ATAR Notes: Forum

Archived Discussion => Mathematics and Science => 2013 => Exam Discussion => Victoria => Mathematical Methods CAS => Topic started by: BubbleWrapMan on November 06, 2013, 01:05:39 pm

Title: [SUGGESTED SOLUTIONS] Exam 1 and 2 Worked Solutions
Post by: BubbleWrapMan on November 06, 2013, 01:05:39 pm: My solutions for both exams are below.
Title: Re: [SUGGESTED SOLUTIONS] Worked Solutions pdf
Post by: waterfords69 on November 06, 2013, 01:15:41 pm: for question 9ci, if we write g(x)=1/3|f(x+1)| does it still count as correct?
Title: Re: [SUGGESTED SOLUTIONS] Worked Solutions pdf
Post by: Damoz.G on November 06, 2013, 01:19:03 pm: Quote from: waterfords69 on November 06, 2013, 01:15:41 pm
for question 9ci, if we write g(x)=1/3|f(x+1)| does it still count as correct?

No, you had to use the actual function of f(x) and make the adjustments to it. Your final answer shouldn't be left with those transformations and "f(x)". If the function is given (which it was), it must be used to get full marks for the question. :)
Title: Re: [SUGGESTED SOLUTIONS] Worked Solutions pdf
Post by: silverpixeli on November 06, 2013, 01:41:21 pm: Sweet solutions thanks man
Title: Re: [SUGGESTED SOLUTIONS] Worked Solutions pdf
Post by: Alienmobman on November 06, 2013, 03:44:41 pm: For 9 ci
I left my answer as a hybrid function, would that be ok?
Title: Re: [SUGGESTED SOLUTIONS] Worked Solutions pdf
Post by: Damoz.G on November 06, 2013, 03:47:34 pm: Quote from: Alienmobman on November 06, 2013, 03:44:41 pm
For 9 ci
I left my answer as a hybrid function, would that be ok?

I believe you would still get the marks as long as the two rules are correct and a domain was included for each. :)
Title: Re: [SUGGESTED SOLUTIONS] Worked Solutions pdf
Post by: Alienmobman on November 06, 2013, 04:12:02 pm: Sick cheers Damoz!
Title: Re: [SUGGESTED SOLUTIONS] Worked Solutions pdf
Post by: mano91 on November 06, 2013, 09:31:49 pm: q8 should be 2+ 4/pi right?

check the negative sign on your solutions.
Title: Re: [SUGGESTED SOLUTIONS] Worked Solutions pdf
Post by: silverpixeli on November 06, 2013, 10:05:00 pm: Quote from: mano91 on November 06, 2013, 09:31:49 pm
q8 should be 2+ 4/pi right?

check the negative sign on your solutions.

Pretty sure it's negative
Title: Re: [SUGGESTED SOLUTIONS] Worked Solutions pdf
Post by: b^3 on November 06, 2013, 10:09:28 pm: I'll do it without simplifying any negatives from the start and showing more working than needed.
$\begin{alignedat}{1}2\sin\left(\frac{\pi}{2}\right)-0-\left[-\frac{4}{\pi}\cos\left(\frac{\pi x}{4}\right)\right]_{0}^{2} & =2\left(1\right)-\left(-\frac{4}{\pi}\cos\left(\frac{\pi}{2}\right)-\left(-\frac{4}{\pi}\cos\left(0\right)\right)\right)<br />\\ & =2-\left(-\frac{4}{\pi}\left(0\right)+\frac{4}{\pi}\left(1\right)\right)<br />\\ & =2-\frac{4}{\pi}<br />\end{alignedat}$
Which is what Tim has.
Title: Re: [SUGGESTED SOLUTIONS] Worked Solutions pdf
Post by: BubbleWrapMan on November 06, 2013, 10:10:57 pm: Also the expected value of $X$ wouldn't be more than 2 since $\Pr(X>2)=0$ from the density function.
Title: Re: [SUGGESTED SOLUTIONS] Worked Solutions pdf
Post by: silverpixeli on November 06, 2013, 10:12:56 pm: It can't be 2+4/pi because it's asking for the mean which surely has to be within the domain of [0,2], also 2-4/pi approximates to just under 1 because 4>pi which makes sense as the mean of a cos distribution if you look at the graph, the first quarter of a cos graph, the mean should be a little to the left of the middle value of 1 because that's where most of the area is
Beaten twice sigh
Title: Re: [SUGGESTED SOLUTIONS] Worked Solutions pdf
Post by: mano91 on November 06, 2013, 10:58:27 pm: My mistake!
Title: Re: [SUGGESTED SOLUTIONS] Exam 1 and 2 Worked Solutions
Post by: BubbleWrapMan on November 07, 2013, 08:22:24 pm: Exam 2 solutions in first post
Title: Re: [SUGGESTED SOLUTIONS] Exam 1 and 2 Worked Solutions
Post by: Damoz.G on November 07, 2013, 08:25:51 pm: Quote from: Timmeh on November 07, 2013, 08:22:24 pm
Exam 2 solutions in first post

Thank you very much!

OMG! I guessed the Equation of the second tangent equation, and I got it correct!!!! :D :D :D :D :D :D :D :D :D :D :D :D
Title: Re: [SUGGESTED SOLUTIONS] Exam 1 and 2 Worked Solutions
Post by: Zoomzoom on November 07, 2013, 10:38:32 pm: Not sure but for 10d)iii. Could the ans be 1/2 at k=8
Title: Re: [SUGGESTED SOLUTIONS] Exam 1 and 2 Worked Solutions
Post by: BubbleWrapMan on November 07, 2013, 10:57:51 pm: Quote from: Zoomzoom on November 07, 2013, 10:38:32 pm
Not sure but for 10d)iii. Could the ans be 1/2 at k=8

For 4diii. you mean? 16/3 is correct.
Title: Re: [SUGGESTED SOLUTIONS] Exam 1 and 2 Worked Solutions
Post by: Zoomzoom on November 07, 2013, 11:00:58 pm: Sorry yes that
Title: Re: [SUGGESTED SOLUTIONS] Exam 1 and 2 Worked Solutions
Post by: Zoomzoom on November 07, 2013, 11:05:55 pm: Why cant it be 8? Since k is between [5,8]
Title: Re: [SUGGESTED SOLUTIONS] Exam 1 and 2 Worked Solutions
Post by: BubbleWrapMan on November 07, 2013, 11:10:36 pm: k=8 gives the maximum area.
Title: Re: [SUGGESTED SOLUTIONS] Exam 1 and 2 Worked Solutions
Post by: Zoomzoom on November 07, 2013, 11:15:33 pm: Oh shoot i mixed them around. Sigh...another few marks gone
Title: Re: [SUGGESTED SOLUTIONS] Exam 1 and 2 Worked Solutions
Post by: AsianNerd on November 09, 2013, 11:15:59 pm: dat feeling when you find the correct tangent for last question but then enter it wrong in calculator and lose the next 6 marks :( :( :( :( :( :( :( :( :( :(
Title: Re: [SUGGESTED SOLUTIONS] Exam 1 and 2 Worked Solutions
Post by: Damoz.G on November 09, 2013, 11:19:15 pm: Quote from: AsianNerd on November 09, 2013, 11:15:59 pm
dat feeling when you find the correct tangent for last question but then enter it wrong in calculator and lose the next 6 marks :( :( :( :( :( :( :( :( :( :(

ORRR that feeling when you GUESS the tangent equation (and get it correct) but don't continue on with the "guessed" equation. :'(
Title: Re: [SUGGESTED SOLUTIONS] Exam 1 and 2 Worked Solutions
Post by: silverpixeli on November 11, 2013, 09:13:31 am: haha yeah, got the gradient and stuffed up the area function, forfeiting the last 6 marks. I realised my mistake but only had time to save 4 of the 6
Title: Re: [SUGGESTED SOLUTIONS] Exam 1 and 2 Worked Solutions
Post by: arush002 on November 11, 2013, 10:02:07 am: Quote from: silverpixeli on November 11, 2013, 09:13:31 am
haha yeah, got the gradient and stuffed up the area function, forfeiting the last 6 marks. I realised my mistake but only had time to save 4 of the 6

You'll get half marks for the rest for giving method though. I did the same thing :( >:(
Title: Re: [SUGGESTED SOLUTIONS] Exam 1 and 2 Worked Solutions
Post by: Damoz.G on November 11, 2013, 10:08:25 am: Quote from: arush002 on November 11, 2013, 10:02:07 am
You'll get half marks for the rest for giving method though. I did the same thing :( >:(

Half marks? The only time you get half marks is if one assessor gives a mark and the other doesn't. But if its one assessor, the full thing has to be correct to get the one mark, otherwise they won't give you the mark.
Title: Re: [SUGGESTED SOLUTIONS] Exam 1 and 2 Worked Solutions
Post by: arush002 on November 11, 2013, 10:13:10 am: Quote from: Caparva on November 11, 2013, 10:08:25 am
Half marks? The only time you get half marks is if one assessor gives a mark and the other doesn't. But if its one assessor, the full thing has to be correct to get the one mark, otherwise they won't give you the mark.

Sorry, let me rephrase. I meant method marks. Even if your solution to 4d)i is incorrect and you find the min/max by making deriv=0 then you will get the method marks but not the answer mark.