Hey everyone!
This unit went by really fast, and since it's the end of the school year, I'm becoming more lazy, so that means that I really haven't been paying much attention to a lot of things happening in class. So I really need to study a lot and make sure I do well on this test! The only thing I really need to review is the day when we learned about graphing parabolic equations since I wasn't in class for that lesson. I have a feeling it's not a hard thing to pick up, so hopefully I learn everything I need to know before our test, which is on friday. Other than that, I think I'll be okay. I'll just have to read through the slides to refresh my memory, and hope that I do well. I guess that's all, good luck! :)
Showing posts with label renster. Show all posts
Showing posts with label renster. Show all posts
Wednesday, May 27, 2009
Thursday, May 14, 2009
BOB
Late bob .. sorry! I just got home from work an hour ago .
Anyway, this unit was easy in the beginning. I mean, it was really easy to understand. The thing the threw me off was the poker part of the unit. I dont even know the poker hands.. Up until last week I thought that I was doing well in this unit. But now, im not so sure .
I guess that there are alot of things we should know for the test tomorrow. Like, knowing which formula to use.... the choose formula or the pick formula. There's also the formula that we use if there are non-distinguishable objects, and circular permutations. I really think that we should've spent more time on the poker questions, because thats the thing that's really bugging me.
Well, I have a lot of studying to do.
Good luck on the test everyone!
Anyway, this unit was easy in the beginning. I mean, it was really easy to understand. The thing the threw me off was the poker part of the unit. I dont even know the poker hands.. Up until last week I thought that I was doing well in this unit. But now, im not so sure .
I guess that there are alot of things we should know for the test tomorrow. Like, knowing which formula to use.... the choose formula or the pick formula. There's also the formula that we use if there are non-distinguishable objects, and circular permutations. I really think that we should've spent more time on the poker questions, because thats the thing that's really bugging me.
Well, I have a lot of studying to do.
Good luck on the test everyone!
Wednesday, May 6, 2009
Permutations of Non-Distinguishable Objects and Circular Permutations
Hello everyone, today we learned about Permutations of Non-Distinguishable Objects and Circular Permutations. Mr. K started the class by splitting everyone into groups and he gave us a problem to solve.
How many four-digit even numbers are there if the same digit cannot be used twice?
We ended up with the answer 2, 290. Now, you're probably wondering how we got this number. Because the same digit cannot be used twice, we have to consider the fact that we cannot have zero as our first digit number. Having zero as our first digit number would give us a three digit number rather than four. So we looked at two different ways, one having the zero at the end, and another not having zero as our last digit number.
If we had zero as our last digit number, that would leave us with 9 different digits to choose from for our first digit number, then 8 for the second digit number, and 7 for the third.
If we multiply these numbers together we would end up with 504 ways of re-arranging the digits to make a four-digit even number if we used zero as our last digit.
Now, If we didn't use zero as our last digit number, we are left with 4 different digits to choose from. Those digits are 2, 4, 6, and 8.
For the first digit number, because we had taken one digit from the ten we originally had, that leaves us with nine choices, but remember that we cannot have zero as our first digit, so now we are left with eight choices for our first digit. For the second digit we will still have eight, because now, we can use zero, and we've only used two out of the ten choices, and as for the third digit, we would have seven choices.
Like what we did previously, we have to multiply these numbers together, and we would end up with 1792 ways of re-arranging the digits to make a four-digit even number, if we didn't use zero as our last digit number.
After, we added the two ways of re-arranging the digits to make a four-digit even number together, we end up with 2296 ways.
NOW, what if the same digit can be repeated?
Because we can use the same digit repeatedly, we don't have to do the same thing we did for the previous question.
For the last digit, there will be five different digits to choose from. Those digits are 0, 2, 4, 6, and 8. These are the only digits we can choose from as our last digit, because the four digit number has to be even.
For our first digit, we only have nine choices, because we exclude zero, for reasons we had stated earlier. For the second and 3rd digit, we can use any of the numbers, so we have ten choices for both. If we multiply these numbers together, we end up with 4500 different ways to re-arrange a four-digit number.
Now, why do we multiply the number of choices for each digit to solve for the number of ways we could re-arrange a four-digit number? It is because of The Fundamental Principle of Counting. The Fundamental Principle of Counting states that if you have M ways of doing one thing, and N ways to do a second thing, then you have MxN ways of doing both things.
Something Mr. K pointed out while we were solving the question above. Make sure to write an explanation as to why you are doing what you're doing.
How many ways can 8 books be arranged on a shelf, if 3 particular books must be together?
Mr. K explained to us that we should look at the 3 books that must be together as one object. So the way he explained it was that you can take those 3 books, and put them in a bag. Now, you have 5 books plus 1 bag, which leaves you with 6 objects. We can solve for all the different ways we can re-arrange those 6 objects. We end up with:
6!
That's not the answer though, remember the 3 books you put in a bag? Well, once we've found a place to put the bag, we're going to have to take the books out of the bag and find the different ways we can re-arrange them. So now, we end up with:
3!
Using The Fundamental Principle of Counting, we can put those two together, and we end up with:
6!3! = 4320
Permutations of Non-Distinguishable Objects
How many different 4 letter "words" can you make from the letters in the word BOOK?
Well, the answer is 12.
You're probably wondering why the answer is 12, when 4! is 24. Well, the word BOOK, has two O's in it. The two O's are NON-DISTINGUISHABLE, in other words, we can't tell apart. The only way we would be able to tell them apart is by writing the O's in different colors.
It is obvious that there are two copies of each word, but the O's had been switched. If those O's were of the same color, we would have two of each words, and we would only count one of the two.
After that, Mr. K gave us a different scenario. What if the word was BOOO, instead of BOOK? Well, if the word was BOOO, we would only be able to make four "words" out of it. That was when we were given this rule:
That is, the number of ways we can re-arrange the object, divided by the number of ways we can re-arrange the non-distinguishable objects.
CIRCULAR PERMUTATIONS
How many distinguishable ways can 3 people be seated around a circular table?
As you can see from the diagram above, the answer is two. The reason is because, when we are arranging with a circle, it has no beginning or end. Whatever is placed first, wherever we place them, or however we place them doesn't matter, we just start arranging around them.
How many distinguishable ways can 3 beads be arranged on a circular bracelet?
Now, a bracelet question is a special case. This is because, it depends on how we put on the bracelet.
Using the table diagram again, we can see that if the table at the top left hand corner was flipped horizontally, it would be the same as the blue table beside it. So that leaves us with only one way of arranging the objects.
So, that's all we learned today. I hope you guys found it helpful!
Homework for tonight is Exercise 30 I believe.
Next Scribe is Jeck!
How many four-digit even numbers are there if the same digit cannot be used twice?
We ended up with the answer 2, 290. Now, you're probably wondering how we got this number. Because the same digit cannot be used twice, we have to consider the fact that we cannot have zero as our first digit number. Having zero as our first digit number would give us a three digit number rather than four. So we looked at two different ways, one having the zero at the end, and another not having zero as our last digit number. If we had zero as our last digit number, that would leave us with 9 different digits to choose from for our first digit number, then 8 for the second digit number, and 7 for the third.
If we multiply these numbers together we would end up with 504 ways of re-arranging the digits to make a four-digit even number if we used zero as our last digit.
Now, If we didn't use zero as our last digit number, we are left with 4 different digits to choose from. Those digits are 2, 4, 6, and 8.
For the first digit number, because we had taken one digit from the ten we originally had, that leaves us with nine choices, but remember that we cannot have zero as our first digit, so now we are left with eight choices for our first digit. For the second digit we will still have eight, because now, we can use zero, and we've only used two out of the ten choices, and as for the third digit, we would have seven choices.
Like what we did previously, we have to multiply these numbers together, and we would end up with 1792 ways of re-arranging the digits to make a four-digit even number, if we didn't use zero as our last digit number.
After, we added the two ways of re-arranging the digits to make a four-digit even number together, we end up with 2296 ways.
NOW, what if the same digit can be repeated?
Because we can use the same digit repeatedly, we don't have to do the same thing we did for the previous question.For the last digit, there will be five different digits to choose from. Those digits are 0, 2, 4, 6, and 8. These are the only digits we can choose from as our last digit, because the four digit number has to be even.
For our first digit, we only have nine choices, because we exclude zero, for reasons we had stated earlier. For the second and 3rd digit, we can use any of the numbers, so we have ten choices for both. If we multiply these numbers together, we end up with 4500 different ways to re-arrange a four-digit number.
Now, why do we multiply the number of choices for each digit to solve for the number of ways we could re-arrange a four-digit number? It is because of The Fundamental Principle of Counting. The Fundamental Principle of Counting states that if you have M ways of doing one thing, and N ways to do a second thing, then you have MxN ways of doing both things.
Something Mr. K pointed out while we were solving the question above. Make sure to write an explanation as to why you are doing what you're doing.
How many ways can 8 books be arranged on a shelf, if 3 particular books must be together?
Mr. K explained to us that we should look at the 3 books that must be together as one object. So the way he explained it was that you can take those 3 books, and put them in a bag. Now, you have 5 books plus 1 bag, which leaves you with 6 objects. We can solve for all the different ways we can re-arrange those 6 objects. We end up with:
6!
That's not the answer though, remember the 3 books you put in a bag? Well, once we've found a place to put the bag, we're going to have to take the books out of the bag and find the different ways we can re-arrange them. So now, we end up with:
3!
Using The Fundamental Principle of Counting, we can put those two together, and we end up with:
6!3! = 4320
Permutations of Non-Distinguishable Objects
How many different 4 letter "words" can you make from the letters in the word BOOK?
Well, the answer is 12.
You're probably wondering why the answer is 12, when 4! is 24. Well, the word BOOK, has two O's in it. The two O's are NON-DISTINGUISHABLE, in other words, we can't tell apart. The only way we would be able to tell them apart is by writing the O's in different colors.
It is obvious that there are two copies of each word, but the O's had been switched. If those O's were of the same color, we would have two of each words, and we would only count one of the two.After that, Mr. K gave us a different scenario. What if the word was BOOO, instead of BOOK? Well, if the word was BOOO, we would only be able to make four "words" out of it. That was when we were given this rule:
That is, the number of ways we can re-arrange the object, divided by the number of ways we can re-arrange the non-distinguishable objects.
CIRCULAR PERMUTATIONS
How many distinguishable ways can 3 people be seated around a circular table?
As you can see from the diagram above, the answer is two. The reason is because, when we are arranging with a circle, it has no beginning or end. Whatever is placed first, wherever we place them, or however we place them doesn't matter, we just start arranging around them. 
How many distinguishable ways can 3 beads be arranged on a circular bracelet?Now, a bracelet question is a special case. This is because, it depends on how we put on the bracelet.
Using the table diagram again, we can see that if the table at the top left hand corner was flipped horizontally, it would be the same as the blue table beside it. So that leaves us with only one way of arranging the objects.
So, that's all we learned today. I hope you guys found it helpful!
Homework for tonight is Exercise 30 I believe.
Next Scribe is Jeck!
Thursday, April 30, 2009
BOB
So, tomorrow is our test, and after reading over our slides over and over again a few days ago, I finally get this unit! Yes, I finally get this unit.
At first, I really really disliked this unit, jut because of the fact that I didn't like exponents. Yes, I know what you're thinking, "Who doesn't like exponents??" Well, i did. I didn't get how negative exponents worked, and now after reading over the stuff, and after I gave it a try, well.. I realized that it wasn't that hard to understand.
There aren't really a lot of things to remember for this unit, except for the fact that A LOGARITHM is an EXPONENT. Another thing to remember would be that an exponential function turns an exponent into a power, while a logarithmic function turns a power into an exponent.
These are the laws that we should know:
The Product Law
logbMN = logbM + logbN
The Quotient Law
logb(M/N) = logbM - logbN
The Power Law
logbMk = klogbM
We should also know that when no base is indicated, the base of the logarithm is base 10 .
Also, remember the
Change of base formula:
some formula's we should know about..
A = P(1+r/n)t
A = Pert
A = A0(model)t
A = A0(m)t/p
Well, yeah, that`s pretty much what we`ve learned in this unit. There are a few more, but I can`t really remember them at the moment. So I guess I`m off to study.
At first, I really really disliked this unit, jut because of the fact that I didn't like exponents. Yes, I know what you're thinking, "Who doesn't like exponents??" Well, i did. I didn't get how negative exponents worked, and now after reading over the stuff, and after I gave it a try, well.. I realized that it wasn't that hard to understand.
There aren't really a lot of things to remember for this unit, except for the fact that A LOGARITHM is an EXPONENT. Another thing to remember would be that an exponential function turns an exponent into a power, while a logarithmic function turns a power into an exponent.
These are the laws that we should know:
The Product Law
logbMN = logbM + logbN
The Quotient Law
logb(M/N) = logbM - logbN
The Power Law
logbMk = klogbM
We should also know that when no base is indicated, the base of the logarithm is base 10 .
Also, remember the
Change of base formula:
some formula's we should know about..
A = P(1+r/n)t
A = Pert
A = A0(model)t
A = A0(m)t/p
Well, yeah, that`s pretty much what we`ve learned in this unit. There are a few more, but I can`t really remember them at the moment. So I guess I`m off to study.
Wednesday, April 22, 2009
DEV Timeline
APRIL 30 – Have the Story Line Finished
MAY 4 – Finalize Question 1 and 2
MAY 8 – Finalize Question 3 and 4
MAY 11 – Start Final Project
MAY 28 – Finish Final Project
JUNE 1 – Figure out how I’m going to publish my project
JUNE 6 – Final Due date
MAY 4 – Finalize Question 1 and 2
MAY 8 – Finalize Question 3 and 4
MAY 11 – Start Final Project
MAY 28 – Finish Final Project
JUNE 1 – Figure out how I’m going to publish my project
JUNE 6 – Final Due date
Wednesday, April 8, 2009
BOB
It's time for another BOB.
I think that this unit was easier than the earlier units that we've studied, and to be honest, I was doing fairly well. But then, Spring Break happened. Yes, spring break. Well, after the pre-test we had yesterday, I realized that I forgot most of the things we learned before the break. So I really have to study study study.
Here are a few things that we should know for the test.
PYTHAGOREAN IDENTITIES
For this unit, unless the question is asking you to solve the problem, never ever put an equal sign. Use the "Great Wall of China" instead. That's why it is important to always read the questions carefully.
Mr. K gave us some strategies we could use to solve Identities in an elegant way, these strategies were:
I really can't think of anything else to say, so I guess I'll end off this Bob post by saying, STUDY!
Good Luck!
I think that this unit was easier than the earlier units that we've studied, and to be honest, I was doing fairly well. But then, Spring Break happened. Yes, spring break. Well, after the pre-test we had yesterday, I realized that I forgot most of the things we learned before the break. So I really have to study study study.
Here are a few things that we should know for the test.
PYTHAGOREAN IDENTITIES
For this unit, unless the question is asking you to solve the problem, never ever put an equal sign. Use the "Great Wall of China" instead. That's why it is important to always read the questions carefully.
Mr. K gave us some strategies we could use to solve Identities in an elegant way, these strategies were:
- Work with the more complicated side of the identity first
- Rewrite both sides of the identity exclusively in terms of sine and cosine
- Use the Pythagorean Identity to make an appropriate substitution
- Simplify complex fractions, or rewrite fraction sums, or differences with a single denominator
- Use factoring (especially in difference of squares)
I really can't think of anything else to say, so I guess I'll end off this Bob post by saying, STUDY!
Good Luck!
Monday, March 16, 2009
BOB ..
Super late B.O.B.
Yes, im bobing the day before the test, shame on me.
Anyway, at first, this unit was pretty easy, but as soon as we started putting everything into word problems, things went downhill for me. During the pre-test earlier, that was the area which I found the most challenging.
I think I will do well on the test, as long as I study and do some practice questions on the areas that I need help in. There are still some things that I have to work on, like graphing reciprocal functions, but my main focus would be on the word problems.
So yeah, i guess i have a lot of studying to do.
Good luck!
p.s. Im going to add on to this when I get home.. hah .
EDIT:
yeah, so much for adding on to this. i fail at this blogging thing. My computer is broken (sadface) .
Yes, im bobing the day before the test, shame on me.
Anyway, at first, this unit was pretty easy, but as soon as we started putting everything into word problems, things went downhill for me. During the pre-test earlier, that was the area which I found the most challenging.
I think I will do well on the test, as long as I study and do some practice questions on the areas that I need help in. There are still some things that I have to work on, like graphing reciprocal functions, but my main focus would be on the word problems.
So yeah, i guess i have a lot of studying to do.
Good luck!
p.s. Im going to add on to this when I get home.. hah .
EDIT:
yeah, so much for adding on to this. i fail at this blogging thing. My computer is broken (sadface) .
Wednesday, February 18, 2009
reflection
Well, I'm not going to go all crazy with my reflection like the first two, but yeah. I still have a lot of reviewing and notes to look over, and I don't think I'll be ready for the upcoming test. Hopefully I get the hang of this whole unit by Friday.
Considering the fact that I can't remember most of the things I learned in Grade 11 and Grade 10 Pre-Cal, this whole review with the addition of the new things we've learned really frustrated me. I don't really have a lot to say, so I guess this will be the end of my reflection? Wish me luck, and I hope I stop getting distracted. That's all.
K bye ~
Considering the fact that I can't remember most of the things I learned in Grade 11 and Grade 10 Pre-Cal, this whole review with the addition of the new things we've learned really frustrated me. I don't really have a lot to say, so I guess this will be the end of my reflection? Wish me luck, and I hope I stop getting distracted. That's all.
K bye ~
Monday, February 9, 2009
Monday, February 9
Hello, Pre-cal Buddies, well my name is Karen and I am your scribe for today. Sorry to disppoint you guys, but my scribe post will be nothing compared to Mr. mest's. I guess you guys are going to start over the whole beating the record for the consecutive Scribe Post Hall of Fame.
So, we started the class by talking about the Scribe Post Hall of Fame, which is pretty much a site "for great scribes". Mr. Kuropatwa talked about what you need on your scribe post to be nominated. Your scribe post should be well explained, engaging, have good content, and you should also have the message delivered properly.
Another thing we talked about before our actual Pre-Cal Lesson started was the website where you can check out the curriculum. It's like an online text book where you can study any courses online.
Here's the link to the website:
webct.merlin.mb.ca
So, we started the class by talking about the Scribe Post Hall of Fame, which is pretty much a site "for great scribes". Mr. Kuropatwa talked about what you need on your scribe post to be nominated. Your scribe post should be well explained, engaging, have good content, and you should also have the message delivered properly.
Another thing we talked about before our actual Pre-Cal Lesson started was the website where you can check out the curriculum. It's like an online text book where you can study any courses online.
Here's the link to the website:
webct.merlin.mb.ca
Log-in: Demo
Password: Demo
so we can rewrite this equation as
Is There A Pattern?
For Sine, as we move up the y-axis, the numerator goes up by 1, and is a square root. The denominator is always 2.
For Cosine, the pattern is the same as the pattern for Sine, except it moves up along the x-axis.
Now, how about Tangent?
Alex had a really clever idea, he said that as you go down, you divide by root3 , and as you move up, you multiply by root3.
Mr. Kuropatwa said that the pattern that he remembered was that Tan was 1/root3 when it was closest to the x-axis. That is, when root3 is down low. When tan was root3/1, that is when it was farthest from the x-axis, that's when root3 is up top.
After talking about Tangents, we had a Mental Math. The following questions were asked:
1.) sin pi/6
2.) cos pi/3
3.) sin 2pi/3
4.) cos 3pi/4
5.) sin 11pi/6
6.) tan pi/4
7.) cos pi/2
8.) sin pi
9.) cos -pi/3
10.) sin -3pi/4
After the mental math, we talked about ...
The "Other Trig Function" is not that hard to understand, they're just the reciprocals of Sine, Cosine and Tangent. An easy way to know which is the reciprocal of which is by remembering that S goes with C, and C goes with S. What I mean by this is that Sine goes with Cosecant, and Cosine goes with Secant.
They would still fall in the same quadrant. These two questions are not the same, but they are related.
-----
Password: Demo
We started today's class from where we left off during Friday's class: Tangents.
Now, how do we get Tangent you may ask?
We all know SOH CAH TOA
Now, how do we get Tangent you may ask?
We all know SOH CAH TOA
From what we've been learning from our previous lessons, we know that
Sine=y-axis and that Cosine=x-axis.
After reading Aldrin's post, you should know that
Sine=y-axis and that Cosine=x-axis.
After reading Aldrin's post, you should know that
so we can rewrite this equation as
Is There A Pattern?For Sine, as we move up the y-axis, the numerator goes up by 1, and is a square root. The denominator is always 2.
For Cosine, the pattern is the same as the pattern for Sine, except it moves up along the x-axis.
Now, how about Tangent?
Alex had a really clever idea, he said that as you go down, you divide by root3 , and as you move up, you multiply by root3.
Mr. Kuropatwa said that the pattern that he remembered was that Tan was 1/root3 when it was closest to the x-axis. That is, when root3 is down low. When tan was root3/1, that is when it was farthest from the x-axis, that's when root3 is up top.
-----
After talking about Tangents, we had a Mental Math. The following questions were asked:
1.) sin pi/6
2.) cos pi/3
3.) sin 2pi/3
4.) cos 3pi/4
5.) sin 11pi/6
6.) tan pi/4
7.) cos pi/2
8.) sin pi
9.) cos -pi/3
10.) sin -3pi/4
After the mental math, we talked about ...
The "Other Trig Function" is not that hard to understand, they're just the reciprocals of Sine, Cosine and Tangent. An easy way to know which is the reciprocal of which is by remembering that S goes with C, and C goes with S. What I mean by this is that Sine goes with Cosecant, and Cosine goes with Secant.Because Cosecant is just a reciprocal of Sine, their signs will not change. So for the question:
They would still fall in the same quadrant. These two questions are not the same, but they are related.-----
After talking about the Other Trig Functions, Mr. Kuropatwa gave this question to answer on the smart board.
To solve this question, we can use the equation of the unit circle, 
And since it keeps on coming up in our discussions in class and because I too, mentioned it earlier, I'm sure that it is drilled into everyone's head that sin=y and cos=x. So, we can re-write this equation as,
-----
That's all I guess, I apologize for the fact that this scribe post was really really really really late, and that it wasn't great. I really just had too much things happening at once, and even if I didn't, I wouldn't have been able to make this scribe post great. For our next scribe, I pick you.. JOHN L.
.. k bye.
To solve this question, we can use the equation of the unit circle, 
And since it keeps on coming up in our discussions in class and because I too, mentioned it earlier, I'm sure that it is drilled into everyone's head that sin=y and cos=x. So, we can re-write this equation as,
-----
The following questions were given to us, and what we had to do were figure out the exact values for each of the following, and multiply/divide/add/subtract them, which ever one the question asks us to do.
And, this last image is just a copy of the second question above, but it was re-written in a better and neater form. It is clear that having a good form when it comes to writing equations comes in handy once you get into way more complex equations. It will be much easier to see what you're doing, and mistakes can be easily spotted.
That's all I guess, I apologize for the fact that this scribe post was really really really really late, and that it wasn't great. I really just had too much things happening at once, and even if I didn't, I wouldn't have been able to make this scribe post great. For our next scribe, I pick you.. JOHN L.
.. k bye.
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