Pre-Cal 40S (Winter '06)
An interactive learning ecology for students and parents in my Pre-Cal 40S class. This ongoing dialogue is as rich as YOU make it. Visit often and post your comments freely.
Friday, June 30, 2006
the last bob
It has been a rollercoaster this semester from trig identities to logs. This math class was special and unique. t he only grade 12 precal class to blog =)... it sounds corny, but has made us all famous lol. good wishes to the grade twelves moving onto universit ;) . Hopefully everyone i knew i S3 for this precal class will take calculus.
HAVE AN AWESOME SUMMER GUYS AND GIRLS !!
i don't know why but i will always remember this math class just as a math class. Maybe because it represents that its the last math class for highschool. The learning experience was much more different compared to recent years. THIS math class was fu n and made you want to learn more =), i sure wanted to learn more.
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. ;-)
Sunday, June 18, 2006
Student Survey Results
We did a little survey in class the day we recorded our podcapsule. The results are below; 18 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 .....
The questions in this section were ranked using this 5 point scale:
|Strongly Disagree||Disagree||Neutral||Agree||Strongly Agree|
The bold numbers after each item are the average ratings given by the entire class.
1. The teacher was enthusiastic about teaching the course. 4.89
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
(This question answered by 17 students.)
4. Students were encouraged to ask questions and were given meaningful answers. 4.56
5. The teacher enhanced the class through the use of humour. 4.50
6. Course materials were well understood and explained clearly by the teacher. 4.22
7. Graded materials fairly represented student understanding and effort. 4.17
8. The teacher showed a genuine interest in individual students. 4.22
9. I have learned something that I consider valuable. 4.33
10. The teacher normally came to class well prepared. 4.83
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. Compared with other high school courses I have taken, I would say this course was: 4.33
2. Compared with other high school teachers I have had, I would say this teacher is: 4.78
3. As an overall rating, I would say this teacher is: 4.78
The questions in this section were ranked using this 5 point scale:
|Very Easy||Easy||Average||Difficult||Very Difficult|
1. Course difficulty, compared to other high school courses: 3.72
2. Course workload, compared to other high school courses: 3.67
3. Hours per week required outside of class:
|0 to 2||2 to 3||3 to 5||5 to 7||over 7|
4. Expected grade in the course:
What was your best learning experience in this course?
|Learning to learn|
Learning real life applications (2)
"Learning is a conversation."
Logs and Exponents
Learning new formulas
|People helping each other|
Math dictionary (4)
Learning was fun and exciting
Group work (7)
Learning cool things
Learning grading methods
Help provided by teacher
What was your worst learning experience in this course?
Learning that I didn't study for tests
|Logs and Exponents (2)|
Online quizzes (5)
Finding links for del.icio.us box
Not understanding lesson (2)
BOB (Blogging On Blogging)
Falling asleep in class
What changes would you suggest to improve the way this course is taught?
More pre-test review
Be more approachable
Make a wiki notebook, edited yearly
Course was well taught (2)
More group work (3)
More bonus questions on tests
|Give "Aim for I Rule! not I can get by" speech|
"Person to person learning"
"Steady level of work"
Have 2 blogs; one for scribes, one for BOBs
Correct tests quicker
Go through every test
|Blog OK, but wiki and del.icio.us too much|
Keep doing what you're doing
No online quizzes
Put del.icio.us button on blog
Homework only every second day
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 ....
Friday, June 16, 2006
Message in a Podcast: Our Podcapsule
The students in our class wrote their final exam on Thursday June 15; 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 (8 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.
Thursday, June 15, 2006
One of the LAST posts of this year
Well its the morning of the exam, and its kind of late, but hope you all had a good nights rest and eat breakfast! Your mind needs the energy to think efficiently so good luck out there as we aim for the HIGH HIGH HIGH SUCCESS LEVEL! Remember what we said guys and girls? 80-100 no exception. Lets prove that we're capable to do what we were aiming for.
Tuesday, June 13, 2006
For today, I was the scribe. But I realized that I was the scribe at the end of second period class so I didnt' actually write anything down. So, I'll do my best to explain some of the stuff we covered for today's class. And sorry for the probably late post that you guys were expecting. But you should get used to that when it's my scribe.lol
Anyways. Back to the blogGing.
For second period, we corrected our tests
-Logarithms and Exponents
If I thoroughly explain everything, I probably won't sleep tonight. So sorry guys. I'm just going to give out the answers.
1) If $5000 is invested in an account that pays 6% compounded continuously, how long will it take the balance to grow to $75000?
Answer: B) 6.8 years
Work that out and you get 6.8 years.
2) The expression e^lnx-lny is equivalent to:
3) In solving the expression 3^2x-1=4^x, which of the following is the exact solution?
Answer: C) log3/log9-log4
Turn it into log formation
4) The solution to the expression 2(3)^3=26 could be:
5) The graph to the right is of f(x)=b^x+k
Answer: D) 0
(sorry guys. Don’t know how to explain this)
6) the graph at right represents the function y=logbase3(x). If the coordinates of C are (9,0), then the area of Triangle(ABC) is:
Since you know y=logbase3(x), you substitute 9 for x, since the x value is nine. Figuring the log out, it turns out t o be 2 after substitution. A is 1.
7) If logbase3(4)=X, then logbase3(64) equals:
Answer: D) 3x
8) A culture of bacteria doubles every 20 minutes. Which of the following is an expression representing the time t, in minutes, it takes for the original amount of bacteria in this culture to triple?
Answer: D) 3=2^t/20
Part III Short Answer
1) If log(x-2) + log(x+7)=1, then x must equal:
X= - 8 x=3-----answer
Because if you plug it back in, it’ll turn out to be zero.
2) Correct to four decimal places, the value of logbase3(7/5) must be:
3) Too lazy to draw the graph so I’ll just give you the answer. Sorry.lol
Part IV Problem Solving
1) Solve for x in each of the following. Write your answers accurate to 4 decimals places.
because plugging it back in will give 0.
2) a colony of what-cha-ma-call-its has a population of 8500. the population is increasing at a rate of 2.5% per year.
a)what will be the population of the colony in 15 years?
b) when was the population 7000?
T= - 7.76624
- 7.7662 years ago
Solve for x exactly without using a calculator:
3x^2e^( - x) = 12e^ -x
X= +/- 2
AND THAT’S THE FIRST TEST DONE. That took about an hour and a half. Haha. Now, Just two more tests and two rehearsal exam things………
TEST ON COUNTING
1) A committee of 4 is to be selected from 4 boys and 3 girls. If both boys and girls must be on this committee, and that is the only restriction, the number of committees that could be formed is:
4c1 * 3c3+ 4c2*3c2+4c3*3c1
2)the number of arrangements of the word COMMUNICATION is:
3)all phone numbers in
4)The fifth degree term in the expansion of (y-3)^7
7c2 y z^5( - 3)^2
21 * y^5 * 9
5)A class of 15 students are to be divided up so 5 students are in group 1, 3 studnets are in group 2, and 7 students are in group 3. the number of ways this can be done is:
Answer: 360 360
7) A juke box has a button for each of the 26 letters of the alphabet, and for each digit 1-9. in order to select a song, you must first enter two letters for the CD, and one digit for the track to be played. The number of songs this juke box could play is:
8)The middle term of the 7th row of Pascal’s Triangle is given by:
Part III Short Answer
1)If n!/(n-2)!=420, the value of n, must be:
n(n-1)(n-2) / (n-2)=420
n= 21 n= - 20
Rejected plugging it in gives 0.
2)in the expansion of (x+2/x)^6, the value of the constant term is:
6c3 (x)^3 (y)^3
6! / 3!3! * 8
3)A car dealer is displaying 5 cars in his showroom. Each car is a different model. Three of the cars are teal in colour, on car is red, and the other is black. The 5 other cars are to be arranged in a line, with none of the teal cars directly beside each other. There are ? possible arrangements of these cars.
3 2 2 1 1 = 12
T T T
4)Four books, W, X, Y and Z are placed on a shelf. The number of possible arrangements if the books W and Z must stay together, but not necessarily in that order is?
PART IV PROBLEM SOLVING
(This is taking too long..sigh..)
1)Algebraically determine the value for n in the expression 7(n-1)! / (n-2)! = 6(n+1)! / n!
7(n-1) = 6(n+1)
2)A class of 18 students includes 8 boys and 10 girls.
a)if the girls line up for a picture, how many pictures are possible if Joan, Jennifer and Jillian, 3 of the girls in the class stay together as a group in the picture?
8!3!= 241 920
b) How many pictures are possible if Joan, Jennifer and Jillian are not together, as a group, in any of the photographs?
10!-8!3!= 3 386 880
c) The 18 students sit in a classroom with 20 identical desks. Express the number of possible arrangements of students as a factorial.
20! / 18!2! OR 20! / 2!
d) four students are going to be selected to represent the class in a school relay. However, the group of four must have more girls represented than boys. How many groups could be formed under these conditions?
10c3 * 8 c1 + 10c4
120 * 8 + 210
960 + 210
3)a chorus consists of 6 singers in red and 6 singers in sliver costumes. In how many ways can they be arranged:
a)in two rows, the red behind the silver?
6!6!= 518 400
b)in a ring facing the centre, the colours alternating?
5!6!= 86 400
The Chinese mathematician Shi Cheh called Pascal’s Triangle by another name; what was it?
THE PRECIOUS MIRROR OF THE 4 ELEMENTS
AND THAT’S THE SECOND TEST DONE. ONE MORE AND TWO EXAM REHERSEALS LEFT.HAHA.YESSS. SLEEP TIME IS SOON.
No body really cared about probability in class it seems because no one raised their hand up for help. And I’m weak in probability so don’t expect any good explanations. lol. Sorry.
PART II MULTIPLE CHOICE
1)a standard six-sided fair die is tossed twice. Find the probability of getting a 2, 4 or 6 on the first toss and a 2, 3, or 5 on the second toss.
2)A jar contains 5 red and 7 blue marbles. What is the probability of pulling out 2 blue marbles in a row, without replacement?
3)A box of eight razor blades contains two defective blades. If two blades are drawn at random, with the first not replaced, what is the probability that exactly one of the two blades will be defective?
Answer: a) 3/7
4)one card is drawn is drawn at random from a deck of 52 cards. What is the probabitlity of drawing an ace or a diamond?
Answer: b) 4/13
4/52 + 13/52 – 1/52(ace of diamonds) = 4/13
5)A rack contains 15 dresses. Five of the dresses are blue, six are green, and 4 are yellow. If selling each of the dresses is equally likely, what is the probability that if six dresses are sold, exactly two will be green?
Answer: a) 6c2 * 9c4/15c6
6)In a car lot, 25% of the inventory are SUV’s, and 75% are passenger cars. 80% of the SUV’s, and 65% of the passenger cars, have air conditioning. What is the probability that a chosen vehicle will be an SUV given the vehicle has air conditioning?
7) A combination lock requires the owner to choose three numbers from 1-40 in order to open the lock. If numbers can be repeated, the probability of an individual correctly guessing the combination to this lock is:
Answer: c) 1/40^3
8)Using the diagram to the right, there are 7!/4! * 3! Possible routs from A to C, given the shortest routes from A to C are traveled. What is the probability that a chosen route will pass through point B, in attempting to get from A to C?
PART III SHORT ANSWER
1)Events A and B have the following probabilities of occurring; 0.2=P(A), 0.5=P(B). if these events are mutually exclusive, the value of P(AorB), correct to the nearest tenth.
P(AorB)=P(A) + P(B)
2)Using the word, FOOD, the probability that an arrangement of this word will begin with the two O’s if all letters are used, correct to the nearest hundredth, must be:
2! * 2! / 2! ----ways the ‘words’ begin with 2 O’s
4! / 2!---arrange letters in food
3)a box contains 100 computer floppy diskettes. The probability of a single diskette being faulty is 0.005. correct to the nearest hundredth, the probability that exactly two diskettes in the box will be faulty is:
100! / 98! 2! (0.005)^2 (0.995)^98
4)Eight students of different heights are seated randomly around a circular table. The probability that the two tallest students are sitting next to each other is:
Arrange 8 students in a circle
# of ways the 2 tallest are together
P(2 tallest together) = 6!2!/7!
PART IV PROBLEM SOLVING
1)Rupert has either milk or cocoa to drink for breakfast with either oatmeal or pancakes. If he drinks milk, then the probability that he is having pancakes with the milk is 2/3. the probability that drinks cocoa is 1/5. if he drinks cocoa, the probability of him having pancakes is 6/7.
a) List a sample space of probabilities using a tree diagram or any other method of your choice
P(mo)= 4/5 * 1/3 = 4/15
P(mp)= 4/5 * 2/3 = 8/15
P(co)= 1/5 * 1/7 = 1/35
P(cp)= 1/5 * 6/7 = 6/35
(draw the tree guys. I’m too lazy right now. You know how…)
b) find the probability that Rupert will have oatmeal with cocoa tomorrow morning.
P(co) = 1/5 * 1/7 = 1/35
2)Josh has purchased a male rabbit and a female rabbit. His research tells him that the breeding conditions the two rabbits will be exposed to dictate that the probability of a single offspring being male, M is 0.53, and female, F, is 0.47.
a) the first litter of rabbits produced 12 offspring, 4 of which were male. Correct to the nearest hundredth, what is the probability of this occurring?
12c4 (0.53)^4 (0.47)^8
b)in the next litter of rabbits, Josh makes the following probability calculation:
7c5(0.47)^5 (0.53)^2 + 7c6 (0.47)^6 (0.53) + 7c7(0.47)^7
This is the probability of having at least 5 females in a litter of 7 rabbits.
3)Five members of a mixed curling team including 2 females and 3 males. Only 4 can be chosen to play in a game.
a)what is the probability that all of the males will play the game?
3c3 * 2c1 / 5c4
b) if the five team members line up for a picture, what is the probability the two females will stand together?
4!2! / 5!
AND THAT’S THE THIRD TEST DONE. YES. SO CLOSE TO THE FINISH. YOU GUYS ARE PROBABLY NOT READING THIS BUT THAT’S OK! I wish I had a scanner. This would be so much easier.
EXAM REHERSEAL COUNTING
1)The number ofdifferent arrangements of 3 boys and 4 girls in a row, if the girls must stand together, is represented by:
Because since you put the four girls in a bag, you have 3 boys plus the bag with gives you 4! Times the girls in the bag which is also 4!.
2)The students in a music department have practiced 6 contemporary and 5 traditional choruses. For their concert, they will choose a program in which they present 4 of the contemporary and 3 of the traditional choruses. How many different programs can be presented, if the order of the choruses does not matter?
6c4 * 5c3 = 150
3)all telephone numbers are preceded by a 3-digit area code. In the original Bell Telephone System of assigning area codes, the first digit could be any number from 2 to 9, the second digit was either 0 or 1, and the third digit could be any number except 0. in this system, the number of different area codes possible was
4)a paperboy who delivers papers on his bike can travel only on the trails represented in the diagram. The number of different trails that the paperboy can take to get from house A to house B with out backtracking is:
*refer to pascal’s triangle.
5)a) how many groups of 3 chairs can be chosen from 7 chairs if the chairs are all different colours?
b)How many different ways can 7 chairs be arranged in a row if 2 of the chairs are blue, 3 are yellow, 1 is red, and 1 is green? (Assume that all of the chairs are identical except for colour.)
7!/2!3! = 420 ways
ONE MORE TO GO
EXAM REHEARSAL EXPONENTS AND LOGARITHMS
1)The expression 3logbase(x) – 1/2logbase(y) is equivalent to:
b)log(x^3/ square root (Y)
2)If 27^x = 9^y-1, what is y in terms of x?
(3)^3X = 3^2Y-2
2)f logbase(b)3 and logbaseb(5)=q, express logbase(b) cubed root of 0.6.
1/3logbase(b)3 * logbase(b)5
1/3p – 1/3q
4)solve for x: logbase(3)x=2 – logbase(3)(x+2)
Logbase(3)x + logbase(3)(x+2) = 2
X^2+2x=9----use quadratic formula
(not sure if this is right. Check with mr.k just in case if you don’t agree with it)
5)the Department of health in a developing country has issued a warning that the number, N, of reported cases of a certain disease is increasing expontentially at an annual rate of 9%. The first years that statistics were collected, 5000 cases were reported.
a)Calculate the approximate number cases reported after 7 years.
9388 cases (sorry guys. Don’t know how to get this but this is the answer)
b)how many years will it take for the number of reported cases to rise to 11 000?
8.7606 years(sorry guys. Don’t know how to get this either)
AND I’M FRIKKIN DONE. Sorry for the language. Anyways, this took too long as I’ve predicted and I did explain some stuff which I said I wouldn’t do but I knew I wouldn’t follow through on my words.haha.
The next scribe will be.
Eehhhh I’ll pick tomorrow. guY =)
Sunday, June 11, 2006
end of the course-afternoon
So today there are two scribes. Marquin for the morning and me for the afternoon. This afternoon we FINALLY finished the course. This afternoon we wrapped up the last unit and also did a exam rehearsal for the Circular Functions unit .
So here's the notes...
Sigma Notation: A shorthand way to write a series.
is the capital sigma (from greek alphabet); means "sum"
- supbscript n=1 means "start with n=1 and evaluate 2n-3"
- superscript 4 means "keep evaluating (2n-3) for successive integral values of n, stop when n=4; then add all the terms."
- (2n-3) is the implicit definition of the sequence
Geometric Series: the sum, to the nth term, of the terms in a geometric series given by:
- Sn is the sum of the first n terms in a geometric sequence
- n is the rank of the nth term
- t1 is the first term
- r is the common ratio
Infinite Geometric Series
END OF COURSE
the next thing we did was the exam rehearsal for ciruclar functions.
1) Through how many radians does the minute hand of a clock turn in 24 minutes.
A) 0.2 pi
B) 0.4 pi
C) 0.6 pi
D) 0.8 pi
2) If cos theta = -3/4 and tan theta <0.>
B) -root 7 / 4
C) 4 root 7 / 7
D) root 7 / 4
3) If y= 2 cos(1/2X) - 3, what is the minimum value of y?
solution: since the graph lies on -3 and the amplitude is two the minimum value is -5. (-3) - 2 = -5
4) if theta=arcos(- root2 / 2), find the value(s) of tan theta?
tan= sin / cos
5) The tide at a boat dock can be modeled by the equation d(t) =-2cos(pi/6T)+8
a) How deep is the water at high tide? low tide?
since the amplitude is 2 you have to add 2 to 8 to get the high tide and subtract 2 from 8 to get the low tide.
low tide: 8-2=6
high tide: 8+2=10
b)How lond is it between one high tide and the next?
pi / 6 = 2 / period
12 = period
c) For how many hours, between t=0 and t=12 is the tide at least 7 feet deep?
7 = -2 cos pi/6T + 8
-1 = -2cos pi/6T
since cos 1/2 is equal to pi/3 and 5pi/3 on the unit circle, we plug it in for cos theta
theta = pi/3
pi/6T = pi/3
theta = 5pi/3
pi/6T = 5pi/3
now you find the difference of 10 and 2...
The tide will be at a dept of atleast 7 ft deep for 8 hrs.
That marks the end of my scribe. Don't mind if i say it again but i just love saying it.. THIS MARKS THE END OF THE COURSE.. haha.. anyways i don't know whole will be scribe tommorow since there was two scribes today. whose gonna pick? me or marquin? we'll just see tommorow..
Saturday, June 10, 2006
Sequences and Series
I guess blogger works right now and im hopping that im not going to lose this work. I should have known that saving thing. Anyways here is what we did Wed. Morning:
A superball is dropped from a height of 160 feet. It bounces to (3/5) of its height after it hits the ground. What is the total vertical distance it has traveled when:
a) it hits the ground for the 4th time?
As you can see that this question have 3 ways to answer.
b) It comes to a rest?
And there is 3 ways to answer this question too.
Soo is the infinite sum of the series
t1 is the first term
r is the common ratio.
And that was all we did in the morning and this what we did in the afternoon:
And that was all we did in the afternoon. Oh we did notes on the morning too. Here they are:
Common Ratio (r): I) the number that is repeatedly multiplied to successive terms in a geometric sequence.
ii) from the implicit definition (r) is the base of the exponential function.
To find the nth term in a geometric sequence
tn is the nth term
n is the rank of the nth term
t1 is the first term
r is the common ratio
Sigma notation: A shorthand way to write a series.
Oh and there is one thing before I finish. The smallest number a calculator can get to is 9.999999999999999*10^(-99)
And the largest number a calculator can get to is 9.999999999999999*10^(99).
(3/5)^1000=0 (its not really 0 but the calculator shows 0 because this number is really small, smaller than that number that's why the calculator shows 0.)
Oh and Thales thought magnets had souls.
anyways that is all for my scribe, you guys have fun.
Thursday, June 08, 2006
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. ;-)