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March 29, 2024, 10:55:02 pm

Author Topic: 3U Maths Question Thread  (Read 1230657 times)  Share 

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RuiAce

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Re: 3U Maths Question Thread
« Reply #435 on: August 03, 2016, 08:24:29 am »
+1
I think I'd swing at Part (v) a little differently, I interpret the question differently. When it says precisely two distances from O, doesn't that mean it has two solutions? The wording is really weird, but I don't think it relates to the distance d given earlier in the question, nothing suggests that. So my interpretation would be that we just need to prove that, provided that the condition on U holds, then there are two values of d which satisfy the other conditions given.

This would make sense, provided the target is moving slow enough, it can hit it on the way up (one distance), or on the way down (another distance). At least I think. I just don't think it relates to the distance d. What do you reckon Rui?  ::)
Yeah seems more legit that way aha I just got completely lost out of the rigour of that question in my fatigue

jamonwindeyer

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Re: 3U Maths Question Thread
« Reply #436 on: August 03, 2016, 10:42:40 am »
+1
Yeah seems more legit that way aha I just got completely lost out of the rigour of that question in my fatigue

I don't blame you, that is probably one of the worst projectile questions I've ever seen  :P

massive

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Re: 3U Maths Question Thread
« Reply #437 on: August 03, 2016, 04:55:13 pm »
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Guys i don't get part d and e. btw i really appreciate the help  ;D

RuiAce

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Re: 3U Maths Question Thread
« Reply #438 on: August 03, 2016, 07:09:01 pm »
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Guys i don't get part d and e. btw i really appreciate the help  ;D
I have to ask this again. What is the source of these questions




Give me a bit, still working on the other one
« Last Edit: August 03, 2016, 07:18:10 pm by RuiAce »

RuiAce

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Re: 3U Maths Question Thread
« Reply #439 on: August 04, 2016, 12:16:12 pm »
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Note that MX1 questions from Pre-2001 are tough. The difficulty/rigour of these questions is WELL beyond that of the current HSC. Post them if have them! But we might not give you a full worked solution, rather, guide you through one for yourself.


In saying that, here are solutions. THSC.

Always feel free to comment further if any part of the provided solutions don't make sense though.
« Last Edit: August 04, 2016, 01:39:56 pm by jamonwindeyer »

conic curve

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Re: 3U Maths Question Thread
« Reply #440 on: August 04, 2016, 01:09:14 pm »
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Can we please refrain from too many past HSC questions before the year 2001? The difficulty/rigour of these questions is seriously getting WELL beyond that of the current HSC.

In saying that, here are solutions. THSC.

Always feel free to comment further if any part of the provided solutions don't make sense though.

Isn't it good that you're doing it because you're exposing yourself to questions harder than the HSC?

RuiAce

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Re: 3U Maths Question Thread
« Reply #441 on: August 04, 2016, 01:24:32 pm »
+1
Isn't it good that you're doing it because you're exposing yourself to questions harder than the HSC?
Sure, if you want to aim that high.

I never went before 2001 and I still did reasonably well anyway. It's becoming really hard to provide concise solutions, or sometimes you just get lost lol.

Sometimes it can be nearing impossible to provide solutions so easily because it's reaching a point where the lateral thinking required is not that prevalent anymore, and demanded by the students today.

jamonwindeyer

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Re: 3U Maths Question Thread
« Reply #442 on: August 04, 2016, 01:34:05 pm »
+1
Sure, if you want to aim that high.

I never went before 2001 and I still did reasonably well anyway. It's becoming really hard to provide concise solutions, or sometimes you just get lost lol.

Sometimes it can be nearing impossible to provide solutions so easily because it's reaching a point where the lateral thinking required is not that prevalent anymore, and demanded by the students today.

Just to give an indication, I did the 1980's-1990's papers for study back in 2014, my average mark in those decades was a good 10 points lower than my average mark for the more recent exams. There is a definite difference in difficulty ;D

That said, there is definitely benefit to doing them. I'd recommend them to anyone aiming for a Band E4 in Extension 1 ;)

Keep posting questions if you have them! Just understand that Rui, Jake and myself might not be able to provide proper solutions to the really hard stuff on occasion, if it really stumps us 8)

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Re: 3U Maths Question Thread
« Reply #443 on: August 04, 2016, 04:20:37 pm »
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Hi, I'm having trouble finding the asymptotes, turning points, inflection points etc to draw these graphs

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Re: 3U Maths Question Thread
« Reply #444 on: August 04, 2016, 04:43:51 pm »
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Hi, I'm having trouble finding the asymptotes, turning points, inflection points etc to draw these graphs

Hey Goodwil! I'm happy to help, I'll help you find the asymptotes for both, then I'll go through the full process for the second one, hopefully you can apply it to the first ;D

Okay, so vertical asymptotes exist where the function is undefined. In both of these cases, that means when the denominator is equal to zero. So, we can do it by inspection if we want, or alternatively:




These are the vertical asymptotes! Let's do the turning points and such for the second function. First, we differentiate using the quotient rule:



To find the turning points, we put this equal to zero (note in the second step we discard the denominator because it can't be equal to zero):



Now we'll need our second derivative for the next step, but I'll be honest, that derivative looks sort of gross. It would be another application of chain rule, but I'm going to use magic (Wolfram Alpha) to get the answer:



Okay, so we do a few things with this. First, we substitute in our x values from earlier to find the nature of the turning points. Doing so, we find that:



We also need to put the second derivative equal to zero to find any points of inflexion:



We already know about this point, but at least we know there aren't any more  ;D

Putting all of that information together, and perhaps plotting a few points and considering some limiting cases near the asymptotes, leads us to this graph here. Notice the asymptotes in the correct spots, the inflexion in the middle, and the two max/min points ;D

So that's the process, it will be an exact replica for the first question! Asymptotes, first and second derivatives, turning points, inflexions, and then sketch ;D

This sort of question, besides the nasty second derivative, is quite standard in MX1 exams so it is handy to know this process really really well ;D does this help?  :)

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Re: 3U Maths Question Thread
« Reply #445 on: August 05, 2016, 10:04:00 am »
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Yeah they're pretty hard, but they're pretty fun at the same time! :P Anyway, how do you find the amplitude for the attached equation (its Simple Harmonic Motion)

RuiAce

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Re: 3U Maths Question Thread
« Reply #446 on: August 05, 2016, 10:26:46 am »
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Yeah they're pretty hard, but they're pretty fun at the same time! :P Anyway, how do you find the amplitude for the attached equation (its Simple Harmonic Motion)



jakesilove

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Re: 3U Maths Question Thread
« Reply #447 on: August 05, 2016, 10:47:43 am »
+1


'Just'. Toughest Amplitude question I've seen
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RuiAce

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Re: 3U Maths Question Thread
« Reply #448 on: August 05, 2016, 10:52:10 am »
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'Just'. Toughest Amplitude question I've seen
I did the exact same question around a month ago

jakesilove

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Re: 3U Maths Question Thread
« Reply #449 on: August 05, 2016, 10:53:05 am »
+2
I did the exact same question around a month ago

Plus you're hard to impress x
ATAR: 99.80

Mathematics Extension 2: 93
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Studying a combined Advanced Science/Law degree at UNSW