ATAR Notes: Forum
Archived Discussion => 2010 => End-of-year exams => Exam Discussion => Victoria => Mathematical Methods CAS => Topic started by: Mao on November 09, 2010, 12:35:05 pm
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Semi-worked solutions. I didn't go into as much detail as enwiabe, but all the key steps are explained.
That was a really difficult exam. So it's not the end of the world, you guys can take a chill pill and now GO STUDY FOR CHEM.
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If not, I guess I will after I get up. You have ~30mins before I start. :)
I think we all trust your answers :) good man.
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Please do my friend :)
Some people said they would but noones published anything.
+Karma if you can post it sometime soon :)
Cheers
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First post updated. Here you go guys.
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MAO SAID IT WAS HARD, WE ARE ALL SAVED! :D:D:D
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THANKYOU MAO!
I can now sleep.
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amazing!!!
quick question, for the expected number of statues, how many marks out of 4 would i get if i used the wrong p value,
for some reason i used 0.7 not 0.75 even though it was given, ultimately i got E(x)=1.1??
thanks in advance =D
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You would get 1 mark off for wrong answer, 2 marks in your favour for method working, and POSSIBLY lose a mark for subbing in the wrong P value... But you at least will get 2/4 - if you pray, and believe in yourself, maybe VCAA will look into their icy, blackened hearts and give you that one mark, axilon! :D
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some of your working out i didnt even understnad T.T . ihope i can get a 30!!! MAO your a genius =D
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fingers crossed!!!!
didn't know they had hearts?? =]
thanks man.
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Great, another mark gone. Guessed the number of S.Ps as 3, because it was quartic lol.
Looking at the last two sections of Q2, they were probably fair game.
Under the pressure of the exam I had no idea what I was doing but they weren't really that hard. Just need to think outside the square a little.
Got completely shit on for the last question though. CAS kept on spitting out errors, and I just left most of the questions with gibberish workings...
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Great, another mark gone. Guessed the number of S.Ps as 3, because it was quartic lol.
Haha same. I immediately thought ooh a quartic *thinks of W shape*
"yes yes yes W means 3 stationary points"
*writes 3*
Assessor: PENS DOWN
"SHIT ITS 2" :(
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i finally figured out how to do the last question and was busy typing it in to my calculator and supervisor says "pens down"
i was tempted to keep going seeing as i was using a pacer... :)
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question 2.2a - it was possible to do this using a tree diagram right? a markov one or whateva
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hey with question 2.3e with dT/dx shouldnt it be a negative sign before 12cos(x)^5sin(x) blabla
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ARGHHHHHHH I FOUND x FOR THE VOLUME QUESTION BUT I ASSUMED IT MUST BE WRONG AND WROTE PI........WHAT A FKN IDIOT I AM.
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Good job Mao +karma
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hey with question 2.3e with dT/dx shouldnt it be a negative sign before 12cos(x)^5sin(x) blabla
Nope, that's a positive.
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in 2.4.b did we have to find the coordinates or was x =1/a and x =(1+ab)/4a an adequate answer?
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in 2.4.b did we have to find the coordinates or was x =1/a and x =(1+ab)/4a an adequate answer?
The question just asked for what x-values are there a stationary point, so i dont think co-ordinates were needed ...
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hey mao, what do you reckon the A+ cut off will be?
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wow - nice solutions.
When I entered that dT/dx question into my CAS. I got 2tan^-1 ((root6 - root 2)/root3). Turns out that is the same as cos^-1(1/root3). Will I lose marks? However, when I found the volume, I got a really long answer haha.
Could you guys please tell me how you got the cos^-1 answer. Even when I try it now, I get the same answer. How did you guys do it?
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in 2.4.b did we have to find the coordinates or was x =1/a and x =(1+ab)/4a an adequate answer?
The question just asked for what x-values are there a stationary point, so i dont think co-ordinates were needed ...
^^this. I stated the coordinates for completeness, and also that later parts required the coordinates.
hey mao, what do you reckon the A+ cut off will be?
I did say I won't be making a prediction. :)
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wow - nice solutions.
When I entered that dT/dx question into my CAS. I got 2tan^-1 ((root6 - root 2)/root3). Turns out that is the same as cos^-1(1/root3). Will I lose marks? However, when I found the volume, I got a really long answer haha.
Could you guys please tell me how you got the cos^-1 answer. Even when I try it now, I get the same answer. How did you guys do it?
If the question just asked for an exact answer, then that should be okay. However if it specified what form it needs to be in, then marks can be taken off
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wow - nice solutions.
When I entered that dT/dx question into my CAS. I got 2tan^-1 ((root6 - root 2)/root3). Turns out that is the same as cos^-1(1/root3). Will I lose marks? However, when I found the volume, I got a really long answer haha.
Could you guys please tell me how you got the cos^-1 answer. Even when I try it now, I get the same answer. How did you guys do it?
It will be accepted. An examiner who runs across this will double check when he/she sees it (if he/she is not an idiot, and they generally tend to be fairly good).
Following the steps of my workings in the solutions, it was just an application of the null factor theorem.
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in 2.4.b did we have to find the coordinates or was x =1/a and x =(1+ab)/4a an adequate answer?
The question just asked for what x-values are there a stationary point, so i dont think co-ordinates were needed ...
^^this. I stated the coordinates for completeness, and also that later parts required the coordinates.
hey mao, what do you reckon the A+ cut off will be?
I did say I won't be making a prediction. :)
Did you find it harder than 07?
*PRAYS* please say yes. By a long shot. *Ends Prayer*
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wow - nice solutions.
When I entered that dT/dx question into my CAS. I got 2tan^-1 ((root6 - root 2)/root3). Turns out that is the same as cos^-1(1/root3). Will I lose marks? However, when I found the volume, I got a really long answer haha.
Could you guys please tell me how you got the cos^-1 answer. Even when I try it now, I get the same answer. How did you guys do it?
It will be accepted. An examiner who runs across this will double check when he/she sees it (if he/she is not an idiot, and they generally tend to be fairly good).
Following the steps of my workings in the solutions, it was just an application of the null factor theorem.
so if you did use inverse tan etc and u got an extremely large expression for the volume will you still get the marks if its unsimpliflied?
the answer took up a whole line lol.
or are we looking at max 3/4??
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wow - nice solutions.
When I entered that dT/dx question into my CAS. I got 2tan^-1 ((root6 - root 2)/root3). Turns out that is the same as cos^-1(1/root3). Will I lose marks? However, when I found the volume, I got a really long answer haha.
Could you guys please tell me how you got the cos^-1 answer. Even when I try it now, I get the same answer. How did you guys do it?
It will be accepted. An examiner who runs across this will double check when he/she sees it (if he/she is not an idiot, and they generally tend to be fairly good).
Following the steps of my workings in the solutions, it was just an application of the null factor theorem.
so if you did use inverse tan etc and u got an extremely large expression for the volume will you still get the marks if its unsimpliflied?
the answer took up a whole line lol.
or are we looking at max 3/4??
same thing happened to me
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^ yep. this. the answer was right, however a moronic examiner might be like mm nope this isnt what i have on my answer sheet! -1 -1 -1 -1 until all your marks are gone
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Good man Mao, I was gonna do it right now coz I finished my exams but yours look great, champ!
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For Q2.3f, will I lose my marks if I gave my answer in degree form?
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Don't predict...but do you reckon lower than 2007? ;)
BTW for the expected value, I drew up the table and got the values for x=0, and x=1 right, but somehow screwed up x=2 :-\, reckon I could scrape 2/4 marks for that seeing as I did show working to find E(X) and also the table?
Also thank you so much for this, I hope the chem ones are this detailed :P
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SHIT! was the possible x values required in degree form? i left it as .81 and the 1.2 whatever
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SHIT! was the possible x values required in degree form? i left it as .81 and the 1.2 whatever
lol I'm just wondering if you could have it in both forms or does it have to be in radians. You would get the marks but I'm not sure I would since I converted it to degrees.
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what a relief i just checked the questoin, the x in terms of radian at the beginning
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lol question 1.b.v I didn't even think of doing that, instead I got the equation of the tangent and subbed in (p,10).
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i did the same as you black hit man,
btw for the question where it says find possible values of x in terms of a, b
we only had to give possible values right not the co-ordinate form , ?????
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Don't predict...but do you reckon lower than 2007? ;)
BTW for the expected value, I drew up the table and got the values for x=0, and x=1 right, but somehow screwed up x=2 :-\, reckon I could scrape 2/4 marks for that seeing as I did show working to find E(X) and also the table?
Also thank you so much for this, I hope the chem ones are this detailed :P
my methods days are so long ago (I did it in 07), I cannot remember what the exam was like.
If I have to rate my distant feelings vs this experience, this one is definitely more calculator intensive. If you didn't know how to navigate calculator errors, or how to use the calculator efficiently, you would have died. In terms of theoretical difficulty and algebraic gayness, this one would also take the crown. Though probability in 07 was definitely a bitch.
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Don't predict...but do you reckon lower than 2007? ;)
BTW for the expected value, I drew up the table and got the values for x=0, and x=1 right, but somehow screwed up x=2 :-\, reckon I could scrape 2/4 marks for that seeing as I did show working to find E(X) and also the table?
Also thank you so much for this, I hope the chem ones are this detailed :P
my methods days are so long ago (I did it in 07), I cannot remember what the exam was like.
If I have to rate my distant feelings vs this experience, this one is definitely more calculator intensive. If you didn't know how to navigate calculator errors, or how to use the calculator efficiently, you would have died. In terms of theoretical difficulty and algebraic gayness, this one would also take the crown. Though probability in 07 was definitely a bitch.
Cool thanks ( I loved the prob in 07 haha, finding maximums in prob O.o) , I hope to god the A+ is low ;D
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I hated this year's exam. I honestly loved my CAS calculator, cause i had known so much and used it oftenly. But my nerves could not be controlled, i was pressing in wrong numbers, like the minimum number i got 1.8 instead of 18, and easy questions just put me off. I mean, at school, considering going to a good school, I got the maths methods award, which they expect a 50 from me but now it's just not the same. I had a breakdown in the 2nd exam and got 60, which was all because my watch had stopped when i hadn't realise as a result of it dropping it on the floor. Terrible day, terrible, day. Irony here, I did better in spesh than methods.
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For question 4 part 1 - will I lose a mark for calling the second stationary point a "local maximum turning point" instead of just a maximum turning point?
Will I lose a mark for using tree-diagrams and not Markov chains, but getting the same answers after all?
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No and No :)
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Thankyou thankyou thankyou! Woo then I'm looking at around ~63 for Exam 2.
Do not know HOW I pulled that outta my ass.
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For Question 2, part ii) ...
I used tree-diagrams to find the probability of each branch of the sample space,
then added these up into sections of S = 0, 1 or 2. Then from THESE probabilities, I forgot to then multiply them by the S values to get the expected value and just said 2 was the expected value (highest prob)
Will I get 2 or 3 marks for this, out of 4?
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Thanks man. I actually did some questions completely different to that :P. And that volume question.... guess it wasn't that confusing, I'd forgotten how trig worked like that :\. Actually, I don't remember doing that at all in Methods, I only remember doing that in AGM. I'm looking at around low 60's, can't remember some of my answers though.
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Wow i think i actually only lost 9 marks overall at the most? (1 for MC and 4 for the E(X) question and 4 for the x value of the pyramid)..
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thanks man.
for the tassy jones questions when u have to prove that p=0.75
i just stated the matrix equation and solved it on my calc...
i didn't expand it by hand. the matrix equation counts as working doesn't it?
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thanks man.
for the tassy jones questions when u have to prove that p=0.75
i just stated the matrix equation and solved it on my calc...
i didn't expand it by hand. the matrix equation counts as working doesn't it?
Yeah man
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I actually didn't use matrix at all for the show p=0.75 question.
I went Pr(SS) +Pr(RS)=0.7
So much quicker than the matrix method (judging by Mao's working out).
Also Mao in that question in your transition matrix, the 2nd row 2nd column should be 1.2-p not 0.8-p...trivial and pointless but thought I'd mention it :buck2:...
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I actually didn't use matrix at all for the show p=0.75 question.
I went Pr(SS) +Pr(RS)=0.7
So much quicker than the matrix method (judging by Mao's working out).
Also Mao in that question in your transition matrix, the 2nd row 2nd column should be 1.2-p not 0.8-p...trivial and pointless but thought I'd mention it :buck2:...
yup i did exactly this too
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thank you Mao! :)
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Yeah, I do apologize for that minor stuff up (0.8-p) insured of (1.2-p). The file is still on my laptop that icbf turning on, lol.
And thank you for your appreciation. It makes life enjoyable :')
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I actually didn't use matrix at all for the show p=0.75 question.
I went Pr(SS) +Pr(RS)=0.7
So much quicker than the matrix method (judging by Mao's working out).
Also Mao in that question in your transition matrix, the 2nd row 2nd column should be 1.2-p not 0.8-p...trivial and pointless but thought I'd mention it :buck2:...
yup i did exactly this too
Same here, just wrote down the matrix equation, and said solve for p, p=.75, if we did that, we wouldn't get dicked a mark for working would we???
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Semi-worked solutions. I didn't go into as much detail as enwiabe, but all the key steps are explained.
That was a really difficult exam. So it's not the end of the world, you guys can take a chill pill and now GO STUDY FOR CHEM.
1.21 'A and B mutually exclusive' implies p+q<1
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Semi-worked solutions. I didn't go into as much detail as enwiabe, but all the key steps are explained.
That was a really difficult exam. So it's not the end of the world, you guys can take a chill pill and now GO STUDY FOR CHEM.
1.21 'A and B mutually exclusive' implies p+q<1
Yep Mao stated that it should have been outlined in the Q
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Semi-worked solutions. I didn't go into as much detail as enwiabe, but all the key steps are explained.
That was a really difficult exam. So it's not the end of the world, you guys can take a chill pill and now GO STUDY FOR CHEM.
1.21 'A and B mutually exclusive' implies p+q<1
Yep Mao stated that it should have been outlined in the Q
the question as it stands is perfectly ok, you don't need to say p+q<1