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October 20, 2021, 02:08:04 pm

Author Topic: VCE Methods Question Thread!  (Read 3730334 times)  Share 

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saransh

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Re: VCE Methods Question Thread!
« Reply #19245 on: September 14, 2021, 10:09:27 am »
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Hey guys,
Does anyone know how to do this question?
Someone on YouTube defined each of the options and then used 'judge' function but I don't have the calculator they have so I'm not sure. I use CAS.

Yup so on the cas: first define f(x) as one of the options
so let's take option A)- define f(x)= 1/(x^2+4)
and then type in the qstn given:  f(2x) = (f(x))^2 -2, (cas will give you an eqtn back)
you basically redefine f(x) and try this for all the options until the calculator says 'true' rather than feedin you back an equation

so if we try option D)-  define f(x)= e^x + e^-x
f(2x) = (f(x))^2 -2 (cas will say true)
that proves that its true for all real x
Hope that clears it up
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Rose34

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Re: VCE Methods Question Thread!
« Reply #19246 on: September 14, 2021, 10:28:04 am »
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Yup so on the cas: first define f(x) as one of the options
so let's take option A)- define f(x)= 1/(x^2+4)
and then type in the qstn given:  f(2x) = (f(x))^2 -2, (cas will give you an eqtn back)
you basically redefine f(x) and try this for all the options until the calculator says 'true' rather than feedin you back an equation

so if we try option D)-  define f(x)= e^x + e^-x
f(2x) = (f(x))^2 -2 (cas will say true)
that proves that its true for all real x
Hope that clears it up


Thank you so much!

LSimons

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Re: VCE Methods Question Thread!
« Reply #19247 on: September 23, 2021, 11:50:20 am »
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Just curious as to everyone's approach when rounding values in a binomial distribution when using the standard deviation. I'm not sure why it seems that the bottom value is always rounded up and the top value is rounded down. I would have thought that both values would round out (small value down and large value up) to ensure that the appropriate standard deviation is included in the interval. See attached, any help would be appreciated.

wingdings2791

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Re: VCE Methods Question Thread!
« Reply #19248 on: September 23, 2021, 01:57:16 pm »
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Just curious as to everyone's approach when rounding values in a binomial distribution when using the standard deviation. I'm not sure why it seems that the bottom value is always rounded up and the top value is rounded down. I would have thought that both values would round out (small value down and large value up) to ensure that the appropriate standard deviation is included in the interval. See attached, any help would be appreciated.

Hello LSimons,
I think the reason for this rounding approach is because underestimation is preferred to overestimation. Since the entire purpose of a confidence interval is to indicate a range where you can be sure that a certain proportion of data (95% in this case) lies, you would want to round to a smaller interval (so that the rounded confidence level is actually >95%), rather than a larger interval (where <95% of data will lie in, meaning your confidence interval is more uncertain than the actual).

Also, the approximation of \(Z\) (1.959963985 \(\approx\) 2) also means that your calculated standard deviation is greater than it actually is. Rounding outwards on each side of the interval would further compound the overestimation of the confidence interval; rounding the bottom up and top down would reflect the actual values more closely.

Hope this helps! Let me know if there are any problems.
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LSimons

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Re: VCE Methods Question Thread!
« Reply #19249 on: September 23, 2021, 02:42:38 pm »
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Hello LSimons,
I think the reason for this rounding approach is because underestimation is preferred to overestimation. Since the entire purpose of a confidence interval is to indicate a range where you can be sure that a certain proportion of data (95% in this case) lies, you would want to round to a smaller interval (so that the rounded confidence level is actually >95%), rather than a larger interval (where <95% of data will lie in, meaning your confidence interval is more uncertain than the actual).

Also, the approximation of \(Z\) (1.959963985 \(\approx\) 2) also means that your calculated standard deviation is greater than it actually is. Rounding outwards on each side of the interval would further compound the overestimation of the confidence interval; rounding the bottom up and top down would reflect the actual values more closely.

Hope this helps! Let me know if there are any problems.

My understanding of confidence intervals is that the smaller the interval the less confident you can actually be. As you reduce the size of the interval there is a greater chance that the expected value would then fall outside of that. This is a practice SAC we completed and the question shows that we found the expected sample proportion and standard deviation then used that to find the probability that it lies within two standard deviations. Again the bottom interval up and the top interval down (even though conventional rounding the the nearest whole is not used) reducing the size of the interval.

S_R_K

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Re: VCE Methods Question Thread!
« Reply #19250 on: September 23, 2021, 03:50:12 pm »
+3
My understanding of confidence intervals is that the smaller the interval the less confident you can actually be. As you reduce the size of the interval there is a greater chance that the expected value would then fall outside of that. This is a practice SAC we completed and the question shows that we found the expected sample proportion and standard deviation then used that to find the probability that it lies within two standard deviations. Again the bottom interval up and the top interval down (even though conventional rounding the the nearest whole is not used) reducing the size of the interval.

I think this might have a pretty simple answer: S = 121 and S = 163 are not within two standard deviations of the expected value, so to answer the question we should calculate Pr(122 ≤ S ≤ 162) rather than Pr(121 ≤ S ≤ 163). In other words, we're just trying to find Pr(a ≤ S ≤ b) where a is the smallest integer that is no more than 2 standard deviations below the expected S, and b is the largest integer that is no more than 2 standard deviations above the expected S.

I don't think there's necessarily a general rule here to round the lower endpoint up and the upper endpoint down - although without seeing the exact question for the first image you posted, it's hard to be sure.
« Last Edit: September 23, 2021, 03:52:06 pm by S_R_K »

wingdings2791

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Re: VCE Methods Question Thread!
« Reply #19251 on: September 23, 2021, 05:10:57 pm »
+2
My understanding of confidence intervals is that the smaller the interval the less confident you can actually be. As you reduce the size of the interval there is a greater chance that the expected value would then fall outside of that. This is a practice SAC we completed and the question shows that we found the expected sample proportion and standard deviation then used that to find the probability that it lies within two standard deviations. Again the bottom interval up and the top interval down (even though conventional rounding the the nearest whole is not used) reducing the size of the interval.

Edit: realise you're right, got confused there xd. What I was trying to say was that you wouldn't want to falsely include data outside of the actual 95%CI in the one you calculate, like S_R_K states. A better explanation is that when you're dealing with discrete data, \(Pr(121.4\leq X \leq 162.6)\approx0.95\) translates to \(Pr(122\leq X \leq 162)\approx0.95\) because \(X=\{121, 163\}\) are not included. This seems like less of a convention specific to binomial distribution/standard deviation, and more of a general rounding method for discrete data- simply because expanding the range is less desirable than rounding to what is accounted for.
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Rose34

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Re: VCE Methods Question Thread!
« Reply #19252 on: September 30, 2021, 11:57:36 am »
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Hi everyone,

Just a quick question, what is the difference between VCAA exams and Northern Hemisphere? and which one is worth doing?

Thank you in advance.

wingdings2791

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Re: VCE Methods Question Thread!
« Reply #19253 on: September 30, 2021, 12:06:16 pm »
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Hi everyone,

Just a quick question, what is the difference between VCAA exams and Northern Hemisphere? and which one is worth doing?

Thank you in advance.

Hey Rose34,
I'm speaking from experience with other subjects (haven't tried Methods), but NHT exams are essentially just the same as VCAA papers; VCAA writes both types of exams. The study designs and difficulties are pretty similar, so the only huge difference is that NHT exams don't provide accuracy stats in the marking scheme (not enough people do NHT VCE for % mark distributions). I would say that the normal VCAA ones probably take priority, but NHT ones are definitely worth doing (as they're still VCAA exams technically, and probably more realistic than company exams as a result).

Best of luck and keep it up!
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arnavg2207

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Re: VCE Methods Question Thread!
« Reply #19254 on: October 04, 2021, 05:12:07 pm »
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Hey, I needed help with this question from MAV 2020 exam 2.

 For part d, why do they sub in (0,3) to find the value of a. I know that this in the y intercept, but why is it that both graphs intercept at their x and y intercepts?

Thanks!
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Re: VCE Methods Question Thread!
« Reply #19255 on: October 04, 2021, 06:59:58 pm »
+2
Hey, I needed help with this question from MAV 2020 exam 2.

 For part d, why do they sub in (0,3) to find the value of a. I know that this in the y intercept, but why is it that both graphs intercept at their x and y intercepts?

Thanks!
Hi for part D we know that the endpoint for \(f\left(x\right)\) is at \((0,3)\) and therefore the endpoint for \(f^{-1}\left(x\right)\) is at \((3,0)\).

Giving these functions a brief sketch or using sliders on your calculator you will be able to see the effect it has on the function and it's inverse as the value of \(a\) varies. You can observe that as \(a\) gets lower and \(f^{-1}\left(x\right)=f\left(x\right)\) gets closer to having three points of intersections - when it starts reaching to having three intersections for a lowest value of \(a\) it approaches these two endpoints as well. Therefore you can sub in the coordinates to get the "lowest" value for \(a\).

Rose34

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Re: VCE Methods Question Thread!
« Reply #19256 on: October 07, 2021, 04:17:38 pm »
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Hi everyone,

Does anyone know what formula is used to calculate the final score of the exam which is out of 50 for methods?

Thanks in advance,
Rose.

S_R_K

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Re: VCE Methods Question Thread!
« Reply #19257 on: October 07, 2021, 04:25:42 pm »
+1
Hi everyone,

Does anyone know what formula is used to calculate the final score of the exam which is out of 50 for methods?

Thanks in advance,
Rose.

?? The final exams are out of 40 and 80, for Exam 1 and Exam 2 respectively. Exam 1 and Exam 2 contribute 22% and 44% respectively to your overall score. (The remainder is your "internal score" which is due to your SAC marks, after your cohort's SAC marks have been standardised to your cohort's exam marks).

Or do you mean how is a study score calculated? There are numerous explanations available for how an overall score is used to calculate a study score, but essentially it's a normal distribution with mean 30 and standard deviation 7.

Rose34

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Re: VCE Methods Question Thread!
« Reply #19258 on: October 08, 2021, 10:50:48 am »
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?? The final exams are out of 40 and 80, for Exam 1 and Exam 2 respectively. Exam 1 and Exam 2 contribute 22% and 44% respectively to your overall score. (The remainder is your "internal score" which is due to your SAC marks, after your cohort's SAC marks have been standardised to your cohort's exam marks).

Or do you mean how is a study score calculated? There are numerous explanations available for how an overall score is used to calculate a study score, but essentially it's a normal distribution with mean 30 and standard deviation 7.

I meant the sudy score.

S_R_K

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Re: VCE Methods Question Thread!
« Reply #19259 on: October 08, 2021, 11:20:14 am »
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I meant the sudy score.

Roughly speaking (because the details aren't important):

All the students in the state doing Methods get an overall graded assessment score (the combination of SACs + Exams). All these students are then ranked in order from highest to lowest. This ranking is then mapped on to a normal distribution with mean 30 and standard deviation 7. So students with the middle assessment score get a study score of 30. Students who get in the top 9% of assessment scores get study scores over 40.