Friday, December 21, 2007
reflection
reflection........
Review
r e f l e c t i o n
reflection
Thursday, December 20, 2007
Reflection
Reflection...
Reflection
Last blog of the year! =O
Good luck everyone!
Answer Key for Review
1. (x+1)/(x)
2. (x-2)/(x)
3. (-2x+2)/(6x2 – 18x +12)
4. (-2x+3)/(3x-1)
5. (x-1)/(x-2)
6. (x-2)/(x-4)
7. (2x2 - 8x)/(x2 - 4x)
8. 1
9. (-3x+5)/(4x+5)
10. 1
11. (x+4)/(-3x-2)
12. (4x2 + 30x – 18)/(– 16x2 + 20x – 6)
13. (2)(x-3) / (x-4)(x+4)
14. 5/3
15. (5)(x+4)(x+3) / (x-5)(x-5)(x-1)
16. (x+1)(5)(x) / (x+5)(x-1)(x+2)
I hope this helps you.
Good luck on the test tomorrow, that's Friday Pacifico, in case you were wondering.
Mrs. Ingram
Reflection : Rational Expressions
PS: Oh and Al, did you really do what I told you?! And Allan, don't cut yourself. That's bad :o. And Ash, don't make a good joke cause your sucky jokes are funnier XD
my reflection on the last day of the year blog ..:o
Well good luck to all and happy holidays!
p.s wish me good luck also..
Reflection
reflection ;D
reflection....
Reflection ;>
Sunday, December 16, 2007
Addition and Subtraction
6/4+7/4 2nd: when you already get the 2 which is the denominator ,multiply it with 3and 2
13/4 3rd: that will be the answer
6/x +7/2x first: find the common denominator
2(6/x)+7/2x 2nd: when you already get the 2 which is the denominator ,multiply it with 6and x
19/2x 3rd: that will be the answer
4/x+3 -5/x-2 first: find the common denominator
x-2(4/x+3) - x+3(5/x-2)2nd : multiply x-2 to 4/x+3 and multiply the x+3 to 5/x-2
4x-8-5x-15/(x-2)(x+3) 3rd: simplify them
-x-23/((x-2)(x+3) 4th :that will be the answer
just always remember that any expression should be simplified before you add it or subtract it.
and if the denominator is like this x2 +2x-15 always factor it then cancel.
EXERCISE NO........49 1-19
ANA SORIA IT'S YOUR TURN
Monday, December 10, 2007
Review
Saturday, December 8, 2007
WELL, i get to take my test on monday with ashley and raia.
This unit has been pretty easy at points and just a bit confusion.
Uhm, this is a pretty short blog. but i dont know what else to say.
Was the test hard you guys? Any questions you guys remember :D ?
Muahahahah, just kidding. Good luck you two.
Sorry Mrs Ingram for not attending two of your classes. Um, we hope to hand in our assignment sheet in the beginning of the class, before we do the test. :)
BYE!
Cheers,
Jenn Lavina
Friday, December 7, 2007
Geometery
reflection
Reflection
*****REFLECTION*****
Reflection
Reflection : Geometry
Thursday, December 6, 2007
r e f l e c t i o n
^-^ reflection -_-;
anyways, this unit was actually pretty easy! i thought it was gonna be reasonably hard because of the previous lessons. but i still did learn some new things like volume of a cone and sphere and surface area of a shpere. One of the most interesting things for me that i learned was the relationship between the area and sides and the whole factors thing. I think i'll do well on this test as long as i dont blank out becasue there were a lot of formulas to remember. but anyways, good luck to all!
P.S. Al if you wanna beat me, this might be the test, but you better try hard because i'm gonna be giving it my all. =D
reflection....
Reflection
reflection
Reflection ;>
GOOD LUCK!!!!!!!!!!!!!!!!!!
Test Reflection on Geometry
Wednesday, December 5, 2007
notes


Question on the left:
ok so the first thing you do with this is 2x -9 = x +5
add 9 to both sides ---- > +9= x +5 + 9
-------------------
now becomes---> 2x= x + 14
the next step is to get the x's on the same side
bring the x on the right to the left. ----> 2x = x + 14
-x = -x
-------------------
now your equation becomes -----> 2x - x = 14
______________
the x is already by itself ------> x = 14
Wednesday, November 28, 2007
Thursday, November 22, 2007
Reflection
reflection
reflection
Reflection : Exponents and Radicals
Good luck!
PS: No emoticons this time AHAHAHAHA
Reflection
REFLECTION
r e f l e c t i o n
Wednesday, November 21, 2007
reflection
*+=reflection=+*
*+=good luck to everyone=+*
+=*LaRlYN*=+
Reflection

***REFLECTION***
reflection
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
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
2√5+2√2
_______
5-2
2√5 + 2√2
________
3
Example #5
__15__ (√14+5)
√14 - 5 (√14+5)
15√14 + 75
__________
√196
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 -
180 - 32√15
________
135 - 64
180 - 32√15
________
71
The next blogger is
Ana
Reflection...
Reflection
r e f l e c t i o n
Reflection
reflection...
! r~e~f~l~e~c~t~i~o~n !
~pj~
REFLECTION
Monday, November 19, 2007
Addition and subtraction with radicals
√<---- 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
Thursday, November 15, 2007


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).
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!!!
Tuesday, November 13, 2007
*Sorry guys if i posted my blog sooo late...*
Radicals
√72 → a value in a radicand
361/2→exponent
Exponent Laws
Multiplying: x3 . x2 = x . x . x . x . x = x5
so xm . xn = xm+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 (xm)n = xmn
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 x1/2 = √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
= 72/3
*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*
Sunday, November 11, 2007
Reflection
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 !
Friday, November 9, 2007
Test post blog
Reflection
reflection
reflection (allans cool)
Reflection : Trigonometry
GOOD LUCK!
Oh, and word problems suck :P
Thursday, November 8, 2007
Reflection
r e f l e c t i o n
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...
reflection
reflection
<(^^<):Reflection:(>^^)>
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~
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
Reflection
Reflection
--refelection--

***REFLECTION ***
Wednesday, November 7, 2007
Reflection...
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* =)
Monday, November 5, 2007
Cosine Law
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 100o. 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
Wednesday, October 31, 2007
It is used when you are solving
a triangle that is not a right triangle
a/sinA = b/sinB = c/sinC
this is the equation we must follow
in Sine Law.
for example:
A triangle has 2 angles and a side,
angleA = 30° and angleB = 65°
side a = 5cm, look for side b.
5cm/sin30° = b/sin65°
b = 5cm/sin30°(sin65°)
b = 9.06cm
sinA/a = sinB/b = sinC/c
this equation is used when 2 sides is given
and you are looking for the angle.
for example:
A triangle has 2 sides and an angle,
side x = 6.8cm
side y = 5.1cm
and angleX = 49°
find angleY.
sinY/5.1cm = sin49°/6.8cm
sinY = sin49°/6.8cm(5.1cm)
angleY = 34.47°
this is how to use the Sine Law.
the next scribe is >> Iana <<
{}(-,-){} zzZ...
Thursday, October 25, 2007
Labelling Triangles
- Use CAPITAL LETTERS for the angles.
- Use small letters for the sides.
Pythagorus Theorom
A² + B² = C²
Sin A = opposite/hypotenues : SOH
Cos A = adjacent/hypotenues : CAH
Tan A = opposite/adjacent : TOA
* adjacent is the side of the triangle, thats beside the opposite of the angle.
Wednesday, October 24, 2007
Reflection
Tuesday, October 23, 2007
-->>reflection<<--
Reflection
reflection :I guess I'm very lucky this day. Our teacher gave us permission to use our formula sheet and it's very useful... whenever I forgot about something, I just look at the formula sheet and I remember all the things that I forgot!!!! kinda weird........ but that's the way it is !!!..... hope I did well on this test and let's wait for the results....... GOOD LUCK !!!
Reflection
Monday, October 22, 2007
Analytic Geometry Reflection
reflection
Reflection
This unit was okay, it wasn't super easy but it wasn't super hard. I learned a lot of new things, and at times I felt kind of confused with the questions, because I wasn't sure what they wanted me to do. But now that I finally reviewed my notes and stuff today things finally click! But it's pretty sad.. But anyways I feel slightly comfortable with the stuff now.
:):):):):):):):):):):):)
reflection.
~Reflection~
This unit was okay? I mean like it wasn't hard but it wasn't easy either. There's quite a few formulas to remember so I guess that makes it kinda hard. The easiest part was probably figuring out the x and y intercepts and graphing the line. The hardest part was probably finding the equation for the perpendicular line? I used so much graph paper in this unit! But, oh well... K so anyways, yea I think I'll do okay on the test yenno as long as I don't mess up on the formulas and getthem mixed up or something? So yea, I guess that's all! Good luck everyone!
~pj~
Thursday, October 18, 2007
Graph the following equations onto one sheet of graphing paper:
y = 2x + 1
y = 2x + 7
y = 2x - 3
y = 2x - 7
This is what it should look like:
(click to view it much better)

Note that..
- all these lines are parallel
- lines that are parallel have equal slopes
- never touch each other
- remains the same distance away to infinity
- equal lines
- cross forming a 90° angle
- the slopes of the two lines will be negative reciprocals
m = 2/1
m"perpendicular" = -1/2
Find the equation of the line to y = 3x + 4 that goes through (7, 16).
m = 3/1
point: (7, 16)
y - y1 = m(x - x1)
y - 16 = 3/1(x - 21)
1[y - 16 = 3/1(x-21)]
y - 16 = 3x -21
y = 3x - 5
Standard Form : 0 = 3x - y - 5
Easy right? Time to use m "perpendicular":
Find the equation for the line "perpendicular" to y = 3x + 4 that goes through (7, 16)
m = 3/1
m "perpendicular" = -1/3
y - y1 = m (x - x1)
y - 16 = -1/3 (x - 7)
3[ y - 16 = -1/3 (x -7) ]
3y - 48 = x + 7
Standard Form: 0 = x + y -55
Homework: Exercise 16: Determining Equations of Lines - 3
Questions 1- 15
Test moved to Tuesday, October 23, 2007
Next scribe is KARENd, heres my other present for you c(:
Her birthday was yesterday everyone, for anyone who didnt know! :P
Cheers,
Jenn (:
Wednesday, October 17, 2007
October 16
1.) Use Slope Intercept
y = mx + b
m = slope
b = why intercept
2.) Point-Slope form
y - y1 = m ( x - x1)
m = 3 P(7, 36)
y - 36 = 3 (x - 7)
y - 36 = 3x - 21
y = 3x - 21 + 36
y = 3x + 15 ---> slope intercept form ( y = mx + b)
Ax + By + C = 0 ---> standard form
3x - y + 15 = 0 ---> (Ax always have to be positive)
Example:
D(6, 1) E (-4, -3)
D(x1, y1) E (x2, y2)
1.) Find the slope
Y2 - Y1
_____
m =
X2 - X1
(-3) - (1)
______
m =
(-4) - (6)
m = -4/-10
m = 2/5
2.) Use point-slope form
y - y1 = m (x - x1)
y - (-3) = 2/5 [x - (-4)]
5 (y + 3) = [2/5 (x + 4)] 5
5y + 15 = 2x + 8
Ax + By + C = 0
2x - 5y - 7 = 0
P(13, -15) m = -7/2
y - y1 = m ( x - x1)
y - (-15) = -7/2 (x - 13)
2(y + 15) = [-7/2 (x - 13)]2
2y + 30 = -7x + 91
Ax + By + C = 0 (standard form)
7x + 2y - 61 = 0
Do exercise 15, 1 - 12
Sorry if this is posted a day late. I had some difficulties with my interent.
next post is jlavina
Monday, October 15, 2007
Today's Lesson 10/15/07
Today's notes:
1. y=mx+b --> m=slope, b=y-intercept
2. Ax+By+C=0 --> Standard form (in general set up so "A" is positive)
3. Ax+By=C
Examples:
m=3 b=2
y=mx+b
y=3x+2
m=-4 b=5
y=mx+b
y=4x+5
Assignment: Ex 13 - All questions but don't do # 13, 14 and 17
Next scribe is: preyes
Wednesday, October 10, 2007
today's lesson 10/10/07
Todays notes:
the equation is set up as y=mx+b
^ ^
m = slope intercept = b
1. Put the equation into y=mx+b
2. Plot the y intercept
3. Use the slop to find a 2nd point
4. Draw a line
eg. -2x+y=-3
y = 2x-3
y =2(0)-3
y=-3
Then plot it out on the graph.
and we received exercise 12, questions 1-9 + 11-15
Oh by the way, look at the comments to see who the next scribe is Laura.
Tuesday, October 9, 2007
Graph Using Intercepts
Graph using intercepts
-needs 2 intercepts
Those 2 intercept are:
1) x- intercept
- the place where the line crosses the " x " axis
y= 0
2) y- intercept
- the place where the line crosses the " y " axis
x= 0
Ex. 1
2x+3y=6
x=0
a) 2x+3(0)=6
2x=6 (divide both side by 2)
x=3
y=0
b) 2(0)+3y=6
3y=6 (divide both side by 3)
y=2
after you solve those 2 intercepts you have to graph it...
(Sorry if I can't make the graph I don't know how to make a graph line here)
Ex.2
2/3x + 6y= 12
x= 0
a) 2/3x+6(0)=12
2/3x=12 (multiply by 3, both side)
x=36/2
x= 18
y= 0
b) 2/3(0)+6y=12
6y=12 (divide both side by 6)
y=2
after yolve graph those 2...
Ex.3
3x-5y=-15
x=0
a) 3x-5(0)=-15
3x=-15 (divide both side by 3)
x=-5
y=0
b) 3(0)-5y=-15
-5y=-15 (divide both side by -5)
y=3
(graph those 2)
assignment
Ex. 11 questions 1-9, 11-16
enjoy!!!!!!! :)
next scribe is... teara :)
Friday, October 5, 2007
A line can be represented by an equation in different ways:
1. Ax + By + C = 0
2. Ax + By = C
3. y = mx + b
Three Ways on how to graph an equation:
a. Table of values
x -1 0 1
y 3 1 -1
Solved for this equation: y=-2x+1
Just simply substitute the x variable above
If x = -1
y=-2(-1)+1
y=2+1
y=3
if x=0
y=-2(0)+1
y=0+1
y=1
if x =1
y=-2(1)+1
y=-2+1
y=-1
So (-1,3) (0,1)(1,-1) plot them in your graphing paper....,,
answer exercise #6 1-12,16-20 :>
raminalyn...............hi!!!!!!!!!!
Tuesday, October 2, 2007
Polynomial Test Results
I finished marking the tests, and would like to let you all know that the class average on this test was 64%. Pretty good for the first pre-calculus test.
Congratulations to all on the test.
Mrs. Ingram
Monday, October 1, 2007
I dont know where my old one went -_-'' For some reason its not on here, but as i said before this unit was a easy to understand, although im pretty careless and then i have to do extra work by doing check on a few questions. Um, next unit seems more familiar to me than this one, so i may have better luck (y)! Good luck for everyone next unit!
Cheers,
Jenn (:
Sunday, September 30, 2007
Review
It seems difficult but it is quite easy once you know what you're doing.
Friday, September 28, 2007
Reflection
Important if you weren't here on friday (09/28/07)
Reflection
Good luck to all.
Thursday, September 27, 2007
Reflection
reflection....
GOOD LUCK:) TO OUR QUIZZ
(WE CAN DO IT!!!)
allan loves math *rollseyes
Reflection
"Reflection"
>>reflection<<
I'm ready...
***reflection***
Wednesday, September 26, 2007
Reflection
Reflection
Unit Reflection...
Reflection =]
Reflection
REFLECTION
Reflection.
Tuesday, September 25, 2007
r e f l e c t i o n
Wednesday, September 19, 2007
Factoring Difference of Squares
(x* - means X squared)
(x + 1)(x - 1) = x* - 1
(x + 2)(x - 2) = x* - 4
(x - 3)(x + 3) = x* - 9
(2x - 1)(2x + 1) = 4x* - 1
Difference of Squares
Example 1:
81y* - 4
(9y + 2)(9y - 2)
Example 2:
x* - 144
(x + 12)(x - 12)
Do exercise 10, questions 1 - 7, 19 & 20
-this is it, work's pretty easy, sorry if its unclear,
- next scribe is William San Diego.
Tuesday, September 18, 2007
Factor Using Grouping
2t*2+t-3
a=2 b=1 c=-3
a X c
2 X -3=-6 ---> what are factors that will add up to 'b' value
-2+3=1
-2X3=6
2t*2 + t -3
2t*2 -2t + 3t- 3
<------> <---->
2t(t-1) + 3(t-1) -----> brackets should be the same
(2t+3) (t-1)
Assignment: Exercise 9 Questions 1-8, 10,11,20
Sorry if you can't understand.
Next scribe is Praisia.
Sorry that's it's posted late didn't know who the next scribe was.
Good luck =)

