Friday, June 26, 2009

So Long ...

We had our graduation exercises today. A gentle push into the world for all of you. I hope you're leaving with the keys to your future in your hand.

I'm so glad we've had this time together,

Just to have a laugh or learn some math,

Seems we've just got started and before you know it,

Comes the time we have to say, "So Long!"

So long everybody!

Farewell, Auf Wiedersehen, Adieu, and all those good bye things. ;-)

Tuesday, June 16, 2009

324th post; It's the end

So I've been meaning to do one final post, forever will I no longer have to blog for school. Exams are over and I'm sure you all did excellent. The school year has ended and it is now time for the exams. Study hard everybody, good luck with the rest of the exams.

I dreaded going to class everyday but I THINK I'm gonna miss it. It's weird that its all finally over. All the memories created through out the semester. As classes went by I think my interest in math sparked.

Thank you Mr.K for educating us so well in math, math wasn't so boring with you teaching us. Those interesting little facts and stories you always feed us. It was awesome how you got each student involved in someway. It is a shame that DMCI will be losing a teacher like you. Congratulations on your new job, take care and good luck in the future.

On the other note were you this type of student? I know I was.
New school semester:

At the first week:

At the second week:

Before the mid-term test:

During the mid-term test:

After the mid-term test:

Before the final exam:

Once know the final exam schedule:

7 days before final exam:

6 days before final exam:

5 days before final exam:

4 days before final exam:

3 days before final exam:

2 days before final exam:

1 day before final exam:

A night before final exam:

1 hour before final exam:

During the final exam:

Once walk out from the exam hall:

After the final exam, during the holiday:

Isn't that cute, I just thought I'd share.

Farewell Pre-cal 40S Winter 2009 Class

Thursday, June 11, 2009

[8]Now that we've come, to the end of the road...[8]

Awwwuh. How sad, it's the last day of math and the semester is almost over. It feels like time has just passed us by so quickly, not even taking a short moment to stop and glance back. And thus, the last few posts for this class blog start to appear.

I will truly miss this class. A whole whack of memories have been created in such a short amount of time that we will all surely remember throughout the course of our lives. In all honesty, I thought this class would be boring at first, but man was I wrong. Each day presented a new challenge Even if some of it was review, things were somehow twisted to create a brand new challenge. I swear, after this class, I will never look at life the same way again. As I go home, or even when I'm out running, I always find myself looking at the math around us all of a sudden. It's as if a whole new light has suddenly been shone on the Earth. One time me and Dion even stopped to count the branches on a tree to see if the way they grew followed the Fibonacci Sequence (and to our surprise, they did). A lot has been taught in this class, not only about math, but about life and other subjects as well.

About my progress throughout the class, all I can say is that I did the best that I could and that's all that I wanted to do. The mark had some importance to me as it made me want to work harder to raise it up but overall, I'd say it was the experience that suddenly became important to me.

Now that I've done a few older exams for practice, I think I have found my strengths and weaknesses in this course. I would have to say my biggest strength is Identities. I think it was because it came really easy to me when we learned it and when I saw how it could take such complicated looking things and turn them into 1 term answers, I was amazed. It made me even more interested in the subject. The hardest thing would've had to have been Combinatorics. Who knew counting could be so difficult?! For me, the most difficult part is probably the Binomial Theorem. It was a hard concept for me to grasp right away, but I think I get it now. Hopefully I will have known it enough for the exam.

Am I worried about the exam? Not too much. I've graded myself on the previous exams I've done and I've gotten pretty consistent marks that I'm proud of. Hopefully I do really well on the exam. I will try to aim for that 100%.

I guess I should end this by saying a few things.

Thank you so much to the rest of the pc40sw09 class. You have all helped to make this semester a lot less stressful. Math was kept fun because we weren't afraid to speak up. The heat of "competition" was kept burning by a small handful (you know who you are) and it made things a whole lot more interesting. We shared each other's struggles and celebrated each other's triumphs. We were always there to help each other out where it was needed. We were like one big happy math family. I'll always cherish the memories from this class.

Thank you to Mr. K. Math would be so boring if it weren't for people like you. So passionate and so energetic. It makes us kind of want to go to math class. I guess the coffee would explain all the energy, but passion, that comes from straight the heart. So many great memories were made in this class and a lot of them involve you like
  • the sine dance
  • Pi Day
  • your block of wood
  • that "ninja" who came to visit
  • your cool tricks on the smart board
  • the snapping thing you taught us
  • that quadratic equation song
  • and a whole lot more!
Your cool little sayings made the day a little more interesting as well. Like that whole "rabbit's foot" thing you say before we take a test or a quiz and that thing you say when you ask if anyone has a question then you ask if anyone has a good joke (even though none of us ever did). Even on a really gloomy and bad morning you never fail to show up with a big smile and a surplus of energy. It amazing, really.

It's such a shame that we must already say our goodbyes after such a short amount of time, right when I was looking forward to AP Calculus, but it's destiny. Even when you leave, remember that you have left your mark at DMCI and you've made a great impact on the lives of many of the people whom you've taught. For that, we all salute you. Congratulations on your new job and good luck.

And lastly, to my D.E.V. partners Mary and Dion. I know this has been said before, but you two really made this semester a lot less stressful, especially when it came down to making our D.E.V. A potentially (non-intentional) stressful project was made really fun because I had the great honor of working with you two. If it had been anyone else, our project wouldn't be the same. Thank you so much for making this experience everything that it was.

It was a great honor and a pleasure to be in a class filled with such brilliant minds. I wish you all the best in your future studies and that you continue to shine. Remember that we'll always have this blog to keep us connected. Good luck to everyone on our exam tomorrow. Everything we have done in this unit has been leading up to this point. Let's knock this one out of the park!

For one last time, peace out!

There are never any final goodbyes and ends, there are only "see you later"s and new beginnings.

Wednesday, June 10, 2009

This is it I guess

Well, this semester of math is coming to a close and I must say that I have greatly enjoyed this class! It's been difficult at many times but for each hard time there has been a greater number of laughs and even more learning. I feel confident going into the exam but that is not what this post is about. It's more about looking back at the year and especially at our great teacher Mr. K.
It's going to be so different with out you Mr. K.
Here are a few memories gathered from your class Mr. K. that we're not going to forget(mostly XD).

These last 2 mornings without you in the room, it's been oddly quiet so we've turned on your music ourselves!!
It's just not going to be the same, "Any questions, complaints, concerns, uncertainties, anxieties.... etc..".
We're going to miss your one lie per class!
The story you told where when you were a little kid, you always wondered how so many people fit "in" the radio.. and they came to YOUR radio, and not someone else's radio!!!!
The time, not long ago, when learning about conics, you took the role of a samurai and amazed us with your skillz and vocabulary! (and calling it a shu-hords)
The time when you wanted to make sure we never forgot this thing... which i forgot... and you went NO NO NO NO NO NO NO NO NO NO NO NO NO all over the smart board!
Someone has just told me that you always wear crocs! Not sure if it's true, is it?!?! If it is why??
Were going to miss your little block of wood with the 3 different views.
Were going to miss your amazing snapping technique!!!!!
Pi day was amazing as was going around sharing the love that was pie to the school.
Your cup of coffee every morning!
The story you told of how pythagorus thought beans had souls!!!
Your mathematical hero is Euler.
Putting blogging into a whole new light for us.
Although I was not there, people are telling me of how you thought
Well, this is it. Have a great summer everyone! Come back and visit Mr. K.!! If anyone has any other stories or memories let me know and I'll update my post!!

Final BOB: Good Luck To All

Hey guys this is the last time I will probably get the chance to blog in this site so I'm gonna take my time saying good luck to everyone who is taking the exam.
Since the exam is tomorrow and today is our last day i wanted to make sure i post a day before the exam just like how we would usually blog on test. The only exception is that this is gonna be the biggest test were gonna have.
In the classes I've spent here I've learned quite a lot of things. Besides math of course we were taught some pretty cool stuff too. For all of you guys who are reading i encourage you to take at least 5-10min from your busy schedule to post up our last blog reflecting this semester.

Why not? For some of us it will be our last time to blog so why not give it a go, for the others well you can probably just say good luck to everyone.
If there is something i do want to reflect on is how inspiring our teacher is. I for one am sure gonna miss him when we depart. We will someday meet again and everything you taught us we will remember in our own ways. The only thing i regret is that our time with you was short, but the memories last for a life time so i guess that compensates it.
Good luck to you our teacher. With patients and skills you taught us what we need to know. Now it is our turn to take the test and try our very best to succeed with the knowledge you provided us.
Once again good luck to everyone who will be taking the exam and don't over strain yourself in studying at the last minute. Take a break, look over the notes, have a little fun, and have plentiful of a good nights rest. When the exams comes your efforts will be tested.
Good luck again to everyone
Hope you do alright

Monday, June 8, 2009

Saturday, June 6, 2009

Scribe...i accidentally put BOB earlier-__-

*note* Mr. K. made a correction to the formula we learned in previous sessions:
the correct formulas are now and
If you look the june 5 slides, pg 6 and 7 shows how we get to these formulas (sorry, my print srn doesn't really work)

On friday, the main thing we learned was solving infinite geometric series!'s the deal...basically, any fraction that is below 1 and over 0, to the power of infinity will be equal to zero...of course it's not REALLY zero, but our calculators don't have the potential to hold a number less than google, and there is no exact value for it since infinity is an idea and not a number...since it's really ultimately infinitely close to zero, we make it equal zero, making our lives easier. Look at the June 5th slides, page 13 for an example. be honest i don't really know what else to add...i'm a little preoccupied thinking finishing up my final project and worrying/studying for the exam...if anyone needs more clarification, just leave a comment within the next week and i'll fix this up some more...

-Jonno out

Friday, June 5, 2009

Thursday, June 4, 2009


Arithmetic and Geometric series.

We started the class with a quick probability question, one that was brought up by a student.

When solving questions like these, always try to go back to the basics. Probability is the number of favorable outcomes over the possible outcomes. From that, we have something to work with.
Finding the possible outcomes, or Sample Space.
  • The question states that "4 men and 4 women" would be chosen. This means that out of the 7 men, 4 will be chosen (7C4), and out of 10 women, 4 will be choose (10C4).
Finding the favorable outcomes.
  • Since the question said that, "Allen and Bridget will be among these 8 chosen people", we already know that they are part of the possible outcomes. They are represented by the green and blue "1"'s.
  • Out of the 7 men, only one has been chosen, (Allen). This leaves us with 6 more men, and 3 more spots for men, 6C3.
  • Out of the 10 women, only Bridget has been chosen. This leaves us with 9 more women, and 3 more spots for women, 9C3.
As a result, you would get what is shown on the image above. (:


Today's class was focused on:
  1. Arithmetic and geometric sequences
  2. Series
  3. Arithmetic and geometric series.
  4. Sigma Notation
Arithmetic sequences
An arithmetic sequence is a sequence (ordered list of numbers), where a fixed number(common difference) is found between two consecutive terms. (negative numbers are added too! )
This means each term is going up or down by the same number.
When wanting to find the nth term in an arithmetic sequence, refer to the equation below. (use Carl Friedrich Gauss's 7year old story to help you remember the equation.)

Geometric sequences
Geometric sequences are like arithmetic sequence, but instead of adding its multiplying. This means instead of a common difference, there's a common ratio.
When finding the nth term in a geometric sequence, refer to...
Series is defined as, the sum of terms in a sequence. (Sn, where S reads as "sum of" and n would be the rank of the nth term. ex. S4 = sum of the first 4 terms.)

If we were to have a sequence of 1,2,3,4,5,6,7 etc, the series would consist of 1,3,6,10,15. Why? Well the first term is a given, 1. The second term would be 3, because that was the sum of the first and second term from the sequence, (1+2). The third term is the sum of the first, second, and third terms from the sequence. (1+2+3). The orange circled numbers in the above picture are the ranks.

Arithmetic series
Arithmetic series is the sum of numbers in an arithmetic sequence. This would be helpful if you are asked to find the "sum of integers from 1 to 5000" for example. Where n would be 5000, because there are 5000 terms, a would be 1, because that is the value of the first term, and d would be 1, because that's the common difference. (numbers are going up by one)
Or you might be asked "What is the sum of all multiples of 7 between 1 & 5000".
What you know:
  • From the sequence of multiples of 7 between 1-5000, first term is 1.
  • Last term is 4998
  • common difference is 7.
What we need to know:
  • number of terms within that sequence.
By using the arithmetic equation, tn = a + (n-1)d, plug in known values, do some grunt work, and you'll be able to find n. (or you can just take the last number, 4998, and divide by 7, to see how many times 7 can go into it.4998/7 = 714) Once you've found the number of terms, plug it into the arithmetic series equation. ta-da~
Now don't get too carried away with questions a and b. These kind of questions wont be asked on the exam, but you'll need to know the methods of a&b in order to solve c. (c = a question likely asked on the exam).

Logic:( The sum of all integers 1-5000) - (sum of all multiples of 7) = sum of all integers not multiples of 7. This "build up" to a question, is called scaffolding.

Geometric series.
Sum of numbers in a geometric sequence.

Sigma Notation
Is the shorthand way of writing a series, also known as the weird looking "E". Sigma is really confusing, if you don't know how to read it. The n=1 tells you the value of the first term, which is 1. The 4 on top of the sigma is nth number of term to stop at. The (2n-3) is the "rule" or equation you follow.

bye guys! good luck on the exams and your DEVs!
The next scribe is jonno!

Today's Slides: June 4

Here they are ...

Wednesday, June 3, 2009

stress impedes learning?!

"What’s your sine? It must be pi/2 because you’re the 1"

just to lighten up the moods for all those who are studying hardcore. As pacifico said,"stress
impedes learning", so cure it with laughter!


Today's Slides: June 3

Here they are ...

June the Third Scribe

First of all we split into groups and Mr.K informed us that we were starting our new unit, sequences. We should be done this unit on Friday or Monday. So be prepared to move really fast!

Okay well apparently today was mostly a review from grade 10 (if you can remember that far back.. good job!)
On the first slide there were four sequences...

4, 7, 10, 13, __, __, __
3, 6, 12, 24, __, __, __
32, 16, 8, 4, __, __, __
1, 1, 2, 3, 5, 8, 13, __, __, __,

Mr. K wanted us to fill in the blanks and explain how we found the missing terms...

4, 7, 10, 13, 16, 19, 22 (Add 3 to the first term to find the second term. This is called an arithmetic sequence. )
3, 6, 12, 24, 48, 96, 192 (multiply the first term by 2 to find the second term. This is called a geometric sequence.)
32, 16, 8, 4, 2, 1, 1/2 (multiply by 1/2.)
1, 1, 2, 3, 5, 8, 13, 21, 34, 55 (this is the Fibonacci sequence! Add the first and second term together to find the third term.)

Now let's take a closer look and try to identify some patterns that can be applied to any other sequence we might encounter in the future.
4, 7, 10, 13, 16, 19, 22

Note: If you are asked to find the 37th term and you plan on adding 3's, you must add 36 threes.How do we get 3n + 1 ?
Well since we found the y-intercept we can graph this.

By looking at this graph we can see that the slope is 3. So for future reference remember that our slope is the constant. So let's make an equation for this sequence.
tn= 3n+1
Where 3 is the slope and 1 is the y-intercept.

Everytime we have an arithmetic sequence it will be a linear function.
This is the graph of our sequence. Here is how you would make that on your calculator! Hit stat, edit. Under L1 enter your rank (1-7) under L2 enter your values (4, 7, 10, 13, 16, 19, 22) Now hit 2nd stat plot (top left corner of the calculator). Hit enter and make sure plot 1 is on, under type make sure the dots are selected. Then hit graph.

Next we covered some definitions:
Recursive: Repeats again and again.
Implicit Definition: This is the teenage way of saying hi, it's an implied hello. Only clear to people who know what they're looking for.
The Common Difference (d): The number that is repeatedly added to successive terms in an arithmetic sequence.
Common Ratio: The number that isrepeatedly multiplied to successive terms in a geometric sequence.

How to find the nth term in an arithmetic sequence.
tn= a + (n-1)d
Where tn is the nth term
a is the first term
n is the rank of the nth term in the sequence
d is the common difference

How to find the nth term in an geometric sequence.
tn= ar^(n-1)
Where tn is the nth term
a is the first term
n is the rank of the nth term in the sequence
r is the common ratio

Here is the next sequence we looked at, 11, 5, -1, -7...
We were asked to find the 51 term.
Look at the difference between the terms.
5-11= -6
-1-5= -6
Therefore we know our constant is -6. Remember we're not subtracting 6 from the first term to get the second term, we are adding -6! :D

Okay so how to find the 51 term. First let's make a formula.

tn= a+ (n-1)-d
Where n is the term. a is the first value and d is the difference. So we have..

t51= 11+ (51-1)(-6)
= -289

Next we looked at the sequence 3, 6, 12, 24, 48, 96, 192
Notice the difference is not constant, so this is not an arithmetic sequence.

To make an equation for this kind of sequence we use the formula, tn= ar^(n-1)
a= the first term r= ratio
The ratio for this sequence is 2 because 6/3=2 and 12/6=2 etc.
So the implicit definition is tn= 3(2)^(n-1)

Next question! 32, 16, 8, 4, 2, 1, 1/2
We multiply by 1/2 to get the next term so 1/2 is our ratio. Now we find the 10 term.
tn= ar^(n-1)
t10= 31(1/2)^10-1)
t10= 1/16

If differences in sequences are different it is NOT arithmetic.
If there are common ratios it is geometric.

And the last slide..

Um next scribe is Mary.

Homework is exercise 44 and 45.

The Egyptians have Scribes.

Hi guys! This is Pacifico, the scribe for today!

Today, we delved deeper into the cancer question, and other things; but mainly the cancer question. We also learned a new formula! And we also get to know another way to solve a certain probability question. Things to remember first:

v Don’t forget to accept the invite to the DEV blog!



v In A|B, | is a shortcut for the phrase, “…given that we already know…”

So, let’s get this scribe started!

For this part, I will only talk more about Q. #4 because Q. #1-3 is a no-brainer for us. Q. #4 starts the semi-complicated things, notably c).

In this slide, it tells us that the probability that person who tests positive for cancer has cancer. Mr. K. used the formula P(C|P) = (4900 ÷ 2400) = 19.76%

P(C|P) is said as: probability of people that have cancer given that they’re already positive.

How did the heck did he get that, you ask?

C = has cancer

H = doesn’t have cancer

P = tested positive

N = tested negative

P(C|P) = P(CP) ÷ [P(CP) + P(HP)] or

Probability of people that have cancer given that they’re already positive is equal to the probability of people that have cancer that is tested positive divided by the sum of the probability of the people that don’t have cancer but is tested positive.


P(C|P) = ( 0.005 × 0.98) ÷ [(0.005 × 0.98) + (0.995 × 0.02)] = 0.1976

So the answer to the question: What is the probability that a person who tests for positive for cancer has cancer is 19.76%

This slide is asking for P(H|N). By reading the question, we know that it’s the same as the last question. So we apply the knowledge that we know already and solve the question!

P(H|N) = P(HN) ÷ [P(HN) + P(CN)]

Answer using this formula!

The next slide is also the same question as the last 2, so I’m pretty sure that you can figure this out on your own (unless this scribe is sucky—which by the way you have to tell me so I can change it!)

Ah… This question…

To find the probability that the couple has at least 2 girls assuming that having a boy or a girl is equally likely events…

We used permutations, from the unit Combinatorics, to find the number of ways of getting 2 girls.

You could use a tree diagram to find the answer, like what is shown below, but that’ll take a long time and it’s going to waste space.


GGBB à 4 “slots” (number of letters) and 2 non-distinguishable object that both have 2 same things.

number of ways to get 2 girls = 4! ÷ (2!2!) = 6

And then, we figure out the probability of getting 2 girls and 2 boys.


P(GGBB) = (½)(½)(½)(½) = 1/16

After that, we multiply the P(GGBB) and the number of ways to get 2 girls.


P(2G) = 6 × (1/16) = 6/16 = 3/8

To compress all that: P(2G) = [4! ÷ (2!2!)] × [(½)(½)(½)(½)] = 3/8

The original question was, “find the probability that the couple has AT LEAST 2 girls.” Therefore, we also calculate the P(3G) and P(4G), which is shown in this slide.

Then to get the final answer, we add P(2G), P(3G) and P(4G) together.


There’s another easier way to find the answer!



P(at least 2 girls) = 1 – [P(1G) + P(0G)]

= 1 – [(1/2)^4 × (4+1)]

= 11/16 <-- answer is the same as adding P(2G), P(3G) and P(4G)


That concludes my scribe post…

Next scribe is… REBECCA! Hurr durr…

Postedit: Sorry for the lateness! I was doing it in Dreamweaver then I fell asleep halfway of the scribe post!

Tuesday, June 2, 2009