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November 20, 2019, 10:16:39 pm

Author Topic: VCE Methods Question Thread!  (Read 2536511 times)  Share 

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MB_

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Re: VCE Methods Question Thread!
« Reply #17970 on: June 23, 2019, 07:38:03 pm »
+1
So if my answer of 47/270725 represents one way the kings could be selected, then why would it be wrong to just multiply my answer by 5! (120)?
It would be wrong as the number of ways of obtaining 3 kings from 5 cards is \(\displaystyle\binom{5}{3}=10\)
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AlphaZero

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Re: VCE Methods Question Thread!
« Reply #17971 on: June 23, 2019, 07:56:37 pm »
+2
So if my answer of 47/270725 represents one way the kings could be selected, then why would it be wrong to just multiply my answer by 5! (120)?

It would be wrong as the number of ways of obtaining 3 kings from 5 cards is \(\displaystyle\binom{5}{3}=10\)

MB_ is right here. There are 10 combinations to consider, not 120.

However, it is worth noting that the only reason this works is because the probabilities of each of the outcomes in the event are equal.

For example, consider the following question:  "Find the probability of obtaining at least 3 kings when drawing 5 cards from a standard card deck without replacement".  Clearly, there are more combinations to consider, and those additional outcomes do not have the same probability as the outcomes for obtaining 3 kings.
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Re: VCE Methods Question Thread!
« Reply #17972 on: June 26, 2019, 06:57:43 am »
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Hey there! I have a doubt from Combinatorics! If u can please help me with it that would be great!!!  ;D

A basketball squad of 10 must be chosen from a group of 8 women and 6 men. How many squads are possible:
a) without restriction?
b) if the squad contains 6 women and 4 men?
c) if the squad must contain at least 6 women?
d) if the squad contains all men?

Now I managed to figure out that this is a "combination" question. I managed to do question a but not b, c and d.

Thanks, much appreciated :).

AlphaZero

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Re: VCE Methods Question Thread!
« Reply #17973 on: June 26, 2019, 11:50:20 am »
+2
Hey there! I have a doubt from Combinatorics! If u can please help me with it that would be great!!!  ;D

A basketball squad of 10 must be chosen from a group of 8 women and 6 men. How many squads are possible:
a) without restriction?
b) if the squad contains 6 women and 4 men?
c) if the squad must contain at least 6 women?
d) if the squad contains all men?

Now I managed to figure out that this is a "combination" question. I managed to do question a but not b, c and d.

Thanks, much appreciated :).

I'm not too great with combinatorics. I could be wrong, so if someone with a little more experience could check this, that'd be great.

Part a
We need to choose 10 players from a group of 14: \[\binom{14}{10}=1001\ \text{ possible squads}\]

Part b
We need to choose 6 women from 8 and 4 men from 6: \[\binom{8}{6}\binom{6}{4}=420\ \text{ possible squads}\]

Part c
We could either choose 6 women and 4 men, 7 women and 3 men, or, 8 women and 2 men: \[\binom{8}{6}\binom{6}{4}+\binom{8}{7}\binom{6}{3}+\binom{8}{8}\binom{6}{2}=595\ \text{ possible squads}\]

Part d
The wording to this question doesn't seem correct. It's impossible to pick a squad so that all 10 members are men since there are only 6 men to pick from. I believe you meant "if the squad contains all the men", in which case, we would need to select 4 women from 8 and 6 men from 6: \[\binom{8}{4}\binom{6}{6}=70\ \text{ possible squads}\]
2015\(-\)2017:  VCE
2018\(-\)2021:  Bachelor of Biomedicine (Human Structure & Function) and Applied Mathematics, University of Melbourne


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Re: VCE Methods Question Thread!
« Reply #17974 on: June 26, 2019, 12:47:12 pm »
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I'm not too great with combinatorics. I could be wrong, so if someone with a little more experience could check this, that'd be great.

Part a
We need to choose 10 players from a group of 14: \[\binom{14}{10}=1001\ \text{ possible squads}\]

Part b
We need to choose 6 women from 8 and 4 men from 6: \[\binom{8}{6}\binom{6}{4}=420\ \text{ possible squads}\]

Part c
We could either choose 6 women and 4 men, 7 women and 3 men, or, 8 women and 2 men: \[\binom{8}{6}\binom{6}{4}+\binom{8}{7}\binom{6}{3}+\binom{8}{8}\binom{6}{2}=595\ \text{ possible squads}\]

Part d
The wording to this question doesn't seem correct. It's impossible to pick a squad so that all 10 members are men since there are only 6 men to pick from. I believe you meant "if the squad contains all the men", in which case, we would need to select 4 women from 8 and 6 men from 6: \[\binom{8}{4}\binom{6}{6}=70\ \text{ possible squads}\]

Thanks so much!!!

P.S. Sorry about the wording of part d (I copied it from the textbook, my bad)

VanessaS

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Re: VCE Methods Question Thread!
« Reply #17975 on: July 05, 2019, 05:45:40 pm »
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Hey, can someone help me with this question? The answer is D but I am not sure how to get to it.
Thanks

AlphaZero

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Re: VCE Methods Question Thread!
« Reply #17976 on: July 05, 2019, 06:22:33 pm »
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Hey, can someone help me with this question? The answer is D but I am not sure how to get to it.
Thanks

This question is about whether you can apply integral properties. \begin{align*}2\int_0^{5a}\left[f\left(\frac x 5\right)+3\right]dx&=2\int_0^{5a}f\left(\frac x 5\right)dx+2\int_0^{5a}3\,dx\\
&=10\int_0^a f(x)\,dx+6\int_0^{5a}dx\\
&=10a+6(5a)\\
&=40a \end{align*}
2015\(-\)2017:  VCE
2018\(-\)2021:  Bachelor of Biomedicine (Human Structure & Function) and Applied Mathematics, University of Melbourne


VanessaS

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Re: VCE Methods Question Thread!
« Reply #17977 on: July 05, 2019, 07:21:54 pm »
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This question is about whether you can apply integral properties. \begin{align*}2\int_0^{5a}\left[f\left(\frac x 5\right)+3\right]dx&=2\int_0^{5a}f\left(\frac x 5\right)dx+2\int_0^{5a}3\,dx\\
&=10\int_0^a f(x)\,dx+6\int_0^{5a}dx\\
&=10a+6(5a)\\
&=40a \end{align*}

How can you get the 5 out of the integral if it is the input in the function? And how does that change the limits?

AlphaZero

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Re: VCE Methods Question Thread!
« Reply #17978 on: July 05, 2019, 08:42:48 pm »
+2
How can you get the 5 out of the integral if it is the input in the function? And how does that change the limits?

The graph of  \(y=f(x)\)  maps to the graph of  \(y=f\left(\dfrac x 5\right)\)  via a dilation by factor 5 from the \(y\)-axis. Note how the area under the black curve is 5 times that of the area under the red curve.

Thus, we have  \(\displaystyle 5\!\int_0^a f(x)\,dx=\int_0^{5a}f\left(\frac x 5\right)dx\).

« Last Edit: July 05, 2019, 08:44:58 pm by AlphaZero »
2015\(-\)2017:  VCE
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VanessaS

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Re: VCE Methods Question Thread!
« Reply #17979 on: July 05, 2019, 11:32:19 pm »
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The graph of  \(y=f(x)\)  maps to the graph of  \(y=f\left(\dfrac x 5\right)\)  via a dilation by factor 5 from the \(y\)-axis. Note how the area under the black curve is 5 times that of the area under the red curve.

Thus, we have  \(\displaystyle 5\!\int_0^a f(x)\,dx=\int_0^{5a}f\left(\frac x 5\right)dx\).

(Image removed from quote.)

Oh ok. That makes much more sense. Thank you so much.

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Re: VCE Methods Question Thread!
« Reply #17980 on: July 06, 2019, 10:04:10 am »
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Hi guys, this is not really a maths-based questions but here i go:

a) from your experience what did you think was the most useful textbook (eg. jacaranda, cambridge, pearson etc.)?

b) how much hours of studying for methods CAS do you think is necessary for a week? (I usually do 15 hours a week just for methods [maths is one of  my  weaknesses with VCE english])

Thanks for your time :)

pugs

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Re: VCE Methods Question Thread!
« Reply #17981 on: July 10, 2019, 03:18:08 pm »
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is the integration of loge(x) still required in the current study design?

i was going through the checkpoints and came across a question from 2009 where you were required to integrate log. as it's pretty old, i'm not sure whether it's still necessary. <and if it is i have absolutely no idea how to do it bc we didn't learn it at school ;/>

thanks!  ;D


2019 vce journal here

pugs

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Re: VCE Methods Question Thread!
« Reply #17982 on: July 10, 2019, 03:25:25 pm »
+1
Hi guys, this is not really a maths-based questions but here i go:

a) from your experience what did you think was the most useful textbook (eg. jacaranda, cambridge, pearson etc.)?
hey! i won't lie, i can't really compare the textbooks as i only use the one our school issued to us (cambridge). however, just regarding this textbook, i find it pretty handy as there are step-by-step solutions somewhere on the web (i'm not sure how i found them, but i did after some searching lolol). with that being said, i'm don't know whether the other textbooks have step-by-step solutions. aside from textbooks, i reckon checkpoints or just going through past exams are extremely useful if you want some extra practise! this is because textbook style questions are quite different from exam style questions

b) how much hours of studying for methods CAS do you think is necessary for a week? (I usually do 15 hours a week just for methods [maths is one of  my  weaknesses with VCE english])

Thanks for your time :)
hmm i don't think it's the hours that matter, but how effective you are because you could spend hours studying yet barely retain any information. i guess it depends on how confident you feel after studying. if you feel like you know the topic well enough, i reckon that's how much study you need, regardless of how many hours it takes

<p.s sorry that my answers aren't straightforward! :(>


2019 vce journal here

Evolio

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Re: VCE Methods Question Thread!
« Reply #17983 on: July 10, 2019, 03:27:07 pm »
+1
is the integration of loge(x) still required in the current study design?

i was going through the checkpoints and came across a question from 2009 where you were required to integrate log. as it's pretty old, i'm not sure whether it's still necessary. <and if it is i have absolutely no idea how to do it bc we didn't learn it at school ;/>

thanks!  ;D
Hi!
You do not need to know how to integrate loge(x) assuming it was an individual question.
Although, you just need to know how to integrate it by recognition. For eg, if they told you to find a derivative of an equation in the first part and then then told you to find the integral, you would do it by integration by recognition. I hope this makes sense.

 :)


2019: Biology, Mathematical Methods
2020: Literature, Psychology, Specialist Mathematics, Chemistry

pugs

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Re: VCE Methods Question Thread!
« Reply #17984 on: July 10, 2019, 05:21:13 pm »
+1
Hi!
You do not need to know how to integrate loge(x) assuming it was an individual question.
Although, you just need to know how to integrate it by recognition. For eg, if they told you to find a derivative of an equation in the first part and then then told you to find the integral, you would do it by integration by recognition. I hope this makes sense.

 :)
ooh okay, thanks!  ;D

also, i hope you don't mind me asking another question, and pls feel free to ignore it as i don't want to post another reply when the question still relates to logs haha

how do you go from one of these logs in the attached image to the other? (sorry if it's a dumb q)


2019 vce journal here