The Last BOB

Hmm, I'm still worried about this sequences test. I understand pretty much everything and I think this unit is quite simple, but I just have this nagging feeling that Mr. K is going to be up to something and make those questions hard on the test, haha. Anyway, wow, this class, course, whatever you call it, was fun. I'll never forget the conversation we had with Eddie and his class from Georgia, the day when the SmartBoard was hooked up (It was pretty funny when Mr. K was trying to learn how to use it. :D sorry Mr. K), and how we implemented it in our class. I wish everyone luck for tomorrow's pre-test, Tuesday's test, and the final exam.

BOB 7

Well, I thought that this probability unit was kinda easy. When we had the quizzes, I was surprised! It was hard, and that led me to think that I needed more practice for this unit. I'm just hoping that the test won't be as quite difficult as the quizzes. Those quizzes really got me surprised. Anyway, I wish everyone luck in the test, we're going to need it.

BOBa Fett

Hi all!

I'm really confident about this unit. I understand everything and whatnot, I feel like everything is going right, but, I get some more practice problems. The links provided by MrSiwWy are good and can help us do better on the test. Remember, perfect practice makes perfect.

Good luck to all!

S-C-R-I-B-E

Good evening to everyone. Sorry if this post is late, I passed out on the couch while watching the hockey playoffs (Buffalo vs. Ottawa) and just woke up, haha. Anyway, here is today's scribe post.

MORNING CLASS

We started off the morning with word problems.

1.
















This problem was solved by yours truly (ahem haha). From the given question, we are given that the foci are (+6,0) and the focal radii is 4 units. Since we know what the focal radii is, we could determine the vertices of the hyperbola by subtracting the focal radii from the foci. Doing those, we should get (+2,0) as our vertices. Thinking about it, the x-value of the vertices are the same as the a value in an equation of a hyperbola. We then get that the a value is 2. We already know the c value of the ellipse equation, so that's enough information to solve for b by using the Pythagorean identity, c²=a²+b². Substituting are values, we then find out that the value of b is the square root of 32, or 4 rt.(2). Now that we have our respective values, we can now write our equation.







In this question, it doesn't matter what form you leave your equation on because it doesn't specify whether you leave your equation in standard equation (the equation above) or in general form (the equation below). Moving on...

2.














This problem should be pretty straightforward as it is like one of the problems we did yesterday/2 days ago.

3.
















This problem is a bit different from the ones we did. In this problem we were given the directrix of the parabola (x-2=0 or x=2) and the vertex (-1, 3). From that we can determine that the parabola opens to the left. Also, from the data given, we can also determine the p value, which is 3. Now that we have enough data, we can determine the equation, which is on the image, in red colour.
Note: the equation underlined in blue is wrong because we forgot to consider the vertex.

4.












Now on to the "real" word problem. This problem requires some thought and some manipulation. From the graph given, we can see that we drew a Cartesian plane on the graph so it would make it a bit easier for us. We plotted out several points on the graph like (10,0), which is the distance from the origin/cliff, (0,40), which is the vertex of the graph/height of the cliff and (?,30) which is the point that we're trying to find. From the solution on the image, we can see that we used the point (10,0) to determine the value of p, which is -5/8. Now that we've found p, it's as easy as substituting the values and solving for x. We then find out that x = +5, but we reject -5 because if we throw -5 distance, we're throwing into the cliff. Also Mr. K pointed out that since it's a word problem, we ALWAYS have to put our answers in a sentence.

5.















This problem seems to be straightforward, but requires a bit of thinking, like any other else. We know that the center is at (0,0) as it is given, and a vertex which is (rt.(6), 0). Thinking back, we know that the x-value of the vertex is equal to the a value in the equation of an ellipse. Now that we know a, we can solve for b by putting in 9 for the x value and 5 for the y value. We then find out that b = rt.(2).

We end our morning class here.

AFTERNOON CLASS

We started our afternoon class with a quiz. I'm kinda hesitant on putting up the solutions here because some of us haven't written the quiz. But if you want to see it, check today's slides. After the quiz, we went to our groups and solved a couple of problems.

1.














This question got most of us wondering. But Grey-M figured it out and once he put up the solution, we were all like, "oooohhh I see I see". It seems pretty straightforward.

2.














We didn't really get to finish this problem because the bell rang, beckoning us to go home and have fun!! But we did the first part of the problem, which seemed pretty straightforward.

The next scribe will be Aichelle.

NOTE: THE PRE-TEST IS ON MONDAY MORNING, THE TEST IS ON MONDAY AFTERNOON. WE WERE SUPPOSED TO HAVE THE PRE-TEST TOMORROW BUT WE HAVE BUS RIDERSHIP TOMORROW SO MR. K MOVED IT ON MONDAY MORNING. TOMORROW'S CLASS WILL BE A WORKSHOP.

BOB

Hmm..

Another unit done and another test coming! Personally I thought that this unit is not hard and not easy at the same time. I kind of like the fact that you have to think about the problems first before you dive and solve it. I'm really not confident about solving those poker problems because I don't know how to play poker (haha) and I just don't understand it. But this morning I think I understand it better. Well I'm off to do my DEV and study for the test. GOOD LUCK TO EVERYONE.

Scribe Post II

Hello everyone!!

We had an unusual start in today's class. When I first came inside the classroom, Mr. K was there, doing his daily morning routine which involves downloading the class' lesson for today. I left to go for a walk. When I came back, Mr. K wasn't there, and when the bell rung, to everyone's surprise, Miss Armstrong and her Grade 10 (Pre-Cal?) class came in. Miss Armstrong was saying that Mr. K is currently in her classroom probably using her computer. She then told us that we were going to do some "math aerobics" and whatnot. Everyone was hesitant at first, but after a while Miss Armstrong got us going and laughing. Richard tried to teach the sine and cosine dance to the Grade 10s and asked everyone to do it, but to no avail. Better luck next time, Richard, haha. ^_^ Mr. K then came in finally, and we started our lesson with the Grade 10s.

We then started off with this problem:
















When we did this problem for the first time, we did not include 0 as one of the possible even numbers for the 3rd problem in the slide. I was wondering at first as to why 0 wasn't included as an even number. That got Mr. K into thinking and we tried to find out whether 0 is an even number. After a couple of minutes, we found out that 0 is an even number and therefore was included as one of the possible even numbers, making us change our solutions and answers.
The solution should go like this:

1.1.5.4.5.1.5 = 500 phone numbers

We were then introduced to Permutations:

















This is pretty much straightforward. We were then introduced to the next problem:


















This problem was solved by one of the Grade 10s (his name is Daniel, thanks Aichelle) that were currently in our class. He figured out that since there were 9 players on the softball team, there could be 9.8.7.6.5.4.3.2.1 or 9! possible batting orders. The first member would have 9 choices when he would bat, leaving the second member 8 choices when to bat. The second member could then choose when he would bat, leaving the 3rd member 7 choices when to bat, so on and so forth. Daniel received a big compliment from Mr. K, who was impressed by the guy's thinking.

On to the next problem:
















This problem got most of us back into thinking, but it's actually quite simple. We could use the Fundamental Principle of Counting, or the Pick Formula. There are 120 rooms in a hotel, and guests have reservations for 66 different rooms. The first guest would have 120 rooms to choose from. After he chooses, the second guest has 119 rooms to choose from, 1 less than the first guest because, well, the first guest has chosen 1 room out of the 120 rooms available, leaving 119 rooms for the second guest to choose from. After the second guest chooses a room, the third guest chooses a room out of 118 rooms, then the fourth guest chooses a room out of 117 rooms, so on and so forth. There are at least 2.63x10¹² ways the rooms can be assigned to guests.

Using the Pick Formula, _nP_r = n!/(n-r)!, we just plug in the numbers, as illustrated in the image.

n = 120 rooms
r = 6 guests

We would also arrive at the same answer. I actually prefer using the Fundamental Principle of Counting as it requires you to really think about it first and you would understand the concept more.

(note: Ms Armstrong came after we solved this problem and picked up the Grade 10s. The classroom felt empty after they left, haha.)

Then, the next problem Mr. K gave us got us into thinking. The word BOOK has four letters. How many "words" could we write using the letters from the word BOOK? Hmmm.. Grey-M said that there are 6 possible "words" that could be formed using the letters from the word BOOK. His reasoning is that since there are 2 letter O's in the word BOOK, some "words" would repeat. Mr. K then told us to actually see how many "words" we could come up using the letters from the word BOOK. Most, or all of us actually came up with 12 "words". Mr. K then explains us why in this slide.


















Why 12? Well, first of all there are four letters in the word BOOK, giving us 4! different "words" that can be made from that word. But, since there are 2 same letters, we divide 4! by 2! (Actually, I don't actually know yet as to why we divide by the 2! if there are 2 same letters , although I understand the concept. I just can't put into words yet. I'll explain further later when I could, haha.), therefore giving us 12 "words". Mr. K then gave us another example, this time he asked as to find how many "words" can be formed from the letters of MISSISSIPPI. Well:













That was pretty much our lesson for today. I'm just covering for Sandy who couldn't do the scribe responsibilities today, so she'll be the scribe for tomorrow. Homework for today is Exercise 29.

BOB

Well I'm not really satisfied with what I can do right now with this unit. This unit started out quite easy but when it came to problem solving and stuff I got confused. I feel like I could do a couple more problem solving questions to fully understand it. I understand how log and ln stuff go on but on the problem solving stuff I just don't know what formula to use. Other than that I think I can do quite alright on the test. Good luck to everyone tomorrow and I hope that everyone does well.

Flickr

What?! I didn't know that the Flickr assignment should be posted on the blog.. well here it is.

http://www.flickr.com/photos/7161763@N05/442769680/

And to continue the theme.. (I haven't seen it!!! You guys are lucky...)

Talladega Nights: The Ballad of Ricky BOBby

Another unit done! Wow, classes fly by so fast it's not even funny. Anyway I think this unit is somewhat complex, in the sense that you really have to look at what you're doing. One lesson I didn't really like in this unit is the proving section. Sure, it could be easy sometimes, but the proof that we did in the pre-test was kinda difficult. Anyway I like the way Mr. K makes the proof seem easy, haha. I dunno, maybe I'm thinking too hard in the problems, maybe that's why I'm having difficulties in proofs and whatnot. Right now my confidence is way down after what happened during the last two tests, so I really need to get a high/good mark in this test to bring my confidence back up again. If I find the test difficult tomorrow, I guess I just have to do it in the best of my talents.

Good luck to you all.

Mr. BOB

This unit went by pretty fast. I understood most of it, but the thing that I'm not comfortable about is the problem solving questions like the one that we did today. I feel like I should do more of those to get some more practice so I could at least understand it better and feel more comfortable and confident about solving those problems. Other than that, I like this unit because I understand it a lot and I'm hoping that I'll do better on this test. Good luck to everyone on the pre-test and test, whenever they may be.

Plotting Piece Functions (is that how you call it?) on Fooplot

Yes, plotting piece functions or whatever you may call it (I forgot haha) works on Fooplot. The thing is, it makes those "weird" lines so I still have to play around with it. A problem that I found with it is that it doesn't accept greater/less than or equal to signs (≤, ≥), apparently it causes syntax error. Haha.

Graphing f(x) = {x²-4; x ≤ 0, x-8, x>0}:













Graphing: f(x) = { -3; -7 ≤ x ≤ -4, x + 1; -4 < x ≤ 3, 4; 3 < x ≤ 7 }













Note: As you can see, it makes those weirdthingy lines that it's not supposed to.. I'll find a way around it. Or maybe someone else will.

Also, a reminder to Mr. K, please put up our Math Dictionary notes. Haha.

B.B.T.T. (blog before the test) or BOB

Hmm.. circular functions.

First I thought it was gonna be quite a struggle for me since I hadn't taken math for a year and that I forgot most of the things I've done last year. It was definitely a struggle for me the first few days because my brain was still in idle mode and I was trying to make my brain get back in rhythm. Fortunately, after a few days of doing math exercises, I was able to finally understand the unit. At first I didn't understand how to convert degrees to radians and vice versa, but after Mr. K gave us the first set of Math Dictionary notes, I finally understood it. The Unit Circle was not that hard to memorize after you work with it after a couple of exercises. Also another area where I was struggling is at graphing trigonometric equations and creating an equation from a graph. From the pre-test last Thursday I finally understood how to scale the graph and from today's class I was finally able to understand the concept of making an equation from a given graph. I'm still not very confident about it, but probably after a few review exercises I should be good.

So, good luck on the test on Wednesday guys and gals!

Scribe for today

First of all, I would like to remind all of you guys and gals that we'll be having our first pre-test on Wednesday. For those new to Mr. K's class, the pre-test starts off with us doing the pre-test first, then after a certain amount of time, Mr. K puts all of us in groups and we discuss all of our answers in our group and we hand in one paper for the group.

Anyway, I'm the scribe for today. Hopefully mine could be as good as the previous scribes.

Today was pretty much just a review of what we did last week, and near the end of the class we started talking about graphing trigonometric functions. First, we started off the class with a couple of questions:

The point (-2, 5) is on the terminal arm of angle θ. Find the exact values of:
a) sin θ b) sec θ

This question is pretty straightforward. First we draw a circle, then put in the coordinates:


















Then we solve for the hypotenuse so we can get the sin of the angle:
a²+b²=c²
(-2)²2+(5)²=c²
4+25=c²
29=c²
c=√29

Now that we know the length of the hypotenuse, we can solve sin θ and sec θ
a) sin θ = opp/hyp
sin θ = 5 / √29

b) sec θ = reciprocal of cos θ
cos θ = adj/hyp
cos θ = -2 / √29
little note: We don't have to rationalize the denominators.

Onto the next problem(s):

a) cot x = -2.3
tan x = 1/-2.3
arctan(tan x) = arctan (1/-2.3)
x = -0.4101, in quadrants II and IV

b) csc x = -2.3
sin x = 1/-2.3
arcsin(sin x) = arcsin (1/-2.3)
x = -0.4498, in quadrants III and IV

But those aren't the answers that we want. We want the related angles. Unless the question gives us a restricted domain, we must solve for all real numbers.

Just to help us in this problem, I made a diagram showing where the two angles are:





















I recall Mr. K telling us to store those angles in our calculator's memory. To store it, press sto> (store), then alpha, then a. We want the positive value though, so we press (-), alpha, a, then sto> (store), alpha, a.

We add/subtract π or 2π to know where exactly the angle is in 0 <x<2π or to know where exactly it is in the circle.

So, to solve:
a) cot x = -2.3
x = -0.4101
a = .4101 (answer converted to positive via calculator [(-), 2nd, ans, sto>, alpha, a])
2π - a = 5.8731 To get the related angle in quadrant II:
π - a = 2.7314
therefore: x = 5.8731 + 2kπ ;k ∈ I
x = 2.7314 + 2kπ ;k ∈ I
Since the angles are only 180 degrees apart, we could leave the answer as:
x = 2.7314 + kπ ; k ∈ I

For csc:
b) csc x = -2.3
sin x = 1/-2.3
arcsin(sin x) = arcsin (1/-2.3)
x = -0.4498, in quadrants III and IV
a = 0.4498
2π - a = 5.8334
This time we add π because the angle is past 180°.
π + a = 3.5914
therefore: x = 3.5914 + 2kπ ; k ∈ I
x = 5.8334 + 2kπ ; k ∈ I

Whew.

After the questions, we jumped in to today's lesson, graphing trigonometrical functions in our graphing calculator, using the values of pi. It's nothing really new to us since we learned this in Grade 11 besides that we're using the values of pi..











On y = sinx, the sinusoidal axis a.k.a vertical shift is 1, which is the maximum value of the function. On y = 2sinx, the vertical shift is 2. Those also are called amplitudes.

To see π values:
1)Press 2nd function, window. Table Setup should appear.
2)Scroll down using your arrow keys to the line that says ΔTBL and put π/2 in it's place.
3)Now press y=, then punch in sin(x).
4)Press 2nd function, table. On the left hand side (X table) you should see different values of π, and on the right hand side (y table) you should see outputs.

I think that's pretty much it. Homework for tonight is ex.6, all of it, and another one that should be posted by Mr. K. The scribe for tomorrow is Tim_MATH_y.
Just comment if there are any mistakes, and I'll change them as soon as I can.