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.
Thursday, January 28, 2010
Class Thursday, Jan 28
Trig intro: U4 intro to trig.pdf (hard copy in class)
HW:
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)
Wednesday, January 27, 2010
Tuesday, Jan 26th Scribe Post
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.
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
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
http://www.theamericanscholar.org/the-disadvantages-of-an-elite-education/
Enjoy!
Mr. O'B
Monday, January 25, 2010
Class Tuesday
Individual first semester reflection
Group advice to a new student
HW:
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
Thursday, January 14, 2010
Revision day
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).
Here is the answer sheet for the midterm.
Use the suggested practice problems from the midterm revision guide (p. 276).
Tuesday, January 12, 2010
Scribe Post
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)}{1-r} "S_n=\frac{a_1(1-r^n))}{1-r}")
.
We also got the formulas that we need for the midterm:
Arithmetic Sequence Formulas:
d "a_n=a_1 + (n-1)d")
,
and "S_n=\frac{n}{2}(a_1 + a_n)")
.
Geometric Sequence Formulas:
 "a_n=a_1(r^{n-1})")
,
}{1-r} "S_n=\frac{a_1(1-r^n)}{1-r}")
,
and
.
Next Time's Scribe is Nathan.
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
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
Midterm exam revision guide
HW
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
Friday, January 8, 2010
Scribe Post 1/8/10
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.
Mr. Obrien showed how to solve the nth term without using the formulas, which was much quicker. For example:
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:
To finish class we filled in the formulas on the yellow sheet which we will use for tonights homework.
Wednesday, January 6, 2010
Monday, January 4, 2010
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