VCE Methods Question Thread!

[lzxnl]

Euler's method, let f(x) = x^1/3, x = 343 and h = 2
Hence f(343 + 2) = f(343) + 2f'(343)
E B

Strictly speaking, it's not Euler's method according to spesh courses; Euler's method is used to solve differential equations and in its general form, is applicable in solving equations of the form dy/dx=f(x,y). However, Euler's method is derived from linear approximation

[Flor]

Hey guys! For exam 2 2010 VCAA section 2 question 1iii I get x = -3.997 and x = 4.8616
All I did was equate 2log10(x+4)+1 = e^x-1/2 -4 and solved for x and my answers are off for some reason. Can someone explain?
HELP

#1stpost

[Phy124]

Hey guys! For exam 2 2010 section 2 question 1iii I get x = -3.997 and x = 4.8616
All I did was equate 2log10(x+4)+1 = e^x-1/2 -4 and solved for x and my answers are off for some reason. Can someone explain?
HELP

#1stpost

The inverse is not

You should also have not on the left hand side

Therefore your calculator syntax should be solve(2ln(x+4)+1=exp(x/2-1/2)-4,x) or simply solve(2ln(x+4)+1 =x,x) as they will intersect on the line y = x

edit: fixed subscript error

[lzxnl]

Hey guys! For exam 2 2010 section 2 question 1iii I get x = -3.997 and x = 4.8616
All I did was equate 2log10(x+4)+1 = e^x-1/2 -4 and solved for x and my answers are off for some reason. Can someone explain?
HELP

#1stpost

The base of your log is incorrect; it's log base e, or ln on the calculator.
Also, it's much easier to solve 2ln(x+4)+1=x on the calculator as it's easier to type in.

[Alwin]

Hey guys! For exam 2 2010 VCAA section 2 question 1iii I get x = -3.997 and x = 4.8616
All I did was equate 2log10(x+4)+1 = e^x-1/2 -4 and solved for x and my answers are off for some reason. Can someone explain?
HELP

#1stpost

IS THAT.... IS THAT.... FLORIASON? =D =D =D
wb! why did you delete your account!!



When you rearrange,

[Flor]

The inverse is not

You should also have not on the left hand side

Therefore your calculator syntax should be solve(2ln(x+4)+1=exp(x/2-1/2)-4,x) or simply solve(2ln(x+4)+1 =x,x) as they will intersect on the line y = x

edit: fixed subscript error

The base of your log is incorrect; it's log base e, or ln on the calculator.
Also, it's much easier to solve 2ln(x+4)+1=x on the calculator as it's easier to type in.

Thanks so much guys!

IS THAT.... IS THAT.... FLORIASON? =D =D =D
wb! why did you delete your account!!



When you rearrange,

I deleted because AN was just too much for me. This is temporary btw.

[Flor]

Hey again! Could someone help me with question 2dii and e section 2? (link below) I know how to find the expected value but I'm kind of confused about how to do it with this particular question. Could someone just explain it to me? http://www.vcaa.vic.edu.au/Documents/exams/mathematics/2010mmcas2-w.pdf

Also, I'm not great with probability, it generally takes me a while to understand what the question is asking. So, you may want to 'simplify' things when explaining.

Thanks in advance!

[TrueTears]

Initially, I found the distribution of x = 4 and x = 5 and got the wrong answer.

That would be finding the joint pmf of X=4, X=5, which is clearly not what the question is asking.

In binomial distributions, what is the difference between finding a particular value of x rather than a series of them and adding them together? What is the significance of this question that allows you to distinguish in what to do?

Question doesn't make sense, please clarify.

What is x? A value of the pmf or a generic pmf itself? By adding, do you mean finding the joint distribution of for (possibly non i.i.id?) observations of the rv x?

[ahat]

Hey again! Could someone help me with question 2dii and e section 2? (link below) I know how to find the expected value but I'm kind of confused about how to do it with this particular question. Could someone just explain it to me? http://www.vcaa.vic.edu.au/Documents/exams/mathematics/2010mmcas2-w.pdf

Also, I'm not great with probability, it generally takes me a while to understand what the question is asking. So, you may want to 'simplify' things when explaining.

Thanks in advance!

There really isn't a quick or 'easy' *actually, I think there is, using matrices, but I have no idea how to do that* method for this - whilst it's straightforward, it takes a lot of work. I'll attach the solution and provide a few comments:

As we know, we can find the expected value by forming a probability distribution table. We know that the probability that we're interested in is the number of Superior Statues, so: Let X = The number of superior statues

Now, we know from the info in the question that on this day, the first statue is regular, so that means another two statues will be produced and they may be regular or superior. So, if we draw a tree diagram and show all of the different possibilities, we can discern the number of superior statues. Starting to click now?

Going back to basics, we can now cram this info into a distribution table. From there, it is a simple application of Expected Value.
Hope that helps.

[Rectophobia]

There are two ways to do part e:
-The way I did it (arguably the longer of the two)
-Plugging in the values straight into Cas.

The reason I chose to take the probability of X being less than 2 and then subtracting it from one is because not doing so would require considering all values of x greater than or equal to 2.

[zvezda]

Hey,
With the determination of steady state probablities using the transition matrix of a markov chain,
Ive come across a question whereby im getting two different answers. Ill explain further.
This is the question:
"A company opens a new factory that uses two suppliers for raw materials to make cyclinders which can be either defective or non-defective. Supplier M supplies 5/8 of the total raw materials and supplier N supplies the remainder. It is estimated that 95% of cylinders manufactured from supplier M are non-defective while 88% of cylinders manufactured from supplier N are non-defective. In the long-run, what overall percentage of cylinders from the new factory are non-defective?"
Now i determined my transition matrix and has M and N in the first and second columns respectively and defective and non-defective in the first and second rows respectively. From the probablities that i then placed in the matrix, i plugged in numbers into the formula for the steady state probablities (which tbh i dont full understand; i just cant grasp how matrices work), and i got an answer that was different to the solution. Upon reversing the rows in the transition matrix (so first row was now non-defective and second row was defective), the formula spits out the answer.
Ive been slaving away trying to understand why this has happened, but im hopelessly lost atm, because usually i just look at the general transition matrix in the essentials textbook and whack in the numbers.
Would anybody be able to explain whats going on?
Help is greatly appreciated

[TrueTears]

tbh i dont full understand; i just cant grasp how matrices work

The wiki entry on Markov chains is especially insightful: http://en.wikipedia.org/wiki/Markov_chain

Have a read of sections 1-5, very detailed explanations.

[shadows]

Just did the 2010 VCAA exam 2. Lol the numbers were pretty horrible.

3e. The question where you had to find the maximum volume of of Pyramid

My cas returned an expression that looked really ugly, so I used "tcollect" (CAS function), and it changed it to something much more workable. Will I still get marks if the derivative looks different but in right format. (They didn't mention anything about it on the assessors reports)

Do you reckon I should just write out the whole expression or just use tcollect? Does the tcollect produce any extraneous error?, cause thats what I'm worried about and I don't know if its reliable.

4a) You had to find the x co-ordinate of the stationary points and state their nature (4 marks)

ON the assessors reports it says that You don't need to draw up a table? (I thought you always had to when they asked for nature of sps.)

So could I just put the 2 x co-ordinates of the sps, and the just state the nature of each of them. WIll that give me full marks?

[BasicAcid]

1) just leave it but if you want, you can simplify it. there no error that can occur lol

2) yes

[zvezda]

The wiki entry on Markov chains is especially insightful: http://en.wikipedia.org/wiki/Markov_chain

Have a read of sections 1-5, very detailed explanations.

Ive had a quick flick through, but cant really find the answer to my question. Isnt flipping the rows of a transition matrix a legitimate thing as long as the probablities in it are converted accordingly?
Cheers