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Tuesday, May 31, 2005

Some Counting Review

Here are some additional exercises on combinatorics. The interactive "tests" here will also give you explanations of why the correct answer is correct. Enjoy!

If you click on the [Back To {topic}] button at the bottom of each quiz you'll be able to find pages that give helpful lessons on each topic.

Monday, May 30, 2005

More Fun

Well, you folks liked the last test so much, try this one on for size (6 questions):

1. What do you put in a toaster? ... Think carefully and scroll down.











AND THE ANSWER IS: The answer is bread. If you said "toast," then give up now and go do something else. Try not to hurt yourself. If you said, "bread," go to question 2.

2. Say "silk" five times. Now spell "silk." What do cows drink? ... Think carefully and scroll down.











AND THE ANSWER IS: Cows drink water. If you said "milk" please do not attempt the next question. Your brain is obviously overstressed and may even overheat. It may be that you need to content yourself with reading something more appropriate such as "Children's World." If you said, "water" then proceed to question three.

3. If a red house is made from red bricks and a blue house is made from blue bricks and a pink house is made from pink bricks and a black house is made from black bricks, what is a greenhouse made from? ... Think carefully and scroll down.











AND THE ANSWER IS: Greenhouses are made of glass. If you said "green bricks," what the heck are you still doing here reading these questions????? ... if you said "glass," then go on to question four.

4. It's twenty years ago, a plane is flying at 20,000 feet over Germany. If you will recall, Germany at the time was politically divided into West Germany and East Germany. Anyway, during the flight, TWO of the engines fail. The pilot, realizing that the last remaining engine is also failing, decides on a crash landing procedure. Unfortunately the engine fails before he has time and the plane crashes smack in the middle of "no man's land" between East Germany and West Germany. Where would you bury the survivors - East Germany or West Germany or in "no man's land"? ... Think carefully and scroll down.











AND THE ANSWER IS: You don't, of course, bury survivors. If you said anything else, you must never try to rescue anyone from a plane crash. Your efforts would not be appreciated. ...... If you said, "Don't bury the survivors" then proceed to the next question.

5. If the hour hand on a clock moves 1/60th of a degree every minute then how many degrees will the hour hand move in one hour? ... Think carefully and scroll down.











AND THE ANSWER IS: One degree. If you said "360 degrees" or anything other than "one degree," you are to be congratulated on getting this far, but you are obviously out of your league. Turn your pencil in and exit the room. Everyone else proceed to the final question.

6. Without using a calculator - You are driving a bus from Downtown Brooklyn (let's say starting at Court Street) to Brighton Beach in guess where (Brooklyn). At Atlantic Avenue, 17 people get on the bus. At Prospect Park, six people get off the bus and nine people get on. At Eastern Parkway, two people get off and four get on. At Newkirk Avenue, 11 people get off and 16 people get on. At Kings Highway, three people get off and five people get on. And then in Sheepshead Bay, six people get off and three get on. And now you arrive at Brighton Beach ... Scroll down for the question.











What was the name of the bus driver? ... Think carefully and scroll down.











AND THE ANSWER IS: Just look back at the question, look at the first line; it was YOU ... "You are driving a bus from..."

Humbling isn't it? And just think, you are among the most intelligent in the population. ;-)

Sunday, May 29, 2005

Just For Fun

I found this "test" over at Teaching and Developing Online. Try it out .... just for fun. ;-)

Below are four (4) questions and a bonus question. You have to answer them instantly. You can't take your time, answer all of them immediately.

OK?

Let's find out just how clever you really are. No looking at the answers in advance.

Ready? GO!!! (scroll down)

First Question:

You are participating in a race. You overtake the second person.

What position are you in?



Answer:If you answered that you are first, then you are absolutely wrong!
If you overtake the second person and you take his place, you are second!

Try not to screw up in the next question.
To answer the second question, don't take as much time as you took for the first question.

Second Question:

If you overtake the last person, then you are...?



Answer:If you answered that you are second to last, then you are wrong again. Tell me, how can you overtake the LAST Person?

You're not very good at this! Are you?

Third Question:

Very tricky math! Note: This must be done in your head only.

Do NOT use paper and pencil or a calculator. Try it.

Take 1000 and add 40 to it. Now add another 1000. Now add 30. Add another 1000. Now add 20. Now add another 1000 Now add 10.

What is the total?

Scroll down for answer.



Did you get 5000?
The correct answer is actually 4100.
Don't believe it? Check with your calculator!

Today is definitely not your day.

Maybe you will get the last question right?

Fourth Question:

Mary's father has five daughters: 1. Nana, 2. Nene, 3. Nini, 4. Nono. What is the name of the fifth daughter?

Answer:Nunu?

NO! Of course not.

Her name is Mary!

Read the question again.

Okay, now the bonus round:

There is a mute person who wants to buy a toothbrush. By imitating the action of brushing one's teeth he successfully expresses himself to the shopkeeper and the purchase is done.
Now if there is a blind man who wishes to buy a pair of sunglasses, how should he express himself?



He just has to open his mouth and ask, so simple.



So simple it is...

Tuesday, May 24, 2005

Fundamental Principle of Counting

This is a good review of the the material we covered in class today. It has step-by-step explanations and solved examples. There are even a few sample questions for you to try!

Here is another good review site from Saskatchewan. You can choose to review the lesson, get extra help and examples or try some practice questions & quizzes. Ignore the Assignment link; it's broken.

Thursday, May 19, 2005

My 2nd Time Blogging

Well its been awhile that i havent blog and i realized that i lost a lot of marks already and i know that it is bad. So Even though its a last minute blogging I still want to get this blogging mark. I really enjoy this unit because I understand it and i'm having fun while I'm answering this kind of questions. I like solving parabolas,circles, ellipse, and Hyperbolas, I think their cool. Just the name "Directrix" makes me think that this unit is interesting. I think I understand this unit very well and the only problem i have in this unit is answering the word problems and that's about it. I admit that I visit the blog once in a while and i know its bad, because it was made for us and we should benefit it. It's that sometimes I'm busy at work and when i got home I'm tired already to go to the computer and blog. Anywayz, i hope that i got my blogging mark this time and I also hope that my blog would make our blog participation a 100%, because I think I'm the only one who's not blogging.

ahh last minute

well i was laying in bed juuust falling asleep and BAM i remembered i TOOOTALLY forgot to blog. so here i am in my pajamas half asleep blogging. lol. this unit i have to admit is pretty tough, its all about the formulas and the graphs. mr.k made a good point today, DONT try to figure out the problem before you draw your diagram. when you draw it out you can visualize what your looking for and then you can also see things you may not see without the picture. im trying my best to understand what each part of the formula does - and i suggest you all do the same because the first step of answering a problem is knowing what your looking for. so i wish you all good luck on the test. and if your up reading this .. GO TO BED!! ... lol night

Wednesday, May 18, 2005

another test, another blog

so tomorrow is the start of our four day long weekend. but before that even commences we must not forget that we also have a test. we shouldn't get too ahead of ourselves. the conics test, in my opinion, a "thinking" unit. you got to pay attention to the formulas because the ellipse and the hyperbola have similar characterists but we shouldn't get them mixed up and lose marks on stupid mistakes. i too get confused, but with the help of the exerices as well as the worksheets you will learn to know the difference =) this unit was difficult but i guess that means that i need more practice right? well i have another test to study for, so i'm going to just end it here. good luck tomorrow.

Pre-Cal 40S

here we go again.. blogs. Some people say that conics are pretty hard and some say its a piece of cake...... well not really. i just said that,lol. Personally I think conics are easier than exponents and logs but it still has its confusing times. I feel that its not as complicated and it doesnt have too much steps unlike logs.. well some people may disagree to this but hey we all have diffirent views and perspective in things. Conics isnt really that complicated if you remember what formula is suitable for the right conic. there's also the part where you have to determine wheter the conic is vertical or horizontal and finding the focus or foci well pretty much i bet you guys all know what i'm talking about so let me tell you something that most of you probably dont even know.. DID YOU KNOW THAT..... - The conics have been discovered by Menaechmus (a Greek, c.375-325 BC), tutor to Alexander the Great. - Appollonius (c. 262-190 BC) (known as The Great Geometer) consolidated and extended previous results of conics into a monograph Conic Sections, consisting of eight books with 487 propositions. - Appollonius was the first to base the theory of all three conics on sections of one circular cone, right or oblique. He is also the one to give the - name ellipse, parabola, and hyperbola. I bet my marbles you didnt know that! Well guys have good night and happy blogging. I wish us all luck for tomorrow's test!

conics

Another test is here! let's see. the moment of clarity was.... well there are a few, except some stand out more than others. i was confused about how you get 'p' for the parabolas and now i get it! i'm pretty sure i get it. and hyperbolas i feel that i really get. but i don't think we have spent much time on circles and that is just something that i have to review over again. the general form is also something i have to look at but i'm sure that that is all in the math dictionary and that's fine because i can always look over it! so it's all good! and so yeah. i feel that this one of the units that i have had most trouble with when i first took this course. and now, i understand it waaaaaay better than i did last year! so it does kind of pay off to actually go over it twice. and just as long as you learn from it then it's worth it right? of course i'm right! well, now that i'm sure that i know more than i knew last year about this topic all i have to do is just study using the companion site and just review, review, and REVIEW! so yes. i must start reviewing now. bye!

hmmm...Another Hard Unit..well SOMEHOW...

Okay. Here i am again explaining how i am doin' in this unit. First of all, conics is a unit where u need to memorize tons of formulas because of hyperbolas, parabolas, ellipses, and circles. However, conics was the first unit introduced to me last semester, as the first unit of the first term. Somehow, it's easier for me the second time around, but i'm still having trouble with the word problems, like usual. I've also learned some things that i've never knew before, like when to graph the hyperbola and which way it's suppose to be pointing at. Well, I guess this is it. 'Til the next blog or test.

Let's Make It 100% This Time!

Test day tomorrow. Get your Blogging mark here!

If you haven't finished the Conics Review on our Companion Review site you should do it now.

I've collected a number of great links to help you learn and study. When you click on each link below you will be able to select:

  • A review lesson on the topic.
  • A selection of problems to review that have been solved step-by-step.
  • An online quiz with immediate feedback.
  • An "assignment" with some more solved practice problems

So here are the things you need to know about for the test with links to the resources described above:

If you like, you can also try this humourous conics quiz. Try it out; you'll learn something!

By the way, what do you think our chances are of hitting 100% blogging participation this time around? ;-) Let's go for it and translate that effort into 100% scores on this test!

Monday, May 16, 2005

Hyperbola Help

Get help with your hyperbola homework if you need it. The site I've linked to has some exercises you can do tied to a java applet. It will show you what changing the values of "a" and "b" in the standard form of the hyperbola's equation will do to the graph. Play with it for a while .... it'll help you get a feel for the geometry behind the algebra. ;-)

Sunday, May 15, 2005

Puddle of Mud

This unit seems pretty hard. I think it’s because I didn’t do really well in analytic geometry in grade 11. A lot of the questions are on this kind of stuff. It feels like this unit is going really fast too. I thought it was just yesterday that we started learning about parabolas, when really we did ellipses. And now hyperbolas? Just when I was starting to get ellipses, Mr. K throws another one of those “folding lessons” on hyperbolas. I just hope that there aren’t any more sections in conics… at least for a little while. On the bright side, I hope I can catch up on these sections over the weekend.

Thursday, May 12, 2005

The Muddiest Point

Most of you seem to have a good grasp of the ellipse! Fantastic! If you need any help with your ellipse homework you can find it here.

By far the muddiest point in our class seems to be the parabola. Here you can play with the parabola as it's defined from the locus definition (which is what we're studying). Play with the java applets, there are two of them, to get a sense of the role "p" plays in the geometry of the parabola.

IMPORTANT: "p" is half the distance between the focus and the directrix when they are perfectly aligned vertically. By dragging the point "B" along the directrix you will sketch out a parabola. Look for when the point "P" is on top of the point "A".

The second applet will show you what happens when you move the focus around. We will discuss these things in class tomorrow, so even if this doesn't entirely make sense to you right now play with the applets so that you will understand what we're talking about in class. ;-)

There were a couple of other questions that came up in our Muddiest Point exercise:

  • about circles
  • arithmetic series
  • changing from general to standard form and back again

We'll be talking lots more about that last point. Please speak to me one-on-one about the first two -- there were only about 3 of you that were feeling muddy about them. ;-)

Monday, May 09, 2005

Parabolic Dishes and The Ellipse Game

Today we discussed parabolas as conic sections in depth. In particular I emphasized how important it is to keep in mind the geometry of the parabola as you work with its equation.

Watch this! Tomorrow I'm going to ask you why parabolas are important in connection with satelite dishes, television and radio signals. ;-)

Tomorrow we will also review circles and begin our discussion of ellipses. Find out more about what an ellipse is and then you'll be ready to play The Ellipse Game:

Your mission, should you choose to accept it, is to find a focus. You will be given an ellipse of random dimensions and you will have to try to click on one of the foci. Should you fail in this mission at first, you will be given some clues. We will deny any responsibility for holes or other damage caused should you decide stick pins into a drawing board or any other item of household equipment.

Ready? Let's play!

Friday, May 06, 2005

test today =)

so the test is today and just like everyone here mentioned, this was a very difficult unit. there are a lot of formulas that we have to know, and although it seems like a lot, just doing the questions and looking at all the info given, you'll eventually know which one to use. and of course attempting to do the questions is key. what i found difficult were actually the word problems, there is some critical thinking involved and i admit that i lack that. i know that i need more practice with them. having the review class yesterday i found was really helpful because you can work with the peers around you and makes studying less stressful when you're working together. my last thoughts are i guess, read questions carefully because knowing what is asked can help you to answer the question. good luck on the test today everyone =)

The Uncommon Ratio

When we first started sequences and bases, I thought that it was going to be easy. It turns out I was wrong. For a long period of time I couldn’t answer most of the word problems in the unit. Eventually, I found out that it was because I was using the “common ratio” right out of the problem. Now, I know that you should write out at least the first two terms in the sequence and divide them to find the common ratio. There still are some small things that I have to remember, like adding the initial values when needed. I almost always forget to do this. I also, have to review some problems like the bouncing ball question. I’m pretty sure that there will be a question similar to this on the test.

Sequences and Series Blog

First of all, I dont see that 100% participation in blogging happening. But at least there is a constant blog by the few individuals who actually visit this site from our class. Anyways, the only difficulty i have in this unit is the long answer problem solving (bouncing ball, army marching, etc.). I have trouble finding which equations to use from the information given, but everything else after that seems easier for me to do. Also remembering all the equations is a somewhat difficult task. I can remember the geometric formulas, but the arithmetic formulas are a little bit of a challenge. But the more i work with these formulas, the easier it will be to remember, so i guess i'll just keep doing more questions.

Thursday, May 05, 2005

Confusing??????

Well, here's my blog for my 1 mark on the test. Let me just say that I was confused in doing this unit. I must admit,that this was a very EASY unit for me. BUT, as the formulas were introduced to me, I got a little confused by the variables being used, such as m and a. The letter m is the number of "Means" required and a is the first term in an arithmetic sequence. I got confused by these letters because I was taught that the variable for the first term is T1, instead of a, but it doesn't really matter that much. It's just that it's easy for me to remember. Also, the letter m is a variable that is new to me and I just hope I can remember what it is. Also, doing word problems are my weakest points, especially those bouncing ball questions. And NO we ain't getting a formula SHEET. HAHA. I guess that's enough. 'Til the next test.

just a blog for just a mark

hmmmm, once again it's another blog, because you know what's coming up! THAT'S RIGHT! ANOTHER TEST! well it's all good. i better make this count and do this fast cuz the show "Friends" is coming up =p so anyways. yes. sequences and series. when we first started this unit, I did not remember that i ever did this unit the last time that i took pre cal! and it still hasn't come back to me if i ever did. but anyways, what i found that was giving the me the most trouble was the problems with the ball. the bouncing one to be exact. and well, what exactly is a bounce? so earlier in class we're just preparing for the test tomorrow and well, it seems as if like i get everything else except for the ball one. i find it very likely there is going to be a ball question. or something very similar to it on the test! this unit isn't one of the hardest ones? but it is one of the shortest ones. and there are many formulas to remember, i hope we get a FORMULA SHEET! tomorrow! and yeah. well, i guess that just in case we don't, i'll try to memorize the formulas or learn how to build them. honestly though, i think i would remember them better if i knew how to build them, but the thing is, i can't remember how they are built. so i am just going to stick to the whole memorizing thing. yes, grammar in this case was very bad, but we're not in english so it's all good =)

Sequences/series

Another test means another blog. Sequences and series seems to be an easy unit with the given information and formulas. But, the most difficult i had was problem solving. Problem solving was always very difficult for me, maybe it's just because it gets you thinking a bit more. The more i understand the more i know what im doing. With the arithmetic and geometric sequences and series, i find easy. Some questions from the review i find harder such as the bouncing ball. I understand every piece of information, but the only part i don't understand is the total distance it will travel before it comes to rest. Hopefully the notes and worksheets from last semester will help me on tomorrow's test.

Wednesday, May 04, 2005

alright well ive managed to reactivate my account and i was about to go to bed but i figured, hey, lets NOT wait until the very last day as usual even though i enjoy being a rebel, and i decided to make my post now. this unit i have to admit it really confusing, this stuff is all new to me and im having trouble memorizing the formulas, actually, reading alexis's post helped me understand common rations and differences - so thanks for that. ive been working on memorizing the different equations but its still tough, but i guess the more i practice the better i will get at it ... and i recommend the same for all of you. dont wait until tomorrow to start studying for this because believe me, this is some tough stuff. i admit ive never really used the blogger reviews because i find them difficult to comprehend, but the ones mr. k just posted helped A LOT! so i suggest you all use them. and with that said ... im going to bed. good luck on the test =)

Moment of Clarity

I found this unit a bit easier then the last unit, the only problem is that I can't remember all of the formulas. I would always have to look back and forth to my dictionary, so without my dictionary I would have been lost. I also find that I sometimes get confused with the word problems. The bouncing ball question really confused me, but it helped a lot when Mr. K explained it on the board. There was a moment of clarity there, now I feel that I can get a really good mark on the test.

Tuesday, May 03, 2005

Geometric Review

As promised, here is a list of reviews for you ....

You can also find a fairly detailed review here with step-by-step solved examples and 8 practice questions with answers.

Don't forget to bring your ruler with you to class tomorrow. You'll need it to play .... ;-)

blog, blog and blog.

Wooo,,.. The test gonna be tomorrow,I need to post something to get my one mark. well, actually, I didn't know what can I post in this unit. formula, difference and ratio are the basic law in this unit. I think the better way to learn this unit is just need to remember those formula about geometric sequences, and arithmetic sequences. If there is a common difference ,then use the formula of arithmetic sequence, and If there is a commom ratio, then use the formula of geometric sequence. It is not hard to memorize these formula. But when you do your exercise, sometime I feel hard to working on thise question, but after you did those question and then do the next exercise, you will fell better and better. I think the more you practise, the more you get familiar with those formula and understand those questions well. Here, I just want to say that those formula is not hard to memorize it, but it was not hard to understand and familiar to use those formula.

Monday, May 02, 2005

G's and A's

let me share a secret to you guys, one thing I keep on mind while doing this unit is that arithmetic sequences are based on slopes also known as the "COMMON DIFFERENCE" (d). The operations used for arithmetic sequences are addition and subtraction. ex: 3,8,13,18.... d=5 *use addition from left to right* *use subtraction from right to left* for geometric sequences just remember that we use COMMON RATIOS and its all about multiplying and dividing. ex: 12, 6, 3, 3/2.... r=1/2 *to be honest the only thing I really do to check if its geometric is that I divide it from right to left, I feel more comfortable doing that.* for sigmanotations and infinite sums(converging and diverging).. That's just something I have to work on to be honest.. And I know 2 days may not be enough but I'll give it my all on wednesday.. I hope my tips helped even a little bit. oh and hey if you already know how to do it and you just find my explanation more disturbing and confusing just stay with what you know and if I have any mistakes please don't be afraid to correct me. =) HAPPY BLOGGING!

Geometric Prompting

The unit test is on Wednesday and the deadline is getting close to get your blogging done. In an effort to make your lives easier ;-) by giving you things to blog about consider this problem:

A student strained her knee in an intramural volleyball game, and her doctor prescribed an anti-inflammatory drug to reduce the swelling. She is to take two 220-milligram tablets every 8 hours for 10 days. Her kidneys eliminate 60% of this drug from her body every 8 hours.

Blogging Prompt
  1. How much of the drug will remain in her body after 10 days, just after she takes her last dose of medicine? If she continued to take the drug for a year, how much of it would be in her system just after she took her last dose?
  2. If the initial dose is halved, what will happen to the stabilization level of the medicine in the body?
  3. If the recurring dose is halved, what will happen to the stabilization level of the medicine?
  4. If the elimination rate is halved, what will happen to the stabilization level of the medicine?

A successful response to this blogging prompt will answer #1 above and at least one of #2 - #4. It will also show all work done to get the answers. If you want to check your work you can use this interactive applet. Instructions on how to use the interactive applet are here.

Have Fun and Happy Blogging!!