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

Title: 2010 MM Exam 2 suggested solutions
Post by: Mao on November 09, 2010, 12:35:05 pm
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.
Title: Re: Is anyone writing the exam 2 answers?
Post by: chopz on November 09, 2010, 01:27:34 pm
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.
Title: Re: Is anyone writing the exam 2 answers?
Post by: 3Xamz on November 09, 2010, 01:27:46 pm
Please do my friend :)
Some people said they would but noones published anything.
+Karma if you can post it sometime soon :)

Cheers
Title: Re: 2010 MM Exam 2 suggested solutions
Post by: Mao on November 09, 2010, 04:07:21 pm
First post updated. Here you go guys.
Title: Re: 2010 MM Exam 2 suggested solutions
Post by: 3Xamz on November 09, 2010, 04:11:54 pm
MAO SAID IT WAS HARD, WE ARE ALL SAVED! :D:D:D
Title: Re: 2010 MM Exam 2 suggested solutions
Post by: lorcan_raven on November 09, 2010, 04:22:53 pm
THANKYOU MAO!
I can now sleep.
Title: Re: 2010 MM Exam 2 suggested solutions
Post by: axilon on November 09, 2010, 04:35:05 pm
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
Title: Re: 2010 MM Exam 2 suggested solutions
Post by: lorcan_raven on November 09, 2010, 04:46:29 pm
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
Title: Re: 2010 MM Exam 2 suggested solutions
Post by: johnson on November 09, 2010, 04:49:52 pm
some of your working out i didnt even understnad T.T . ihope i can get a 30!!! MAO your a genius =D
Title: Re: 2010 MM Exam 2 suggested solutions
Post by: axilon on November 09, 2010, 04:50:25 pm
fingers crossed!!!!
didn't know they had hearts?? =]
thanks man.
Title: Re: 2010 MM Exam 2 suggested solutions
Post by: stonecold on November 09, 2010, 04:50:48 pm
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...
Title: Re: 2010 MM Exam 2 suggested solutions
Post by: 98.40_for_sure on November 09, 2010, 04:52:46 pm
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" :(
Title: Re: 2010 MM Exam 2 suggested solutions
Post by: cypriottiger on November 09, 2010, 04:55:24 pm
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... :)
Title: Re: 2010 MM Exam 2 suggested solutions
Post by: lisafaustina on November 09, 2010, 05:05:27 pm
question 2.2a - it was possible to do this using a tree diagram right? a markov one or whateva
Title: Re: 2010 MM Exam 2 suggested solutions
Post by: lisafaustina on November 09, 2010, 05:07:19 pm
hey with question 2.3e with dT/dx shouldnt it be a negative sign before 12cos(x)^5sin(x) blabla
Title: Re: 2010 MM Exam 2 suggested solutions
Post by: lisafaustina on November 09, 2010, 05:09:53 pm
ARGHHHHHHH I FOUND x FOR THE VOLUME QUESTION BUT I ASSUMED IT MUST BE WRONG AND WROTE PI........WHAT A FKN IDIOT I AM.
Title: Re: 2010 MM Exam 2 suggested solutions
Post by: Whatlol on November 09, 2010, 05:15:06 pm
Good job Mao +karma
Title: Re: 2010 MM Exam 2 suggested solutions
Post by: Mao on November 09, 2010, 05:19:14 pm
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.

Title: Re: 2010 MM Exam 2 suggested solutions
Post by: becca92 on November 09, 2010, 05:34:08 pm
in 2.4.b did we have to find the coordinates or was x =1/a and x =(1+ab)/4a an adequate answer?
Title: Re: 2010 MM Exam 2 suggested solutions
Post by: jane1234 on November 09, 2010, 05:35:30 pm
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 ...
Title: Re: 2010 MM Exam 2 suggested solutions
Post by: lisafaustina on November 09, 2010, 05:37:30 pm
hey mao, what do you reckon the A+ cut off will be?
Title: Re: 2010 MM Exam 2 suggested solutions
Post by: luffy on November 09, 2010, 05:52:51 pm
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?

Title: Re: 2010 MM Exam 2 suggested solutions
Post by: Mao on November 09, 2010, 05:54:24 pm
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. :)
Title: Re: 2010 MM Exam 2 suggested solutions
Post by: jimmy999 on November 09, 2010, 05:54:51 pm
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
Title: Re: 2010 MM Exam 2 suggested solutions
Post by: Mao on November 09, 2010, 05:59:11 pm
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.
Title: Re: 2010 MM Exam 2 suggested solutions
Post by: jayna on November 09, 2010, 06:02:22 pm
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*
Title: Re: 2010 MM Exam 2 suggested solutions
Post by: axilon on November 09, 2010, 06:02:57 pm
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??
Title: Re: 2010 MM Exam 2 suggested solutions
Post by: Whatlol on November 09, 2010, 06:16:25 pm
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
Title: Re: 2010 MM Exam 2 suggested solutions
Post by: 98.40_for_sure on November 09, 2010, 06:25:23 pm
^ 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
Title: Re: 2010 MM Exam 2 suggested solutions
Post by: TrueTears on November 09, 2010, 06:27:23 pm
Good man Mao, I was gonna do it right now coz I finished my exams but yours look great, champ!
Title: Re: 2010 MM Exam 2 suggested solutions
Post by: sajib_mostofa on November 09, 2010, 06:40:12 pm
For Q2.3f, will I lose my marks if I gave my answer in degree form?
Title: Re: 2010 MM Exam 2 suggested solutions
Post by: Blakhitman on November 09, 2010, 06:50:56 pm
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
Title: Re: 2010 MM Exam 2 suggested solutions
Post by: Jdog on November 09, 2010, 06:52:05 pm
SHIT! was the possible x values required in degree form? i left it as .81 and the 1.2 whatever
Title: Re: 2010 MM Exam 2 suggested solutions
Post by: sajib_mostofa on November 09, 2010, 06:53:20 pm
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.
Title: Re: 2010 MM Exam 2 suggested solutions
Post by: Jdog on November 09, 2010, 06:54:23 pm
what a relief i just checked the questoin, the x in terms of radian at the beginning
Title: Re: 2010 MM Exam 2 suggested solutions
Post by: Blakhitman on November 09, 2010, 07:01:40 pm
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).
Title: Re: 2010 MM Exam 2 suggested solutions
Post by: Jdog on November 09, 2010, 07:09:26 pm
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 , ?????
Title: Re: 2010 MM Exam 2 suggested solutions
Post by: Mao on November 09, 2010, 07:13:04 pm
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.
Title: Re: 2010 MM Exam 2 suggested solutions
Post by: Blakhitman on November 09, 2010, 07:18:15 pm
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

Title: Re: 2010 MM Exam 2 suggested solutions
Post by: awesome2damax on November 09, 2010, 07:47:08 pm
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.
Title: Re: 2010 MM Exam 2 suggested solutions
Post by: lorcan_raven on November 09, 2010, 08:34:44 pm
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?
Title: Re: 2010 MM Exam 2 suggested solutions
Post by: sajib_mostofa on November 09, 2010, 08:35:29 pm
No and No  :)
Title: Re: 2010 MM Exam 2 suggested solutions
Post by: lorcan_raven on November 09, 2010, 08:36:41 pm
Thankyou thankyou thankyou! Woo then I'm looking at around ~63 for Exam 2.
Do not know HOW I pulled that outta my ass.
Title: Re: 2010 MM Exam 2 suggested solutions
Post by: lorcan_raven on November 09, 2010, 08:41:46 pm
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?
Title: Re: 2010 MM Exam 2 suggested solutions
Post by: camrenis on November 09, 2010, 08:57:35 pm
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.
Title: Re: 2010 MM Exam 2 suggested solutions
Post by: darkphoenix on November 09, 2010, 10:03:35 pm
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)..
Title: Re: 2010 MM Exam 2 suggested solutions
Post by: sheno on November 09, 2010, 11:30:16 pm
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?
Title: Re: 2010 MM Exam 2 suggested solutions
Post by: sajib_mostofa on November 09, 2010, 11:34:44 pm
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
Title: Re: 2010 MM Exam 2 suggested solutions
Post by: Blakhitman on November 09, 2010, 11:44:48 pm
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:...
Title: Re: 2010 MM Exam 2 suggested solutions
Post by: Whatlol on November 10, 2010, 08:36:15 am
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
Title: Re: 2010 MM Exam 2 suggested solutions
Post by: lizzi on November 10, 2010, 11:59:15 am
thank you Mao!  :)
Title: Re: 2010 MM Exam 2 suggested solutions
Post by: Mao on November 10, 2010, 06:11:34 pm
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 :')
Title: Re: 2010 MM Exam 2 suggested solutions
Post by: ulbasour on November 10, 2010, 09:07:12 pm
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???
Title: Re: 2010 MM Exam 2 suggested solutions
Post by: itolduso on November 10, 2010, 10:17:08 pm
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
Title: Re: 2010 MM Exam 2 suggested solutions
Post by: sajib_mostofa on November 10, 2010, 10:20:00 pm
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
Title: Re: 2010 MM Exam 2 suggested solutions
Post by: itolduso on November 10, 2010, 10:39:08 pm
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