2 Core questions, 1 Matrices question. 2007 VCAA.

[brenden]

Hey guys I just completed 2007 VCAA Exam 1 (36/40). Two of them I don't know how to do and one of the questions I got right was a guess so for anyone kind enough to open the exam and read on, that would be much appreciated

http://www.vcaa.vic.edu.au/Documents/exams/mathematics/2007furmath1.pdf
(Please refer to page 8, and  then page 40 of that link).

Core

On Page 8, question 9 they want me to apply a Log Y transformation and then find the least squares regression line. The answer is D which I worked out by process of elimination and a bit of dumb luck. How do I apply a Log transformation to any of my lists?

On Page 8, question 10 they want me to choose the best graphical display for a set of data. I cannot consistently get these questions correct and I can't work out why their answer is correct instead of mine. If anyone has a method that would let me determine answers with more consistency I would jump for joy.

Matrices

Page 40, Question 7. Correct answer is E. Looking at the 3 diagonal zeros and seeing the columns sum to 1 I recognise this is correct but I don't know how I would prevent future mistakes like this. Why are those numbers the way they are?


Thanks for even opening the thread, and even more if you answer it

[Kaille]

for your first problem, what calculator do you use? i use classpad and so i won't be of much use if you use the ti ahah

[brenden]

I've struck luck - I use the classpad too

[Kaille]

cool!

I'm not very good at explaining so i'll write down steps
1. put x values into list 1
2. put y values into list 2
3. then if you look below the lists, in the last row it should say cal.
3. Go to list three and in that cal box for list 3, type in log(list2) (list two contains your y values)
4. press exe.
5. transformed y values should come up.
6. Go to the 5th little square box from the top left (it should have a graph and a coloured and non coloured dot), select it
7. then you should get a list saying xlist, y list so on. So since the x values have remained the same, just keep x list- list1.
However, your y values hav been changed so go ylist-list3
8. then set and read new slope and y intercept values.

Hope you can understand, there is a pretty good page of instructions on pages 180-181 of essentials if you have it

[brenden]

Fantastic! Thank you very much, +1.
The steps were a great explanation =]

[Kaille]

awesome! glad i could help

[ashoni]

Core Question 10
I'm not sure which textbook you have for further, but my textbook(Essentials) has a table where it shows which type of data,whether it be numerical or categorical, is displayed best graphically. (See attachment)
Now with the question, both variables are categorical (ordinal), which by looking at the table is best displayed using a segmented bar chart OR percentage segmented bar chart (selection E). Make sure you copy out this table in your bound reference!

Matrices Question 7
This question is purely testing your basic knowledge of transition matrices. The question says that "They never go to the same place two years in a row" which tells us that there is a 'diagonal 0 line' going from the top left corner to the bottom right corner. We are then left with only selection D and E. Then you would have to recognise that the columns in transition matrices must add up to 1. This only leaves the selection E. As for the values within the matrix, I think they were just random. I remember doing this question thinking "WHERE DID THEY GET THE .1 AND .9 FROM?!?"

Hope this helped!

[brenden]

Core Question 10
I'm not sure which textbook you have for further, but my textbook(Essentials) has a table where it shows which type of data,whether it be numerical or categorical, is displayed best graphically. (See attachment)
Now with the question, both variables are categorical (ordinal), which by looking at the table is best displayed using a segmented bar chart OR percentage segmented bar chart (selection E). Make sure you copy out this table in your bound reference!

Matrices Question 7
This question is purely testing your basic knowledge of transition matrices. The question says that "They never go to the same place two years in a row" which tells us that there is a 'diagonal 0 line' going from the top left corner to the bottom right corner. We are then left with only selection D and E. Then you would have to recognise that the columns in transition matrices must add up to 1. This only leaves the selection E. As for the values within the matrix, I think they were just random. I remember doing this question thinking "WHERE DID THEY GET THE .1 AND .9 FROM?!?"

Hope this helped!

Hahaha yeah I was just so confused at the values lol. That helped a lot, thanks heaps for the table! And for the answer +1. Thank you both very much!

[ashoni]

Your welcome!

[Yendall]

Each year, a family always goes on its holiday to one of three places; Portland (P), Quambatook (Q) or
Rochester (R).
They never go to the same place two years in a row. For example, if they went to Portland one year, they would
not go to Portland the next year; they would go to Quambatook or Rochester instead.
A transition matrix that can be used to model this situation is

Main thing you should be looking at is: "if they went to Portland one year, they would not go to Portland the next year; they would go to Quambatook or Rochester instead"
You now know that a 0 will signify that they aren't travelling there in the next year. The rest of the information is irrelevent, as long as the sum equals 1.

That leaves two possible answers:
D)

E)

Now remember that in Transition Matrices, the sum of each column must equal "1".

In matrix D, column 1 (0.3 + 0.5) = 0.8, Column 2 (0.2 + 0.6) = 0.8 and Column 3 (0.8 + 0) = 0.8, none equal 1, therefore it cannot be an appropriate Transition Matrix.

In Matrix E, column 1 (0.5 + 0.5) = 1, column 2 (0 + 1) = 1, column 3 (0.1 + 0.9) = 1

The answer must be E

Hope that helps man