Here is the project:
http://pre-apcalculusw2.obrienfamily.sent.com/Q4%20Project.pdf
Monday, May 17, 2010
Wednesday, May 12, 2010
May 12th Math Class a.k.a. 13 days until Kayla's birthday!!
First we started off having open revision time. We did problems, used Mr. O'B, and avoided second semester senior distractions :-).
Next we went over the HW Quiz. This showed that the ambiguous case is something we all may need to go over before the test. Know the rules for the ambiguous case and how to find values for b to make the triangle have a. one solution b. two solutions and c. no solution. In order to have a triangle the third side has to be between the sum and difference of the other two sides. For the example if a=9 and b=13 c has to be between 22 and 4.
The test covers: Chapter 5&6. Page 419 has a list of topics in chapter 5 that we need to know. We will be given sum/difference formulas, so no need to memorize. Section 5.5 all the bullets are on the test except for the second and the fourth bullet. It's a very doable test, just learn the basics. There aren't going to be that many finally crafted, so get the basics down. Page 481 tells what's on the test for chapter 6. 6.1Know the law of sines and area. 6.2 Know the law of cosines and the Heron's area formula. 6.3 know all. 6.4 know the dot product formula. Try to memorize all of the formulas but if not Mr. OB may help us. We will get the vector projection formula. We do not need to know the last bullet on 6.4 and 6.5 will not be on the test.
Last we finished up with doing problems and practicing our skills.
Remember study hard for the test on Monday. Put all of your homework together, corrected, marked, and in order.
Next scribe: Angus P.
Next we went over the HW Quiz. This showed that the ambiguous case is something we all may need to go over before the test. Know the rules for the ambiguous case and how to find values for b to make the triangle have a. one solution b. two solutions and c. no solution. In order to have a triangle the third side has to be between the sum and difference of the other two sides. For the example if a=9 and b=13 c has to be between 22 and 4.
The test covers: Chapter 5&6. Page 419 has a list of topics in chapter 5 that we need to know. We will be given sum/difference formulas, so no need to memorize. Section 5.5 all the bullets are on the test except for the second and the fourth bullet. It's a very doable test, just learn the basics. There aren't going to be that many finally crafted, so get the basics down. Page 481 tells what's on the test for chapter 6. 6.1Know the law of sines and area. 6.2 Know the law of cosines and the Heron's area formula. 6.3 know all. 6.4 know the dot product formula. Try to memorize all of the formulas but if not Mr. OB may help us. We will get the vector projection formula. We do not need to know the last bullet on 6.4 and 6.5 will not be on the test.
Last we finished up with doing problems and practicing our skills.
Remember study hard for the test on Monday. Put all of your homework together, corrected, marked, and in order.
Next scribe: Angus P.
Monday, May 10, 2010
May 10: Vector Projections
We spent the first 40 minutes on the quiz. This was the last homework quiz of the year!! But still make sure you're keeping up with your homework because we have a test coming up!
We then looked at the proof for the vector projection of u onto v
(I would type all of the proof except I'm not the best with that equation editor..Ask someone for notes if you need it)
Mr. OB told us that it was not necessary to memorize the proof (he'll put it on the test).
Our homework questions took up the rest of the time.
Example:
#59.
u = <3,5>
Find 2 vectors orthogonal in opposite directions
Possible answers: <-5,3>, <10,-6>
In order to be orthogonal u dot v must equal zero
Next Scribe: Kayla
We then looked at the proof for the vector projection of u onto v
(I would type all of the proof except I'm not the best with that equation editor..Ask someone for notes if you need it)
Mr. OB told us that it was not necessary to memorize the proof (he'll put it on the test).
Our homework questions took up the rest of the time.
Example:
#59.
u = <3,5>
Find 2 vectors orthogonal in opposite directions
Possible answers: <-5,3>, <10,-6>
In order to be orthogonal u dot v must equal zero
Next Scribe: Kayla
Thursday, May 6, 2010
5/6/10 - Noelle
Final New Material of PAP!!!!
Today we started off with a warm up using the first link on the blog to find the sum of vectors:
a) <3,2> + <2,4> = ? = <5,6>
b) <3,2> + <-5,1> = ? = <-2,3>
Then we worked on this problem from the book (which also answered the homework question #69)
Pg. 467 (70)
To solve this you can graph on paper or use geogebra. First you're supposed to find the magnitude of the vectors, which is 
. From this you can use the pythagorean theorem to find the hypotenuse, which is 
. Then, by using the law of cosines, set up the following equation: %5E%7B2%7D%3D%5Cleft(%20%5Csqrt%7B5%7D%20%5Cright)%5E%7B2%7D%2B%5Cleft(%20%5Csqrt%7B5%7D%20%5Cright)%5E%7B2%7D-2%5Csqrt%7B5%7D%5Csqrt%7B5%7Dcos%5Ctheta%20)
, and by solving algebraically, you get that theta is 90 when cosine of theta is 0.
We went over problem 73 from the homework on page 456:
We discovered you can use vector properties OR use the law of cosines to find the answer. The answer was 398.32 lbs of force at a 12.8 degree angle.
(make sure to try and memorize the formula for the law of cosines for the quiz/test coming up, unless you don't mind the sting of losing a point by asking for it)
*possible test connection, make sure you understand how to do this problem*
Dot/Scalar Multiplication:
if 
" class="ee_img tr_noresize" eeimg="1" style="vertical-align: middle; "> and 
" class="ee_img tr_noresize" eeimg="1" style="vertical-align: middle; ">, then 
.
Scalar is a number, while a vector is a directed line segment. When Vectors are dotted (multiplied together), then they become scalars.
There are 5 Properties of Dot Multiplication that can be found in the book or with detailed explanations at: http://en.wikipedia.org/wiki/Dot_product#Properties.
Angle Between 2 Vectors:
If theta is the angle between 2 vectors, then u*v= (magnitude of u)*(magnitude of v)*cos(theta).
another way to write this is 
magnitude of u)*(magnitude of v)*cos(theta).
This can be explained in more detail at this site: http://en.wikipedia.org/wiki/Dot_product#Proof_of_the_geometric_interpretation
Things to Remember:
Study for the Quiz on Monday!!!
Test on the 17th!
Supercorrections...
and then the final project!!
Homework: HW #12:
* p. 467/1, 13, 29, 33, 35, 43, 49, 53, 57, 59 (and study)
Tuesday, May 4, 2010
May 4, 2010
Today we started class with a WARM UP....
We worked on finding the component form, magnitude, and direction angle of vectors. Finding the component form of the the vectors was not too hard. Mr. O'Brien showed us a trick to help us remember how to find the component form. Terminal - Initial = Component Form.. (T-I!) Someone suggested that thinking of our super T-I 83 or 84 calculators could be a helpful reminder of how to find the component form.
Vector AB
Vector CD
Direction angle seemed to be the one part of the warm up that confused the class. We used Geogebra to help us visualize where the direction angle was.
The angle shown in both triangles is subtracted from 360˚ to find the directional angle.
That was only the first part of the warm up.....
For the second part we worked on finding the value of 3 x vector u.
Mr. O'Brien shared another helpful hint with us, he told us that if the magnitude of vector u and (theta) are given then the component form isu x cos(theta), magnitude of vector u x sin(theta)>.
Also, when a vector is multiplied by a number it is called a scalar. When the vector is multiplied by a number it is dilated geometrically.
We also looked at the result of two vectors added or subtracted, and their relation to 3(vector u) with Geogebra.
The three segments in the image above are: 3 x vector u, vector u - vector v, and vector u + vector v. The discovery that we made with Geogebra is that the three segments make up a triangle!!
We also went over the quiz that we took last class. Mr. O'brien stressed to make sure that the answer that you found while working through a problem was an answer that the question was looking for.
**Besides some silly/careless errors, Mr. O-Brien said that overall, we are showing great progress with our homework quizzes! way to go
Homework Questions.... were #59 and 61 on Pg. 456. These questions were addressed when we went over the warm up.
Keep on top of your homework! Due next class: pg. 456 #15-20, 25, 31, 43, 49, 53, 69, 73
Reminder: Quiz Monday 5/10
TEST Monday 5/17
Next Scribe: I'm not really sure who hasn't done a blog post recently... any volunteers??
We worked on finding the component form, magnitude, and direction angle of vectors. Finding the component form of the the vectors was not too hard. Mr. O'Brien showed us a trick to help us remember how to find the component form. Terminal - Initial = Component Form.. (T-I!) Someone suggested that thinking of our super T-I 83 or 84 calculators could be a helpful reminder of how to find the component form.
Vector AB
Vector CD
Direction angle seemed to be the one part of the warm up that confused the class. We used Geogebra to help us visualize where the direction angle was.
The angle shown in both triangles is subtracted from 360˚ to find the directional angle.
That was only the first part of the warm up.....
For the second part we worked on finding the value of 3 x vector u.
Mr. O'Brien shared another helpful hint with us, he told us that if the magnitude of vector u and (theta) are given then the component form is
Also, when a vector is multiplied by a number it is called a scalar. When the vector is multiplied by a number it is dilated geometrically.
We also looked at the result of two vectors added or subtracted, and their relation to 3(vector u) with Geogebra.
The three segments in the image above are: 3 x vector u, vector u - vector v, and vector u + vector v. The discovery that we made with Geogebra is that the three segments make up a triangle!!
We also went over the quiz that we took last class. Mr. O'brien stressed to make sure that the answer that you found while working through a problem was an answer that the question was looking for.
**Besides some silly/careless errors, Mr. O-Brien said that overall, we are showing great progress with our homework quizzes! way to go
Homework Questions.... were #59 and 61 on Pg. 456. These questions were addressed when we went over the warm up.
Keep on top of your homework! Due next class: pg. 456 #15-20, 25, 31, 43, 49, 53, 69, 73
Reminder: Quiz Monday 5/10
TEST Monday 5/17
Next Scribe: I'm not really sure who hasn't done a blog post recently... any volunteers??
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