BOB

I gues it's time to BOB! Well, about the design and measurement unit, i wan't having any difficulties with the problems having just the basic objects, but when we were given complex problems, I got confused because they are too complicated. About sequences, at first I can't understand on how to do the problems because I missed a class. Anyway, as we go along, I am kind of getting the stuff that we were doing. The fractals look cool. they look nice and it's also interesting that we can see and find sequences aruond us. Good luck in the test! =)

Friday's class

I'm sorry for the delay.. Here's my blog for June 1st..


The next scribe is... donna

BOB

The unit that we just finished about periodic functions is not that hard. We just have to read the questions carefully and understand what each value in the situation means. Just remember the word "DABC", like what Mr. K. said to help us remember. Mr. K. mentioned that quadratic equations are used in the real world, for example in tides, temparature, etc. which I found interesting. I think i am understanding the unit pretty well, and I hope I'll do good in the test tomorrow. =)

BOB

Personal finance is not a hard unit. We just have to read and understand the problems. This unit helped me learnned about the real world for example, in buying a car or house, or if buying is better than renting, etc. It gave me idea on what to do in the future if I'm in the same situation in the problems that we did in class. I think know what to do. I didn't have that much difficulty during this unit. Hope I did good... =/

May 8, 2007

In today's class, we formed five groups and solved problems together about purchasing a home for us to understand the things that we were not clear of and to allow others our ideas on how to solve that certain problem.

This was the first problem that we worked on in our groups...

First, list all the additional expenses that the Dirkson family had in purchasing a home.

Appraisal $ 125.00

Survey $ 300.00

Insurance $ 325.00

Taxes -> (2125/12) * 7 = $ 1,239.58

Dry wall -> (650/2) = $ 325.00

Washer & Dryer $ 920.00

Moving Expenses $ 320.00

Legal Fees $ 965.00

Morting $ 1,437.50

Total Cost $ 5,957.08 -> The total cost the Dirkson family had in purchasing a home.

The next problem was...

- To calculate the monthly payment, we can use the Finance Application in our TI-83 calculator, having N=300 which is 12 * 25, 7.25% as the interest rate, $121,000 as your principal value, and the compounding periods per year is 2 because it's Canadian Mortgage, then find the amount of payment every month. The monthly payment is $866.26.

- Multiply the monthly payment to the total number of payments for 25 years.

$866.26 * 300 = $259,878 -> This is the total amount paid for the mortgage.

- To find the total amount of interest paid when mortgage is repaid, subtract the mortgage from the total amount paid for the mortgage.

$259,878 - $121,000 = $138,878

- To determine the monthly payment, we can again use our calculator. and the monthly payment is $948.52.

- The total amount paid for the mortgage is calculated by multiplying the amount of monthly payment to 240 which is the product of 12 * 20. The total amount is $227,644.80.

- The total amount of the interest paid is $106,644.80. we got this by subtracting the required mortgage from the total amount of mortgage.

- By repaying the mortgage in 20 years instead of 25 years, the Jamison family saves $32,233.20.




The next scribe is Chris...

BOB

Sorry, my BOB is late because of our trip...
The last unit that we learned was about vectors. This topic is not new to me because i have learned it in my physics class. I didn't have much difficulty in this lesson because of its introduction in physics which have problems more complicated than those that we had. I now have a much better understanding of vectors. Some of us in class had a hard time understanding on how to tell the direction of the vectors, but we all helped each other if we don't get a problem. I think i don't have any difficulties in this unit because in problem solving, you just have to read and understand the question word for word. I'll ask Mr. K. if I can write the test tomorrow and I hope I get a good mark in it. ;-)

BOB

In the unit of Statistics, everything is pretty complicated. Analyzing the problems carefully is one thing that we should always do. This unit also involves probability, which makes it more complex in understanding. The topic that I am comfortable and confident with are z-scores and the confidence intervals. Learning Statistics also involves different calculator functions which will be remembered if we understand the meaning of the problems that we have. Statistics is also important because it is used by different professionals in the real world like teacher applying that knowledge in the marks of their students. Speaking of marks, I hope I get a good mark in our upcoming test tomorrow??.. Oh well, good luck to us! ;-)

Confidence Interval

On Thursday, we talked about confidence intervals.

A confidence interval gives an estimated range of values which is likely to include an unknown population parameter, the estimated range being calculated from a given set of sample data.

We had this problem…

Some Senior 4 students in a large high school want to change a tradition at graduation. Instead of wearing the usual cap and gown, they want to wear formal clothes. A quick survey of 96 randomly selected students shows that 41 prefer formal wear.

To answer this question, construct a “confidence interval”, most often a “95% confidence interval”.

Find the probability (P), the mean (µ), and the standard deviation (σ) first.
p = 41 / 96
= 0.43


µ = n ∙ p
= 96 (0.43)
= 41.28



σ = √ n ∙ p ∙ (1 - p)
= √ 96 (0.43) (1 – 0.43)
= √ 23.5296
= 4.851

For data that have a normal distribution with mean and standard deviation, a 95% confidence interval is:

µ ± 1.96σ

This is the range of values that lie within 1.96 standard deviations of the mean. The probability that a particular data value lies in that range is 0.95. This is shown in the graph.

95% confidence interval = µ ± 1.96σ
= 41.28 ± 1.96 (4.851)
= 41.28 ± 9.508

---

= 41.28 – 9.508
= 31.772

or

= 41.28 + 9.508
= 50.788

We write it this way: (31.772, 50.788)

= (31.772 / 96) × 100
= 33%



= (50.788 / 96) × 100
= 53%

And we write it this way: (33%, 53%)

With 95% confidence, we know that between 33% and 53% of 96 students prefer formal wear.
Now, find the Margin of Error and Percent Margin of Error.

The margin of error is the proportion that we add to, and subtract from, the mean to construct the confidence interval.

For a 95% confidence interval: Margin of Error = ± 1.96σ

1.96 × 4.851 or 9.508 represents the half-width of the interval. This is the margin of error. To express this as a percent, we divide it by the sample size, which is 96, and multiply by 100.

% Margin of Error = ± (9.508 / 96) × 100
= ± 9.904%

Is it possible that a majority of students prefer formal wear?
** Yes, but not likely, because the high end of the 95% confidence interval is just 3% over the half of the sample size and the Margin of Error is a little bit high. When you conduct a survey, the smaller the Margin of Error, the better the results of the survey.

The next scribe is Donna (",)

Probability on Flickr

Just click on the image to go to my flickr.. (",)

Probability

This unit about probability is harder than the last unit about matrices. At the beginning of the unit, problems are plain and easy, but as we move to different chapters in this unit, we encounter more complicated stuff. The Math dioctionary really helps, knowing what the terms mean. There were probelms that we had in class that were difficult to solve, but I think that I just have to read the question or the problem carefully. Working with groups also helps in understanding the concept of probability, because I can ask the group members if I don't get something, and vice versa. We are having our pre-test tomorrow. I hope I do good in it, so that I know that I can also do good in the soming test. =)

BOB - Matricies

In the first week of class in Applied Math, learning about matrices is new to me. At first, it was a little bit confusing because it was my first time encountering this lesson.. but after some examples shown and discussed in class, I had that "moment of clarity" that Mr. K. was saying. I understood the lesson more when we were assigned to do problems involving matrices. I learned that matrices are used to solve real life problems, which I found interesting. We learned about multiplying matrices and transition matrices. About transition matrices, I did not get it at first because I missed one class, but i caught up and I am comfortable with it now. And now this unit is over, we are having a unit test on monday. Hope I get a good mark. =) >> Kristel

Multiplying Matricies

In mathematics, a matrix (pl. matricies) is a rectangular table of numbers, generally a table consisting quatities that can be added and multiplied. In today's class, we learned about the 2 kinds of multiplication in matricies. These 2 kinds are:

• Scalar Multiplication - is multiplying a matrix by a number.

Given a matrix A and a number n (which is 2), the scalar multiplication cA is computed by multiplying the scalar c by every element of A.

For example:

A

• Matrix Multiplication - is the multiplication of two matricies where the number of columns of the left matrix is the same as the number of rows of the right matrix. This involves both multiplication and addition.

For example:

2 x 3 2 x 2 2 x 2

A B C

If A is 2 x 3 matrix and B is a 2 x 2 matrix, then the resultant matrix C is a 2 x 2 matrix. Why? Look at the dimensions of the 3 matricies. The inner dimensions are the number of rows and columns of matrix A and the outer dimensions, as we can see, are the dimensions of the resultant matrix C. Is this example commutative? Yes, because in this example, the outer dimensions are the same, which means we can multiply the matricies. In our examples in class, the inner dimensions of the matricies should be the same to multiply them.

And the next scribe is... Jennifer