Communicating using technology, Japanese Vending Machines....and some more Binomial Theorem

We started the class with a discussion about how beneficial (or not) a ban on cell phones would be in schools, and how some people have lost the connection with people around them, by only talking to there "friends" on their phone or computer. Just something to think about...Back to math class we did mental math today. We did more examples of using the Binomial Theorem and had a matherific time! Remember that smoking and meatbelts are stupid.

Assignment is Exercise #35 Questions 3,4,5,6,7

Binomial Theorem

Binomial theorem is defined as (a+b)^N where N equals a natural number.

See these terms??? (look up), well, look at the cool patterns within them (look down)

Here is an example showing how to use the binomial theorem:

Here is an example showing how to find a certain term within an expansion:

Here is another example showing how to put the binomial theorem to use:

This nifty picture down here is Pascal's Triangle. What you'll notice is that if you add any two numbers beside eachother, their sum is the number found directly below it. Example: 6+15=21

Homework:

Exercise 32, Questions 1-10

Exercise 33, Questions 1-10

Exercise 34, Questions 1-10

Below is a calendar of our next few weeks of school before the end of the semester.

-November 29th to December 1st we will be learning BINOMIAL THEOREM
-December 2nd to December 8th we will be learning CONICS
- December 8th and 9th we will be given time to review
-December 10th will most likely be our test
-December 11th to December 17th we will learning PROBABILITY
-December 18th we are off for Christmas Holidays!

-January 4th to January 11th we will be learning SEQUENCES

-January 12th to the 19th we will be doing review, but remember PILOT EXAM IS JANUARY 14th, and our FINAL EXAM IS JANUARY 20th

KRISTIN HANSFORDS TEST QUESTION

Question: Simplify: (log210)(log48-log3)

Solution: (log10/log2)(log16)
=(1/log2)(log2^4)
=4log2/log2
=4

Test Question

1st question (2 marks)

Convert expression into a single expression logarithm:
½ln(x) - 2 ln(x-1) - 1/3 ln (x²+1)
=ln √(x) - ln(x-1)² - ln ³√(x²+1)
= ln (√x)/ [ (x-1)² * ³√(x²+1) ] <--- Log Law #2.
surprisingly, thats all you have to do for that question (simplify)

2nd question (1 mark)

Express log 6 1/216= -3 in exponential form
6^-3= 1/216

3rd question (1 mark)

Evaluate ln ( 1/ 4√e)
*multiple choice here guys..
a) ¼
b) -¼
c) -4
d) 4

Thursday Test Question

This is my test question:
Solve for x: ln6+ln(x−2)=−2
(Express your answer correct to 3 decimal places.)
This question is worth 3 marks as well
Here is the method I used to get the answer:

ln[6(x-2)]=-2
ln(6x-12)=-2 (1 mark here)
(e^-2)=6x-12
6x=(e^-2)+12
x=(e^-2)+12/6 (1 mark here)
x=2.022 556
x=2.023 (1 mark here)

(that's where the marking guide said the marks should be awarded)

I would suggest to everyone that you go over all the test questions mentioned on here. This way you know what you will have to answer and how to do it. Good Luck to everyone!

My Text Question

http://www.edu.gov.mb.ca/k12/assess/archives/pc_mg_june_06.pdf

page 58.

(3 marks)

Transformations Questions

Questions: #13 - 2 marks (1 per letter)
#14 - 3 marks (1 per letter)
http://www.bmlc.ca/Math40S/Pre-Calculus%20Math%2040s%20Standards%20Test%20-%20Transformations%20QUESTIONS.pdf
Answers Link:
http://www.bmlc.ca/Math40S/Pre-Calculus%20Math%2040s%20Standards%20Test%20-%20Transformations%20ANSWERS.pdf

Test Questions

Here are my questions for our test tomorrow:


1) Point P is a point on the terminal arm of an angle Θ in standard position. If cscΘ<0 and sin theta=-15/17, deterine the value of the other five trigometric functions.

2)P(Θ) is a point on the unit circle. If secΘ<0 and tan(theta)<0, and the coordinates for P are (x, 2root6/7)

a. Find the value of x
b.State the coordinates of P(Θ+pi)

Solutions:

1)step 1: Determine quadrat-(quadrat III)
step2: Find sinΘ=1-(-8/17)squared=-15/17
Step3: Determine other 4 trig. values
sec=-17/8
csc=-17/15
tan=15/8
cot=8/15

2) a.
step1: determine quadrat-(quadrat 2)
step 2:1-(2√6/7)²=-5/7
b.step1: determine quadrat-(quadrat 4)
step 2: determine integer values for x and y: (5/7, -2root6)

My question.

These questions are pulled from the Mickelson book.The solutions can be found on pages 198 and 199.

Page: 179

Number:16)

Letter: c)

Evaluate(worth one mark):

10! 4! / 8! 6!

= (1*2*3*4*5*6*7*8*9*10)(1*2*3*4) /

(1*2*3*4*5*6*7*8) (1*2*3*4*5*6)

= 9 * 10 /

5 * 6

90 / 30

= 3

Second question (page 180, number 23) (worth two marks):

How many different groups of four letters can be made from the letters A, B, C, D, E, and F if the letters can only be used once?

P(6, 4) = 6! / (6 - 4)! = 6! / 2! =

1 * 2 * 3 * 4 * 5 * 6 /

1 * 2

= 3 * 4* 5 * 6

= 360

We can create 360 groups of four letters from A, B, C, D, E, and F if the letters can only be used once.

TEST QUESTION!

HERE WE GO GUYS...QUESTION ON THE FUNDAMENTAL COUNTING PRINCIPLE (FCP)

This is out of the Mickelson (hmm i always thought it was nickleson) book. pg 176.

There are 4 roads between cities A and B, and 3 roads between cities B and C.
a) How many ways can a person travel from A to C through city B??
(4)(3) = 12
b) How many ways can a person make a round trip from A to C and back to A, through city B?
(4)(3)(3)(4) = 144
c) How many ways can a person make a round trip from A to C and back to A through city B, without using any road twice?
(4)(3)(2)(3) = 72

Alright, hope that helped and you all do great

Brett's Test Question

Question:

1. a) How many 6 letter arrangements can be made using the letters M A T T E R ? Give your answer as a whole number. (1 mark)

b) How many 6 letter arrangements end with T T? Give your answer as a whole number. (1 mark)

c) How many 6 letter arrangements can be made if the letters M T T R must be together? Give your answer as a whole number. (2 marks)

Solutions:

1. a) 6!/2!= 360


b) _ _ _ _ T T
4!= 24


c) (3!) (4!/2!) = 72

**3 groups, 4 consonants, 2 t's


GOOD LUCK THURSDAY!

My test question!

I just got this from accelerated math, so i'll write it out for you as opposed to posting a link!
(Worth 2 marks)

Write as a logarithm of a single expression:
2log5x + 3log5(x+6)

Answer:
= log5x^2 + log5(x+6)^3
= log5x^2(x+6)^3

Taaa Daaaa!

Test Question for Nov 26 2009

http://www.bmlc.ca/Math40S/Pre-Calculus%20Math%2040s%20Standards%20Test%20-%20Transformations%20QUESTIONS.pdf

Question #2
a) Worth 2 marks
b) Worth 2 marks
c) Worth 2 marks
Question #11 Part A, B, C and D


Answers can be found here...

http://www.bmlc.ca/Math40S/Pre-Calculus%20Math%2040s%20Standards%20Test%20-%20Transformations%20ANSWERS.pdf

my test questions

HEYYYYYYYY YOUUUUUUU GUYYYYYYYY'S
If you would like the advanced edge on tomorrows upcoming test, here it is.
I Picked two questions, one from exercise 3 and one from exercise 5.
from exercise 3, I picked question 1, part e), which was
find the exact value of tan(7pi/4), show work, ie. unit circle

from exercise 5, question 1
Solve for thaeta where the domain is the set of all reals.
sin thaeta=1/2
answer is pi/6+2kpi where k is an integer
and
5 pi/6 + 2kpi where k is an integer

dont forget to show how you got those answers. ie unit circle

In class today Mr. Max gave us more examples on Perms and coms. The first example that we were given showed us how to create possible cases for one question, but after creating the possible cases you combine them together to get the final answer.
Next, we were given the term and definition: Sample Space- some display, rendition, showing all probability outcomes. "has everything" Scrabble was used as the example to explain sample space, which is shown below.
Test has now been moved to Thursday everyone, and there is tutoring today after school with Mr.Max. The Test questions should be posted on to the blog by wither today or tomorrow, where we will be able to see the problems and solutions. Good luck everyone!

Tuesday November 24, 2009- More Perms and Coms!

First of all, TEST MOVEMENT! Instead of Wednesday, we're moving this to Thursday.
What happens if the orderings of perms/coms are circular? i.e) people around a table; bracelets; necklaces; basically things that require objects in sequence on a round form of something.

ex) How many ways can you sit 4 people around a table?
*moving to the cafeteria to do some shananigans around the tables.
-How many things are actually moving?
ANSWER- 3 things are actually moving, which makes the equation 3!
Final answer- 3!= 6 ways
FORMULA: (n-1)!, where n= number of things to order in a circular way.


ex) Regarding this necklace, how many ways can we make this thing unique?
Thinking the same as the previous example? If so, that is incorrect. The 3D object can be flipped around, as shown in the picture. FORMULA: (n-1)!/2















ex) 5 people around a circular table
a) if person A and person B have to sit together?
{(n-1)!} *2 <--- because they can switch around (A-B, B-A) b) if person A and person B can not sit together? FORMULA: (All ways)-(undesired ways)= Answer.
4! - 3!2! = 12 ways

c) person A and person B together; person C and person D together.
2! (from the n-1 ! formula); 2! ways to organize A/B; 2! ways to organize C/D
2! * 2! *2!= 8 ways.

Ordering identical things-
ex) "How many different 'words' are possible with these letters?"
Z O O M
*thinking the answer is 4! ? 24 ways? Wrong, again!
MOZO* is the same as MO*ZO..
FORMULA: total number of ways / "total number of identicals"! = desired ways
ex) S T A T I S T I C S
10 !/ {(3!)(3!)(2!) = 50400 UNIQUE words

Friday Nov 20. Work Period.

Friday we had a work period to catch up on Accelerated Math, Cumulative Exercises and to work on our 2 questions of our choice picked from Old exams, Cummulitave Excercises, Accel Math, ect to be submit for the test on Wednesday.

It would be wise to be into the Probility on Acell Math and have the following Cummulative Exercises completed prior to Wednesdays test...

**Up to and including**

Ex 1 #1-12
Ex 2 # 1-12
Ex 3 # 1-7
Ex 4 #1-8
Ex 5 #1-12
Ex 6 #1-16
Ex 7 # 1-10
Ex 8 #1-10
Ex 9 # 1-14
Ex 10 # 1-6
Ex 11 # 1-12
Ex 12 # 1-10
Ex 13 #1-10
Ex 14 #1-11
Ex 15 # 1-14
Ex 16 # 1, 2, 4, 6-13
Ex 17 # 1-12
Ex 18 # 1-18
Ex 19 # 1-10
Ex 20 # 1-13
Ex 21 # 1-12
Ex 22 #1-10
Ex 23 # 1-12
Ex 24 # 1-10
Ex 25 # 1-15
Ex 26 # 1-16
Ex 27 # 1-10
Ex 28 # 1-10
Ex 29 # 1-10

Deeper Thinking...

Yesterday in class Mr. Max had us do a different style of assignment. We were to read an article online (link is below in his post) and write our own blog post based on our thoughts on the topic. It was about an agreement made between 2 students and a teacher about having a No Homework agreement where the 2 students would get, well, no homework. Ever.

So, your homework is to write a blog post on what you think about having no homework. Ironic?

We spent the rest of the block working on accelerated math. Try to get that done guys, I know I myself am super far behind and its just taking me ages to get caught up, but once I complete an objective I really do feel like I know what I'm doing for the most part.

REMINDER: Test is next Wednesday, so lets get our study on guys!

Pilot Exam

I forgot to post this when I scribed for the class on Monday. For anyone who missed Monday's class, we were told that there is going to be a pilot exam (practice exam) for our Grade 12 Pre-Calculus exam after holiday break. This takes place at 12:30 on January 14th. I think this is a great opportunity to get a feel for what the real exam is like as well as to find find out where we need to improve before the actual exam. It is going to take place in Mr. Maksymchuk's room.

Perms and Coms

Yesterdays class, we learned more about perms and coms. Permulations are the number of possible orderings of a set, provided that the order of set elements matters. An example would be 281-0563 218-0563 560-3812 or books on a shelf, locker combos. The BEST EXAMPLE EVER of a perm, is create 5 letter words from the alphabet no repeats. So you pick any 5 letters, and then you would times 26(because there is 26 letters in the alphabet) then 25 because you used a letter, then 24 b/c you used another letter...etc. you get 7893 600. At that point we learned the formula : 26!/21!=n!/(n-r)! n being the number of items to select from and r being selecting items r at 2 time. "n things, permulated 5 at a time". The second part of THE BEST EXAMPLE EVER is: pizzas. you have peperoni pinapple and ham, either order you put it in, its still the same pizza.