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March 30, 2024, 12:46:21 am

Author Topic: 3U Maths Question Thread  (Read 1230706 times)  Share 

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jamonwindeyer

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Re: 3U Maths Question Thread
« Reply #630 on: August 28, 2016, 02:36:01 pm »
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For the last one ii) the binomial identity, i've tried integrating, factoring out the x then subbing in x equals -1 and it gives you the lhs but not the rhs :/
Will work on this further

But wait! After integrating and subbing in x=0 you get the entire lhs equals to 0 and the rhs equalling 1/n +1

Summing the two would give the final identity. I think I might have broken a maths law haha could someone check?

Yeah Rui is right, no math laws broken, you are all sweet ;)

Spencerr

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Re: 3U Maths Question Thread
« Reply #631 on: August 28, 2016, 03:16:20 pm »
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Ah yes definite integrals gives the answer. I didn't consider the constant term when I indefinitely integrated it. All good :)
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Mei2016

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Re: 3U Maths Question Thread
« Reply #632 on: August 28, 2016, 10:09:02 pm »
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Thanks Jamon, Spencerr and Rui for you help!

For the 1992 q, for the definite integral, how would you know to use 0 and -1 or does any combo of 1/-1/0 still work fine?

For the 1996 q, is the pic below the kind of working out required for the 2 marks of the questions?

Thanks.

RuiAce

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Re: 3U Maths Question Thread
« Reply #633 on: August 28, 2016, 10:28:39 pm »
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Thanks Jamon, Spencerr and Rui for you help!

For the 1992 q, for the definite integral, how would you know to use 0 and -1 or does any combo of 1/-1/0 still work fine?

For the 1996 q, is the pic below the kind of working out required for the 2 marks of the questions?

Thanks.
Just quickly regarding the definite integral question (I'm busy right now)

You can use an indefinite integral. But using anything that's not 0 to evaluate your +C is never a good idea.

-1 is then chosen because the signs alternate!

Mei2016

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Re: 3U Maths Question Thread
« Reply #634 on: August 28, 2016, 10:35:44 pm »
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So from the textbook questions, Q9 can be solved in a similar way to the 1996 question, but how would you solve Q7?

Also, again in the pic is the working to Q9. Is this how you would set out the working to 'show' the given equation?

Mei2016

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Re: 3U Maths Question Thread
« Reply #635 on: August 28, 2016, 10:45:21 pm »
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Hi Rui, thanks for answering. I understand why we use x=0 and x=-1 for the indefinite method, but previously, I couldn't see why you had chosen these from a quick glance at the question with the definite method, because I'm used to using to definite method with resisted motion questions where the limits of the integration are given with the initial and final conditions.

I really like this method because it's really quick :D Thanks for your time.

jamonwindeyer

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Re: 3U Maths Question Thread
« Reply #636 on: August 28, 2016, 11:24:09 pm »
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So from the textbook questions, Q9 can be solved in a similar way to the 1996 question, but how would you solve Q7?

Also, again in the pic is the working to Q9. Is this how you would set out the working to 'show' the given equation?

Hey! That working is definitely sufficient for the marks, a little messy in the middle, you can just not worry about that box if you don't want to, it's obvious what you are up to ;D

That question you posted has me a bit stumped. We consider two successive coefficients (the two and three's come from the terms inside the bracket):



Perhaps I'm a bit tired, I can't see how to proceed from here! Do we even have enough info to answer? Happy for someone to tag in ;)

RuiAce

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Re: 3U Maths Question Thread
« Reply #637 on: August 29, 2016, 12:02:50 am »
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Ok I'm back in action
Thanks Jamon, Spencerr and Rui for you help!

For the 1992 q, for the definite integral, how would you know to use 0 and -1 or does any combo of 1/-1/0 still work fine?

For the 1996 q, is the pic below the kind of working out required for the 2 marks of the questions?

Thanks.
For your equating coefficients thing, you can just say that the coefficient of xsomething in the expansion of ... is ...

You don't have to explicitly expand (1+x)4 or (1+x)13

RuiAce

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Re: 3U Maths Question Thread
« Reply #638 on: August 29, 2016, 12:03:46 am »
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Hi Rui, thanks for answering. I understand why we use x=0 and x=-1 for the indefinite method, but previously, I couldn't see why you had chosen these from a quick glance at the question with the definite method, because I'm used to using to definite method with resisted motion questions where the limits of the integration are given with the initial and final conditions.

I really like this method because it's really quick :D Thanks for your time.
Just pick 0. Usually if your thing is tidy then 0 is involved.

But yeah -1 was like I said, because the signs alternated.


Sorry but can you mention what year and exactly which question which part for anything else you wish for help with?
« Last Edit: August 29, 2016, 12:08:00 am by RuiAce »

amandali

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Re: 3U Maths Question Thread
« Reply #639 on: August 31, 2016, 03:17:13 pm »
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how to do part b ii)

jakesilove

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Re: 3U Maths Question Thread
« Reply #640 on: August 31, 2016, 03:26:24 pm »
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(Image removed from quote.)

how to do part b ii)

Hey! My solution is below :)



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RuiAce

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Re: 3U Maths Question Thread
« Reply #641 on: August 31, 2016, 03:42:27 pm »
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Hey! My solution is below :)

(Image removed from quote.)

Jake
Just check your working out again. Your answer gets A > (3√3) / 2

The correct reasoning is that because (2A+3√3)/(3√3) is strictly positive, the other must be positive as well.


@amandali if this question is hard to understand I can offer up a GeoGebra simulation if you need it later on. I'm in a lecture now to give a comprehensive solution.

RuiAce

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Re: 3U Maths Question Thread
« Reply #642 on: August 31, 2016, 07:13:51 pm »
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If you play around with GeoGebra you'll see what we're trying to do. Notice how as A gets larger, the stationary points seemingly poke outwards more. We are basically telling it to not poke over the x-axis.

jakesilove

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Re: 3U Maths Question Thread
« Reply #643 on: September 01, 2016, 10:22:07 am »
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(Image removed from quote.)





If you play around with GeoGebra you'll see what we're trying to do. Notice how as A gets larger, the stationary points seemingly poke outwards more. We are basically telling it to not poke over the x-axis.


Truuuueeee I didn't actually look at the question (noting that it was a cubic), and then just basically worked backwards from what I expected. Thanks Rui!
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anotherworld2b

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Re: 3U Maths Question Thread
« Reply #644 on: September 02, 2016, 07:06:38 pm »
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I was wondering how do you do these two questions?