Developing Expert Voices

Question #1 Personal Finance Unit

Shaiana wishes to invest $2000.00 given by her grandfather. She has an option guaranteed earning investment certificated of 8.5%, compounded quarterly, or a savings bond of 9%, compounded semi annually.

Which investment should she choose?


If each investment is termed 5 years, what will the difference of their values be at the end of the term?


Question #2 Matrices Unit

On the soap opera, the young and the mathematical Ann is in love with Buck and Dash. Dash is in love with Ann, Charlotte and Elvira. Charlotte who just broke up with her fiancé after learning that he was dating the University of Winnipeg women's basketball team, has fallen in love with Frank, not realizing that he is actually her step brother who has returned to Winnipeg with amnesia and major plastic surgery after the tragic explosion of a graphing calculator at a secret CSIS cryptography lab. Frank is in love with Elvira. Buck is in love only with himself. Write a connection matrix detailing the relationships among the six named characters. Include labels and other explanations to make your work clear.

Time Line:
May 23: Rough Copy for Questions & Solve Questions
May 24: Create visuals for project
May 25 - 31: Put together all visuals on computer
June 1 - 6: Complete Project
June 7: Hand in Project

April 30, 2009

According to Mr. K the world has been visited by alliens! hahaaaaa =)

back to reality..

Today Mr. K started the class off by introducing us to a new program which he had on his calculator, it is called "TRISOLV2." Providing the program with atleast 3 bits of information, either angles or sides, the TRISOLV2 program can solve the entire triangle. Meaning the program solves the remaining unknown sides or angles.

He then gave us connecting cords for our graphing calculators and he sent the program to some of the students, from there we were to send the program throughout the rest of the class. Once we all had the program on our graphing calculators Mr. K continued on with the lesson.

He first reviewed adding vectors with the class, here is an example..

Find vector A+B

vector A is 6 km east

vector B is 10 km south

These vectors should look as shown below..

1 cm = 1 km

**Remember when using the triangle method the vectors are arranged tip-to-tail.**

The resultant of this vector addition would be the missing vector which connects all the vectors together by creating a triangle (3 sided figure)

1 cm = 1 km

Now to find the length of the resultant vector you can use pythagorean theorem. You can only use pythagorean theorem if one of the angles equals 90 degrees. In this case it does since the vectors go from east straight down to south.

The resultant vector equals 11.66 cm

Next Mr. K gave us another vector addition to solve, we were to use the triangle method aswell. But not just trying to find the length of the resultant vector, Mr. K also showed us how to solve for the angles of the triangle too. Here is the example that he used

Find vector A+B
vector A is 3 m east
vector B is 4 m north

1 cm = 1 m

These vectors should look like this..

The resultant vector is shown in the next image

Using pythagorean theorem as used in the example above, we find the length of the resultant vector as 5 cm.

Since the direction of the vector A goes east and vector B goes straight up to north, a 90 degree angle is created.

So the information that we are given all together would be side-angle-side (3cm-90 degrees-4cm)

Therefore, we must use the tri-function inverse TAN to find angle B

Now that we know that angle B equals 53.1 degress we are now able to use the TRISOLV2 program on our graphing calculator to determine the remaining unknown sides and angles of this triangle! All you have to do is open the TRISOLV2 program enter in the 2 sides and the angle into place as labled on the program. (What I mean is make sure that sides a b and c match whats on the diagram above and also the same goes for angles A B and C) Once you have entered in the known sides and angle press solve and the program should look a little somthing like this.

This tells us that angle A = 36.87 B = 53.13 and C = 90

also side a = 3 b = 4 c = 5

I have explained all that I understood and if you have any inputs please tell moi! =)

I CHOOSE KYLE TO SCRIBE NEXT =P

Statistics Reflection

This unit on statistics was pretty challenging for me and I’m pretty sure that it was pretty challenging for the rest of the class. I think that I have quite a grasp at what each command does, like the inversenorm, normalcdf, binocdf etc. But I think that for me to fully understand this unit, I would need about an extra week or two more to fully understand it. From our last class I think that I was finally able to talk to my other group members to clarify what I had problems with, and that was VERY helpful for me. In about two hours our math test will take place, and hopefully everyone is prepared! Good luck to everyone!

Today during class we did our "Pre-test" for our current unit of probability. The pre-test prepares us for our upcomming unit test which takes place tomorrow March 19. The format of our pre-test was 2 multiple choice questions, 2 short answer questions, and 1 3-step problem. We were given about 35-40 minutes to write our pre-test and after that Mr. K split us up into groups to compare answers. After about ten minutes of comparing answers, Mr. K went over the questions and showed us step by step how it came out to the answer.


In my group there were a couple a questions that stumpted my group members and I, but now I understand why and how we got the answer.

Here is one question that we didn't quite get right..

Using the word FOOD, find the probability that an arrangement of this word will begin with the two O's if all the letters are used. Correct to the nearest hundreth.

So to start off, you need to make sure that the two O's are stuck together at the front of the four letter combination. A way that Mr. K would refer it to would be "take the two O's and put them in a bag."


And this is what the 4 letter word combination can look like..




The first 1 stands for the 2 O's which are "stuck together," they are first because the question requires for them to be at the front of the four letter combination. The 2 stands for the choice of either F or D. And the last 1 stands for the left over of the previous two. (Say I choose F for the second space, then the last space would be a D and vice versa.)

So now you are required to multiply 1 by 2 by 1 in order to find out the number of ways for the combination. The answer is 2.

Now you take the the amount of ways that the four letter word can be rearranged(2 differnt ways) and you divide it by 4 factorial(representing the total number of letters) divided by 2 factorial(representing the 2 O's)

You would do it like so..



The result would be 2/12 then would reduce into 1/6, and because the question says around to the nearest hundreth, you must express the faction into a decimal which is 0.17.



* JUST A REMINDER * our unit test is tomorrow!
For further review Mr. K posted up extra questions.

I choose Kayla for the next scribe!

Today's class was our "pre-test" for our Matrices unit. This pre-test prepares us for our up comming unit test which will take place on Friday.

We were given about half the time in class to write the pre-test. After that, Mr. K split us up into groups and following that we were to compare our answers with our group members. After comparing our answers we were to hand in one pre-test for our whole group which will be worth marks. The paper each group chose to hand in was the modified test paper (meaning the answers were looked over, and corrected by what the entire group felt was the right answer within reason.)

After that, Mr. K went over every single question and explained each question step by step.

Here is an example of a similar problem which was on the pre-test.

At a local grocery store, there are 2 available sizes in which milk can be purchased in. There is the 2 litre carton, and there is a 4 litre jug. Research shows that 23% of the 2 litre carton buyers switch to the 4 litre jug on their next purchase. And 41% of the 4 litre jug buyers switch the the 2 litre carton on their next purchase. The original market share is 40% of the 2 litre carton and 60% of the 4 litre jug.

a.) What is the market share for each the 2 litre and the 4 litre in the next round of purchases?

Well in order to find the next market share for the next round of purchases, you must write the initial state matrix, and you must also write the transition matix. After that, you must multiply the two together inorder to firgure out the market share for the next round of purchases.

The inital state matrix is the original percentage market share, which is 40% for the 2 litre and 60% for the 4 litre. Also, you must remember that the percentages in a state matrix should always be expressed as a decimal.

Let's call the initial state matrix " I "


Now we must figure out the transition matrix.

The information given states that 23% of the 2 litre carton buyers switch to the 4 litre jug on their next purchase. And 41% of the 4 litre jug buyers switch the the 2 litre carton on their next purchase.

So since 23% of the 2 litre buyers switch to the 4 litre, 77% remain as a 2 litre buyer. And since 41% of the 4 litre buyers switch the the 2 litre, 59% remain as a 4 litre buyer.

Lets call our transition matrix " T "



Now we must multiply the two matrices together (I*T) in order to get the market share for the next round of purchases. Lets call the resultant matrix "R"


Now the resultant is..

Meaning the market share between the two is 55% for the 2 litre carton and 45 % for the 4 litre jug.

b.) In the long term, what would the market share be for both sizes?

Well, in order to find the long term market share you must chose a large amount of years. Lets say 50. And then you must multiply I by T to the power of 50.

So it should look like this.
L is the resultant.


Now, we must put up the power by 1 making it 51 to clarify that the percentages have stabilized.

So we now find that the matrice has stabilized. Making the final market share 64% for the 2 litre carton and 36% for the 4 litre jug.



*JUST A REMINDER! *



The final unit matrices test is on Friday, Febuary 20. Remember to study and to be prepared!



I choose K_Hannah to scribe next:)!