Applied Math 40S (Winter 2009)

So Long ...

noreply@blogger.com (dkuropatwa) — Tue, 28 Jul 2009 22:02:56 PDT

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. ;-)

Class Survey

noreply@blogger.com (dkuropatwa) — Tue, 09 Jun 2009 12:02:51 PDT

The exam is over and we did a little survey in class. The results are below; 17 students participated. If you'd like to add another comment on what you see here email me or leave a comment below this post.

Without any further ado, here are the results of our class's survey. Please share your thoughts by commenting (anonymously if you wish) below .....

Classroom Environment
The questions in this section were ranked using this 5 point scale:

Strongly Disagree	Disagree	Neutral	Agree	Strongly Agree
1	2	3	4	5

The bold numbers after each item are the average ratings given by the entire class.

1. The teacher was enthusiastic about teaching the course. 4.59

2. The teacher made students feel welcome in seeking help in/outside of class. 4.35

3. My interest in math has increased because of this course. 3.35

4. Students were encouraged to ask questions and were given meaningful answers. 4.29

5. The teacher enhanced the class through the use of humour. 4.24

6. Course materials were well understood and explained clearly by the teacher. 4.18

7. Graded materials fairly represented student understanding and effort. 4.12

8. The teacher showed a genuine interest in individual students. 4.12

9. I have learned something that I consider valuable. 4.47

10. The teacher normally came to class well prepared. 4.65

Overall Impression of the Course
The questions in this section were ranked using this 5 point scale:

Very Poor	Poor	Average	Good	Very Good
1	2	3	4	5

1. Compared with other high school courses I have taken, I would say this course was: 4.06

2. Compared with other high school teachers I have had, I would say this teacher is: 4.12

3. As an overall rating, I would say this teacher is: 4.35

Course Characteristics

1. Course difficulty, compared to other high school courses:

Very Easy
0%

Easy
5.9%

Average
35.9%

Difficult
52.9%

Very Difficult
5.9%

2. Course workload, compared to other high school courses:

Very Easy
0%

Easy
17.6%

Average
58.8%

Difficult
11.8%

Very Difficult
11.8%

3. Hours per week required outside of class:

0 to 2
29.4%

2 to 3
35.3%

3 to 5
17.6%

5 to 7
17.6%

over 7
0%

4. Expected grade in the course:

F
0%

D
11.8%

C
52.9%

B
29.4%

A
5.9%

Specific Feedback
[Ed. Note: Numbers in parentheses indicate the number of students that gave the same answer.]

What was your best learning experience in this course?

Learning many things on my calculator
Developing Expert Voices Project
Group Work (5)
Class Discussions
Sharing Ideas
Made learning easier and fun
Solo in-class work
SMARTboard
Technology
Pre-Tests
I could listen better
Personal Finance Unit (3)
Probability Unit (2)
Helping each other
Being able to sit not taking notes because they would be online
Able to learn from students as well as teacher as if it were feedback on my mistakes
Being encouraged to contribute to the learning environment

What was your worst learning experience in this course?

Blogging (3)
None (2)
Blog was sometimes unsteady because notes needed to be written when scribe didn't post
Not having Mr. K. in class
Probability Unit (2)
When I didn't get anything
Vectors Unit (4)
Statistics Unit (2)
Sequences Unit
Periodic Functions Unit (2)
When one student wasted time arguing
Using technology in assignments
Being expected to work hard, few teachers care — I appreciated this "negative" experience

What changes would you suggest to improve the way this course is taught?

Have more students at front showing work to get more ideas and feedback from peers
I think this course was taught great and really enjoyed the online work
A little more explanation in every topic
Less online homework
I suppose maybe look at how you can help individuals do better. Most do better in groups or by talking. I can't learn like that so this class sucked for me.
Nothing really, I thought this course was great and fun; thanks for teaching us.
Any suggestions I have would only make the course pander to laziness.
Watch if the scribe was done on time.
State that reflection posts and delcious links are both done, not one or the other, more clearly.
Try to teach slower, sometimes you go through lessons way too fast for me to understand.
This has been the only math class I've done well and felt confident in both at the same time. Thanks Mr. K!

It's interesting to compare the items that were considered both the worst and best learning experiences. Also, take a look at the list of worst learning experiences compared to suggestions for next year. Help me do a better job next year by commenting on what you see here ....

Today's Slides: June 5

noreply@blogger.com (dkuropatwa) — Fri, 05 Jun 2009 13:39:07 PDT

Here they are ...

Applied 40S June 5, 2009

View more Microsoft Word documents from dkuropatwa.

My D.E.V. Project

noreply@blogger.com (Eugene) — Sun, 07 Jun 2009 20:16:10 PDT

Question #1

George wants to invest $10,000 into an account. He has two options, the first bank offers to invest it at a 7.2% rate for 7 years. His second option from another bank is to invest it at a 9% rate but for only for five years. He wants to know which investment will give him more money after the time is up. Which investment will give more and by how much?George then plans to invest his money a second time at a 12% rate for two years. What will be George's final amount of money in both scenarios? All of Goerge's investments are compounded yearly

Option # 1

N=7
I%=7.2
PV=-10000
PMT=0
FV=16269.09883
P/Y=1
C/Y=1
PMT: END BEGIN

Option #2

N=5
I%=9
PV=-10000
PMT=0
FV=15386.23955
P/Y=1
C/Y=1
PMT: END BEGIN

The first option will give him more by $882.86 (16269.09883-15386.23955)

WHY & HOW

The numbers in "N", "I%" and "PV" come directly from the information in the question.
"P/Y and C/Y" are 1 because the money is compounded yearly and not semi annually or quarterly. Semi annually is compounded twice a year. Quarterly is compounded four times a year.

The second Investment

N=2

I%=12
PV=-16269.09883
PMT=0
FV=19300.49889
P/Y=1
C/Y=1
PMT: END BEGIN

George's final amount will be $19300.50 in scenario one.

N=2
I%=12
PV=-15386.23955
PMT=0
FV=20407.95757
P/Y=1
C/Y=1
PMT: END BEGIN

George's final amount will be $20407.96 in scenario two.

Question #2

When you walk home from the big bridge there is a pizza place and a chicken place. Calculate the total amount of ways home. The P(passing the pizza place), P(passing pizza and chicken place).

There are 336 ways home

The P(passing pizza place) is 38.7%(130/336)

The P(passing pizza & chicken place) is 32.7% (110/336)

Click here to see WHY? & HOW?

Today's Slides: June 4

noreply@blogger.com (dkuropatwa) — Thu, 04 Jun 2009 11:50:49 PDT

Here they are ...

Applied 40S June 4, 2009

View more Microsoft Word documents from dkuropatwa.

Niwatori-san's Corner (Sequences)

noreply@blogger.com (Niwatori-san) — Wed, 03 Jun 2009 21:27:18 PDT

Anyong-hi jumuseyo

!!!!For Ya Imfomation. . . . . . !!!!!!
Blue anecdotes sorta inportant
Red anecdotes Stuff to check/IMPORTANT STUFF take it however you will
Green is for formulas/any calculator stuff!

Remember that your projects are due the midnight of Sunday. So make sure to get it in quite
soon!

Well Getting back to the topic of Sequences the main topic tonite is FRACTALS!

You remember the "Trippy" show of the fractal of the island
(ok i don't remember the name of the island
off my head) yes well like in class how it was discussed that the fractal can be
divided into similar shapes
by dividing the whole shape into subsequent pieces equal to one another.

**** When looking at a fractal such things can follow through your head like:

* Will this fractal diverge/converge? (grow/come to one point)
* What's the area of the shaded areas? (If asked this question)
* What's the implicit and recursive definitions of this fractal
(the "exponential equation" and the
"general definition" through means of finding a common ratio between the
2nd and the 1st numbers in a geometric sequence)

And so forth.... (im sure there are more but for now this is all i can
manage to pull out of my hat
sorry I couldn't pull a bunny rabbit but better luck next time =p)

All is done through a number of series of "careful" observation and analysis of
the fractal finding the pattern to the piece. Or more rather the point of it all.

Well right now you can see that the slides haven't been posted yet so
don't be blaming Mr.Kuros if it didn't sink in to your minds to what
was done in class. And sorry if I sounded rude but it's how blunt i need
to be for the understanding of the course.

All in all my good mates around the world watching us and to my fellow
bloggettes/student peers "Math is the Science of Patterns" - Mr . Kuros

Follow looking for similar paths along your way in life and in the progression
of your studies/classes. The more patterns you have the more easier it is for
you to solve the mysteries of your own "CASE"

And Im yet again sorry folks but I totally forgot to inform about the solving
of the "Shaded Areas" I was sorta stuck between the path to finding
the shaded area and it's a little sketchy about the details but Im sure Ill
get it right away and clear this passage just for your info *pinky promise*

Anywho this ends the night until another day and another time.
Niwatori-san signing off -__-

GO AND SCRIBE CUZ I CHOOSE YOU ----"Daniel"----
*throws pokeball misses and then walks away* (utter defeat)

quote from Niwatori-san -
"The sun is the open pinnacle to enlightenment by revealing the shadows
of your talents"

Today's Slides: June 3

noreply@blogger.com (dkuropatwa) — Thu, 04 Jun 2009 06:24:40 PDT

Here they are ...

Applied 40S June 3, 2009

View more Microsoft Word documents from dkuropatwa.

noreply@blogger.com (iamamanda) — Sun, 07 Jun 2009 22:09:53 PDT

FRACTAL

What is a fractal? Generally "a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole,"

We have not yet learned much about fractals but what they can look like, and how to make one.

An example of a fractal can be like this…

An example of one you can make would be as follows...

The blue would be your first box. Then you would make the purple ones which are a reduced size of the first. Then you'd make the green boxes which would be a reduced size of the purple. This can almost go on for infinity, however the size will eventually get to small to be significant or too small to see. We would eventually have to stop because of that factor.

The next scribe is Carmel

Today's Slides: June 2

noreply@blogger.com (dkuropatwa) — Tue, 02 Jun 2009 14:10:10 PDT

Here they are ...

Applied 40S June 2, 2009

View more Microsoft Word documents from dkuropatwa.

Today's Slides: June 1

noreply@blogger.com (dkuropatwa) — Mon, 01 Jun 2009 21:50:16 PDT

Here you go ...

Applied 40S June 1, 2009

View more Microsoft Word documents from dkuropatwa.

noreply@blogger.com (don) — Thu, 28 May 2009 21:55:35 PDT

so in class today we went over some of last nights homework, and some of the homework on periodic functions a couple days before we learned sequences. the unit periodic functions, well lets say I'm the brightest in that unit. i still don't get the whole concept. so I'm going to try and explain how to answer one of the questions we did for homework.

EXAMPLE

Jud was working with a sinusoidal data, but lost all of it except for two points. A maximum point was (3, 13) and a minimum point next to it was (7, 1). Write a sinusoidal equation that matches Jud's data.

This is the sine formula

f(x) = AsinB( x - C ) + D

What does this formula mean?

"check Lamael's most recent post to find out what it means"

To help you write a sinusoidal equation, the best way is to draw what information that has been given to you.

In this question the maximum point is (3,13) and the minimum is (7,1)

what does this mean? remember in grade like 9, when the the first number would tell us the point on the X- axis and the second would be on the Y -axis? well this is exactly that.

this is how your drawing should look like.

After your done that, you figure out what the sinusoidal axis is. Sinusoidal axis equals the average and that average equals out to be your D in the sine formula.

the sinusoidal axis usually lays on the y -axis creating a straight line in between the minimum and maximum point.

In this case the minimum point is 1 and the maximum is 13. Add those two numbers up and divide by 2 and you get the sinusoidal axis which is equal to 7.

So now we got the sinusoidal axis. having that we can figure out the amplitude or A in the sine formula. The amplitude is the distance from sinusoidal axis to a maximum or minimum point.

In this case, we would subtract our sinusoidal axis from a minimum or maximum point. Here, our sinusoidal axis is 7 so we subtract that from our maximum which is 13 and get a difference of 6 which is equal to our A in our sine formula.

This is how our graph looks like now.

Why does the graph look like this your wondering? remember were dealing with periodic things, so it always goes up and down at a steady pace. like a bug on a wheel.

where did the 11 come from? well on the x - axis the points are going up by 4 so you add another 4 to 7 and you get 11.

the two variables were missing now is B and C.

Lets find B. B in our sine formula is NOT the period it determines the period according to this formula.

PERIOD = 2Pi/B OR B = 2Pi/PERIOD

The period is the difference between two maximum points. In this graph the maximum points are always at 13. At point 3 on the X - Axis the graph is at its maximum point and as you keep going down the line on the X - axis to find the next maximum point you find it to be 11. The difference between 3 and 11 is 8. So our period is 8. we then plug our period into our period formula to figure out what the variable B is.

B = 2Pi/PERIOD

Then.. B= 2Pi/8

Reduced.. B = Pi/4

The last variable were missing is C. C is called the phase shift, or horizontal shift on the graph. in this case, there was no horizontal shift so we leave C as 1.

So our sinusoidal equation looks like this..

f(x) = AsinB( x - C ) + D

f(x) = 6sin(Pi/4(x-1)) + 7

Hopefully my scribe has helped some people. Doing this scribe has helped me understand the unit a little better.

PERIODIC FUNCTIONS TEST TMRW! STUDY STUDY STUDY!!!

next scribe is..
Amanda

Today's Slides: May 28

noreply@blogger.com (dkuropatwa) — Thu, 28 May 2009 10:49:35 PDT

Here they are ...

Applied 40S May 28, 2009

View more Microsoft Word documents from dkuropatwa.

May 26th's and Today's Notes

noreply@blogger.com (Roe) — Thu, 28 May 2009 01:11:14 PDT

As of the notes of Periodic Functions on May 26, we have learned and relearned of clarifying the amplitude, the period, and the phase shift.

To identify the amplitude, simply clarify the difference between the sinusodial axis and the maximum or mininum.

A period is determined through of the fraction 2(pi)/b. The parameter itself can be identified by switching 'b' with the period shown.

Parameter C is the phase shift. The phase shift moves the graph either left or right on the sinusodial axis, it is normally subtracted from x. The phase shift is identified as either a whole number or pi/c if the starting point value is less than a whole number.

We were also taught of the cosine function. But it bears a very close resemblence to the Sine function, so we'll only be learning of the Sine function this year. The difference from the Sine function is that it's starting point is pi/2 units apart.

For today's notes, we learn of Sequences, a list of numbers that follow a certain pattern. We learn of two types of Sequences, Recursive and Implicit. A recursive sequence, is a list of numbers generated by continuously adding the difference to the first term. Such an equation would be y= 3 ( n - 1 ) + 4, the 3 would be identified as the difference. Take note that n would be rank. An implicit sequence is basically a list of numbers generated by a linear equation. More or less y = 3 n + 1. The difference in an linear equation would be the slope.

With that said, this scribe will now bid you adieu. As he is sleep deprived, the next scribe will be Don. Please, the person that is to take care of the scribe list, please update it regularly. This is also for anyone next year as well. If, the scribe list is used again.

Today's Slides: May 27

noreply@blogger.com (dkuropatwa) — Wed, 27 May 2009 13:01:16 PDT

Here they are ...

Applied 40S May 27, 2009

View more Microsoft Word documents from dkuropatwa.

Today's Slides: May 26

noreply@blogger.com (dkuropatwa) — Wed, 27 May 2009 06:39:22 PDT

Here they are ...

Applied 40S May 26, 2009

View more Microsoft Word documents from dkuropatwa.

Transformation of the Sine function

noreply@blogger.com (Lamael) — Mon, 25 May 2009 23:43:54 PDT

Today in class, we learned what each parameter in the sine function does.

This is what a sine function formula looks like:

but.. what does the formula mean?

Let's start with Parameter D:

Parameter D shifts the graph up and down
- a (+) value shifts the graph upwards by
x number of units
- a (-) value shifts the graph downwards

so..if D = 2, the graph shifts up 2 units
if D = -2, it shifts down 2 units

Parameter A:

Parameter A controls the amplitude of
the graph

* The amplitude gets higher when the value of
gets bigger. A negative value will flip the wave
upside down, but the height of the wave does
not change.

Example:

-the black wave is what a basic
function looks like
- the blue wave represents the function with
a negative A value (A=-2)
-the red wave represents the function with a
positive A value (A= 2)

Parameter B:

Parameter controls the width of the
graph. It also multiplies the copy of
the wave.

normal sine function : period = 2π
so...B= 2 is the same as 2π/2 or π
* the value of B becomes divides the
normal sine function.

Example :

- black wave : sin(X)
- red wave : sin (2X)
Parameter C:

Parameter C shifts the graph
left and right
- a (+) value shifts the graph
to the left by x number of
units.
- a (-) value shifts the graph
to the right.

Example:

- black wave - represents the basic
sine function
- red wave - represents a positive C
value ( C=2)
- blue wave - represents a negative C
value (C= -2)

That's it for today's blog. I hope it helped you guys understand the today's topic.

The next blogger will be... Roe.

Today's Slides: May 25

noreply@blogger.com (dkuropatwa) — Mon, 25 May 2009 12:52:29 PDT

Here they are ...

Applied 40S May 25, 2009

View more Microsoft Word documents from dkuropatwa.

My Project Thing

noreply@blogger.com (K_Hannah) — Sun, 24 May 2009 20:22:32 PDT

for one of the questions (since my computer wont let me view past posts/videos, i am just remembering back to a question i remembered from matrices about trips between cities.
I will figure out the details once i get with my partner.

My second question is from the unit of probability.
On the board game you can move pieces diagonally forward.
a) determine the number of different pathways from the game piece to each of the squares on the other side of the board.
b)assume the player is equally likely to go left or right. what is the probability it will land on each destination.

My timeline is the same is chelsias

Today's Slides: May 22

noreply@blogger.com (dkuropatwa) — Fri, 22 May 2009 14:09:56 PDT

Here they are ...

Applied 40S May 22, 2009

View more Microsoft Word documents from dkuropatwa.

Today's Slides: May 21

noreply@blogger.com (dkuropatwa) — Thu, 21 May 2009 14:01:37 PDT

Here they are ...

Applied 40S May 21, 2009

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Developing Expert Voices

noreply@blogger.com (jason) — Thu, 21 May 2009 07:05:54 PDT

Questions:

a.) Statistic Problem

For boys, the average number of absences in the first grade is 15 with a standard deviation of 7; for girls, the average number of absences is 10 with a standard deviation of 6.

In a nationwide survey, suppose 100 boys and 50 girls are sampled. What is the probability that the male sample will have at most three more days of absences than the female sample?

b.)Vectors

Draw scale diagrams of the following vectors using pencil, ruler, protractor, and paper. Label the diagram. Be sure to indicate the scale you used.

(1.) Tiffany walks 13 blocks in a direction East 13 degrees South.

(2.) A boat is headed 300 degrees at 45 km/h.

Time line

May 22 - rough draft questions
May 25 - consult with partner(s)
May 29 - rough copy
June 03 - completion of the project
June 04 to 05 - hand in the project

Developing Expert Voices

noreply@blogger.com (MAC) — Wed, 20 May 2009 18:40:29 PDT

Question 1 : Personal Finance

Debt. Equity Ratio = Total Liabilities - Mortgage / Networth

Lebron is married with two childen. He wants to borrow money to make a major purchase.
His financial advisor prepares a net worth statement for his family with the following.
Lebron and his family live in an $80,000 home on which there is an outstanding mortgage of $52,000.00. He owns a car valued at $20,000.00 and owes 12,000.00 on a 2-year loan he took to buy the car. He has $5000 and a short term personal loan for $2500.00. The family has $1500.00 in a chequing account and another $3000.00 in a savings account. He owns a boat worth $5000.00

Question 2 :

Timeline

May 24: Rough Copy for Questions & Solve Questions
May 25: Create visuals for project
May 26 - 31: Put together all visuals on computer
June 1 - 6: Complete Project
June 7: Hand in Project

noreply@blogger.com (iamamanda) — Tue, 19 May 2009 18:42:51 PDT

STUDY.STUDY.STUDY.

Hey guys we have a test tomorrow so make sure you study, study, study :)

Today we learned that that net worth = assets-liabilities.
Assets is money you have or things of value that you own. There are three kinds of assets:
Liquid Assets: Money you can access easily (cash amounts)
Semi-Liquid Assets: Longer term investments (stocks, mutual funds, or some real estate)
Non-Liquid Assets: Material goods (cars, houses) you have to sell it to make money.
Liabilities is amounts of money that you owe. There are two kinds:
Short Term Debts: Must be paid in the next twelve months.
Long Term Debt: Payments that will take more than a year (mortage).

We also learned today that the Debt/Equity Ratio = (Total Liabilities - Mortage) / Net Worth

You want the outcome of the Debt/Equity Ratio to never be bigger than .5 or 50%. If it is even half a percent higher you will have a hard time finding a bank if you can that will give you a loan. But not is all lost, if it is larger than 50% you may try to get a lower loan, find the money in some bond or somewhere else, take a smaller loan then get another after, or even pay off another debtin order to get that percent 50 or lower.

There a few really good examples of this in the slides Mr.K has put up, so if you feel you need more feel free to also look there.

Wish everyone luck on tomorrows test :) and the next scribe is...Lamael

Today's Slides: May 19

noreply@blogger.com (dkuropatwa) — Tue, 19 May 2009 10:35:58 PDT

Here they are ...

Applied 40S May 19, 2009

View more presentations from dkuropatwa.

Developing MY Voice.

noreply@blogger.com (Daniel) — Wed, 03 Jun 2009 08:55:14 PDT

That's problem one. Problem two will be based on a suggestion Mr. K made about the probability of being drafted. I don't think we ever actually did a question of it though...

Timeline:

By May 25th I will have completed my questions. By June 3rd, I will have filmed portions to be embedded in a prezi presentation. By June 6th, I will have completed my prezi and published it to the blog.