Scribe : Spheres (Volume/Surface Area)

Click the image to view!

Well that's all to it. Have fun with that!
The next scribe I choose is Nounith ....your turn =)

Reflection

I think that the unit Exponents and Radicals seems easy. The first time I saw these questions it was hard but later I started to understand. The only hard part of the radicals were the ones on the triangle. I hope that I do well on this test. Good luck. =)

reflection

well easy well notthis unit was pretty reallly but it kindda was. The multiplying was difficult through some points but i pretty much got it. well good luck to all and have a good test day

reflection

I think that i will do well on this test. I thought the whole unti was pretty easy, but sometimes i got confused and i didnt get it. Now, i understand it because i looked over everthing, and asked if i didnt. Hopefully i do well, and good luck to all.

so this a last minute thing too cause i was in a rush -.- but yeah. There was a couple of things that i thought was pretty difficult in this unit like multiplying radicals that have different bases and things like that. some easy things that i liked were adding and subtracting the radicals. and i guess thats it so good luck to everyone on the test!

Reflection : Exponents and Radicals

Lol, Ms. Ingram just reminded us (me and Karen). That was funny! Anyways, the unit was cool. I learned alot. And I mean alot. I actually hand in assignments now. The one's that there's a radical inside a radical are the challenging ones. I hope I get high marks.

Good luck!

PS: No emoticons this time AHAHAHAHA

Reflection

Yeah, I don't think I did as well as I expected but yeah, good luck to everyone and I hope you guys didn't forget to do the radical triangle thing that is due!!

REFLECTION

last minute blogging? uh yeah. this unit was pretty easy. Nothing hard, radicals are pretty easy to understand. This is probably the easiest thing to understand out of all the math units. yuhp. I actually like this unit :D

r e f l e c t i o n

i didn't have a hard time understanding this unit. this was easier than the past beacause there are no formulas to remember, and the steps in solving a problem are short. good luck to everyone on our test!! :)

Reflection

I didn't have a hard time about Radicals
and I really learned all things about this stuff
hope I would pass the test.

reflection

Radical? This unit is quite easy though, and i hope that i can pass the text this time. LOL!By the way, good luck to everyone! ^^

*+=reflection=+*

Radicals is more easier than others its like you were just playing games and having fun with it...but I hope in our test tomorrow doesn't have the cosine law or sine law I'm really having trouble in that one...tomorrow we got test and I hope this time I can get the higher marks.. cuzzzz, lately I'm having trouble here in my pre cal class.but I hope this time its my turn to go up and have higher marks for this...GoOd LuCk To mE!!!




*+=good luck to everyone=+*





+=*LaRlYN*=+

Reflection

'Radicals' is actually an easy unit for me. I understand most of the steps to get the right answers, but radicals with fractions and divisions confuse me at times. Hopefully I do well tomorrow ! goodluck to everybody..

***REFLECTION***

ummmhhhh....... we have another test tomorrow ??? I guess I have to prefer for that... Well, solving radicals is quite hard for me,,, sometimes,,, I find it very confusing... But I think I can pass this test,,, pretty confident uhh!!!.... no I'm not... I'll just do what I can.... hmmmm.... well,,,, Good Luck to all of us!!!!

reflection

This unit was difficult in some ways and easy in others. Some of the stuff towards the end was more complicated and/or confusing; but all in all it wasn't too bad. The rules just take some getting used to. I think I'll do fine on the unit test tomorrow.

Rationalizing Radicals

Ok, now for the exciting topic of rationalizing radicals.

Example #1
__3__
√2+1

STEP ONE

Multiply both the numerator and the denominator by the conjugate. This is the same as the denominator, just with the second term's sign reversed. If there is only one sign in the denominator, don't change the sign.

__3__ (√2-1)
√2+1 (√2-1)

=

3√2-3
_____
2-1

STEP TWO

Solve the rest of the problem. REMEMBER TO REDUCE (if possible)!

3√2-3
_____
2-1

3√2-3
_____
1

= 3√2-3

Do the same for the rest.

Example #2

(√5 + √2)(√5-√2)

multiply the terms together

√2x - √10 +3√2-3
√2x- √10 + √10 - √4
5-2=3

Example #3

_7_ (√3-1) <-----conjugates
√3+1(√3-1) <-----

7√3 - 7
_____
3 - 1

= 7√3-7
______

2

Example #4

__2__ (√5 + 2)
√5 - √2 (√5+2)

2√5 + 2√2
_______
√25 + √10 √10 - √4

2√5+2√2
_______
5-2

2√5 + 2√2
________

3

Example #5

__15__ (√14+5)
√14 - 5 (√14+5)

15√14 + 75
__________
√196 + 5√14 - 5√14 - 25

15 √14 +75
_________
14 - 25

15√14 + 75
_______
-11

Example #6

4√15 (3√15 - 8)
______
3√15 + 8 (3√15-8)

12√225 - 32 √15
____________
9√225 - - 24√15 +24 √15 - 64

180 - 32√15
________
135 - 64

180 - 32√15
________
71

The next blogger is
Ana

Reflection...

I almost forgot to post a blog, but here it is. Well, the unit was pretty ok. I did better on this unit than the other unit that we had. I didn't expect to learn "Radicals" that fast, and I thought that this unit will end my pre-cal career(as if im good). lol just kidding. But my point is, it's kind of unbelievable that I didn't struggle with math THIS TIME! Yay for me! And I hope i'll do good on the test tomorrow. That's it! Goodluck to all!

MY REFLECTION:

This unit was not as easy as i thought itd be. I mean its simple, the facts and its pretty basic. Yet its confusing towards rationalozing the radicals. I just need to be careful, and hopefully ill do well. Good luck to everyone, and and. :) Yeaah... =P

Cheers,
Jenn Lavina

Reflection

Reflection again.. This unit was pretty average for me because some topics are difficult and some are not. And the crazy thing is when to use this and that. when to do this and when to use that. The Square Root Puzzle was fun but tricky. I hope our next unit will be as fun as this one. Okay everyone.. GOOD LUCK.. STUDY WELL..

r e f l e c t i o n

This unit wasn't bad...the only thing that I was having trouble with was knowing when to use what. For example, I did not know when I should simplify or multiply. But, now it's all cleared up. But other than that, I just need to remember what I need to do for each type.

Reflection

This unit has been a breeze! I actually paid more attention in class, and then everything felt kinda simpler. AND, I think the hardest part for me was when i had a cubed square root, I kept getting confused -_- . Besides all of that, I think this unit was good.

reflection...

ahhhhh!! we have test again.... ahm,, well I feel excited for tomorrow's test because I think it's easy, so I don't feel nervous for the test... I also learned this radicals when I was in Philippines so it's easy for me, I think... GOOD LUCK EVERYONE!!!!

! r~e~f~l~e~c~t~i~o~n !

Wow... we are just zooming through this course! lol. Well it's test time again. Radicals was alright I guess. It was sort of easy because you didn't have to put anything in decimals. You could've just left it in it's square root form or w/e it's called. The annoying part was rationalizing radicals. That probably took the longest, even though it was only 10 questions. I think I'll do well on the test? But you never know what could happen! Good luck everyone!

~pj~

REFLECTION

ah!!!!!!!!! another test but I'm pretty sure that i really understand this topic this is much easier than the previous topic.I love doing this stuff ,I'm really excited tomorrow...,,! GOOD LUCK!!!!!!!!!!!

Addition and subtraction with radicals

*NB: You can only add and subtract radicals if they are the same.
√<---- this is the radical sign just incase anyone is wondering.

Ex. √3 + √2=√3 + √2
√3 + √3 =2√3 <---because the radical is the same. Therefore, they can be combined.

Try: 1) 2√5+ 3√5 + 6√5=11√5
2) 5√7 +3√7-2√7=6√7


-What if the radical is different?

Ex. √12 + √18 - √27 + √8
Step one: Simplify if you can.

√12 √18 √27 √8
4x3 9x2 9x3 4x2 <----the first number always has to be a square root.
√4 x √3 + √9 x √2 + √9 x √3 + √4 x √2<---square root the first number.
2√3 + 3√2 - 3√3 + 2√2
Step two: Combine like terms.
2√3 - 3√3 +3√2 +2√2
-1√3 + 5√2

Ex. √12 + 2√8 -3√75 + √2
4x3 2√4x2 3√25x3 √2
√4 x √3 + 2√4 x √2 -3√25 x √3 + √2
2√3 + 2x2√2 - 3x5√3 + √2
2√3 + 4√2 - 15√3 + √2
=-13√3 + 5√2

Try: 1) √12 + √27
4x3 9x3
√4 x √3 + √9 x √3
2√3 + 3√3
= 5√3

2) √28 - √27 +√63 + √300
4x7 9x3 9x7 100x3
√4 x √7 - √9 x √3 + √9 x √7 + √100 x √3
2√7 - 3√3 + √3 x √7 + √10 x √3
= 5√7 + 7√3

Exercise # 34
Questions 1-9, 11, 13, 14

the next person to scribe is going to be..Katherine

Here are some other examples that I got on the internet

(a)

(b)

(c)

(d)

(e)

Solution

To evaluate these we will first convert them to exponent form and then evaluate that since we already know how to do that.

(a) These are together to make a point about the importance of the index in this notation. Let’s take a look at both of these.

So, the index is important. Different indexes will give different evaluations so make sure that you don’t drop the index unless it is a 2 (and hence we’re using square roots).

(b)

(c)

(d)

(e)

As we saw in the integer exponent section this does not have a real answer and so we can’t evaluate the radical of a negative number if the index is even. Note however that we can evaluate the radical of a negative number if the index is odd as the previous part shows.

Sorry for the delay of my scribe b'coz I didn't know i was the next... So... here it is now... I hope you'll understand the first examples that i wrote there....

By the way, our great teacher asked us to answer Exercise # 26 1-7 , 9-11 , 17-20
For the next scribe,,,,, I chose.................FRANCA !!!. good luck!!!

*Sorry guys if i posted my blog sooo late...*

Radicals

√72 → a value in a radicand
36^1/2→exponent


Exponent Laws

Multiplying: x³ . x² = x . x . x . x . x = x⁵
so x^m . xⁿ = x^m+n


Dividing: x⁵ ÷ x³ = x . x . x . x . x . x = x²
-------------- x . x . x

Power raised to a power:
(x³)² = (x . x . x)(x . x . x) = x²x² = x⁶
so (x^m)ⁿ = x^mn


Multiple base values:
(xy)³ = xy . xy . xy
= x . x . x . y . y . y = x³y³
so (xy)ⁿ = xⁿyⁿ


Examples of radicals:
√9 . √ 9 = 91
9^? . 9^? = 9¹
½ + ½ = 1

*Square root of fractional exponent form is x^1/2 = √x


3√27 . 3√27 . 3√27 = 271
27^? . 27^? . 27^? = 27¹
? + ? + ? = 1
1/3 + 1/3 + 1/3 = 1
³√x = 1/3
³√62 = 1/3
³√72 = (72)^1/2
= 7^2/3

*For assignment, answer Exercise 21 #1-15, 18-20*
*The next scribe will be inoj… im not even sure if this person hasn’t posted a scribe yet. =p*

Reflection

trigonometry

This unit's been easy for me, again, I forgot to blog. For me Trigonometry is the easiest. Hopefully I did well on the test. Word problems are the ones that are hard. Not all of them though. I wish everything in math were as easy as triangles !

Test post blog

I think this unit was quite easy. I learned how to do some easy ways to find angles and sides by using sine law and cosine law. At first it was quite hard but i understood it after doing some of the assignments. well good luck to everyone on there test

Reflection

Umm...yeah, this unit was easy. I think i will do good on this test. Pretty basic stuff. I think if you did your homework everyday then you should be fine and you wouldn't even need to study. Well, that all i got to say. Can't wait for the next unit....

reflection

This unit had some easy and some not so easy stuff in it. I found the Pythagoras theorem and SOH CAH TOA easy, while the cosine law was a little more difficult for me. Sine law was pretty easy too. I think I'll do pretty well on the test -- I think I'll get an A. I studied and practiced for it.

reflection (allans cool)

well this unit we are in is pretty hard they call it trigonometry but I call it "complicated" ! well since i was in mexico and i wasn't here for most of the trig stuff I probably won't do very well in the quiz today but i'll try my hardest. Yesterday while was studying trig i found it very easy for the sine and cosine and pythagoreous stuff but for the problem solving I think it was hard.... well good luck guys and have a good time doing the quiz-___-"

When we first learned how to do sine and cosine, my first thought after the lesson was "Letters should stay in the alphabet and out of mathematical equations!" But after a few questions and lessons it was easy. I thought it would be a lot harder, especially cosine, but I find it quite easy.. as long as I have a calculator near by. =)

Reflection : Trigonometry

The unit for me was kinda easy o.oa... I don't know why but evens out with the harder questions.... Anyways, like Ash said, pretty straightforward »» Cosine law takes a bit of time to do [talking about the angle ones XD]. I think I will do good in the test [don't give factor questions please >_>]
GOOD LUCK!

Oh, and word problems suck :P

Reflection

I think that this unit was a bit hard and easy. The only part that I think that is easy is Soh Cah Toa and a bit of Sine Law and Cosine Law. I think that using word problems is kind of hard for me because when you have to draw it out, it could be wrong or you are just confused. I hope I did well throught this unit and I hope I did well on the test. Good luck everyone on the test =)

r e f l e c t i o n

i was about to fall asleep. good thing, mrs. ingram popped in my head. that was just the time that i remembered we need to create a pre-test blog. -_- so even though i'm sooo sleepy now, here's my reflection..

at first, this unit was really confusing for me. i have studied only SOH CAH TOA last year so the sine and cosine laws were new to me. the exercises really helped me understand the things that were difficult to me. other than that, i found it fun to solve trigonometry questions. i hope we all do well on the test. good luck to all! :))

zzzZZ..

reflection...

ahhh!!! tomorrow is our test... I hope I can pass the test... well I know trigonometry is an easy unit but sometimes it's hard for me to visualize the diagram, so I'm a little bit nervous for tomorrow's test.. hehhe,, But if you guys can do it I think I can do it too right? hehhe!! well good luck to our test tomorrow.... :)

reflection

hmm.. i think i was pretty comfortable with this unit? i had a little trouble at the beginning because i kinda forgot how to do everything? lol.. but yeah. i think i should do pretty well on this test.. as long as i dont have a mental block.. like always.. but overall, i think this was a pretty straight forward unit. good luck everyone! =)

reflection

trigonometry, this unit was alright. i find it pretty easy. the only thing i have problems with is finding the side using cosine law. hopefully i get the hang of it by tomorrow. Everything else was pretty easy, and i didnt have much problems with it. but then, there are word problems, and sometimes i mess them up. hopefully i do well on the test. yeah.. now im gonna go study cosine law

<(^^<):Reflection:(>^^)>

Wow! Another test already? It seems like our last test was just yesterday!
lol. k so anyways, trigonomerty was pretty easy. i learned part of it last year so that kinda helped. the easiest part was SOH CAH TOA. that part was pretty basic. but then sine law and cosine law came just to make things harder. cosine law was confusing at first but then i got it afterwards. i think that ill do well on my test, but i dont want to be over-confident. so i guess that's all i have to say for now!
GOOD LUCK EVERYONE!!!

~pj~

Before i go with my mother and brother to refill our fridge :)
This is my reflection:

Trigonometry is an easy unit for me. It makes math fun. Soh Cah Toa is a real easy method to use compared to the sine and cosine law. However the real trouble i had are the word problems where you had to draw out the triangle's distances and angles, and when the diagram is not given. It's the only type of questions that im really worry about. I'd like to say good luck everyone :) I really enjoy this class. Haha!


Cheers,
Jenn Lavina

REFLECTION

I think our test will not be so hard ,because of the equation that we had solved in the game it really help me to know my mistakes and were should I focus , GOOD LUCK !!!!!!!!!! maybe I need to study our math lesson now higher MARK that's my aim............!!!!!!!!!!!!!!!!byE!!!!!!!!!

Reflection

The unit we are doing is Trigonometry. I understand most of what we've been taught and I think I will be doing well on this test. The only thing I had troubles with was the two triangles in the beginning and doing Cosine law with finding the angle. But now I understand how to do those things and I feel comfortable with doing the test tomorrow.

Reflection

Tomorrow we have a Trigonometry math test!! For this unit I think I was doing okay slightly better than the last unit. The only trouble I had was where to put the numbers. I'm not sure how to explain what I don't understand. Okay, well studying a little bit to refresh my memory is going to help me for the math test tomorrow, everyone will do fine!!!

--refelection--

Again we're going to have another test tomorrow. Which is about Trigonometry, triangles and stuff. The review did help me for tomorrow's test. This unit is the average one I guess. Because we took it last year but not everything. And the problem solvings are pretty hard but yet it did practice us for tomorrow's test. Argh.. okay that's all for now.. Lotsa things 2 do.. go0d luck evry1.. STUDY HARD..

***REFLECTION ***

Hhmmmmm..... we have a test tomorrow!!! and I don't know what to say.... hhmmmm... I think I'll pass on this test even though this unit gave me so much headache... but still, I'm not sure about that... Solving word problems is very hard for me and sometimes I make mistakes in making diagrams because I don't quite understand the problem very well... so I hope this test doesn't contain much of that...heh...heh...heh...I'm very busy today and there's a lot of things to do.... I HAVE TO STUDY NOW!!!!! GOOD LUCK!!!!!

Reflection...

* Im posting just to make sure*

I'm feeling kinda nervous about the trigonometry test on Friday. I know i found the Sine law and the Cosine law not that difficult, but i don't know how im gonna do on the test, but i'll try my very best to pass the test. Good luck to all, and keep up the good work guys!

*Im the next scribe person and im still waiting for a new lesson to use for my scribe, so don't post any scribes yet. Thanks* =)

Cosine Law

It is only used if you have SAS or SSS.

Important:
~> Only use cosine law once, then use sine law to finish question.

If you are looking for side a, the following equation must be used:
a² = b² + c² -2bc cosA

If you are looking for side b, the following equation must be used:
b² = a² + c² -2ac cosB

If you are looking for side c, the following equation must be used:
c² = a² + b² -2ab cosC


Example:

You have a triangular-shaped garden that you want to fance. You know two sidesare 50 m and 80 m and the included angle (angle between the sides) is 100^o. How many meters of fencing do you need?











b² = a² + c² - 2ac cosB


b² = 80² + 50² - 2(80)(50) cos100


b² = 6400 + 2500 - (8000).34


b² = 6180


b = 78.61




Here's a sample problem looking for an angle using the cosine law:

Find C where a = 200 m, b = 155 m, c = 172 m.

c² = a² + b² - 2ab cosC
172² = 200² + 155² - 2(200)(155) cosC
29584 = 40000 + 24025 - 62000 cosC
29584 - 64025 = -62000 cosC
-34441 = -62000 cosC
------------------------
-62000
cosC = 0.56
C = 56.3

Mrs. Ingram also asked us to answer Exercise 25, numbers 1-7.

Next scribe.. Rochelm!! Bet you didn't see that coming! :D