog posts, then started the lesson.

Lesson 8.2: Inverses of Relations

3 Important things to know about inverses of relations:

Suppose f is a relation and g is the inverse of f;

1) A rule (or equation) can be found by switching x and y (solving for y if necessary)

2) A graph for g is found by reflecting f over y=x,

3) The domain of g is the range of f, and the range of g is the domain of f

An example of inverse relation is this;

Let f = (1,4) (2,8) (3,8) (0,0) (-1,-4)

The inverse relation of this would be;

(4,1) (8,2) (8,3) (0,0) (-4,-1)

Another thing to note, is that the f is a function but the inverse of f is not.

This is because when you reverse x and y, there becomes (8,2) and (8,3) which means it is not a function.

You can also find out if the inverse is a function by seeing if it passes the horizontal line test.

The domain of f is ( 1, 2, 3, 0, -1) and the range is ( 4, 8, 0, -4)

The domain of the inverse is (4, 8, 0, -4) and the range is (1, 2, 3, 0, -1)

You should note that the domain and range swap when it is the inverse.

Another example is f 9x0 = 1/2x + 4

The work I did to find the inverse is;

I rewrote the equation to be y = 1/2x + 4

Then rewrote it as x = 1/2y + 4

Then I subtracted the 4

So its now x - 4 = 1/2y

Then I multiplied both sides by 2 to get ride of the fraction

So it would now be 2x-8 = y which is the final answer.

I hope this helps!

Homework :

802 and the 3 problems on the back of the worksheet.

The next scribe will be Leah.

March 03, 2011

It has been yet another wonderful day in Mr.Cope's second period Advanced Algebra class.
First we started our day off by getting a homework quiz, which usually either helps your grade or hurts it. Along with going over our partner quizzes, that were not so phenomenal according to Mr.Cope and the would not count for points, so hurray for those who did not so great. We then received our very structured and helpful Chapter 7 review sheet that we did in class, and Mr.Cope so kindly reminded us that we should access Moodle, that has many helpful resources, such as extra copies of our green cards that we are allowed to use for tomorrow's Chapter 7 test, and there are also review sheets and answers on Moodle for those that are interested.

Don't forget to study for our Chapter 7 test tomorrow, :)
Good luck.

btw, Mikaela your next.

3/1/2011

Hey everyone! Today in class we went over the homework (708 A & B) and then we took a partner, open-note, no calc quiz! Also, we talked more about this blog and what we think of it. There were varying opinions on it, ranging from 'I don't think this is going to have any affect on anyone' to 'I really like that we will get to interact and almost talk to each other!'

Okay, so Victoria G is going to post the next one! :)

Reflections from Class

I just wanted to say thank you for your honest reflections today in class about what this blogging process will be like.  I do want it to succeed, but I don't have any delusions that it will be amazing and revolutionary right away.  If it turns into something great, it will take time and effort on both of our parts.  We will need to reflect on and share what is working well and what needs to be improved.  I appreciate your patience and your willingness to give it a try.