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March 29, 2024, 12:47:43 am

Author Topic: 3U Maths Question Thread  (Read 1230258 times)  Share 

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ATWalk

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Re: 3U Maths Question Thread
« Reply #105 on: April 04, 2016, 03:22:05 pm »
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Thanks Jake! Unfortunately I've also got another question that I'm finding difficult and I'd be grateful for help... Hopefully this one is easier to solve. Could I have help just with part i? Part ii I'll attempt later.

jakesilove

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Re: 3U Maths Question Thread
« Reply #106 on: April 04, 2016, 06:52:24 pm »
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Thanks Jake! Unfortunately I've also got another question that I'm finding difficult and I'd be grateful for help... Hopefully this one is easier to solve. Could I have help just with part i? Part ii I'll attempt later.

Hey!

I'm sorry that I don't have time at the moment to figure out where I went wrong: That is the general structure, and I hope it helps! You're asking some crazy hard questions.



Jake
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Goodwil

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Re: 3U Maths Question Thread
« Reply #107 on: April 07, 2016, 04:55:22 pm »
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Hi there, I'm having trouble with these two questions. Any help would be appreciated. Thanks

1. Show that f(x)= x^3+2x-4 has only 1 root
2. Given log(xy^3)=m and log(x^3y^2)=p, find log(sqrt(xy)) in terms of m and p (all logs are base 'b')

jakesilove

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Re: 3U Maths Question Thread
« Reply #108 on: April 07, 2016, 05:22:38 pm »
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Hi there, I'm having trouble with these two questions. Any help would be appreciated. Thanks

1. Show that f(x)= x^3+2x-4 has only 1 root
2. Given log(xy^3)=m and log(x^3y^2)=p, find log(sqrt(xy)) in terms of m and p (all logs are base 'b')

Hey! These are some seriously tricky questions, but once you've noted the general technique you'll be able to approach similar questions with ease. Take a look at my working!



Jake
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katherine123

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Re: 3U Maths Question Thread
« Reply #109 on: April 09, 2016, 10:34:48 am »
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Should i be taken the positive velocity since v>0 when t=0

ans for part ii)1-e^-t

jakesilove

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Re: 3U Maths Question Thread
« Reply #110 on: April 09, 2016, 10:58:20 am »
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Should i be taken the positive velocity since v>0 when t=0

ans for part ii)1-e^-t

Hey! My proof is below :) this question is mainly about applying the relevant velocity/displacement formulas, and then ensuring you integrate correctly. I hope the solution helps!



Jake
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Happy Physics Land

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Re: 3U Maths Question Thread
« Reply #111 on: April 09, 2016, 06:02:42 pm »
+1
Hey! My proof is below :) this question is mainly about applying the relevant velocity/displacement formulas, and then ensuring you integrate correctly. I hope the solution helps!

(Image removed from quote.)

Jake

Actually I had almost the same question in my 3u exam, the hard part in this question for a lot of my mates was actually to realise the fact that you have to implement natural log in the integral
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RuiAce

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Re: 3U Maths Question Thread
« Reply #112 on: April 10, 2016, 09:07:38 am »
+1
Actually I had almost the same question in my 3u exam, the hard part in this question for a lot of my mates was actually to realise the fact that you have to implement natural log in the integral

There is a very VERY subtle trick placed there that reveals that an exponential might've been needed.

If you look closely at the initial equation, recalling that v is just dx/dt, this is actually motion in the form of exponential decay. The final answer was virtually doomed to have an exponential within it. The consequence is that because we find dt/dx before dx/dt, we find t = f(x) + C first. Because f(t) and g(x) are bound to be mutually inverse functions (or even just by looking at the inverse function theorem dx/dt dt/dx = 1) it's essentially unavoidable that the natural log must appear halfway through.

You can try explaining this to those kids at your school if you wish

katherine123

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Re: 3U Maths Question Thread
« Reply #113 on: April 16, 2016, 01:50:31 am »
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a particle moves in SHM of period 8 hours and amplitude 6 metres. When t=3 hours, x=4m  by using x-b=asin(wt)   find centre of motion

RuiAce

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Re: 3U Maths Question Thread
« Reply #114 on: April 16, 2016, 09:18:48 am »
+1
a particle moves in SHM of period 8 hours and amplitude 6 metres. When t=3 hours, x=4m  by using x-b=asin(wt)   find centre of motion



lazydreamer

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Re: 3U Maths Question Thread
« Reply #115 on: April 17, 2016, 07:02:10 pm »
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Hi, need some help with this differentiating trig func. question :)
wasn't sure which thread this question should go but...here~
thanks in advance!


jakesilove

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Re: 3U Maths Question Thread
« Reply #116 on: April 17, 2016, 07:44:30 pm »
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Hi, need some help with this differentiating trig func. question :)
wasn't sure which thread this question should go but...here~
thanks in advance!

Hey!

This was quite a tough one: I did it wrong twice, working through methods that ended up being way easier, but gave you a different result that became even more difficult to prove equaled the RHS. In the end, brute forcing the entire thing was the easiest way to go! I hope my answer below is helpful: If you're ever unsure, just attack the question using the rules you know!



Jake
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RuiAce

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Re: 3U Maths Question Thread
« Reply #117 on: April 17, 2016, 10:58:59 pm »
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Hey!

This was quite a tough one: I did it wrong twice, working through methods that ended up being way easier, but gave you a different result that became even more difficult to prove equaled the RHS. In the end, brute forcing the entire thing was the easiest way to go! I hope my answer below is helpful: If you're ever unsure, just attack the question using the rules you know!

(Image removed from quote.)

Jake


« Last Edit: April 17, 2016, 11:00:34 pm by RuiAce »

jakesilove

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Re: 3U Maths Question Thread
« Reply #118 on: April 17, 2016, 11:16:09 pm »
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Wow I can't believe I missed that: A really simple solution to what is otherwise quite a difficult question. Thanks for pointing this out!

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Re: 3U Maths Question Thread
« Reply #119 on: April 18, 2016, 10:10:02 am »
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Hey!

This was quite a tough one: I did it wrong twice, working through methods that ended up being way easier, but gave you a different result that became even more difficult to prove equaled the RHS. In the end, brute forcing the entire thing was the easiest way to go! I hope my answer below is helpful: If you're ever unsure, just attack the question using the rules you know!

(Image removed from quote.)

Jake
oh i didn't try to approach it from the RHS...my bad haha



Mind=blown xD

thank you both for your help!