Mr. O'Brien's 2009-10 White Pre-AP Calculus

Scribe Post 10/1/10

2010-10-01T14:31:00.003-04:00

https://docs0.google.com/document/d/1lifUs_-b3c2aoNERQQKVsFh5y1C6iyUjJRJ65fZYAtg/edit#

Final Exam Revision

2010-06-02T09:02:00.000-04:00

Here is the study guide.

Q4 Project

2010-05-26T10:03:00.002-04:00

Here is the project:

http://pre-apcalculusw2.obrienfamily.sent.com/Q4%20Project.pdf

Miles Last Scribe Post, May 11

2010-05-11T13:43:00.001-04:00

We began class with the quiz. It focused mostly on the law of cosines and vectors. We then checked the O'Brien answers to the quiz. We were reminded that the unit test will take place next tuesday the 18^th. We then went into vector projection. Tricky stuff to be sure. There were properties and such. A good derivation for Dot Products can be found at:

http://www.math.oregonstate.edu/home/programs/undergrad/CalculusQuestStudyGuides/vcalc/dotprod/dotprod.html

He fired up his trusty TI-84 Plus Silver Edition. With a flurry of button pushing, he proved beyond a shadow a doubt that theta does, in fact, equal 75 degrees. He then noted that cleverness was a key prerequisite to succes on the unit test. Bad news for Tyler.

Did you ever want to find the projection of vector u onto vector v? Well wait no longer True Believer, the magic formula, for the vector projection of vector u on vector v is:
Ta-Da!

See you next time Dan and O'Brien.

Scribe Post May 7

2010-05-07T09:33:00.004-04:00

warm up:

1.
use applet to show:

a) <3,2> + <2,4>
b)<3,2> + <-5,1>

2.
Do p. 457/70

1.
We plugged in the two coordinates for each problem into the applet, and we added them together (found the sum). We observed the movements of the vectors and concluded that...

(vector between two terminal points of two vectors = Terminal - Initial)

A+(-B) = A-B
B-A=-(A-B)

v=i+2j = <1,0> + 2<1,0> = <1,2>
w=2i-j = <2,-1>

for the homework quiz on Monday we must remember:

we reviewed homework problems, and learned that when the magnitude of the vector sum must be 3. This is because the magnitude of cos60º and sin60º is 1. The coefficient of 3 then changes the magnitude's value to 3.

73:
<300,0>

" class="ee_img tr_noresize" eeimg="1" style="vertical-align: middle;">

" class="ee_img tr_noresize" eeimg="1" style="vertical-align: middle;">

to find the vector of A+B use...

because you have found the parallelogram created by the vectors of <300,0> and " class="ee_img tr_noresize" eeimg="1" style="vertical-align: middle;"> . knowing that one side of the parallelogram is 300 and the other is 125 use the given formula above to find the vector/resultant of "x".

Dot Product Notes:

if u= and v= then =u1(v1)+u2(v2)

ex/ u=<3,4> v=<-2,7>

=3(-2)+4.7

=-6+28
=22

p. 460/ 5 properties:

1. =
2.
3.
4.
5.

all variables above are vectors other than: all c's and last "o" in property 2
however, when you "dot" the vectors together your product is a scalar.

definition of "dotted products": take two components multiply them together and then add them

scalar is a real number = 17
vector is a directed line segment = ------>

1st Cool Result:

where theta is the angle between u and v

if = 1, vectors in same direction = parallel
if = -1, vectors in opposite direction = parallel
if = 0, vectors are perpendicular = orthogonal

orthogonal = perpendicular

2nd cool result:

the projection of u onto v (see u, in applet) is given by:

this 2nd cool result will be in class discussion on Tuesday

Links for Friday, May. 7

2010-05-07T09:33:00.000-04:00

http://www.ies.co.jp/math/java/vector/vsum/vsum.html

http://jwelker.lps.org/lessons/geogebra/vector_projection.html

5/5 Scribe Post

2010-05-05T09:32:00.010-04:00

Today we started with a warm up involving vectors. The first question was to find the component form, magnitude, and direction angle for vector AB and CD, with given points A(1,1) B(4,-1) C(-5,3) D(-2,1) .
The component form of both the vectors was <3,-2> and the magnitude was . To find the direction angle you create an axis with the initial point as the vertex. The direction angle is then measured counter clock wise. The direction angle is then,, so the two vectors AB and CD are equal. This means that two vectors with the same component form are equal to each other.
Mr. O'Brien showed us the formula to find the component form:
Terminal Point - Initial Point. After this warm up problem we went over problem 59 from the homework. We found out that the component form can be found by , usin> where u was 7/2 for problem 59.

The second warm up question: given u = <2,1> and v = <-1,4>
a. find 3u
b. Graph u and 3u on Geogebra, What do you notice?
c. Repeat a. and b. for u + v
d. Repeat a. and b. for u-v
For this problem we discovered that vector addition is done "tip to tail". So when vector u, vector v and vector u+v are combined they form a triangle. When a vector is multiplied by a number, it is a called a "Scalar multiplication" and it lengthens or shortens the vector.
ex. <3,4> to make a unit vector in the same direction:

Quiz:
After we completed the warm up we discussed the upcoming quizes and tests and decided to review the warm up at the end of class. Next we reviewed the quiz we took last class. Mr. Obrien showed us how to solve problem 1 on the quiz using a calculator only, but wanted to make sure that we could do this problem without a calculator using the sum and difference identity. To solve problem 1 you need to use the sum and difference formulas, then cancel and simply the equation. For problem 2 from the quiz Mr. Obrien recommended that we draw the triangles to start this type of problem. Problems 1 and 2 could both appear on a non-calculator section of a test. Problem 3 you needed to use factoring then an identity to simplify the expression. On problem 4 you needed to remember that there were two answers, . Problems 5 involved using the Area of a triangle formula, A = 1/2 b x h or for this certain problem, A = 1/2 cbsinA. For problems 6 and 7 most people didn't have problems using the double angle formulas and the Law of Sines. The last problem, #8 gave people more trouble. It is important to use the correct fundamental identites.

Link for Wednesday, May 5th

2010-05-05T09:23:00.002-04:00

http://www.pa.uky.edu/~phy211/VecArith/index.html

2010-05-03T10:07:00.012-04:00

Today we started with a homework quiz.
Then we proved why

We used Pythagorean theorem for the right triangle:

and we got that:
Then we used Pythagorean theorem for the left triangle:

also we used to get
Then we substituted everything from the left triangle in the equation we got for the right triangle. So the final equation is:
It works with SSS and SAS.

The next part of the unit were vectors.
In math the vector is a segment with direction, also called directed line segment:
The first point of the segment is called initial point (A), and the last point is called terminal point (B). a, b are components of the vector -
The length is sometimes referred to as magnitude,
Using Pythagorean theorem we could write it as:
The angle of the vector, θ is called direction angle.

examples:
1)Find the component form for a vector with initial point (-2,4) and terminal point (3,1).
The answer is <5,>

2)Find the component form for and θ=45º
, so
, so
The answer is

The rest of the class we went over hw.

2010-05-02T21:44:00.002-04:00

Today in class we did a lot of things. We started with a warm up that asked us to find the triangle with these given sides and angle:
A=26º
a=5
b=8
This gave us an ASS (angle, side, side) case, which we know presents an ambiguous case. An ambiguous case provides you with information that you could use to create two different triangles. During this warm up we were asked to solve each angle and side of this triangle along with its area. Students could have solved for two different triangles with these given sides and angle. After the warm up we explored and proved the ambiguous case by constructing a visual of these possible triangles on Geogebra.

As you can see in the visuals there are two different triangles with values:
A=26º
a=5
b=8
This proves the ambiguous case.
We calculated the other possible sides and angles using the theorem that:

By Monday we are to prove that (when given SSS or SAS):

(and also find the largest angle when given SSS)

And for Bonus points we have the option to prove Heron's Area Formula (when given SSS) of:
, where s is the half perimeter.

Homework for 4/29

2010-04-30T20:11:00.004-04:00

Some of us didn't understand problems 41 and 43 from the previous hw. Could you please post them here? Thanks.
Petra

Links for Thursday, April 29th

2010-04-29T08:33:00.001-04:00

http://www.geogebra.org/en/upload/files/english/dtravis/ssa_ambiguous.html

http://home.comcast.net/~paulbirdsall/class/ambig.html

Scribe post, 4/27/10

2010-04-27T09:30:00.007-04:00

We started with a warm up where we had to
1. Solve on [0,2π)
sin2x-cosx=0
2. Find the exact value of cos105˚
3. Use the figure to find tan2u

We went over how to figure out if our answer is right when we finally get an answer.
For number 1
sin2x-cosx=0
2sinxcosx-cosx
cosx(2sinx-1)=0
so cosx = 0 and sinx = 1/2

for number 2
cos(105˚)

we then went over the Law of Sines which is and
we started deriving the law of sines

then we proved that they are all equal for all triangles

We also talked about the added bonus which is

we tried this on a random triangle from GeoGebra where (using AAS therom)
A=59.85˚
C=26.05˚
c=4.78 units

so B =180˚-A-C
B=94.1

so a = 9.41

b=10.86
for the last 10 minutes of class we did our homework

April 16 scribe post

2010-04-16T09:56:00.000-04:00

Mr. O' Brien reminded us to spend a solid hour on math homework, so that on quizzes we would not be stuck on the problems by not knowing what to do in the beginning as the first step.

We began class with a warm-up:

We were asked to attempt to graph this without technology. So...

This is what we would have gotten if it originally was a positive tan. However, the negative makes it more difficult.

Therefore...

This makes us able to graph this equation by hand.

After the warm up we went over homework problems. We covered #33,77,29,75,

While doing this we went over the identities that we needed. #75 is the most important question on the homework, and there will probably be a question like this on the unit test. Make sure that you know how to do this problem!!! Remember to draw a triangle to help you get through it. If you don't know how to do this problem yet, then go to the download and try to work through it until you think you have more of a handle on it, then try and do it by yourself until you know that you could do this problem by yourself on a quiz or test.

While still working on this problem 75 we started to learn to put the sin, cos, and tan answers into the calculator up on the board. Then, we checked all three of these on our own using our own calculator. The sin, cos, and tan were:

inverse sin(-4/5)
inverse cos(-3/5)
inverse tan(4/3)

Put them all into your calculator and you can see for yourself that they are correct, and that the inverse sin and the inverse tan equal the same value.

The last thing we did in class we all took out our quiz and the homework's it related to Mr. O'Brien came around to people individually to help us understand what we missed.

Our Goals were:
Correct Each..
Quiz questions
either on quiz or in notebook using HW #3,4,5

Class was only an hour because we have the Bunny Bowl later on today.

Collin will be the scribe for next class.

April 14 Scribe Post

2010-04-15T18:14:00.005-04:00

Class begin with more work on the trigonometric identities packet

sin2x = 2sinxcosx

cos2x = (cos^2)x - (sin^2)x
this can also be written as:
1-(sin^2)x - (sin^2)x
thus,
cos2x = 1- 2(sin^2)x
written solely in terms of cosine,
cos2x = 2(cos^2)x - 1

To derive the identity for tan2x:
tan(x+x)
= (tanx + tanx)/(1-tanxtanx)
tan2x = (2tanx)/(1-(tan^2)x)

Next, we derived identities for sin(x/2) and cos(x/2)
cosx = 1- 2(sin^2)(x/2)
2(sin^2)(x/2) = 1 - cosx
sin(x/2) = +/- sqrt((1-cosa)/(2))
sin(x/2) = +/- sqrt((1-cosa)/(2))

cosx = 2(cos^2)(x/2) - 1
2(cos^2)(x/2) = 1 + cosx
cos(x/2) = +/- sqrt((1+cosx)/(2))
cos(x/2) = +/- sqrt((1+cosx)/(2))

Finally, we derived an identity for tan(x/2)
(+/- sqrt((1-cosx)/(2)))/(+/- sqrt((1+cosx)/(2)))
= +/- sqrt((1 - cosx)/(1 + cosx)) * (sqrt(1-cosx))/(sqrt(1-cosx))
= +/- sqrt(((1 - cosx)^2)/(1-(cos^2)x))
= +/- sqrt((1-cosx)^2/(sin^2)x)
= (1-cosx)/(sinx)
tan(x/2) = (1-cosx)/(sinx)
This concluded the work we did on the trigonometric identities packet [sorry if it's hard to visualize, but I couldn't get the online equation editor's html code to show up on the blog for some reason].

HW Questions We Reviewed:

13.
cos2x - cosx = 0
cos2x = cosx
(cos^2)x - (sin^2)x = cosx
cos^2(x) - (1 - (cos^2)x) - cosx = 0
2(cos^2)x - cosx - 1 = 0
(2cosx + 1)(cosx - 1) = 0
2cosx + 1 = 0
x = 2π/3, 4π/3
or
cosx - 1 = 0
x = 0

49.
sinu = 5/13, π/2 <> cos u = -12/13
sin(u/2) = sqrt((1-cosu)/2) = sqrt((1+12/13)/2) = (5sqrt(26))/26
cos(u/2) = sqrt((1+cosu)/2) = sqrt((1- 12/13)/2) = (sqrt(26)/26
tan(u/2) = (sinu)/(1+cosu) = (5/13)/(1-12/13) = 5

19.
6sinxcosx = 3(2sinxcosx) = 3sin2x

25.
tanu = 3/4, o <> sinu = 3/5 and cosu = 4/5
sin2u = 2sinucosu = 2(3/5)(4/5) = 24/25
cos2u = (cos^2)u - (sin^2)u = 16/25 - 9/25 = 7/25
tan2u = (2tanu)/(1-(tan^2)u) = (2(3/4))/(1-(9/16)) = (3/2)(16/7) = 24/7

11.
4sinxcosx = 1
2sin2x = 1
sin2x = 1/2
2x = π/6 + 2πk
x = π/12 + πk
x = π/12, 13π/12
or
2x = 5π/6 + 2πk
x = 5π/12 + πk
x = 5π/12, 17π/12

23.
sinu = -4/5, π <> cosu = -3/5
sin2u = 2sinucosu = 2(-4/5)(-3/5) = 24/25
cos2u = (cos^2)u - (sin^2)u = 9/25 - 16/25 = -7/25
tan2u = (2tanu)/(1 - (tan^2)u) = (2(4/3))/(1 - (16/9)) = (8/3)(-9/7) = -24/7

We finished off class with the Chapter 5 Quiz #2

Scribe for next class will be Nate

April 12 Scribe Post

2010-04-12T09:39:00.009-04:00

We began class with a warm up. In our warm up we did part a of the Sum, Difference, Double, and Half Angle Identities.
First, we discovered how we could write a sin graph in terms of cosine, which was
sinx=cos(x-pi/2)
this can also be cos (pi/2-x). it is complementary.
To write cos in terms of sin:
cosx= sin (x+pi/2)
These relate to the confunction identites, but are not the same.

Next, we figured out how to write cos(-a) in terms of cosa. We know that cos is even, so cos(-a) does not equal -cosa.

We then looked at #1 on the same sheet.
We drew in three angles. a,b, and a-b. We then labeled four points. Point A was (1,0), point B was where angle b intersected the circle (X1 ,Y1,), point C was where angle a-b intersected the circle (X2, Y2,), and then point D is where angle a intersects the circle (X3, Y3,).

Then, on #2, we figured out that by using pythagorean theorem and the equation of a circle, that for our points B, C, and D, x^2 + y^2 = 1.

#3 asks why X1= cosb and Y1 = sinb, which is because cos =x value on the unit circle and sin = y value on the unit circle. From that, you can derive the values.

They are points on the circle with points

#4 asks why arcs AC and CD are the same length, which is because they have the same angle and the same radius, so the arc length is the same.

COSINE
In #5 we must use the distance formula, which in our case, is square root ((X2-1)^2+Y2^2). On its own, the distance formula is: d= square root((X2-X1)^2+(Y2-Y1)^2).
Since one of our points has an X value of 1, and Y of zero, we were able to insert these into the first distance equation which is catered to our situation (but does not work if you aren ot on a unit circle!)
Since we are trying to find a formula for cos(a-b), we could put this in for the X2 value.
So, if we want to see if AC and BC line segments are the same length, we would put these two equal to each other, getting:
X2^2 - 2X2 + 1 +Y2^2 = X3^2-2X1X3+ X1^2 + Y3^2-2Y1Y3 + Y1^2.
We can take out all our value that equal one, which would be all the X^2 + Y^2 or just 1. We have 2 of these on either side, so we can -2 from each side.
We then have
-2X2= -2X1X3-2Y1Y3
After dividing each by -2, we get
X2= X1X3+Y1Y3,
which is the same as
cos(a-b)= cosa*cosb+sina*sinb

This is called the "mother" of all identities.

We can also say that cos(a+b) is the same as cosa*cos(-b) + sina*sin(-b) (by using the mother of all identities) and can then be written as
cosa*cos-sina*sinb

SIN
Now we want to get the identity for sin (we just got the identity for cos.)

Since we know that we can rewrite sin in terms of cos, we can write sin(a-b) as cos((a-b)-pi/2).

We then want to regroup the terms inside the cos function. This gets us
cos(a-(b+pi/2)).
Then, using the mother if all identities again, we will get
cosa*cos(b+ pi/2) + sina*sin(b+ pi/2).

Since we know how to break apart a cos we can turn the cos(b+pi/2) to cosb*cos(pi/2) - sinb * sin(pi/2),
so our whole function is
cosa* cosb*[cos(pi/2) - sinb * sin(pi/2)] + sina*cosb

We can reduce the cos and sin inside the [] to 0-1 because of the location on the unit circle. So the value in the [] is just -1.

So, this = cosa (-sinb) + sina* cosb
which =
sina*cosb - cosa*sinb.
SIN(A-B)= SINACOSB - COSASINB
To find sin (a+b), we will use both sin(a-b) and cos(a+b) as reference to reduce the process.
SO,
sin (a+b)=
sin(a-(-b))=
sinacos(-b)-cosasin(-b)=
sina*cosb +cosa*sinb

TANGENT
tan(a-b) can be found by remembering tan=sin(a-b)/cos(a-b), so
sin(a-b)/cos(a-b)=
sinacosb-cosasinb/ cosacosb+sinasinb.

This would be fine, but we want to find this in terms of tan, instead of sin and cos.

SO, we must use a FuFoo.

sinacosb-cosasinb/ cosacosb+sinasinb * (1/cosacosb/1/cosacosb) (this is the FuFoo).
Some values cancel out, so we are left with

tana-tanb/ 1+ tana tanb.

SO, TAN (A-B)= TANA-TANB/ 1+TANA TANB

To find tan (a+b), we will use the same trick as in finding sin(a+b) and cos (a+b), replacing the b with a -b. So
Tan (a+b)= tana +tanb / 1-tana tanb

After this, we went over a few problems from the homework (p. 404).
Problems we went over: 19, 29, 37, 47, 53, 65, 71:

19.
13pi/12
sin (13pi/12)
Change to "nicer" values, so...
sin (3pi/12 + 10pi/12), these reduce to
sin (pi/4 + 5pi/6)
sinpi/4 cos 5pi/6 + sin 5pi/6 cos pi/4=
(sqrt. 2)/2 * (sqrt. 3)/2 + (sqrt. 2)/2 1/2=
(sqrt. 2 - sqrt. 6)/4

29. tan 2x + tan x/ a+tan 2x tanx

By using the mother identity, we can find that
= tan(2x+x), which = tan3x.

37.
sin (u+v) = sinu cosv +sinv cosu
sinu = 5/13
cosv=-3/5
u=arcsin 5/13
v=arccos -3/5
u and v are both in quad. II, and we must turn arcsin into pi - arcsin so it will be in quad. II instead of quad. I.

we will then have:
(5/13)(-3/5) + (4/5)(-12/13)= -63/65

47.
tan (u-v) = tanu -tanv/ 1+ tanutanv
sin u = -7/25 cos v = -4/5
= (7/24 - 3/4)/[ 1 + (7/24) (3/4)]
= (-11/24) / (39/32)
= 44/117

53.
cos(arccosx+arcsinx)=
cos(arccosx) cos(arcsinx)-sin(arccosx)(arcsinx)
= x (sqrt 1-x^2)- (sqrt 1-x^2)x
= 0

65. cos (3pi/2 - X)
cos 3pi/2 cosx+ sin 3pi/2 sinx
= 0(cosx)+ -1(sinx)
= -sinx

71. cos (x+ pi/4) - cos (x-pi/4)= 1

Simplifies to
1 = -2 sin(x) (sqrt.2)/2
1= -sqrt. 2 sinx
sinx= 1/(sqrt. 2)
x= 5pi/4, 7pi/4

After we went over the homework questions we began to look at sin2a and cos2a.

Sin2a:
= sin (a+a)
= sinacosa + sinacosa
= 2sinacosa

Cos2a:
= cos (a+a)
= cosasina cosasina
= cos^2a - sin^2a
= 1-sin^2a - sin^2a
= 1- 2sin^2a
= cos^2a - (1-cos^2a)
= 2 cos^2a -1

Homework Quiz next Class!

Scribe for next class is Kyle.

April 8th

2010-04-12T08:33:00.007-04:00

At the start of today's class Mr. O'Brien gave us two warm up problems to do, to be solved by hand and then checked using technology. Here's the first problem:

After the warm up problems we went over questions people had from the homework. Number 73 is below:

Next, Mr. OB handed back our first quiz on unit 6! In general, I think most people did fairly well. Remember the two identities on the back are very similar because they use the same identities. If you understand one you should be able to figure out the other. Also, if you still have questions about the information we've covered so far, look over the sections in the textbook or come in to see Mr. OB!

Finally, we took notes on a new set of identities. These are called the sum, difference, double and half angle identities.

Cos(a-b)=Cos(a)Cos(b)+Sin(a)Sin(b)
Cos(a+b)=Cos(a)Cos(b)-Sin(a)Sin(b)
Sin(a-b)=Sin(a)Cos(b)-Cos(a)Sin(b)
Sin(a+b)=Sin(a)Cos(b)+Cos(a)Sin(b)

You can also find these identities on the front inside cover of your textbook!

Homework p. 404/5, 19, 29, 33, 37, 47, 53, 63, 65, 71

The scribe for next class is Sophie.

Homework question

2010-04-08T03:53:00.001-04:00

So I understand problem 55 up until you come out with sin x = {3/4, 1/3}. However, I simply did arcsin(3/4) and arcsin(1/3) and came out with x?{.8481,.3398}. However, the book showed two other answers that I should get, and I understand that they are also points on the arcsin graphs. However, I don't understand why we use two of them on each graph. Shouldn't the arcsin function only have one value for x? And even if it did use more than the one, then how would I know which to use when there are infinite points on the arcsin graph? Furthermore, how would I calculate the other value? It gives ~2.2935 as one of the values, and if I enter in sin(2.2935), i get ~.75. But I don't know how to find that without having it in the book. Thanks!

-Molly

Scribe Post from Daniel Mynick

2010-04-06T10:19:00.003-04:00

Please click here for the scribe post.

Quarter 3 projects

2010-04-06T09:48:00.000-04:00

Please take the time to look at the one or two quarter projects from your classmates:

http://math-ob.wikispaces.com/Pre-AP+Calculus+Quarter+3+Projects+2009-10

While I was impressed with them all, Annie's in R3 and Andy's in W2 are particularly well done.

Friday, April 2, 2010

2010-04-06T08:51:00.000-04:00

We spent a good deal of class working on the warmup problems. Basically, it was the application of the Fundamental Trigonometric Identities. The primary benefit of the exercise was that it gave us a chance on making our proof format more acceptable. Format work included using the equals sign in a transitive manner, and making sure everything was thoroughly explained. If you’re not evidently applying a property, it’s best to leave a side note for thorough explanation. For example,

If cotx + csc= cos/(sin^2), you couldn’t make the leap to “cos/(sin^2)=cos/(sin^2)” without first explaining your manipulation of cotx and cscx.

On concept that came up several times throughout the warm-up was the technique of multiplying by fufoos to get lowest common denominator. This can be particularly useful with complicated fractions.

After we had learned to write proofs in a more explanatory manner, we started work on the homework problems.
While working on the homework, there was some reviewing of how to derive the other pythagorean identities. For those who need a reminder, just divide the values on both sides by (sin^2)x or (cos^2)x. Basically, working on the homework solidified strategies we had previously gone over, like multiplying by fufoos.

Then, we worked on Solving Trig Functions. Instead of trial and error, we worked with technology to solve the equations. Note that some of the solutions to these trig functions looked similar to the format used in our Francois worksheet.

At the end of the class, we briefly talked about future algebraic solving.

Andy Schleb's scribe post

2010-03-31T10:08:00.004-04:00

We started the class with the Supercorrection Follow-up test. That took the first 30 minutes of class. After that, Mr. Obrien put up 7 problems from the homework on the board. He let us go up to the board and do them, and then we went over each one.

A few key things:

• Use pythagorus to convert sin to cos (sin^2+cos^2=1), so (sin^2=1-cos^2, and vice-versa)

• Remember arithmetic (multiply/dividing fractions, equalizing denominators)

We then began work on a worksheet with four problems on it, to try and understand proofs. The goal was to turn the left hand side of the equation into the right hand side.

Finally, we had a class challenge in which we were given sections of trigonometric proofs. We had to arrange the in the correct order. It was a fun class!

Scribe Post 3.25.10

2010-03-25T10:11:00.007-04:00

We worked on our Quarter 3 projects for 35 minutes at the beginning of class.

We went over the fact that we have a regular textbook homework assignment assigned today, but that on Monday even though juniors won't have class because of the science exam, our homework assignment will be to finish our final draft of the project. That is due on midnight on March 31. March 31 is also our supercorrection follow-up test.

Today we started Unit 6, which is continuing on with trigonometry. Mr. O'Brien put an equation on the board, and asked us to solve it either by graphing or by using a table:

We decided that x is all real numbers, except π/2 + πk, k∈Z

We then started working on proofs, and proved that the two sides of the equation were equal.

We looked in our textbooks at page 374 (the beginning of chapter 5.1) at the list of fundamental trigonometric identities. This included the reciprocal identities, quotient identities, Pythagorean identities, cofunction identities, and even/odd identities. I won't post them here because you can find them in your textbook. We went over the fact that:

Mr. O'Brien explained that

We went over the identities, and then looked at the examples in the book.

Ex. 1: Mr. O'Brien pointed out that the book doesn't use a triangle, but rather uses the identities. He said that he doesn't really care if, going forward, we use triangles or identities.

Ex. 3: Mr. O'Brien suggested that it could be easier to substitute a variable such as u for tan θ to factor something like this.

Scribe post 3/17

2010-03-17T15:42:00.003-04:00

Today we got our tests back, reviewed question 9, and spent the rest of class doing supercorrections. Next class we will also have time to work on them, be ready to turn them in on Tuesday the 23rd. The homework is to work on supercorrections. Remember that our rough draft's of our quarter 1 projects are due on Tuesday the 23rd as well.

Weds. March 10, Last Day of Unit 5

2010-03-10T16:30:00.010-05:00

Today, we began class by finding the equations for two mystery graphs. The first one had the equation which caused the graph to look like this:

The second graph's equation was which caused the second graph to look like this:

After discovering the equations for the two mystery graphs; we turned our attention to number 21 and 22 of Francois and his Pedometer. For number one we noted that =. After evaluating number twenty two we discovered that his set for all distances was 2.42 + 2k where k is an integer but also at 3.86 + 2k where k is also an integer.

Following the warm-up, our class reviewed Quiz 4 of Unit 5. The two numbers that we paid special attention to were number 1 and 4. For number 1, we noted that if you take and you added you would get , but if you added another you would end up with . This means, that all you have to do next is find the sin() which is . For number 4, one thing to keep in mind is that in functions, there is an opposite order of operations. This means that the easiest way to solve the problem is by finding your a, b, and c value then plugging them into a equation which looks like this: , the next step is to distribute your which makes a=2, b= and c=-.

Once we finished going over the Unit 5 Quiz 4 and any questions students had trouble on, we took the review quiz. The quiz will only count towards your quarter grade if you want it to. The quiz questions were the exact same as the ones on the previous quizzes. Next class, there will be the unit test covering chapter four. Mr. O'Brien suggested to students that they should challenge themselves while studying for the test by working on more complex and conceptual questions than the basic review.

The next class Scribe will be Tyler.

Homework question P. 359 #33 B

2010-03-09T17:38:00.002-05:00

Hey Mr. O' Brien,
I am really confused about 33 B on page 359. I looked at the answers you have posted, but I was still really confused. I don't understand all the different aspects of the work to get the answer, like the B, Y, C, D, and other variables.

Scribe post

2010-03-08T09:41:00.004-05:00

I'm sorry this is late but I've been having troubles with this posting thing.
To start the class we did a warm up where we had to evaluate

cos^-1(√3/3)
a) you would be looking for an angle and since you are looking for an angle where the inverse cos is a -√(3)/2 then it would be 150˚it is also possible to get an answer of 5π/6 algebraically you could do x=cos
cosx=-√3/2
sin(cos^-1 √5/5)
b) in this one the answer will be a ratio ø=cos^-1 sqrt(5)/5
cosø=sqrt(5)/5 sinø=(√20)/5

we also had to evaluate the graphs of
y=arscin(x-1)
a)y=arcsin(x-1) this is just a sin graph only with the restricted domain to make it a function and the negative 1 makes it move 1 unit to the right and the minimum and maximum is π/2
y=tan(3x-6/π)
b) you can set this up as an inequality because the period of tan is π so -π/2<3x-π/6<π/2>2π/9 y="sec^-1" secy="x" cosy="1/x" y="arccos^-1(1/x"

Consider Engineering

2010-03-08T09:37:00.001-05:00

Great opportunity from University of Maine for this summer:

http://www.mainepulpaper.org/considerengineering/considerengineering.htm

Thursday, March 4 Class

2010-03-08T09:00:00.005-05:00

We went over quiz, noting several things...

First, when Mr. O’brien says to graph both and angle and its reference angle in standard position, the initial sides of both angles must be on the x-axis. Second, much as sin(90º-θ)= cosθ, sec(90º-θ)= cscθ

After going over the quiz, we went on to discuss the inverse trig functions.

y=sin^-1x

y=cos^-1x

y=tan^-1x

Notation problems: sin-1x does not equal (sinx)-1

Because of this potential confusion, there are other notations to represent the inverse functions:

arcsin (x)
arccos (x)
arctan (x)

We saw that on grapher, arcsin(x) isn’t a function. On our graphing calculators we saw the inverse trig function is a portion of the entire function. We consider the inverse trig functions to be a collection of all the points possible while still being a function.
The same applies to Cosine, which doesn’t pass the horizontal line test any more than the Sine function does. A single Tangent wave passes the horizontal line test, and that is all that’s graphed of the arctan function.
Of course, all three graphs look different from the originals, since they are inverse functions, and therefore have reverse (x,y) coordinates.

Here are links to the three inverse functions. This should help make their domains and ranges pretty clear.

http://www.math.rutgers.edu/~greenfie/mill_courses/math151a/gifstuff/arcsin.gif

http://www.intmath.com/Analytic-trigonometry/arccosx.gif

http://upload.wikimedia.org/wikipedia/commons/f/f6/Arctan_plot_real.png

arcsin (x)
Domain: [-1, 1]
Range: [-π/2, π/2]

arccos (x)
Domain: [-1,1]
Range: [0, π]

arctan (x)
Domain: [all real numbers]
Range: [-π/2,π/2 ]

Use of inverse functions: We can plug in coordinate points along the unit circle, and the inverse function gives the angle. It gives angles in quadrants where that particular function (sin, cos, tan) is positive.

Then we took the quiz, which brought us to the end of class.

According to the tags on the side, Collin has only done one scribe post, so now it's his turn for next class.

Friday February 26th Class

2010-03-03T18:52:00.002-05:00

Today in class we started off by taking the quiz.
After the quiz we went over some questions on the homework. We did problems 27 and 55.
27.

To graph these two functions we first looked at a standard sin graph.
http://fooplot.com/index.php
Then we took the f(x) function and altered the graph by moving the Y values of 1 to -2, and the Y values of -1 to 2. (Red)
We added on to that axis the g(x) function onto the same graph. This transformed the original sin graph by changing all the Y values of 1 to 4 and Y values of -1 to -4. (Blue)
file:///Users/student/Desktop/sin.tiff
The period is still 2π, and the symmetry is odd, as it is for all sin graphs. This means sin(-x)=-sin(x)
The transformation of these two functions changed the amplitude of the sin function.

55.
We then changed this to to make it simpler to graph.
This graph looked like: file:///Users/student/Desktop/cos.tiff
The period was 4π and the amplitude was changed, along with the graph being condensed. This graph originally (before being transformed) had was even, being symmetrical across the Y axis as all cos graphs originally are.

After reviewing the homework we moved on and looked at the graphs of the trig functions. We noticed that the sin graph and cos graph were very similar, but just shifted over to the right a bit. Both had a domain of -1 to 1 and a range of all real numbers.
We spent most of the rest of class playing with these graphs. We also looked at the graphs of the other trig functions as well and looking at the periods and amplitudes of the graphs.
We also looked at the tan graph which looks like:file:///Users/student/Desktop/tan%20graph.tiff

The csc graph which looks like:file:///Users/student/Desktop/csc%20graph.tiff

And the sec graph which looks like:file:///Users/student/Desktop/sec%20graph.tiff

But we did not get into why they are the way they are. That will be learned later and is in Dan's scribe post of class on 3/2.

Scribe Post: March 2, 2010

2010-03-02T09:38:00.005-05:00

Go to http://docs.google.com/View?id=dfhptqmz_194dd56p3dn view the scribe post.

scribe post, petra, trigonometry

2010-02-24T10:06:00.010-05:00

We started the class with a warm-up quiz on quizlet. Then we worked on a few problems: example:
We went over hw problems we didn't know.
83)a which is so the answers are:
19) 0"> from the function value we get that
We decided that it's in the IV quadrant. We calculated hypotenuse using Pythagorean theorem. The answer is:

27) 2x-y=0, quadrant III we made a slope -> y=2x and found the sides of the triangle. Then using the sides of the triangle found all six trigonometric functions.
Then we went on the site for a Ferris Wheel. http://maine.edc.org/file.php/1/AssessmentResources/FerrisWheelUnitCircle32_L.html
We tried to make a graph where height was on y-axis and time on x-axis.
Then we used a function
We found it's domain: all real numbers
and range: [-1, 1]
Then we made a graph where f (θ) was on y axis and θ was on x axis.
We then used GeoGebra and made a graph for g(θ) = cos (θ), where we used different values for θ in radians.
At the end we used a function:
to define amplitude of sine and cosine curves -> amplitude = |a|
and to define a period of sine and cosine curves ->

Links for Wednesday, Feb. 24

2010-02-24T10:02:00.002-05:00

Warm-up quiz
Ferris wheel applet
Transformations of the sinusoid wave

February 22

2010-02-23T21:03:00.011-05:00

Today in class we discussed the visual location of the tangent, sine, cosine, and cosecant on the unit circle. We played around with this idea using Geogebra and Mr. O'Brien drew up some notes on the board. Here's a nice visual I found online:

Next, we went over the second unit four homework quiz. Mr. O'Brien reminded us to make sure our calculators are in the correct unit (degrees/radians) when you answer a problem.

Some other concepts we reviewed were converting angle measurements to decimal degree form (and vice versa). Here are some examples:

Decimal Degree Form to Angle Measure:
87˚ 18' 30"
87 + 18/60 + 30/3600
= 87.308

Angle Measure to Decimal Degree:
-2.58˚ (times .58 x 60)
= -2˚ + 34.8 (times .8 x 60)
=-2˚ + 34' + 48"
=-2˚ 34' 48"

Mr. OB also said that a helpful formula to remember is that the Area of a Sector = , which was especially useful in solving problem 4.

The remaining time left in class was spent working on new HW:
* p. 318/1, 3, 7, 13, 15, 19, 21, 23, 27, 41, 53, 61, 81, 83, 89, 91
*Read the last two pages of the six page notes handout to learn where the sine function gets its name.
*Have a think about the quarter project
*Keep working on your memorization of the common radian-degree conversion and the 198 trig values

I noticed that the trigonometric identities never made it up onto the blog, so I snagged Kayla's from the Red day class in case anyone needed them.

Identities:
Reciprocal: sinθ=1/cscθ cscθ=1/sinθ
cos θ=1/secθ secθ=1/cosθ
tanθ=1/cotθ cotθ=1/tanθ

Quotient: tanθ=sinθ/cosθ
cotθ= cosθ/sinθ

Co-Function: sinθ=cos((π/2)-θ)
cosθ=sin((π/2)-θ)
secθ=csc((π/2)-θ)
cscθ=sec((π/2)-θ)
tanθ=cot((π/2)-θ)
cotθ=tan((π/2)-θ)

Pythagorean: sin²θ+cos²θ=1 then divide both sides by a sin²θ
which makes it: 1+cot²θ=csc²θ
and also: 1+tan²θ=sec²θ

Remember that there's a homework quiz on Friday! The scribe for next class is Petra.

Links for Thursday, Feb. 11

2010-02-11T06:35:00.002-05:00

Quizlet.com for 98 flash cards of the common trig values

Quizlet.com for all 198 common trig values!

sine function of any angle applet

cosine function of any angle applet

our unit circle applet

Quarter 3 Project

Scribe post 2.5.10

2010-02-09T09:36:00.001-05:00

Well today we started with a small class, which was very surprising. However, as the class went along, more people filed in. AT the start of the class we had a fun warm-up in which we attempted a quizlet and Mr. Obrien tried to stump us BUT HE DIDN'T. We are much better than his expectations. After our warm-up, we began work on going over problem 108 on our homework.

Notes on Trig. Functions

We then conducted an experiment using this neat function program on the internet.

It was a nice visual!

Finally, Mr. Obrien allowed us to do a cosine version of the above applet:

Scribe Post 2.9.10

2010-02-09T09:34:00.012-05:00

We started the day with a warmup using the trig basics Quizlet. During the class, Mr. O'Brien wants to talk about patterns, tan π/6 vs. tan π/3, sec 5π/3, quadrants, reference angles, even/odd, periodicity, identities: reciprocal, quotient, pythagorean, co-function. We went back to the applets (found here: sine box, cosine box, and unit circle).

We used the sine box to go over finding different values without a calculator. Mr. O'Brien reminded us the sine value is the y and the cosine value is the x. He also told us that the x values (cosine) are positive in Quadrant I and Quadrant IV, and that the y values (sine) are positive in Quadrant I and Quadrant II. He also told us that the tangent values are positive in Quadrant I and Quadrant III. Mr. O'Brien gave us a mnemonic to remind us which values are positive: All Students Take Calculus. This tells us that in Quadrant I, all values are positive. In Quadrant II, sine values are positive. In Quadrant III, tangent values are positive. And in Quadrant IV, cosine values are positive. Mr. O'Brien gave us a table to show patterns that help us remember some of the values:

After this we went over the difference between tan π/6 and tan π/3.

Then we moved on to the all 198 trig values Quizlet and discussed identities. Andy showed the which trig functions are which, copied below:

We went over the reciprocals of trig functions. You can find a table of the trigonometric identities here (it includes reciprocal, Pythagorean, quotient, and co-function identities, as well as others that we don't need). Note that it uses an upsilon (υ) instead of a theta (θ). We worked through a few values, such as the ones below:

Example: If we have a value like sec(135˚), we know that it's positive because of all students take calculus. We know that the reference angle is 45˚, and that it corresponds to cosine. So, we know that it's the reciprocal of cos(45˚) which is -√2.

Mr. O'Brien told us that if we want to use our calculator to evalute something such as secant, we have to enter it as cos(x)^-1. He told us that cos^-1(x) is not the same as sec(x). He also told us that

and that you have to enter the latter in a calculator, as it won't allow you to enter the former.

In the last two minutes of class, we went over the homework problems. For #29, we just had to recognize that sin 5π=sin π. For #43, he reminded us that we had to change our calculator from degree to radian mode. To do this, simply hit the [MODE] button on the calculator, and select radian. Katherine brought up the point that if we have our calculators in degree mode, then we can simply enter sin π/4 into the calculator as sin (√2/2).

Links for Tuesday, Feb. 9

2010-02-09T06:18:00.001-05:00

Quizlet.com for 39 trig basics flashcards

Quizlet.com for 98 flash cards of the common trig values

Quizlet.com for all 198 common trig values!

sine function of any angle applet

cosine function of any angle applet

our unit circle applet

Friday, Feb. 5th links

2010-02-05T07:53:00.001-05:00

Quizlet.com for the common radian-degree conversion values warm up

six trig function definitions in quizlet.com

sine function of any angle applet
cosine function of any angle applet
our unit circle applet

HW:

p. 299/1-51 odd
Keep working on your memorization. Here are some more resources you can use:

Feb. 3 Scribe Post

2010-02-04T15:55:00.003-05:00

We started off the class with a review on angular and linear speed.
The example of a bicycle wheel was used.
A 29 inch wheel at 2 revolutions a second.
Linear Speed?
Take into account that distance = speed * time

182.2 (inches/second) = 10.35 mph

note: Stoichiometry can take care of all unit conversion before you really start the problem:

Angular Speed?

Additionally, it was proven that: radius * angular speed = linear speed, which will be useful for problems in the future.

We finished up class with the first Unit 4 quiz in Ms. Ferlauto’s room.

Links for Monday, Feb. 1

2010-02-01T06:49:00.001-05:00

The interactive unit circle.

The quizlet flashcard site.

Homework problems are posted on the class website/ical: http://math-ob.wikispaces.com/Calendar+Pre-AP+Calculus+White.

Jan. 28 scribe post

2010-01-28T10:54:00.000-05:00

We started class by going over the homework which was the Francois and his Pendometer sheet. We went over question #2 which was the first graph. We learned that it was periotic, which is how long it takes to repeat, in this case it was 8 units. There didn't seem to be a lot of questions from the class on these first graphs. Next, we went over #6 c and looked at x(1362). To do this you divide: 1362/8 then find the remainder. The next problem was #9, and here there seemed to be more problems for the class. I didn't fully understand this problem. I think the k as a variable threw me at first. I didn't realize that you must take the smallest non negative number and then add k. Many people did this in different ways such as writing it in sequent notation. Mr. O'Brien said it was fine because it was a homework, but from now on we should write it as set notation, which we will learn more later on in the unit. Next on the list was #11, and we learned that it could be and infinate amount of answers. Dan asked a question about k∈Z. And, the answer was that Z is the set of integars, and ∈ is the element. When I was doing this homework I to was confused on what this meant by this, but after this discussion I know what is meant by it. We skipped down to to the last page because there weren't any questions , and the last page is where it got more complicated. π/4 is half of π/2, using this and drawing a 45,45,90 triangle in the circle to find what 1/8 of the circle is and it will make it easier to solve question #17. Next we learned what FuFOO is which is funny form of 1. Did all you guys understand all this on the last page before today's discussion? because I know that I didn't. For question 18 there was problems as well. Again we took the circle and divided it into fourths, then drew a 30,60, 90 into the circle, and found out the length of the sides my looking at the ratios.
Fraction of Circumference:
30/360 * 2π
1/12 * 2π
π/6

For # 21 and 22 Mr. O'brien said to hold off on them.

Next we took out our laptops and used Geogebra, and he handed out a packet of notes labeled Introduction to Trigonometry Notes . These will be all of our notes for the next couple of days. People may want to look over these and make sure that they are comfortable with all of this information.

Using Geogebra: We first made an angle using a ray. We can't use a line because a line goes on forever. Therefore use a couple rays to make an angle. Select the one point, then the vertex, then the other point to measure the angle. To change the angle click on a point and drag it to change the measurement of it. When measuring one ray is called the initial and the other is the terminal. It is always measured from initial to the terminal. It is possible to go past 360 degrees for an angle. We learned that we can't break sin. Its domain is all real numbers. Standard position is what we next learned but I don't think I fully really understand what this is... I think you measure from right to left.

Radian Definition: θ = arc length/ radius

To make an arc we first select the center then the point on one ray, then the point on the other ray. This is after going up into the tool bar and finding the right selection to make arcs.

180 degrees = π rads which works out with Francois. 90 degrees = π/2. These answers were our answers in the Francois problems as well.

On the blog there are two links under the homework for next class that would be good to look at. The first shows a circle with points that you can quiz yourself on. Also there is a link to quizlet for flashcards.

Collin is the scribe for next class.

Class Thursday, Jan 28

2010-01-28T07:47:00.001-05:00

Trig intro: U4 intro to trig.pdf (hard copy in class)

HW:

Do p. 290/1-69 odd (I don't want this to be busy work- if you feel that you learn best by just doing one from each section, then feel free to do so)
Memorize the common radian-degree conversion: this flashcard site may help you to quiz yourself and this circle will help you visualize the angles (turn off the coordinates if they get in the way)

Tuesday, Jan 26th Scribe Post

2010-01-27T12:29:00.001-05:00

We began by going over the midterm exam, section a. Congratulations to Sophie and Petra on grabbing the top two scores. We went through each problem one at a time. Most of the first two pages can be solved easily using algebra or the calculator, and the majority of the class got these correct. We went over #5 in detail, since only a third of the class got it correct. We first looked at it graphically. 3100 is the y-intercept, and we are looking for where the graph reaches the y-value 6200. Algebraically, we found K, then we were able to plug the entire equation into the calculator. Next, we tested the different answers as y-variables, finding 44.3 to be correct. Questions six through eight were correct for the majority of the class. On section B, nine and ten were overwhelmingly correct. Most of the class missed #11. 12- 17 were answered correctly by most of the class. #18 was more difficult. #20 was also quite difficult.

Now to second semester. We will be studying trigonometry. Sin, cos, tan, and the inverse of each of these. We will look at a function such as f(x)= sin x

We will study certain types of triangles, such as the 45, 45, 90, or isosceles. Triangle side lengths of a,b, and h. h= a multiplied by the square root of 2.

Another type is the 30, 60, 90 triangle. We can think of this triangle as half of an equilateral triangle. Triangle sides of a, b, and h. a=1, b=square root of 3 h=2

Brief review of circle properties. To find arc length, given radius and angle. C=2(pi)(radius). Take the ratio of the angles, angle/360 multiplied by the circumference. This will give you arc length. Our homework is the Francois Pedometer packet. Nate will be the scribe next class.

A great read

2010-01-27T05:16:00.001-05:00

Heading off to an elite school after CHRHS? You should definitely read this article:

http://www.theamericanscholar.org/the-disadvantages-of-an-elite-education/

Enjoy!

Mr. O'B

Class Tuesday

2010-01-25T15:19:00.001-05:00

Individual first semester reflection

Group advice to a new student

HW:

Course methodology: take another look as we start the second semester
Finish Francois and his Pedometer
Check your Francois answers

Revision day

2010-01-14T06:17:00.003-05:00

Please fill in this feedback form.

Here is the answer sheet for the midterm.

Use the suggested practice problems from the midterm revision guide (p. 276).

Scribe Post

2010-01-12T09:35:00.009-05:00

Today we reviewed the Midterm Study Guide to start out with. OB explained what the exam will look like (25 multiple choice questions), and when it will be (2nd period Tuesday). Logically, we should have 3 minutes per question, and 5 extra minutes. We'll have Chapter 1, 2, and, as well as Section 9.1-9.3 which we just worked on. We'll have calculator for some portions, and some without. OB explained how the answer sheet will work. We'll have to rank the questions, in order for which we think is most likely. We'll get 8 points for a first choice being correct, 4 points for a second choice being correct, 2 for a third, 1 for a fourth, and none for a 5th. Hopefully, we should have at least a point on every question, meaning that we were able to identify which one was wrong every time.
OB gave us problems that we can use to review for the mid-term. We can bring in one 3x5 card, with anything we want to use, except for examples with actual problems in them, and they have to be in our own handwriting. We can also get extra points from out cards if we are on the 'border' or changing our grade higher. We then calculated fake grades, with Q1=85, Q2=83, and Exam=69, with a semester grade of 79, etc...
After we played around with our imaginary grades, we got our Homework, which is our "Sequences & Series Practice" Sheet. All we have to do is do the Sheet, and the homework at the bottom for next class. We reviewed questions 19, 29, 53, 57, 79, 63, 77, 73, 83, and 89 from last class's homework. Most of this was review, but we introduced another factor to a previous equation. When we are dealing with, we have to include, If .
Otherwise we should use .
We also got the formulas that we need for the midterm:
Arithmetic Sequence Formulas:
,
and .

Geometric Sequence Formulas:
,
,
and .

Next Time's Scribe is Nathan.

HW and midterm revision guide

2010-01-12T06:07:00.001-05:00

Midterm exam revision guide

HW

Sequences & Series revision sheet
Be prepared for a homework quiz covering all Unit 4 homework, including revision sheet (time to ask questions before the quiz)
Organize Unit 4 homework to be submitted by 2:15 Friday

Scribe Post 1/8/10

2010-01-08T09:26:00.004-05:00

At the beginning of class people had questions with the homework problems at the end of the assignment using the sum of the first n terms of any arithmetic sequence formula, #67, 69, 71, 85. We started with the warm-up which was doing the half-sheet of arithmetic sequences and series which was passed out to us last class. Mr. Obrien explained how make a table with arithmetic sequences to find the common difference. The graph of a arithmetic sequence has a linear graph, y = mx + b. He also reminded us to always check our answers for n by simply testing it.

Mr. Obrien showed how to solve the nth term without using the formulas, which was much quicker. For example:,, 9d + = , 9d + 16 = 43, 9d = 27, d = 3. So instead of using formulas you can find without them. = 3n + 4. Because 3 is the difference so it is the nth term, then since you know = 16, 4 x 3 = 12 + 4 = 16, so you found the nth term without using the formula.

We learned about Gauss's formula of finding how to find the sum of numbers 1 through 1000. So 1001 x 500 = 500500. The formula for this is: .

Next students put up the answers to the questions from the homework that students had questions on. Mr. Obrien explained that there are three numbers between 10 and 12, 10, 11, 12. This sounds simply, but it is helpful to understand when doing problems such as #69 on the homework. Next he passed out a yellow half-sheet. We started by defining a geometric sequence:
= r x
To finish class we filled in the formulas on the yellow sheet which we will use for tonights homework.

HW

2010-01-08T06:30:00.001-05:00

HW:

p. 669/5, 11, 19, 25, 29, 35, 41, 53, 57, 63, 73, 77, 79, 83, 89

HW for Fri

2010-01-06T05:38:00.001-05:00

HW:

p. 659/1, 9, 11, 16, 19, 21, 27, 37, 39, 41, 45, 67, 69, 71, 85

HW

2010-01-04T06:41:00.003-05:00

HW:

Check out this link for a revision of function and sequence mode on your calculator and this link for a revision of finding summations on your calculator.
p. 649/1, 3, 5, 7, 23, 25, 37, 43, 51, 53, 54, 57, 73, 77, 81, 93, 97

Unit 3 test

2009-12-19T02:29:00.001-05:00

Here's a blank copy of the Unit 3 test to use as practice before Tuesday's follow-up test:

Unit 3 test

Wednesday and Friday

2009-12-15T04:33:00.002-05:00

You have all class to work on Supercorrections and prepare for the follow-up test next Tuesday. Please feel free to use this document to discuss problems:

http://etherpad.com/HwRSczyOkJ

If you'd like me to jump into a discussion, just let me know with an email.

Although I will be in London for the rest of the week, I am available via email. Just shoot me your questions!

Update: I'm now in the UK (Wednesday)- if you use the Etherpad link above, I can contribute to your discussion.

Scribe Post for 10/10/09

2009-12-10T09:35:00.015-05:00

Mr. O'Brien passed the Unit 3 Quiz #2 tests back today, and we went over them for the first part of class. While going over the test, Mr. O'Brien stressed the importance of considering the order of operations while condensing logarithms. He also explained some of the simplifying, and explained why an expression such as

is not fully simplified, and should be further simplified to:

Mr. O'Brien also emphasized that we should use "=" only when the equation is completely equal, and "≈" if the equation is approximately equal. For example, if you have the equation x = 12/13, the equals sign is appropriate. But if you make 12/13 a decimal, it should be written as x ≈ .923 because the decimal is being rounded. He also pointed out that people were losing points for not following directions (for example, rounding to four decimal places when the problem specified to round to three decimal places).

He also explained problem #9 in detail, as follows:
ln 4x = 14/13 can be rewritten as

either by thinking of it as just directly translating it into this form, or by making each side of the equation raised to a power of e, like this:

He then explained checking it without a calculator. He also said to beware of extraneous solutions for our test. A problem can be done perfectly correctly, but then the solutions can be extraneous. This means we should be careful to check our answers by substituting the values back into the equations. He later said how we need to use common sense in checking our answers. For example, if we're doing a carbon dating problem and we get a negative answer for the time, there's obviously a problem with our math.

We then went to p. 270 of the textbook, which went over all of the things we're expected to know for the test. The themes of the test are the basics, as well as real-life problems. Note: we do not have to "recognize the five most common types of models involving exponential and logarithmic functions". We have to be able to use things from section 3.5, but we don't have to have them memorized.

After this, we reviewed homework questions. Mr. O'Brien talked about how, in order to minimize the amount of time we spent on problems during math tests, we should go through the problems to see if there are things we can recognize. For example, repeated calculations can use the "function machine" on our calculators. (Enter the function into the y= on our calculator, and then use a table that's set to ask for the independent variables.)

He also reviewed the correlation between

with the first equation being used for daily, monthly, yearly, etc. compounding, and the Pert equation being used for continuous compounding. (We will not need to have these equations memorized for the test).

Then we reviewed using the [STO→] key to store long values to letters in our calculators. To store a value (for example .56273) to a letter (or example A), type [.56273][STO→][ALPHA][A]. Then to recall the value, simply type [ALPHA][A].

Remember that % decrease is (amount of decrease/total amount). The amount of decrease is the difference of the two values.

For homework, we have to correct all our homework to turn in next class, do 8 problems from the Chapter 3 Review Test to include with our homework packet, and revise for the test next class. Mr. O'Brien said that the test will have a lot of word problems.

Scribe for next class is Andy.

HW

2009-12-10T06:35:00.002-05:00

Purplemath.com log links (scribe?)

HW:

Choose 8 problems from the Chapter 3 Review/Test. Include them with your homework packet.
Organize your homework- make sure each assignment is completely checked and corrected and that each has your name, date, and the assignment at the top. Stack your homework ordered from oldest to newest with the homework cover page on top. Staple your stack in the lower right hand corner. You will hand in your homework on the day of the test before you take your test.
Revise for the test. Rest. Psych yourself up. Don't be late and don't be sick- Monday is game day...

Scribe Post 8.12.09

2009-12-08T10:27:00.004-05:00

We started off with reviewing our Quiz from last class, and our Homework from last class. Then we took a Quiz regarding Log's. Our Quiz lasted for most of the class, but then we moved on to the next chapter.

We started off on pg.265, with problem #26 concerning the half-lives of Radon, and graphing the function y=ae^(-bt), where t is the length of time, b is the horizontal dilation, a is the vertical dilation, and y is the final value of the Radon. We subbed in values as t=1599, y=50, a=100, and then calculated for b, which was b=ln(1/2)/-1599. We then reversed our process, and calculated a with the values of 1.5=ae^-1000[ln(1/2)/-1599], which gave us the value of a=2.3g. We then filled in the values on TI-SmartView, which graphed the equation as a decaying function.

We then confirmed that the function did match the graph. Our homework deals with these functions tonight, but we don't have to memorize the functions for a test.

Next times scribe is Molly.

2009-12-08T04:27:00.001-05:00

HW:

* p. 265/15, 17, 19, 25, 27, 35, 39, 41, 43, 45, 51, 55, 59, 63

Tyler's Late Post

2009-12-07T20:47:00.002-05:00

In class on Friday we took the first quiz on chapter 3 and then we went over our homework on pg. 253. The majority of the class time was consumed by the quiz. We did not go over any new materials, however we stressed a few laws of log to remember for the next quiz (which is tomorrow).

Notable Points:

1. The base property:

2. ln=e

I hope the class found everything else easy to follow with log. I apologize for the post being so late, most likely it wasn't any help to any of you. Homework for tomorrow is to study for the quiz. Review the HW from pg. 243, and 253 to study. There is also a HW assignment on pg. 253 due for tomorrow. Good luck to everybody on the test.

Here is a website that looks very useful for studying the rules of log: http://www.themathpage.com/aPreCalc/logarithms.htm

2009-12-04T10:12:00.002-05:00

HW:

* p. 253/101, 97, 95, 91, 87, 59, 55, 53, 39, 33 (whichever are not finished in class)
* Be sure other homework is up to date

Unit 3 Logarithms, Scribe Post

2009-12-02T10:39:00.005-05:00

Today we began class by a quick discussion of the mid-term, Mr. O’Brian mentioned that some of the questions on the test will be multiple choice. He also mentioned that students need to understand the concepts we have gone over so far this year.
Next we looked over the Unit 2 test, Mr. O’Brian stressed that students check all answers and make sure that you answer the question that is being asked. When your are supercorrecting pick apart the problem, see how many connections you can make, and show many different ways you can solve it. One note to make is anytime you have a test question concerning a function, you need to have a equal sign and function name with the solution. Mr. O’Brian explains that the questions on the supercorrection follow-up test are the problems he believes to be the most important, the problems he wants to “stick” in student’s minds.
Next, we took notes on the Big Three Log Properties. The first is . The seconds is . The third is .

Next we created a proof for: .
Proof:
Let and
So:
Multiply:
Simplify:

Therefore:
Q.E.P.

We next proved the second of the Big Three Log Properties which is similar to the first proof but changes the multiplication and addition.
The third proof is almost similar to the second property applied multiple times. Mr. O'Brian said that for bonus, students should prove the third Log property.
Next, we looked at the other log properties on page 230 of our textbooks. Mr. O’Brian said that students should say the properties out loud in words to make sense of them.

We took notes on the Change of Base Formula which is .
Proof:

Take the log of both sides:

Therefore:
Q.E.P
In the last 15 minutes of class Mr. O'Brian let us work on the homework problems.

Next Class: Mr. O’Brian noted that students should check their answers for the homework to prepare for the quiz because “there is no fudging with logs”. Quiz on friday will be non-calculator. Mr. O'Brian said that for bonus, students should prove the third of the Big Three Log Properties.

Tyler will be the next class scribe

2009-12-02T07:04:00.003-05:00

HW:

* p. 243/47-59 odd, 69-79 odd, 80
* p. 253/12, 14, 30, 56, 86, 94
* p. 253/9-23 odd, 27, 29, 35, 49, 57, 65, 81, 93, 99
* Look over your homework in preparation for the quiz next class

Unit 3 logarithms, Scribe post, Collin Downs

2009-11-30T11:08:00.003-05:00

Today we started class with the super correction follow up test for the first 25 minutes of class. We then jumped to (1+1/x)^x which is also called e and what happens to it when it gets very large and how neither the base or the power wins and makes the function go towards 1 or a large number. We used this to show the transformation from A=P(1+r/n)^nt to A=Pe^rt because you can substitute n/r for x and 1/x= r/n so you can substitute e for 1+r/n and get A=Pe^rt. We then went on to homework where we talked about #21 with reference to the purple math visual of turning a log into an exponential. The last thing we learned today was the big three log properties with reference to the mystery function worksheet.
1. log(a*b)=log(a) * log(b)
2. log a^n= n*log a
3. log a/b= log a - log b
These will be used in our homework tonight which is p. 243/11-45 odd, 61-67 odd.

2009-11-30T05:37:00.003-05:00

HW:

p. 243/11-45 odd, 61-67 odd

2009-11-23T09:46:00.003-05:00

Today we did a warm-up with a liftoff function. example: g5(125)= g5(5^3)=3. Then we had to sketch y=4^x and use it to sketch a graph of a) y= 4^(-x) - 3, b) y=16*4^x and c) y=4^(0.5x). In b) 16=4^2 which makes y=4^2 + 4^x = 4^(x+2). In c) 4=2^2 which makes y= (2^2)^(0.5x)= 2^x. Then we discussed exercises 55 and 59 from hw. We used a formula A=P(1 + (r/n))^nt and GDC. Then we also used A=Pe^(rt) formula. Then we did the last page of Mystery function. Then we realized that mystery function and liftoff function is log. Definition: x=b^y means the same as y=log (b)^x. We went to http://www.purplemath.com/modules/logs.htm.
example: log(27)^9, in words: "The power you raise 27 to to get 9"
Then we found the inverse of exponential: f(x)=b^x then: y=b^x, then inverse: x=b^y, then solve for y: y= log(b)^x. So f^(-1)(x)=log (b)^x

Monday, November 23rd, 2009

2009-11-23T06:07:00.005-05:00

Lift-off function

Check out the log definition graphic over at Purple Math.

HW:

p. 236/1-29 odd, 33, 39-44 all, 49-69 odd
Be sure you are ready for the Supercorrection Follow-up Test (blank copy of the test available here)

2009-11-06T10:31:00.002-05:00

Today we did a warm-up with rational functions. We reviewed graphing and simplifying, and molly wrote up a google-doc on 'steps to graph rational functions.' We also discussed the equation 0/0=0, and pondered whether or not the answer would be 1, or whether it would result in an error on your calculators. We calculated our asymptotes for our warm-up using division to find the end-behavior. We explored rational functions using grapher, and added extra x's on the numerator's using our previous equation's from our warm-ups. We also fooled around with adding 7x, 5x, 12x, etc. and 2x, etc. on the numerator and denominator (respectively) to change the horizontal asymptotes. What we ascertained is that when there is a larger power on the denominator than on the numerator, the end behavior reached closer and closer to 0, regardless of the numerator's behavior. We can find the end behavior of our graphs by using division if the numerator's power is higher than the denominator's power, if the powers are the same then the lead coefficient of the numerator divided by the lead coefficient of the denominator is the horizontal asymptote for the end behavior, and if the power in the denominator is higher than the highest power in the numerator, then the end behavior is y=0. We finished by graphing the functions with all of the above information. We then calculated f(x) is less than or equal to 0. We used molly's steps to solve and graph our second equation. We revised our steps by adding that you can cancel portions of equations if it is possible. We changed our equation from g(x)=(2-x)(2+x)/(x-2) =-x-2, x does not equal 2. Mr. O'Brien went over what to expect for the test, and gave us the revision problems for the test, and encouraged us to do extra problems if we wanted to. Mr. O'Brien corrected the notion that Juniors will be in class on the 17th when the Supercorrections are due, and we spent the rest of the class reviewing any homework problems we wanted to.

2009-11-04T09:54:00.004-05:00

We started class with a radical function warm up. After we did this problem, but before we went over it, we went over the quiz for the first half of class, and learned some ways to use our calculators to solve for i or find a complex conjugate. Next we went over the homework problems from two nights ago, on page 179. We went over problems 43 and 47, finding the roots over rational numbers, real numbers, and complex numbers for #43. For #47, we solved by factoring by grouping, then solving for zero. We learned how to factor a number that is the sum of two squares. So (x^2 +25) becomes (x+ 5i) (x-5i), which is the difference between two squares. When a complex number is a root, another root will be the complex conjugate. So since 5i is a root, - 5i is too. After going over those two problems we went back to the warm up. To help solve this problem, we went to http://calc101.com/webMathematica/long-divide.jsp This website can do long division, and it will show you the steps as well. We then went over how to find a slant asymptote. To find the slant asymptote, you can use the form of the radical function where there is and x + c outside of the fraction. To find the y-intercept it is easiest to use the original, unfactored form. All the x values will cancel out, and you will be left with the c values, which have no x value. This is the y intercept. We then talked about a removable asymptote, which is when a factor cancels out of a radical function, but should still be in the domain. For example: (x^2 + 1)(x + 1) ( x-3)/(x-2) (x-1) (x-3) The (x-3) will cancel out, but x cannot equal 3, so you must draw an open circle at this point on the graph.
There is no quiz on Friday, but the Unit 2 test is on Tuesday.

Class Lesson 2.6: Rational Functions

2009-11-02T09:56:00.018-05:00

We started class with the 2.3-2.4 homework quiz, which took 20 minutes to complete. The homework from the previous class, which was on page 179 of the textbook, was not entirely reviewed. However, students had questions on exercises 43 and 47.

Before beginning the major lesson, Mr. O'Brien showed us how to enter imaginary numbers into TI graphing calculators. Afterwards, we began a group exploratory/lesson. Using the computer program Grapher, we graphed to functions, and began discussing them in small groups, trying to find domain and range etc.

As a class, we reviewed that rational numbers are numbers that can be written as decimals that end. We learned that rational functions, in fraction form, always have a polynomial over another polynomial.

We looked at both of the functions on the Smartboard, beginning with the second one. We saw that when zooming very far out, the function appears similar to f(x) = x. Upon zooming in to an area around 9800 on the x axis, we saw that it still appeared linear in that area, even at a closer zoom level.

After looking at the graph, we began to look at the problem numerically, both with the table in the TI-84 Plus calculator, and in the computer program Numbers, which is similar to Excel. We began in Numbers by creating an x/y chart, and putting in integer numbers on the x side. Then we plugged in the first formula, and instead of using x, we used B(matching number). So, to represent X in square C3, we would plug in B3. This created a chart on the computer that allowed us to examine the function numerically.

This showed us that 1, 2, and 3 were not values (the warning triangle on the computer = the "ERROR" message on the calculator's table). Then Mr. O'Brien talked about zeros and domain, showing us these by typing in x values in Numbers. We discussed the concept of asymptotes, as well as there application and relation to why a formula like the ones we were looking at could appear linear from very far out. We looked at a horizontal asymptote of 1. We discussed why when a very high (50000000000) value was put in the x axis, 1 was displayed - was it rounded, or did it actually reach 1? Applying what we had just learned, Mr. O'Brien walked us through graphing the function by hand. Then came the announcements.

I do not know who wants to be the next scribe.

2009-10-29T12:54:00.003-04:00

To start class, we went over the quiz we took Wednesday. Number four was found to have a cost of zero when x=80. Therefore, Mr. O'Brien gave the option of making a note on this problem if we got it wrong for this reason, and passing it back in. We then switched gears, and looked at the projects done by our classmates. We then went over the previous night's homework, involving imaginaries. Mr. O'Brien pointed out that with imaginaries there are often multiple ways to solve the problem. This discussion lead us to the fundamental theorum of algebra. Counting multiplicity, every nth degree polynomial has n complex zeros. We were then introduced to the rational roots test. This states: If a polynomial function has rational zeros, then they must be of the for a/b, where a is a factor of the constant term and b is a factor of the leading coefficient.

Friday, October 23rd

2009-10-29T07:40:00.001-04:00

We warmed up with two simple questions, one from the book and one that Mr. O’brien came up with. The problem from the book was number 42, a cubic function with three different roots. The other one was a quartic function, and we were able to solve it through the use of Wolfram alpha, or guess and check, but lead to our later exploration of Polynomial Long Division and Synthetic Division later in the class.
Before we refreshed on these two forms of division, we went over homework, which was composed of problems from section 2.1 and 2.2. since this was our first time looking over chapter two homework together, we refreshed on some basics, like finding the Axis of Symmetry (of quadratics) and and the roots of polynomial functions etc. This will be the material present on next class’ quiz.
Our lesson regarding Synthetic Division and Polynomial Long Division showed us that while both were effective, each had their time and place. Synthetic Division was more simple, but Polynomial Long division could be used regardless of what the polynomial is being divided by. We then saw how the remainder theorem can help one find function values.

Scribe Post 10/27/09

2009-10-27T16:57:00.004-04:00

At the start of class we had a quiz on the 2.1-2.2 homework. This took us up to 10:05, and from there we began going over some of the more recent homework problems, including pg. 159 (13, 23, 49, 25, 59, and 37). Problem 37 segued nicely into a discussion of the remainder theorem, which as we learned can be used to quickly find specific values of a function such as f(5). Next, we did a review of complex numbers, proceeding with a Venn-diagram of the various types of numbers and the relationships between them. This lead discussion towards terms such as rational, irrational, pure imaginary, etc.; we also reviewed operations involving complex numbers, including a brief discourse on complex conjugates. This took us right up to 10:50, our homework being p. 167/17, 19, 21, 29, 33, 37-51 odd, 65, 71. I haven't gotten a chance to talk to anyone about being the next scribe yet, so I'll do that at the beginning of next class.

Homework for 10/27/09

2009-10-26T23:31:00.002-04:00

I was unclear on how to do pg. 159(37). Could we go over this in class? Thanks!

- Molly W.
W-2 Pre-AP Calc

HWK assigned10/18

2009-10-20T21:08:00.003-04:00

I had trouble on problems p.134/23 ,79, p.149/21, 29, 33, 41. I forgot how to put parabolas in standard form and also forgot what a and b are in the equation for the axis of symmetry.
-Henry W-2

Pre-AP Calc 10/19/09

2009-10-19T10:02:00.003-04:00

Class summary and notes!

The first 2o (it was ACTUALLY 25) minutes of class we spent taking the Suppercorrection quiz. Then we worked in our books on page 134, going over a matching-function-to-equation exercise. We saw the definition of polynomial function, which we won't need to learn, phew (it's REALLY complicated-looking). Then we went on to learning about polynomial functions. WolframAlpha!

•Linear functions are a special type of polynomial functions

•Every polynomial function has the property that they always are ARN

•As x approaches infinity, the function itself also approaches infinity

•As x approaches -infinity, the function also approaches -infinity.

•An odd degree means that the end lines go in opposite directions.

•An even amount of turning points means the end lines go in opposite directions.

•The amount of turning points is AT MOST one less than the exponent.

•Double roots (or roots with multiplicity).

•Even routes make a smooch.

Scribe Post for 9/29/09

2009-09-29T19:53:00.002-04:00

We started off today's class with a competition using our knowledge of transformations (translations, dilations & reflections) to formulate equations for graphs shown on the overhead. (The Kings won extra credit!) We then went over the answers from the quiz last class and talked about the unit test on Thursday.

THE TEST will cover all assigned homework and content learned in chapter 1. When you come to class that day you should have all of your homework organized as specified on the class website so you can take a full eighty minutes to complete the test. You should study by: making sure you understand the points explained in the chapter summary, doing six questions of your choice from pgs. 117-122, and reviewing all hw, notes, and quizzes.

In the last ten minutes of class Mr. O'Brien answered the questions we had on today's homework which covered inverse functions. The questions included problems 21, 23, 27, 61, and 63 on page 99. If you still have any more questions on the homework or on any part of chapter 1 you should see Mr. O'Brien or email him. Good luck on the test!

--The scribe for next class will be Andy--

Scribe Post for 9/25/09

2009-09-25T15:46:00.002-04:00

We started the class by going over some problems that we'd forgotten from the last time. Then we spent thirty minutes on the test. After that we went over some problems from the homework for this class. Some people weren't clear on the (fog) and (gof) problems, but we went over them. Then we took notes on inverses until the end of class.

Scribe for the next class is Sean.

Scribe Post for 9/23/09

2009-09-23T09:46:00.003-04:00

We spent the first 10 minutes or so going over the GeoGebra homework packet from last class. After that we discussed translation, reflection, and dilation. After this, we discussed problems from the homework: p. 70 (53, 55, 56) We took a break from going over homework, so Mr. O'Brien could pass back our quizzes. We quickly went over the answers. Mr. O'Brien also answered why calculators see -4² as being -16 -- and that to fix that we should enter the problem as (-4)² to get the answer of 16. Then, we went over p. 79 (25d, 31bd, 47, 55, 56, 53), and GeoGebra (20-22). In the last five minutes or so of class, we filled out a brief survey from the National Council of Teachers of Mathematics.

Scribe Post for 9/21/09

2009-09-21T10:12:00.002-04:00

We took the test for the first thirty minutes. People had questions on p.71/31, p.71/53, 55, 56, p.79/65, p.79/31b and d. People also had question on 53-60 on how to write the new equation. The concepts of these problems are what most people seemed to need instruction on. Also as I said on my other post, I don't understand how to put the equation into words. Some people had trouble finishing the classwork in class. People also had trouble figuring out the parabola equations.

Homework for 9/21/09

2009-09-20T15:38:00.001-04:00

Hey Mr. O'Brien. Can we go over 79/25d, 31d, and 61 in class? Thanks!

- Molly

Tuesday's class

2009-09-17T09:22:00.003-04:00

In the beginning of the class we took out all of our homework that we have completed so far this year. Which was three assignments. Then, we took out our graphing calculators, and while going over problems Mr. O'Brien taught us how to use the calculators in more detail. We got our first quiz handed back to us and then went over it. We were given a chance to ask questions about problems that didn't understand. While going over all of these we were all shown how to get the answers by using the graphing calculator. People had trouble with problem 35 on page 49; problem 33, 57, and 59 on page 61; problem 71 and 103 on page 119. All these problems were gone over
in class. Then, after all of this we went onto the symmetry sight off the class website, and downloaded the page. We then learned about symmetry proofs. And the ten problems on these pages was our homework.

Collin will be the next scribe.

How to find a line of best fit on TI-84 Plus

2009-09-15T12:28:00.005-04:00

Someone asked how to find a line of best fit on the graphing calculator, so I'm putting it on here... This is how I do it on my TI-84 Plus, but it's probably similar for everything else.

Linear Equation
To find the line of best fit for a linear equation, pretend we had the points: (-2, 5) (1, 11) (3,15)
Go to STAT > Edit... Under L1, enter all the x-coordinates. Under L2, enter all the y-coordinates. Then hit STAT > CALC > LinReg. Hit ENTER. You'll see something like this:

LinReg
y=ax+b
a=2
b=9
This means y=2x+9.

Quadratic Equation
Say you have a quadratic with these points: (-2, 3) (0,-5) (2, 11) (3, 28)
Go to STAT > Edit... Under L1, enter all the x-coordinates. Under L2, enter all the y-coordinates. Then hit STAT > CALC > QuadReg. Hit 2nd>1 (L1), then enter a comma, and then 2nd>2 (L2). Then hit ENTER. It will give you something like this:

QuadReg
y=ax²+bx+c
a=3
b=2
c=-5

This means that the equation is y=3x²+2x-5

Cubic Equation
For a cubic equation, enter the points. Pretend they're (-2, -8) (-1, -6) (0, -6) (1,4) (2, 36)
Go to STAT > Edit... Then enter all the x-coordinates under L1 and the y-coordinates under L2. Then hit STAT > CALC > CubicReg. Type 2nd>1 (L1), comma, then 2nd>2 (L2). Hit ENTER. You'll see something like this:

CubicReg
y=ax³+bx²+cx+d
a=2
b=5
c=3
d=-6

This means it's y=2x³+5x²+3x-6.

Good luck :)

Homework for 9/15

2009-09-15T08:50:00.003-04:00

Could we go over problems p.49/89 and p.63/47. I got an answer, but I would like to review them. Also I could use a quick review on graphing calcs. Tyler from my W-2 class gave me a good overview on how to use them on the homework problems, but I don't know how to use them for other types of problems.
Thank you,
Henry W-2

Friday September 11th's class

2009-09-13T06:15:00.000-04:00

Some students were struggling using these calculators. They could not find the “abs” or figure out how to graph these equations. Seeing that the focus of todays class was using these graphing calculators, we need further instruction on how to use the different utilities on these calculators. Some forgot how to graph palaboras, solve quadratics, and use domain and range. Solving quadratics to find the domain of equations was another struggle we had. Few kids can remember the equations such as point slope, distance formula, midpoint formula, and others. When in front of us we can use them, however remembering why they work (as you explained in class) is different. We should go over the definitions of intervals (relative minimum/relative maximums) and odd/even functions. Other than those things the class did not have many questions. None of these stuck out as a great problem other than using the calculators.

The Scribe List

2009-09-09T13:14:00.041-04:00

This is The Scribe List. Every possible scribe in our class is listed here. This list will be updated every class. If you see someone's name crossed off on this list then you CANNOT choose them as the scribe for the next class.

This post can be quickly accessed from the [Links] list over there on the right hand sidebar. Check here before you choose a scribe for tomorrow's class when it is your turn to do so.

IMPORTANT: Make sure you label all your Scribe Posts properly (Your Name, Unit Title, Scribe Post) or they will not be counted.

Extra Credit: Tyler

Cycle 3

~~Nathan~~

~~Katharine~~

Collin

Sean

Henry

Miles

Amber

Marcel

Tyler

~~Daniel~~

Kyle

Petra

~~Sophie~~

Andy

Molly

Katharine, Functions, Scribe Post

2009-09-09T09:48:00.004-04:00

Mr. O'Brian,
Overall the class believed that the homework went well and was a fair amount of problems. Some sections that the class had trouble with was pg. 49 (65, 75-78) The class seemed to not clearly understand domain. More importantly the class did not know how to find the domain easily, we were wondering if there was a equation to help solve the problem. On problems, 75-78, the class also wondered if there was a equation to find the solution, instead of simply guess and check. One of our class questions for the quiz next class is if we are able to have a note card to write the formulas on?
Hope your feeling better,
Katharine

Note: Tyler will be the next class scribe

Superfluous technology use

2009-09-09T09:48:00.003-04:00

We have spent far too much class time subscribing to your blog.

On Step #1

2009-09-09T09:36:00.000-04:00

This is my comment.

Welcome

2009-09-09T09:00:00.000-04:00

Welcome to our class blog. This will be our space to discuss mathematics. There are a few basic guidelines to posting online. First, read this post from another blog about personal branding and the internet. Remember the blogging is a very public activity and your writing may be read by anyone on the internet- for as long as it exists. So, please be sure to use your first name only, and do not use a photo of yourself. If you like, you may use an image of something to represent you but that is not you (an avatar).

After each class, the scribe will post a synopsis of the day's events (Scribe Post). A student at another school described the role of a scribe as this:

A scribe post is basically like you are teaching the class again, but this time in your words in a way that other people can understand it. You can also recap other important things that we talk about in class (like Pi Day) so that if someone was away in our class, they would know what they missed. Also don't forget that when you scribe, you get the power to choose the next scribe.

You will also use this blog to post your revision questions before a unit test revision (Revision), and you may make a posting to share at any time (On My Mind).

Your contributions to the class blog consist of a quiz grade (rubric on the class website). To ensure that you receive credit for your contributions, please ensure that any post you make has exactly three labels:

Your first name.
The unit of study, e.g. Functions
The type of post: either Scribe Post, Reflection, or On My Mind.

Below are some guidelines for student bloggers that another teacher, Bud Hunt, came up with:

Students using blogs are expected to treat blogspaces as classroom spaces. Speech that is inappropriate for class is not appropriate for our blog. While we encourage you to engage in debate and conversation with other bloggers, we also expect that you will conduct yourself in a manner reflective of a representative of this school.

Never EVER EVER give out or record personal information on our blog. Our blog exists as a public space on the Internet. Don’t share anything that you don’t want the world to know. For your safety, be careful what you say, too. Don’t give out your phone number or home address. This is particularly important to remember if you have a personal online journal or blog elsewhere.

Again, your blog is a public space. And if you put it on the Internet, odds are really good that it will stay on the Internet. Always. That means ten years from now when you are looking for a job, it might be possible for an employer to discover some really hateful and immature things you said when you were younger and more prone to foolish things. Be sure that anything you write you are proud of. It can come back to haunt you if you don’t.

Never link to something you haven’t read. While it isn’t your job to police the Internet, when you link to something, you should make sure it is something that you really want to be associated with. If a link contains material that might be creepy or make some people uncomfortable, you should probably try a different source.

To kick us off, add a brief comment to this post- thoughts or additions to the above discussion of privacy and blogging.

Note: This blogging model is courtesy of Darren Kuropatwa.