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Author Topic: VCE Methods Question Thread!  (Read 4802257 times)  Share 

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Re: VCE Methods Question Thread!
« Reply #16890 on: September 16, 2018, 09:29:42 pm »
+2
can someone help me with question 2. theres no worked examples in my book for it.
this is methods units 3 & 4

2. Sammy and Guido play racquetball each week. In any one game, Sammy has the probability of
winning of 0.7. The outcome of any one game between the two is independent of the outcome of the
previous games played.
a. If the play 8 games, what is the probability, to four decimal places, that Sammy wins 5 out of 8
games?
b. What is the probability, to four decimal places, that Guido wins at most 6 of the 8 games?
c. What is the probability, to four decimal places, that Sammy only wins the second, fourth, fifth,
seventh and eighth games?
d. Compare the value obtained in part (a) with that of part (c). Explain the result.
e. How many games do they need to play so that Guido has at east 80% chance of winning at least
one game?
let 'S' be the random variable 'Sammy wins a game' and let 'G' be the random variable 'Guido' wins a game
a. S~Binomial(n=8,p=0.7) i.e. S follows a binomial distribution where the number of trials is 8 and the probability of success is 0.7
Solve Pr(S=5) using the cas or by hand using the binomial formula
b. G~Binomial(n=8,p=0.3) i.e. G follows a binomial distribution where the number of trials is 8 and the probability of success is 1-0.7=0.3
Solve Pr(G ≤ 6) with the cas or you can do it by hand by using the binomial formula and adding up Pr(G=1) + Pr(G=2) ... + Pr(G=6)
c. Think you can use a tree diagram for this one so
let S=sammy wins and G=guido wins
G*S*G*S*S*G*S*S
d. (c) would be lower than (a) due to the order Sammy wins or loses mattering in part (c) compared to (a) where the order does not matter i.e. Sammy can still get 5 wins without winning the second, fourth, fifth, sixth or eighth game resulting in a different combination.
e. Pr(G≥1)≥0.8
G~Binomial(n=?, p=0.3)
put in random trial values into the binomial cdf function until you find a value close to 0.8 as it says at least 80% but not below it
binomCdf(n=8,p=0.3,lower bound=1, upper bound=n=8) = 0.94 so too high
binomCdf(n=5,p=0.3,lower bound=1, upper bound=n=5) = 0.83
binomCdf(n=4,p=0.3,lower bound=1, upper bound=n=4) = 0.76 so too low
So the minimum number of games Guido needs to play to have at least 80% of winning is 5

Not sure if these are all correct so someone please correct me if they're wrong
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yourdavid

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Re: VCE Methods Question Thread!
« Reply #16891 on: September 17, 2018, 11:30:02 am »
0
can i please get some assistance on this question, my sacs in 3 hours ish and this is related to the sac

3. The resistance heating elements produced by an electrical firm are normally distributed with the mean 50 ohms and standard deviation 4 ohms.
a. If the specifications require that acceptable elements shall have a resistance between 45 and 50 ohms, find the probability, to four decimal places, that a randomly selected element has these specifications .
b. Find the least resistance, to four decimal places, the 85% of heating elements would have?
c. The profit on an acceptable element, that is, on whose resistance is within the specific limit, is $2, while unacceptable elements result in a loss of $0.50.
If P dollars is the profit in a randomly selected element produced by the firm, find the mean and variance of P. Correct to four decimal places.
d. Find the approximate percentage of the heating elements that you would expect to have resistance between 42 ohms and 54 ohms.



S_R_K

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Re: VCE Methods Question Thread!
« Reply #16892 on: September 18, 2018, 10:50:24 am »
0
can i please get some assistance on this question, my sacs in 3 hours ish and this is related to the sac

3. The resistance heating elements produced by an electrical firm are normally distributed with the mean 50 ohms and standard deviation 4 ohms.
a. If the specifications require that acceptable elements shall have a resistance between 45 and 50 ohms, find the probability, to four decimal places, that a randomly selected element has these specifications .
b. Find the least resistance, to four decimal places, the 85% of heating elements would have?
c. The profit on an acceptable element, that is, on whose resistance is within the specific limit, is $2, while unacceptable elements result in a loss of $0.50.
If P dollars is the profit in a randomly selected element produced by the firm, find the mean and variance of P. Correct to four decimal places.
d. Find the approximate percentage of the heating elements that you would expect to have resistance between 42 ohms and 54 ohms.

a. You are finding the probability that a normally distributed variable, with mean = 50, sd = 4 is between the values 45 and 50. Use the normal CDF function on CAS.
b. This question can be paraphrased as: if Pr(X < k) = 0.85, find the value of k. Use the inverse normal function on CAS.
c. Define a new random variable, P, where P is the profit made on an element. Pr(P = 2) is equal to the probability of randomly selecting an acceptable element; Pr(P = -0.5) is equal to the probability of randomly selecting an unacceptable element. This gives you the probability distribution of P, from which you can calculate the mean and variance.
d. 42 ohms is two standard deviations below the mean, and 54 ohms is one standard deviation above. Hence, you can use the 68-95-99.7% rule for normal distributions.

Hope that helps.

f0od

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Re: VCE Methods Question Thread!
« Reply #16893 on: September 18, 2018, 02:37:33 pm »
0
Hey! I'm not really sure how to figure out the answer to this binomial distribution question

Each week a security firm transports a large sum of money between two places. The day on which the journey is made is varied at random and, in any week, each of the five days from Monday to Friday is equally likely to be chosen. (In the following, give answers correct to four decimal places.) Calculate the probability that in a period of 10 weeks Friday will be chosen:
a) exactly 2 times
b) at least 2 times
c) exactly 3 times, given it is chosen at least 2 times

thank you so much in advance!

here are the answers
a) 0.3020
b) 0.6242
c) 0.3225
class of 2019

Bri MT

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Re: VCE Methods Question Thread!
« Reply #16894 on: September 18, 2018, 04:48:20 pm »
+3
Hey! I'm not really sure how to figure out the answer to this binomial distribution question

Each week a security firm transports a large sum of money between two places. The day on which the journey is made is varied at random and, in any week, each of the five days from Monday to Friday is equally likely to be chosen. (In the following, give answers correct to four decimal places.) Calculate the probability that in a period of 10 weeks Friday will be chosen:
a) exactly 2 times
b) at least 2 times
c) exactly 3 times, given it is chosen at least 2 times

thank you so much in advance!

here are the answers
a) 0.3020
b) 0.6242
c) 0.3225

There are 5 options that are equally likely to be chosen, so for each one the chance of that specifically is 0.2.
This choosing process occurs 10 times

so p=0.2  and n=10

hint: binompdf and binomcdf

Bell9565

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Re: VCE Methods Question Thread!
« Reply #16895 on: September 18, 2018, 06:13:22 pm »
+1
Hey! I'm not really sure how to figure out the answer to this binomial distribution question

Each week a security firm transports a large sum of money between two places. The day on which the journey is made is varied at random and, in any week, each of the five days from Monday to Friday is equally likely to be chosen. (In the following, give answers correct to four decimal places.) Calculate the probability that in a period of 10 weeks Friday will be chosen:
a) exactly 2 times
b) at least 2 times
c) exactly 3 times, given it is chosen at least 2 times

thank you so much in advance!

here are the answers
a) 0.3020
b) 0.6242
c) 0.3225

Also, to add to miniturtle's response, remember to use the conditional formula (Pr(A|B)=Pr(A∩B)/Pr(B))   :)
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NEV0008

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Re: VCE Methods Question Thread!
« Reply #16896 on: September 18, 2018, 08:16:05 pm »
0
Hi,
I was wondering if anyone has bought the bound reference from mathmethods.com? Is it good?

f0od

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Re: VCE Methods Question Thread!
« Reply #16897 on: September 20, 2018, 11:42:18 am »
0
There are 5 options that are equally likely to be chosen, so for each one the chance of that specifically is 0.2.
This choosing process occurs 10 times

so p=0.2  and n=10

hint: binompdf and binomcdf
Also, to add to miniturtle's response, remember to use the conditional formula (Pr(A|B)=Pr(A∩B)/Pr(B))   :)

thank you guys so much!!
class of 2019

snowmanrace

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Re: VCE Methods Question Thread!
« Reply #16898 on: September 21, 2018, 10:32:30 am »
0
For the multiple choice questions in exam 2 where you are given functions in terms of constants like "a" and "b", and given information like a>0, b>0 etc, is it a good idea to sub in numbers for a and b and then use trial and error with each of the options, or would this be too time consuming for exam 2?
Thanks
« Last Edit: September 21, 2018, 10:37:20 am by snowmanrace »

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Re: VCE Methods Question Thread!
« Reply #16899 on: September 21, 2018, 11:49:00 am »
0
For the multiple choice questions in exam 2 where you are given functions in terms of constants like "a" and "b", and given information like a>0, b>0 etc, is it a good idea to sub in numbers for a and b and then use trial and error with each of the options, or would this be too time consuming for exam 2?
Thanks

Depends. Personally, I will always use my CAS for the function properties ones, see VCAA 2016 Exam 2 Q11. I typically cant work out what properties are necessary to make the statement true. However, if I know exactly what to do in the questions, I will typically solve it as it is usually quicker. If I have any doubt though, its probably best to define some kind of function and do trial and error. Really shouldn't take longer than 90 seconds per question.

DBA-144

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Re: VCE Methods Question Thread!
« Reply #16900 on: September 21, 2018, 01:06:48 pm »
+1
Hi,
I was wondering if anyone has bought the bound reference from mathmethods.com? Is it good?


Going to just say that spending the time to make your own bound reference is going to help you a lot more. For example, you might like to put in examples of questions you know you struggle with and putting in key reminders for things that you might forget. The process of making the bound reference yourself is also a good revision technique, but you should probably get onto that if you have not done so already!

Really though, it is up to you to consider which option you should take, as I am also just a student trudging thru the course.
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Yertle the Turtle

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Re: VCE Methods Question Thread!
« Reply #16901 on: September 21, 2018, 04:30:00 pm »
+1
Regarding the concept of a bound book:

I personally agree with DBA-144 on this, since writing all the things down will strengthen your memory of them. However, I also find that there is no way I would write down everything, and therefore I find that having the textbook as my bound book works really well, if I want to I can write notes in there, and it is packed with examples that you can use. Of course to have this as an effective resource, you have to know your textbook layout very well. Just a hint, the glossary is really useful for finding out the concepts that you need really quickly.

In summary, writing your own notes is really important for refreshing your long-term memory, but having a more comprehensive bound book (such as the textbook) can be really useful, if you add your own notes. Commercially available bound books, in my opinion, lack the comprehensiveness of the textbook and the memory retention of the personal bound book.

Hope this helps! :D
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DBA-144

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Re: VCE Methods Question Thread!
« Reply #16902 on: September 22, 2018, 09:42:27 am »
0
Regarding the concept of a bound book:

I personally agree with DBA-144 on this, since writing all the things down will strengthen your memory of them. However, I also find that there is no way I would write down everything, and therefore I find that having the textbook as my bound book works really well, if I want to I can write notes in there, and it is packed with examples that you can use. Of course to have this as an effective resource, you have to know your textbook layout very well. Just a hint, the glossary is really useful for finding out the concepts that you need really quickly.

In summary, writing your own notes is really important for refreshing your long-term memory, but having a more comprehensive bound book (such as the textbook) can be really useful, if you add your own notes. Commercially available bound books, in my opinion, lack the comprehensiveness of the textbook and the memory retention of the personal bound book.

Hope this helps! :D


With maths, methods especially, I don't really think that memory retention is the issue here. In my opinion, the bound reference is there to help you out if you forget something, say, for example, if you forget the formula for the quotient rule, or, if you encounter a question in your preparation that you get wrong, you can put the solution to that question in there, so you know how to do it, in case a similar question comes up on the exam. Remember Yertle the Turtle, that often the textbook has examples that are quite basic, almost nothing like what could pop on the exam. Furthermore, the textbook is filled with exercises, meaning that you have the question there, but no solution.

I think it is also important to consider that the bound reference is for Exam 2, where you are going to be asked some very difficult questions.

Hope this helps. Again, this is my opinion only, and I am just a student as well.
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snowmanrace

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Re: VCE Methods Question Thread!
« Reply #16903 on: September 22, 2018, 11:02:16 am »
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Is it a good idea to bring the textbook in as a bound reference?
Also, what grade would a 45/80 on a heffernan methods exam 2 correspond to vcaa?
Thanks ;D

Lear

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Re: VCE Methods Question Thread!
« Reply #16904 on: September 22, 2018, 11:19:05 am »
+1
Is it a good idea to bring the textbook in as a bound reference?
Also, what grade would a 45/80 on a heffernan methods exam 2 correspond to vcaa?
Thanks ;D

In my personal opinion textbook is a bad resource to bring into an exam considering it is full of questions and basic examples. You see the purpose of a textbook is to individually teach you certain areas (eg Trig functions, log laws, differentiation of power functions) separately so you can master the basics. Exams on the other hand require you to synthesise everything you have learnt over a year and therefore the chapter based examples in the textbook are useless if you are aiming above 30. Furthermore textbooks can be very tricky to navigate even with a number of dividers of some sort and are in general very, very inefficient.
Personally for this year what I did is made my own concise notes typed up for all three sacs on the same document. Essentially I just added more and more to the same document and by the end of my third methods SAC I had a complete bound reference. The key here is being concise. I only have in there the things that I NEED to have in there such as what end points to include in approximating area under a curve using rectangles and how left-end or right-end is over estimation or underestimation depending on the nature of the function. Its these little yet vital things that should make up your bound reference, not something like what an x^2 graph looks like. You can just draw that on your cas if you really need it. Now these notes are only about 9 pages. Very easy to navigate in comparison to a textbook.
Ex

I have stapled these notes at the back of an ordinary exercise book. The rest of this exercise is book is full of mistakes and tricky questions I have ever come across. This, in my opinion, is far more important than the notes at the back which are simply there for confidence and the rare confirmation. Having those tricky questions there means
1. You actively went through the effort of writing down what you did wrong or found hard and in turn learnt from it and
2. You can access it if you come across a tricky question similar in nature

This sort of bound reference is many many times more valuable than a textbook with notes in it.

Re: Heffernan
Heffernan exams are known to be at or if not below the difficulty of VCAA exams. Imo you can can consider a 45/80 on Heffernan to be a 45/80 on VCAA or below.
« Last Edit: September 22, 2018, 11:24:30 am by Lear »
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