Thursday, June 29, 2006 

The Adventure Continues ...

Our adventures in blogging continue....

Watch for 3 new blogs going live September 6, 2006 ...




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Wednesday, June 28, 2006 

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! Watch this space in the fall for pointers to new blogs for each of my classes.

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




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Sunday, June 18, 2006 

Student Survey Results

We did a little survey in class the day after we recorded our podcapsule. The results are below; 17 students participated. So, without any further ado, here are the results of our class' 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 DisagreeDisagreeNeutralAgreeStrongly Agree
12345


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

1. The teacher was enthusiastic about teaching the course. 4.88

2. The teacher made students feel welcome in seeking help in/outside of class. 4.65

3. My interest in math has increased because of this course. 3.76

4. Students were encouraged to ask questions and were given meaningful answers. 4.53

5. The teacher enhanced the class through the use of humour. 4.47

6. Course materials were well understood and explained clearly by the teacher. 4.47

7. Graded materials fairly represented student understanding and effort. 4.24

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

9. I have learned something that I consider valuable. 4.29

10. The teacher normally came to class well prepared. 4.59

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

Very PoorPoorAverageGoodVery Good
12345


1. Compared with other high school courses I have taken, I would say this course was: 4.65

2. Compared with other high school teachers I have had, I would say this teacher is: 4.65

3. As an overall rating, I would say this teacher is: 4.53

Course Characteristics
The questions in this section were ranked using this 5 point scale:

Very EasyEasyAverageDifficultVery Difficult
12345


1. Course difficulty, compared to other high school courses: 3.35

2. Course workload, compared to other high school courses: 3.31
(This question answered by 16 students.)

3. Hours per week required outside of class:
(This question answered by 16 students.)

0 to 22 to 33 to 55 to 7over 7
25%44%12%19%0%


4. Expected grade in the course:
(This question answered by 14 students.)

FDCBA
0%29%29%36%7%


Specific Feedback
What was your best learning experience in this course?

Pre-tests
Vectors
Probability
Design & Measurement
Real life applications of math (2)
Almost everything
Online tools
All but Statistics
Stories about the Greeks and infinity
Scribes (3)
Blogging (4)
Wiki assignment
"Say it six times"
Group work (2)
Learning to use graphing calculator
Using the internet for learning
How teachers love teaching


What was your worst learning experience in this course?

Statistics
The exam
Using the iMac lab for the Personal Finance unit
None (4)
Not getting tests back quickly
Fear of asking questions
Homework quizzes
Personal Finance (2)


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

More stories and extra topics (2)
Blog
Math dictionaries
More Projects
None (3)
Give notes on using the graphing calculator
Give tests back quickly (4)
Give regular grade updates
More jokes
More wiki work
Teach Personal Finance using only the graphing calculator


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 ....




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Friday, June 16, 2006 

Message in a Podcast: Our Podcapsule

The students in our class wrote their final exam on Wednesday June 14; they ended their high school mathematics careers. We made a podcast to celebrate! We left ourselves a "podcapsule" instead of a "time capsule." We left our future selves a message; hopefully it will help us improve our learning.

Here is our Podcapsule (5 minutes, 52 seconds). Please leave any questions, concerns, complaints, compliments, confusions, uncertainties, anxieties or other inquiries in the comments to this post.

You can also leave us an audio message if you wish. ;-) (You'll need a microphone.)

This isn't our last post yet -- I've got at least two more I want to get out before the end.




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Tuesday, June 13, 2006 

SCRIBE!!!

HELLO EVERYONE! This is Jessica, I haven't been the scribe in a while so I decided to volunteer again! This morning we had our first part of our exam and hopefully everyone did well!! Tomorrow morning we have our second part of our exam, everyone don't forget we need two pencils, an eraser and a geometry set. BE READY! In class today a couple of us recorded our podcapsule and the rest of us continued making our notes on our sheets.

Thats all for today! GOOD LUCK EVERYONE ON THE EXAM TOMORROW!




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The password to the wiki is rwgtktea.

.. Just in case anyone was unclear.




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Monday, June 12, 2006 

Scribe ; The Day Before Provs!

Hellooo everyone. Unbelievably I am scribe, once again -_-' But that's fine, not much to report anyway. But here is something very, very important: As everyone should know by now, tomorrow is the start of the Provincials! Everyone should be infront of the Imac Lab @ 8:45 am, due to the fact that pen should be on paper by 9:00 am. MAC LAB, 8:45 am. That also goes for the continuation of exams on Wednesday. So today for first period, we were handed one yellow sheet of paper on which we were able to write anything that we thought could help us for the exams. We could have written on the sheet, back to back if we wanted. The thing is, seeing as how we have 'tools' such as our blog and thinkfree and everything else we've been taught during the course, we'll legitimately be able to access these websites for the exam as well. So for second period, a Wiki was created in which we started to put the information from our dictionaries. I believe it was Cait who initiated this, I'm not entirely sure actually..But there we have it, our very own Wiki! So hopefully, everyone contributes a little bit so that we have good notes to refer to incase we need to for the exam.


Goodluck to everyone. Study well. It was great being in this class =)




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UNITS

Matrix Modelling - feb
Probability - feb/mar
Variability and Statistical Analysis - mar/apr
Vectors - apr
Personal Finance -may
Applications of Perodic Functions - may
Sequences -may/ june
Design and Measurement-june




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Sunday, June 11, 2006 

Scribe Post for Friday, June 9

We had one class for math on friday and everyone got to choose which units to review for the exams.

Nobody chose to review Matricies and Sequences. So we are to review these units: Design & Measurement, Statistics, Probability, Personal Finance, Vectors, and Periodic Functions.

Today we did a worksheet on design & measurement.







(a) COST OF FLOOR COVERING: (show all work.) (1 mark)
Vinyl flooring is sold in 6-foot widths. The area under the tub will not be covered and the flooring is to be installed in one piece. What length of flooring do you need to buy?

10 - 2.5 = 7.5 ft



(b) PAINT COSTS: (show all work) (5 marks)
The walls are 8 feet high and the dimensions of the door are 30 inches by 78 inches. The walls require 2 coats of paint. The second coat will require 2/3 as much paint as the first coat. The area behind the tub and vanity do not need to be painted.

* Calculate the area of the walls to be painted.

Walls:
10 * 8 * 2 = 160 square ft
6 * 8 * 2 = 96 square ft
160 + 96 = 256 square ft

Area behind bath tub: 2 * 2.5 * 2 + (6*2) = 22 square ft
Area behind sink vanity: 3 * 3 = 9 square ft
Door: 2.5 * 6.5 = 16.25 square ft
Total: 22 + 9 + 16.25 = 47.25 square ft

Area to be painted: 256 - 47.25 = 208.75 square ft


A 4L can of paint covers 120 square ft at a cost of $42.99. A one litre can of paint covers 30 square ft at a cost of $14.99.

* What combination of cans of paint do you need to buy in order to minimize the coast? What is your final cost?

With both coats of paint: 208.75 * 1(2/3) = 347.92 square ft

347.92 / 30 square ft = 11.59 L or 12 L

Cheapes combination of cans:
Three 4L cans
3 * $42.99 = $128.97



(c) BASEBOARD COSTS: (show all work) (2 marks)
The baseboards are sold in 8-foot lengths at a cost of $5.36 each. Determine the number of 8-foot baseboards needed and calculate the total cost of the baseboards. State any assumptions you have made.

Assumption: Baseboards are around the tub and vanity
6 ft + 7.5 ft + 7.5 ft + 3.5 ft + 4 ft = 28.5 ft
Cost: 28.5 / 8 = 3.56 lengths --> 4 lengths * $5.36 = $21.44

OR

Assumption: No baseboard in front of the tub or vanity
7.5 ft + 4.5 ft + 3.5 ft = 15.5 ft / 8 = 2 lengths
2 * $5.36 = 10.72 + 0.75 + 0.75 = $12.22



(d) BUDGET:
You have a $300.00 budget for the entire bathroom project. How much money will you have left for the floor covering after you have considered the paint, baseboards, GST and PST?

Paint: $128.97
Baseboards: $21.44
SUB-TOTAL: 128.97 + 21.44 = $150.41 * 1.14 = $171.47

Amount left for flooring: $300.00 - $171.47 = $128.53




That was all the work we did and the NEXT SCRIBE is...

STEPH




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Thursday, June 08, 2006 

One steals on my hammer, the other one is skating

Hello all... Today I had the honor bestoded upon my of being the scribe... joy...
well its not like we did too much *rolls eyes* just finished two subjects, and got some closure on a couple questions, like the Ice Rink one, apparently people paint the ENTIRE surface of their ice rinks, hmmm...

First off
^2 = squared, ^3 = cubed... etc.

Sequences - If I Had A Hammer


Three nails, each 6 cm long, are hammered into a board until the head of the nail is flush with the surface of the board.

Note: To be flush, the head of the nail must not be more than 0.10 cm above the board's surface.

Nail 1 Moves 0.90 cm into the board with each hit of the hammer

Nail 2 Moves 0.90 cm into the board with the first hit of the hammer.
After each successive hit, the visible part of the nail is 80% of its previous
height.

Nail 3 Moves 0.90 cm into the board wiht the first hit of the hammer.
After each successive hit, the nail moves 0.30 cm less than it moved
previously.


Task A.
How may hits of the hammer will it take to drive each nail into the board? Support your answer for each nail.

(My answer)
Nail 1: uMin = 1
u(n-1)-0.9
u(nMin) = 6

7 Hits @ -0.3 cm

Nail 2: uMin = 1
0.8u(n-1)
u(nMin) = 5.1

19 Hits @ 0.09187 cm

Nail 3: Stops at the height of 4.2 cm


Task B
Which of these three situations is least likly to occur and why?

(My answer)
Nail 3 is least likely to occur


Task c
Create a new scenario where a 10 cm nail is hammered until it becomes flush with a board using from 19 to 21 hits (inclusively). The nail cannot move more than 1.5 cm on the first hit.
Support your answer.

(My answer)
nMin = 0
u(n) = u(n-1)-0.5 cm
u(uMin) = {10}


So that was that... lets move on....

---------------------------------------------------------------------------------------------
Samantha's Ice Rink
Samantha wants to have an ice rink built in her backyard. In order to do this, she must:

  • Hire someone wiht landscaping equipment to level her back yard. This costs $2.50 per square metre.
  • Flood the ice with enough water to form ice to a depth of 12 centimeters. As water freezes, the volume of ice formes is about 1.1 times the volume of the water. The price of the water is $2.10 per 1000 liters. Note: 1 m^3 = 1000 liters
  • paint the ice with ice paint that costs $8.99 per litre. One litre covers eight square meters.
  • allow $65 for miscellaneous materials she need to buy.
  • pay PST and GST , both at 7 percent, for all materials, and only 7 percent GST for labour (having their yard landscaped).
  • pay her children for flooding the rink. Water flows through the garden hose at 20 litres per minute, and the children insist on receiving $3.50 per hour for flooding. Samantha pays no PST or GST on this expense.
Samantha has a budget of $400 to build this rink. Determine the maximum-size rink she can build for that amount. What would be a suitable shape of rink to design? What are the dimensions of the shape you suggest?

ok... that took forever, now the answers:
because everything can be split to fractions of the whole except for the paint, so we used the amount of area that the paint can can cover as the base number for the price quotes and then just divide the anoumt of money by the base price... you'll understand afer its all written down

Land scaping $2.50/m^2 + GST
Water $2.10/1000L = $2.10/m^3 + PST &GST
Paint $8.99/8m^2 + PST & GST
Misc $65 {assuming the taxes are included]
Flooding $3.50/h 1200L/h

For 8m^2
Landscaping 8 X 2.50 + Tx = $21.40
Water 0.8727 X 2.10 + Tx = $2.09
Paint $10.25
Misc $65
Flooding $2.55
Total..............$36.29 per unit

For water:
12 cm = 0.12 m
Vice = 8(0.12)
= 0.96m^3

Amount of water to make 12 cm of ice
1.1w = Vice
1.1w = 0.96
w = 0.96/1.1
w= 0.8727 m^3

How many liters is that?
1000L/1m^3 = XL/0.8727m^3
X = 272.7L

How many hours will that take to fill?
872.7/1200 = 0.72725 hr or 42 minutes and 36 seconds (I belive)

So all said and done how big can we go?
well $400 - $65 = $335
335/36.29 = 9.28

or 9.28 meters by 8 meters, but because we cant buy partial cans of paint, well have to go with 9m X 8m with this budget

-----------------------------------------------------------------------------------------------
Ok... the next question is from a while back, about 2 weeks I think

A water tank is a sphere with a diameter of 3.6m. Estimate the volume of water in the tank if the depth of the water is 24 cm.

Vcone is cone of water
Vcone = Pir^2L/3
=(Pi(0.8979)^2(0.24)/3)1.1
= 0.2228m^3
















Well thats it for today, and that on took forever :)
thanks for reading
Shane

Next Scribe is......... Andrew




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Create a Scribers Guide to Scribing

Two days ago I received this email from a teacher friend of mine, Mr. Harbeck.

I would like to congratulate you[r classes]. Every scribe post I read is like taking part in your class. The students take tremendous pride in creating their posts and are all scribing at Hall of Fame levels. It would be interesting for them to reflect on their scribing and come up with a criteria for making the Hall of Fame. They know how much effort they put into their posts and what is worthy or not. As an outsider teaching 13 year olds who have no choice but to be in my class I do not see the devotion these scribes put forth every day. Everyone takes a turn and does a great job.

I would be curious if you did a "bob" on reflecting about scribe posts. The first to the last. What made a difference from the beginning of the course to the end. My topic was a dry etc one...this is how I spiced it up.

Could they create a scribers guide to scribing?

This is a talented bunch of students. Use them while you still have them. The Next bunch could be even better.


So here it is folks. You've more or less created this art form, now you can write the book on it. In the comments to this post answer these questions:

  • How do you go about writing a scribe post? Do you do anything differently in class when it is your turn to scribe? If so, can you describe what you do differently in class when you are scribe?

  • What makes a scribe post worthy of entry into The Scribe Post Hall Of Fame? Specifically, what should be included in the post for it to achieve this recognition?

  • Compare the first scribe post you wrote to the most recent one. What, if anything, did you do differently?


Your replies, and those of my other classes, will be collated and posted on a special page in The Scribe Post Hall Of Fame. Do yourselves proud. The world is watching; teach them how it's done. ;-)




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Wednesday, June 07, 2006 

SCRIBE,SCRIBE,EBIRCS,EBIRCS

Hey all, it is i todays scribe NIKKI!! Yeah today we didnt dooo tooo much all we did was had a quiz and were assigned questions, i will be posting the questions from the Quiz and tellin u about wat we will be doing tomorrow k KOOL :)!!!!

QUIZ 1 on Sequences and Series

1.Write the first 3 terms of the sequences generated by each of the following functions:

(a) f(x)=4x-3 (b) g(x)=2X3^x
4(x-3)=1 2X3^x=6
8(x-3)=5 2X3^2=18
12(x-3)=9 2X3^3=54
1,5,9 is the answer 6,18,54 is the answer

2.Write the function that generates each of the following sequences:

(a) 1,-2,4,-8,16... (b) 10,5,2.5,1.25...
Tn=T1-2^(n-1) Tn=T1(1/2)^(n-1)

3.Consider the following sequence: 3,6,12,24...

(a) Find the 8th term of the sequence.
n Min= 1 The 8th Term is 384
u(n)=u(n-1)*2
u(nMin)={3}

(b) Find the Nth term of the seqence.
Tn= T1(n-1)*2

4.An army is marching in a triangular array: 1 soldier in the first row, 3 in the second row, 5 in the third row, 7 in the fourth row. etc.

(a) If each soldier requires 4 feet of space in a row, how long is the 53rd row?
nMin=1 The 53rd row is 105
u(n)=u(n-1)+2 To get the length of the 53rd row u take 105 and multiply it by 4.
u(nMin)={3} 105*4=420 Ft.

(b) What is the total number of soldiers in rows 22 through 87?
nMin=1 u(1,87)-->L1
u(n)=u(n-1)+2 sum(L1,22,87)
u(nMin)={3} =7128

I hope all of my answers were correct cause i didnt do too wellon the Quiz :)!!! BUt yeah thats wat we did for the Quiz it wasnt long but it was spur of the moment!!!!

Now for homework we have to do Pg.295 #1-7!!!!!!!!!
For tomorrows class we will be taking up Design and Measurment cause we never really learned it in class n thats for tomorrow!!!!
A few tips for the Exam:
1) Make sure you lay out your exam in the outmost detail, like dont forget a degree sign or anything like that because those can cause u to lose critical marks on the exam!!!!
2) For our exam on the 13th it will be on Design and Measurment and on Sequences!!!1
3) Dont forget to read all your homework and study paper at least 6 times through because your going to need all your work to be engraved into your memory!!!!!
4) STUDY STUDY STUDY STUDY STUDY STUDY!!!!!!!!!!!

Well thats all for now i hope you take these tips into consideration and dont forget exams are only next week so take this weekend to prepare!!!!!!!

ps sorry for the late scribe post :)

Next Srcibe will BEEEEE!: SHANE





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Tuesday, June 06, 2006 

Scribe: Sequences

Sorry guys my scribe will not be up till tommorow because im not sure if my answers are right. SORRY for those who are waiting. Ill post the scribe as soon as i can tommorow promise. :b




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Monday, June 05, 2006 

Fractals

hi everyone,
This scribe is for Monday, june/05/06. We had only one class and the subject that was taught is about fractals.
We started off with the following diagram.

Fractal:A mathematically generated pattern that is reproducible at any magnification or reduction.

In this diagram the green square is twice as big as the blue one. And the blue one is twice as big as fuchsia and so on........ .
The question is wether these triangles ever pass the edges of the paper.
Answer: If we go to infinity it will cross the paper.
And a sequence is created by the following formula.
(n-1)
tn=t1(r)
(n-1)
tn=8(1/2)
Area
64+32+16+8+2+1/2
It is a geometric sequence they have common difference. Some times the first number in this case 64 does not fit the sequence so we start with second number 32.
u(1,100)store in (L1)
HOME WORK IS ON THE BLOG
Next scribe: Nikki (if not avaiblable then shane)




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Fractal Homework

Draw the following fractals. Be sure to save your drawings and bring them to class tomorrow. Draw them centered, one fractal per page.

(1) Draw a rectangle that measures 12 cm by 8 cm, and shade the inside of the rectangle. Construct the midpoints of each side of the rectangle, and then draw a quadrilateral by joining these points. Shade the quadrilateral white. Now continue the process by finding the midpoints of the quadrilateral, drawing the rectangle, and shading it the same colour as the first rectangle. Draw six generations. (The initial rectangle is the first generation.)


(2) Create a fractal that begins with a large square 20 cm on each side. Each pattern requires that the square be divided into four equally sized squares, that the bottom-left square be shaded, and the process continues in the upper-right square. Repeat the process four times.


(3) Create a fractal where a square is inscribed in a circle. The diameter of the original circle is 16 cm. Shade the area between the circle and the square. Inscribe a circle inside the resulting square, and then inscribe a new square inside that circle, and shade the area between the new circle and square. Repeat this process three times.




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Fractal Homework

Draw the following fractals. Be sure to save your drawings and bring them to class tomorrow. Draw them centered, one fractal per page.

(1) Draw a rectangle that measures 12 cm by 8 cm, and shade the inside of the rectangle. Construct the midpoints of each side of the rectangle, and then draw a quadrilateral by joining these points. Shade the quadrilateral white. Now continue the process by finding the midpoints of the quadrilateral, drawing the rectangle, and shading it the same colour as the first rectangle. Draw six generations. (The initial rectangle is the first generation.)


(2) Create a fractal that begins with a large square 20 cm on each side. Each pattern requires that the square be divided into four equally sized squares, that the bottom-left square be shaded, and the process continues in the upper-right square. Repeat the process four times.


(3) Create a fractal where a square is inscribed in a circle. The diameter of the original circle is 16 cm. Shade the area between the circle and the square. Inscribe a circle inside the resulting square, and then inscribe a new square inside that circle, and shade the area between the new circle and square. Repeat this process three times.




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Friday, June 02, 2006 

THURSDAY JUNE 1ST CLASS

Two weeks before the exam. This is how today’s class began. Mr. K discussed how the exam is going to take place, that we going to do two question in the mac lab. And correct me if I am wrong. He also said the question are based on "design and measurement" and "Sequences". If you missed today’s class, then you missed Mr. K dripping Words of Wisdom. I am going to share little of his dripping words of wisdom. He said " You can't just walk out of the class if you wanted to. To walk out of the class, you have to walk half the distance from the exit (door), then again half of that, then half of that. Etc.... it also got something to do with sequences. The second thing was an ordinary man and his donkey. mmm. I think I better keep the rest to myself. i have shared enough. To get more of Mr. K dripping words of wisdom comment on the blog page, or if you are Mr. K student ask him in class tomorrow. Ok lets get business started. The notes are as follows:

Sequences & Series

Sequence: an ordered list of numbers that follow a certain pattern (or rule).


Series: the sum of numbers in a sequence to particular term in the sequence.


Example: Given the sequence: 3, 6, 12, 24, 48, ............

the series S5 denotes the sum of the first 5 terms:

S1=3 thus we have the series:
s2= 3+6= 9 3,9,21,45,93...
s3=3+6+12=21
s4=3+6+12+24=45
s5=3+6+12+24+48=93


in general, Sn denotes the sum of the first n terms.



Arithmetic Sequence:


i) Recursive Definition: an ordered list of numbers. Generated by continuously add a value.
(the common difference). to a given first term.
ii) Implicit Definition: an ordered list of numbers in the list is generated by a linear equation.

Common Difference: (d) i) the number that is repeatedly added to successive terms in an arithmetic sequences.
ii) From the implicit definition it is the slope of the linear function.

To find the n^th term in an arithmetic sequence.

tn= t1 + ( n - 1 ) d tn is the n^th term
t1 is the first term.
n is the rank of the n^th term.
d is the Common difference.

Geometric Sequence:

i) Recursive Definition: an ordered list of numbers generated by continuously multiplying a given first term by a particular value (common ratio)

ii) Implicit Definition: an ordered list of numbers where each number in the list is generated by an exponential function.

Common Ratio: (r) i) the number that is repeatedly multiplied to successive terms in a given sequence.



Geometric Sequence:

ii) from the implicit definition it is the base of the exponential function.


to find the n^th term in a geometric sequence.


tn= t1 (r) ^(n-1) tn is the n^th term
t1 is the first term
n is the Rank of the n^th term.
r is the (common ratio).

just don't forget that you can't have a series without a sequence.



Convergence and Divergence

When |r| > 1 the sum of an infinite geometric series Diverges. i.e. grows without bound.

When |r| <>

** Reminder that after the exams we do have classes, and we also going to do a pod cast. Basically it is kinda interview, don’t get scared. it not another exam. Mr. K is going to ask us couple of question, actually two questions to discuss. 1. What is something you would wish you would do better.
2. What thing would remind you of this class, that’s going to help you in future, studies i.e. university, and finally any closing comment.




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