Binomial Distribution

Yesterday we had a snow day.
Today we started off the class with a Christmas Trivia. After that we did Mental Math, then Mr. Max gave us the Binomial Distribution booklet. There are 12 questions that are due tomorrow. We aren't sure when the test is still, if we are having it on Thursday or after the Christmas Break.

Z-Scores

Big Idea:

*Relative scores(your score compared to others in the same data set*

Formula:

Z=(x-xbar)

Std.Dev.

*Z-Score values should be between -3.5 and 3.5*

Normal Distributions

Normal Distributions are "theory and practice", they are frequently polygons and histograms.

Characteristics of Normal Distributions:

*Theoretical(approximation)*

*Symmetry about the mean*

*Follows the rule - 68-95-99.7*

*mean=median=mode*

Ways to figure out Normal Distributions:

*www.ronblond.com-Gr.12-areas under the normal distribution/x&z values*

*Graphing calculator: 2nd-vars-normal cdf-low value, high value, mean, standard deviation*

Ungrouped Vs. Grouped Data

Ungrouped-All data values are present and accounted for.

Grouped-Frequency tabled

A frequency table looks like this:(Using the same data for how far we live from school)

The class marks column is the median for the boundary

Population Standard Deviation

Population Standard Deviation(little sigma x)- the measure of variability within a data set.
Range-also a measure of variability(the highest subtract the lowest)

We can find this number with our calculators. Go into STAT, edit, and edit a list. Once done that, go to STAT, CALC, 1-Var Stats, then select the list you edited.
It can also be done on the spreadsheet we made, found in my math folder.

Standard Deciation measures how varied the data is, relative to itself(how spread out the numbers are) The formula is too hard to type out, but is "the square root of the quotient between the sum of all x subtract x bar squared, divided by n"

Variability and Statistical Analysis

On Friday we looked at the measures of central tendency.

Median-Known in the calculator as med. "The middle number when ascending or descending." If the middle of the data is 2 numbers, the median is the average of those 2 numbers.

Mean- Know in the caclulator as an x with a line over it(x bar). "The sum of all the x-values divided by n"

it = SIGMA x

n

Mode-Known in the calculator as mode. The most frequently occuring. Note that the mode may not exist, or there may be multiple modes.

Computer Down

Yesterday Mr. Max's computer was down for the first half of class at least so we just worked on our Probability Exercises and Accelerated math. We have our test on Thursday, so to make sure we do good on the test we should do the accelerated math.

Vector Projects

On Thursday we continued to work on our vector projects. We had a work period to put our finishing touches on it. I finished mine and handed it in on the flash drive.

Independant/Dependant Events

Independent Events- 2 or more events occur that have NO effect in each others outcomes at all(with replacement)

Dependant Events- Probability events that occur and later events ARE affected by previous events(no replacement)

**The probability of something an event happening is slightly lower with dependant events**

Probability-Sample Spaces and Complimentary Events

Sample Spaces-any complete representation of all probability outcomes in a probability experiment(some measurable event)
Examples of sample spaces would be coordinate points, tree diagrams, charts, words saying each possible outcome.

Complimentary Events- P(A)+P(A)'=1
This means the "probability of event A" +"Not the probability of event A" =100%

Factorial Notations-Into Perms&Coms

Permutation- an ordering of objects in which order matters.
Combination- an ordering of objects in which order doesn't matter.
*The exclamation mark is "factorial"*

Perm VS. Com
We did examples to show the differences between Perms and Coms:

1- How many 5 letter "words", using the alphabet, no repeats?
26*25*24*23*22=7893600
26!=(26*25*24*23*22)*21!
SO 26*25*24*23*22=26!
21!
Divide it by 21(the 6th number) because there are only 5 spaces for the letters to go into.
You can do this on the calculator with this equation:
nPr= n!
(n-r)!
SO 26P5= 26!
(26-5)!
=7893600
Part 1 is a permutation because the order of the letters matters since there are no repeats.

2-How many poker hands are there with hearts/diamonds only?
There are 26 hearts/diamonds alltogether in a 52 card deck, so we go like this:
26*25*24*23*22 = 7893600 = 65780 unique poker hands using hearts/diamonds only.
5 * 4 * 3 * 2 * 1 120
You can do this on the calculator with this equation:
nCr= n!
(n-r)!*r!
SO 26C5= 26!
(26-5)!*5!
The extra *5! is to divide out all combinations with the same 5 elements(the same 5 cards, but in different orders)
Part 2 is a combination because the order doesnt matter.

Probability-Fundamental Counting Principal

F.C.P.-Fundamental Counting Principal

**...if you can do event A in a ways, and B in b ways, etc... then the number of ways to do event A, followed by number of ways to do event B, etc...**

This means: Number of ways to do A, B, C, ....=a X b X c....

Probability Intro..

Yesterday we did our Probability introduction and I was the class blog scribe. All the information is on that blog, with pictures too.

Vector "tricks"

Yesterday Mr.Max showed us some Vector templates.
To open them you have to first open Euklid, then get to the "stuff you can use on your exam" folder.
In that folder there are 2 templates, one is the Triangle Method, and the other is the Parallelogram Method.
For each method you can move the 2 vectors to where they are supposed to go and to what length to calculate the resultant vector.

Vector Exercises

Yesterday we just had a work class. We worked on the exercises 1-4 some more.
Here are some pointers:
For the triangle method, the tail is stacked onto the head of the previous vector.
For the parallelogram method, the tails are placed on the tail of the other vector.

Parallelogram Method

Parallelogram-a 4 sided polygon with opposite sides parallel.
We use the parallelogram method when there are situations with simultaneous vector addition, NOT stacked/chronological order.
Steps:
1)Create V1 with the tail on the origin
2)Create V2 with the tail on the origin.
3)Create 2 parallel sides to make a parallelogram
4)Create the resultant vector starting from the tail of V1 and V2(the origin) to the intersection of the parallel sides

Vectors Project

Nov. 10/09
We were given a vectors project that is due on November 27th at 4:00 p.m.

The project includes:

-Starting with a known resultant vector

-5 scenarios that have their answer as the resultant vector.

-Each scenario has to have a minimum of 2 vectors(with magnitude and direction scaled for each)

-Title page, table of contents, intro, references(if any), discussion(if any), conclusion, *diagrams

*Format is negotiable*

Vector Addition

We started vector addition today. These are the steps for the triangle method:

1-Starting from some origin, create a vector(to scale), that has the tail on that origin

2-From the head of the original vector(v1), square it(make another origin) for measurment.

3-Create V2, V3, V4, etc... and "square up" each vector head for measurment.

4-Create the resultant vector from the origin(starting point) to the head of the last "added" vector.

*Resultant vector is a vector from the tail of the original vector(origin), to the head of the last added vector*

We did an example on Euklid, and to "square up", in the construct tab there is a "parallel" button. Click that, then click the point you want to square up(the head of the last vector), then the X or Y axis to make it parallel.

Vectors on Euklid

Today Mr.Max showed us how to do vector questions on Euklid. It's actually really simple, and way faster than how I did it in Physics last year. All you have to do is make a fixed length line segment(to scale, with the scale legend typed onto the graph), and then measure the angle from a point on the axis, to O, to the end of the vector. To switch the line segment into a vector, you hit the vector button, then click on the ends of the line in the direction that it is going.
And that is pretty much all that we did today. Exercise 2 of the vectors booklet given to us yesterday is due on Thursday, not tomorrow because we have our first grad meeting tomorrow during block 1.

Vectors!

Today we started off on the Vectors unit. We learnt how to use the Euklid program, how to make lines with a fixed measurement, and measure angles. Once we finished that lesson we were given a Vectors exercises package to work on. We should be done the unit by next week.

Picnic Table Question

For the picnic table question we had to find the cheapest way to purchase lumber for a picnic table using the given dimensions.

I first took the top view to find out that I needed 4 7ft 2X12 boards. That works to 2-14ft-2X12's.

I then took the side view to find out how many pieces of what lengths I needed, and came up with 6 3ft lengths, and 2 5.5 ft lengths of 2X4 boards. To find out what lengths of boards I would need to purchase, I made a diagram to find out lengths of boards I would need, and came up with 1 16ft board to accommodate 5 ft lengths, and a 14ft board to accommodate both 5.5 ft lengths, and the last 3 ft length.

I figured out the cost with the cost of miscellaneous hardware and came up with the total price.

The second part of the question was to find out the cheapest way to build 2 picnic tables.

First I got 4-14ft-2X12's for the table top. I then got 2-14ft-2X4's so each one can get 2-5.5ft pieces for the seat supports and 1-3ft piece for the table supports. That leaves 10-3ft pieces still needed, which works nicely to 2-16ft boards with 1 ft waste on each. I then multiplied the boards by the cost of each, and added the miscellaneous cost onto it as well.

That was the question for the portfolio!

Finish Driveway Problem

Yesterday we finished the driveway question for homework and were to start on the picnic table question on page 11. It is due by the end of class today.

Driveway Question-Portfolio

At the start of class we had conversations about starting a Facebook group for our math class, and then watched a video on Media Literacy. The video showed us how far technology has come in the last 6 years(with Facebook and My Space), and how in 25 years something like a computer could fit in a blood cell, thats how small it could be.

When we finished the video Mr.Max showed us a few steps to finish the Driveway question from our Portfolios. -First we had to figure out the area of the driveway.

-Then for each method we figured out how much would have to be dug down for the excavation.

-Once you have done that, you find out the cost of each type of material for each method needed in cubic yards(1 yard cubed is equal to 27 feet cubed). To find the cost I multiplied the depth by the area to find feet cubed, then divided the answer by 27 to get yards cubed. After I did that I multipled it by the price per cubic yard.

-When you have calculated the cost of materials and the cost for excavation for each method, you find the total cost it would be without taxes or labour costs.

The rest of the question was due for the next day

Portfolio Continuation

First thing this morning we got our Matrices tests back. I did really good on the test, no troubles.
After we got our tests back we were to do a question in the portfolio's on page 6. We had to look at 2 methods of how to do a driveway and find the total cost of either driveway. The question is due for tomorrow.

Spot Check

In yesterdays class I was given the spot check work booklet to finish when I have the chance from missing Monday & Tuesday. There was also a formula sheet for Sequences/Series & Personal Finance that was assigned.

We got a Design & Measurement Portfolio booklet. We started to go over the questions, we were to do the 1st part of question 2 on page 4 of 4. The question was to find out how many ceiling tiles you need to complete the ceiling of a room, with the square tiles laid in the center of the room.

To do the question I divided the dimensions of the ceiling into 4 quarters. I then figured out how many full tiles I would need, and how many partial tiles(for each tile that was less than half, I used 1 full tile cut into 2 partial tiles) for each quarter. Then, I multiplied that number by 4quarters to find out how many complete tiles I would need for the full ceiling. Once I got the total number of tiles I would need, I figured out how many packages I would need, and from that I got the price of the total price ceiling tiles.

Surprise Test

Today we had a "test". We went over some provincial math exam questions.
One of the questions showed us that doing the questions through the calculator can give different answers than Excel. Through the calculator it gives you a more accurate number because you can change how many times the amount is compounded semi-annually which changes your answer. So when there is a question with different compounding it is easier to do it on the calculator.
We also did a question that needed the Statement of Net Worth. There are templates on the coursework drive with this statement so we don't have to make our own:)

Personal Finance-Tricks

Tricks:
There are some tricks you can use on the calculator to help you do a certain part in a question. You can find these in the applications part of the calculator. They have a weird E looking symbol in front of the first 3 letters of the function.

Sum of Interest-Gives you the total interest paid between 2 points in time

Sum of Principal-Gives you the total amount paid on the principal between 2 points in time

Balance-Gives you the balance at one point in time.

Templates-Personal Finance

Today we went over the 3 templates:

1)Net Worth Statement

NW=Own-Owe or NW=Total Assets-Total Liabilities

2)Debt Equity Ratio

D.E.Ratio=(Total liabilities-Mortgage on your home) x 100

Net Worth

*Most desirable ratio is 0%*

3)Gross Debt Service Ratio

GDSR=(Monthly Rent/Mortgage+Monthly Taxes+Monthly Heat) x 100

Gross Household Monthly Salary

*Usually associated with housing costs and not to exceed 32%*

Homework Check Day

When Mr.Max went to do the homework check yesterday most of the class hadn't done the 2 questions that were assigned over the long weekend. So we were given time to try and finish the questions, and then we went over question 5 together as a class.

For Fridays class we continued to review the personal finance unit. We went over question 8 kind of as a class. We were given questions 3&5 to do for Monday morning. Mr.Max said that he doesn't want to see nothing when we show up on Monday.

Personal Finance-Excel

Today the day started off with a little bit of snow on people's cars in town. Winter has arrived..
Mr.Max showed us how to make an excel spreadsheet that gives us the same information that we figured out with the TVM method yesterday, but on excel you can see the progress of the loan(how much still owing by when, etc.)

Personal Finance unit.

Class started off with Mental Math. When that was done we had to calculate our average out of 8 quizzes and hand it in to get marked.

When we finished that, we started our next unit:

Personal Finance

Tools that we will be using for this unit are the:

TVM solver(calculators)

Excel

*Web Applets from Canada only*

Today we started with the TVM solver. This allows us to put info from taking out a loan etc in the calculator and from that we can calculate monthly payments, costs of borrowing, etc. We went over an example question of buying a car, and we figured out what the monthly payments would be for the car with a 5 year loan.
From there we were given some practice questions

Sequences

Today we started off with Mental Math, then we were told we have to complete 2 questions from the Sequences Review Questions and hand them in for a test mark. I wasn't here for the last few days from getting my wisdom teeth removed, but I have to get it done as soon as possible to hand in.

Sequences & Series cont...

Today we learnt more about the 4 methods to figure out sequences and series.
Shodor- There is a link www.shodor.org/interactive/activities/Sequencer where you can put in your information from the question and it shows you the graph, and gives you the number values below the graph
Sequence mode-You turn your calculator's mode to Sequence. You can fill in the y=, set the window, see the graph, see the table

"Sequences & Series

This unit is split into two parts:
1)Geometric/Arithmetic sequences and prediction, stability, exponential growth.
2)Fractal(self similarity-reduced size of the whole, split) Analysis
Fractal-Sierpinski has examples(triangle and square)

There are 4 methods to solving these problems. Mr. Max gave us the first two, and for homework we were to find the other 2.

1-Calculator Home Screen Method

2-Excel(making a chart with answers and another with formulas)

3-Sequence mode on the calculator

4-Shodor

Matrix Modelling is over!

On Friday we were supposed to write our test, but at the start of class we found out we had an assembly to say that the Swan Valley is going to host the 2012 Manitoba Summer Games. When we got back from the assembly we had a choice to write the first half of the test or study, and yesterday we finished writing the test.

Matrix Modelling Review

Today we started off the class with our review. Mr.Max divided the unit into 4 parts:
1)Matrix Info-vocab, naming, calcuators, matrix operations(+,-,scalar X, matrix X)
2)Matrix Multiplication in context(fast, avoiding nonsense calculations), word problems
3)Transition Matricies-RowXSquare, [B]X[A]^n(stability), loopies, decimals in matrices, 1 sum(each row=1)
4)Networks-Directed(node, direct route, at most, exactly) and Non-Directed(two-way)
We then went over some provincial exam questions from previous exams for some more review. For the test tomorrow we are allowed to bring a 8.5X11 formula sheet.

Directed Networks

Today we started class with Mental Math, and went over a question that was for homework yesterday. Also, there was a big conversation on homework being due, and if a person doesn't get their homework done the first day, it can be made up when they have the chance.

With Direct & Indirect networks:
Matrix A^1=direct-1 leg stop
Matrix A^2=indirect-through exactly 1 node
Matrix A^3=indirect-through exactly 2 nodes(2 stops before reaching the destination)
Directed Networks:
If the question asks you for the number of ways each point can get back to itself using no more than "x" relays, you have to make all the matricies you can. The first matrix is direct connections, the second is through one relay, ect until you reach the total numbers of nodes you can go through. Once you have made all the matrices you can, add them together and you will get the total number of node to itself connections through AT MOST "x" relays.

For the remainder of class we are to look at old provincial exams and do some questions from them for practice, and as a study tool for the test on Friday.

Networks & Matricies

Today we learnt about Directed(one-way streets) and Non-Directed networks(two-way streets). To do so, we started with a diagram that had routes to the nodes. We had to figure out how many ways we could get from one place to the next either directly, or indirectly(through another node). After we did this for a half hour, Mr.Max showed us how to do it easily on the calculator by taking the direct route matrix and squaring it to get to the second matrix that was from one place to another through one other node.

Transition Matricies

Today we went over one of our homework questions on transition matrices. To continue to the "next transition" you first multiply the row by the square, and to continue you multiply the resulting matrix by the original and can continue pushing enter to see the next matrix.
There is now a link on the class blog to previous provincial math exams. And we also have a test on Friday.

Transition Matricies

A transition matricies question has the info moving around(students changing their minds over what restaruaunt they prefer). There is a chart showing what people stay at which restaraunt, and what ones they switch to.
The first step is to create a nXn matrix using decimal equivalents to show the switches and input them in the calculator. Headers for the rows and columns are very important to keep track of.
The second step is to create a row matrix with either A)Real # values or B) the % of some distribution, which is also put in the calculator.
The third and final step is to multiply the row matrix by the nXn matrix which gives you the answer of the next transition. This can be continued until stability is reached. To prove stability you can do the transition to the power of 50, then 51 to see if any digits change.

Matrix Multiplication Question

We were given a question yesterday to do with matrix multiplication and were asked to post our thoughts through it on our blogs to look at in the future.

There are 3 factories of type A that makes 30 kitchens each week and 40 bathrooms, as well as 8 factories of type B with 10 kitchens each week and 15 bathrooms. This information could be made into a 2X2 matrix with row headers "Kitchen" & "Bathroom" and column headers factories"A" &"B". The first part of the question asked for total weekly production of both suites from both kinds of factories. To do so, the 2X2 matrix had to by multiplied by a 2X1 matrix so the inside numbers were the same. The next part of the question was to find the market value of all suites per week. To do this, the total of each suite had to be multiplied by the total value of each suite. The 2X1 had to be multiplied by a 1X2 matrix with values to work, resulting in a 1X1 matrix with the total value of the goods purchased

Two-Finger Method

The two finger method is used for Matrix Multiplication. To form it, the left hand is a thumbs up with the index finger pointing to the right, and the right hand forms a backwards "L".

The right hand uses all columns up before the left hand moves to the next row. Each row & column's product is an element in the resulting matrix.

First Few Days of Class-Matrix Modelling

Sept 14th 2009:
The third and forth parts to matrices are "Scalar" multiplication(matrix multiplied by a scalar quantity measure), and "Matrix" multiplication. Matrix multiplication can only be done

when the inner dimensions match

or

the # of rows in the 2nd matrix matches the # of columns in the 1st matrix

*This is where the "Two-Finger Method" is used*

Sept 11th 2009:
On the second day of class we were taught about Matrix Modelling. Every matrix has Rows&Columns(listed in this order) and the numbers in each is an element. The first 2 parts to Matrices are addition and subtraction, which cannot be done unless they have the same number of rows and columns. To do so, thinking of the numbers overlapped will allow you to see the end result.

Goals!

Specific
Measurable
Attainable
Realistic
Timely
Goals:
~To acheive marks of 80% or higher in the remainder of my High School courses
~To decide on a career that I will enjoy that allows me to help others within the next 3 months
~To be accepted to UofM or UofW
~To not rely on my parents for more money than already put aside for my education
~To be a good role model for my younger siblings and try to help them make smart choices