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March 29, 2024, 12:00:43 pm

Author Topic: 3U Maths Question Thread  (Read 1230470 times)  Share 

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RuiAce

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Re: 3U Maths Question Thread
« Reply #2070 on: May 25, 2017, 12:15:44 am »
+1
Hi um stuck on integrating 2^lnx pls help :)
Bit bizarre for 3U


Can be simplified in a variety of ways to match what's given on WolframAlpha
Hey! Tricky one this, we have to take an exponential/logarithm at the same time and then use the Log Laws to manipulate. See if this makes sense:



And that is just a power of \(x\) - Integrate that as normal! The power of \(x\) will be \(1+\ln{2}\) ;D


I feel weird about this

These two integrals don't seem to match up properly and I can't get my head around why

chelseam

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Re: 3U Maths Question Thread
« Reply #2071 on: May 25, 2017, 06:19:41 pm »
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Hi! What would I need to do to find part b of this question? Thank you in advance :D
HSC 2017: Chemistry / English Advanced / English Extension 1 / Legal Studies (5th in NSW) / Math Extension 1 / Math Extension 2

RuiAce

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Re: 3U Maths Question Thread
« Reply #2072 on: May 25, 2017, 06:34:23 pm »
+2
Hi! What would I need to do to find part b of this question? Thank you in advance :D
Please provide progress on previous parts in the future


bluecookie

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Re: 3U Maths Question Thread
« Reply #2073 on: May 26, 2017, 09:16:03 am »
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I've always wondered, why is the 2nd derivative written d^2y/dx^2? I've always assumed it was d^2y/d^2x, but recently realised it wasn't xD

RuiAce

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Re: 3U Maths Question Thread
« Reply #2074 on: May 26, 2017, 09:54:55 am »
+2
I've always wondered, why is the 2nd derivative written d^2y/dx^2? I've always assumed it was d^2y/d^2x, but recently realised it wasn't xD

At the same time, you can just blame the mathematicians from centuries ago for the convention

hanaacdr

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Re: 3U Maths Question Thread
« Reply #2075 on: May 26, 2017, 06:56:50 pm »
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Does anyone know how to do this question??

bluecookie

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Re: 3U Maths Question Thread
« Reply #2076 on: May 27, 2017, 12:04:45 am »
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At the same time, you can just blame the mathematicians from centuries ago for the convention

Thanks!

RuiAce

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Re: 3U Maths Question Thread
« Reply #2077 on: May 27, 2017, 09:09:23 am »
+1
(Image removed from quote.)


Does anyone know how to do this question??
You may find answers to past HSC questions here. Carefully note that this came out of an Extension 2 paper so I will not address it here

K9810

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Re: 3U Maths Question Thread
« Reply #2078 on: May 27, 2017, 05:13:57 pm »
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Hey! Need help with this probability question: Twelve people arrive at a restaurant. There is one table for six, one table for four and one table for two. In how many ways can they be assigned to a table?

jamonwindeyer

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Re: 3U Maths Question Thread
« Reply #2079 on: May 27, 2017, 05:22:43 pm »
+1
Hey! Need help with this probability question: Twelve people arrive at a restaurant. There is one table for six, one table for four and one table for two. In how many ways can they be assigned to a table?

Hey! Choose and arrange the table of 6:



Then do the same for the next table of four:



Then the table of two can really only be chosen and seated one way - So just multiply the two of those together ;D

Note: I've assumed the arrangements are circular, perhaps not in shape, but in that it is the people you are sitting next to that matters, not necessarily what seat you are in - So we do the usual \(\left(n-1\right)!\) thing :)
« Last Edit: May 27, 2017, 05:24:40 pm by jamonwindeyer »

K9810

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Re: 3U Maths Question Thread
« Reply #2080 on: May 27, 2017, 05:54:01 pm »
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Hey! Choose and arrange the table of 6:



Then do the same for the next table of four:



Then the table of two can really only be chosen and seated one way - So just multiply the two of those together ;D

Note: I've assumed the arrangements are circular, perhaps not in shape, but in that it is the people you are sitting next to that matters, not necessarily what seat you are in - So we do the usual \(\left(n-1\right)!\) thing :)

Thank you so much!

chelseam

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Re: 3U Maths Question Thread
« Reply #2081 on: May 28, 2017, 02:00:10 pm »
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Hi! I've heard that there are cases where using Newton's method wouldn't work. Are there ways to recognise when it won't work? Thank you :D
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RuiAce

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Re: 3U Maths Question Thread
« Reply #2082 on: May 28, 2017, 02:04:49 pm »
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Hi! I've heard that there are cases where using Newton's method wouldn't work. Are there ways to recognise when it won't work? Thank you :D
The Cambridge 3U textbook summarises these quite well

chelseam

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Re: 3U Maths Question Thread
« Reply #2083 on: May 28, 2017, 02:14:20 pm »
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The Cambridge 3U textbook summarises these quite well

Thanks Rui :)
HSC 2017: Chemistry / English Advanced / English Extension 1 / Legal Studies (5th in NSW) / Math Extension 1 / Math Extension 2

RuiAce

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Re: 3U Maths Question Thread
« Reply #2084 on: May 28, 2017, 02:17:54 pm »
+2
Worthwhile considering:

Of course, in the modern day we have computers to do everything for us now. But back then, the best way to estimate the values was to use a combination of bisection (halving the interval) and Newton's method. This usually collapses the flaws in Newton's method.