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March 29, 2024, 10:35:20 am

Author Topic: 4U Maths Question Thread  (Read 659917 times)  Share 

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jamonwindeyer

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Re: 93 in 4U Maths: Ask me Anything!
« Reply #15 on: February 11, 2016, 07:42:35 pm »
+2
Damn Jake, looks like I missed out on some delicious polynomial questions :/

I love that you described a polynomial question as "delicious." Absolutely fantastic  8)

xXCandyDXx

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93 in 4U Maths: Ask me Anything!
« Reply #16 on: February 11, 2016, 09:27:17 pm »
+2
Thank you Jake! I think that's the same method a friend of mine used! But I don't understand it very well... I'll have to keep looking HAHA HOWEVER I have accidentally come across the same solution using a different method and I think this may benefit others too! Here it is! Also, would this be a valid method to use??? oh wait I think I understand what you've done in the working out (THANK YOU!) but I don't know if I will know when to use them ... Are there indicators to use those 'sum of roots' equations :s ? I still feel pretty blind...
« Last Edit: February 11, 2016, 09:32:53 pm by xXCandyDXx »

jakesilove

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Re: 93 in 4U Maths: Ask me Anything!
« Reply #17 on: February 11, 2016, 09:32:36 pm »
0
Thank you Jake! I think that's the same method a friend of mine used! But I don't understand it very well... I'll have to keep looking HAHA HOWEVER I have accidentally come across the same solution using a different method and I think this may benefit others too! Here it is! Also, would this be a valid method to use??? (Image removed from quote.)

Hey hey!!

That's actually a fantastic method! Definitely a valid method, and use whatever you understand more. Remember, there are always heaps of ways to solve a question.

Thanks for posting that answer though! Very beneficial to the community.

Jake
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Re: 93 in 4U Maths: Ask me Anything!
« Reply #18 on: February 11, 2016, 09:37:55 pm »
0
Thank you !!

jamonwindeyer

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Re: 93 in 4U Maths: Ask me Anything!
« Reply #19 on: February 11, 2016, 11:23:01 pm »
+2
Hey xXCandyDXx! Glad Jake could be of help!

In addition, a tip for spotting when to use the "sums of roots" formulae. Pretty much, if a question follows the following template:

Find the roots of ____________________ given that __________________

or even

The roots of ___________________ form an arithmetic series. Find the value of k (some unknown in the polynomial))

Essentially, if you are given a polynomial with something to find, and all you are given is some information about the roots, chances are that these formulae will help you. They are very powerful in surprising ways.

While I'm here, I have an issue with the method you posted above. It's very possible I am misunderstanding, but it seems like the notions of root and factor are being confused. Remember, factors can be multiplied together to get back to the original, roots are just solutions to the polynomial equal to zero.

So, in the first few lines, we multiply the roots together and then form an identity with the original polynomial. This doesn't make sense to me. We could do it with factors, but multiplying the roots of a polynomial together has no relationship with the original, besides the relationships highlighted in the formulae used by Jake's method.

The factor rule makes perfect sense. The first part of the solution however, while the correct answer is obtained, does not make as much sense to me, and I would argue that it is incorrect. I'd love to hear others interpretations on the matter!  ;D

jakesilove

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Re: 93 in 4U Maths: Ask me Anything!
« Reply #20 on: February 12, 2016, 09:36:28 am »
+2
Hey xXCandyDXx! Glad Jake could be of help!

In addition, a tip for spotting when to use the "sums of roots" formulae. Pretty much, if a question follows the following template:

Find the roots of ____________________ given that __________________

or even

The roots of ___________________ form an arithmetic series. Find the value of k (some unknown in the polynomial))

Essentially, if you are given a polynomial with something to find, and all you are given is some information about the roots, chances are that these formulae will help you. They are very powerful in surprising ways.

While I'm here, I have an issue with the method you posted above. It's very possible I am misunderstanding, but it seems like the notions of root and factor are being confused. Remember, factors can be multiplied together to get back to the original, roots are just solutions to the polynomial equal to zero.

So, in the first few lines, we multiply the roots together and then form an identity with the original polynomial. This doesn't make sense to me. We could do it with factors, but multiplying the roots of a polynomial together has no relationship with the original, besides the relationships highlighted in the formulae used by Jake's method.

The factor rule makes perfect sense. The first part of the solution however, while the correct answer is obtained, does not make as much sense to me, and I would argue that it is incorrect. I'd love to hear others interpretations on the matter!  ;D

Hey Jamon!

Thanks for clarifying when to use the sum and product formulas for Polynomial questions!

Also, I agree that her method is actually incorrect, but as luck would have it gets to the right answer. Here's why




Jake
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Re: 93 in 4U Maths: Ask me Anything!
« Reply #21 on: February 12, 2016, 11:15:56 am »
+1
Hey Jamon!

Thanks for clarifying when to use the sum and product formulas for Polynomial questions!

Also, I agree that her method is actually incorrect, but as luck would have it gets to the right answer. Here's why

(Image removed from quote.)


Jake


Jake you are such a god what an elaborative response!
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Re: 93 in 4U Maths: Ask me Anything!
« Reply #22 on: February 13, 2016, 10:22:56 pm »
+1
Please send help Almighty Jake when you are available!!! This has been screwing me over!!!  :-[




Thank you so much Jake! <3 (I dont know why the images are sideways doe...)
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xXCandyDXx

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Re: 93 in 4U Maths: Ask me Anything!
« Reply #23 on: February 13, 2016, 11:20:39 pm »
0
Sorry for the very late response!!! >~<
Thanks Jamon and Jake for clearing it up ... I guess it is luck that I got the answer this time hehe ... But YEP thank you guys! I understand a lot more about polynomials and how they work .. Kinda HAHA I'm getting there! But i totally get where you're coming from in the sense that I suddenly multiplied the roots and equated them ...( clearly I don't understand ) but yeah I was actually thinking of trying to multiply the factors together which I totally mistook ... for the roots ahh... But yeah !!! Thanks again !!! I won't be making the same mistake in the future for sure

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Re: 93 in 4U Maths: Ask me Anything!
« Reply #24 on: February 13, 2016, 11:22:01 pm »
0



Jake you are such a god what an elaborative response!
He really is a god

jakesilove

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Re: 93 in 4U Maths: Ask me Anything!
« Reply #25 on: February 14, 2016, 12:18:30 am »
+4
Please send help Almighty Jake when you are available!!! This has been screwing me over!!!  :-[

(Image removed from quote.)
(Image removed from quote.)

Thank you so much Jake! <3 (I dont know why the images are sideways doe...)
CLICK HERE TO SEE THE IMAGES/QUESTION


Hey HPL.

Typical you giving me incredibly difficult 4U maths questions at Midnight. Couldn't resist though, so this is the solution I came up with! An extremely, extremely difficult graphing question, and I definitely may have missed some components, so if anyone in the community wants to correct me please do.







Like I said, if anyone has any corrections, suggestions, or anything like that, please feel free to post below. Extension 2 is an incredibly difficult course, one that even University professors often struggle with.

Still, this is a lot of fun (to me, I know I'm a bit of a nerd) so keep posting, and keep answering questions! We're starting to build a real community, and I love watching it grow.

Yours,

Jake :)
« Last Edit: February 14, 2016, 10:13:08 am by brenden »
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jakesilove

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Re: 93 in 4U Maths: Ask me Anything!
« Reply #26 on: February 14, 2016, 12:19:46 am »
0
He really is a god

Aha thank you all, although I wouldn't go so far as to say that. My head still hurts sometimes when I try to do Extension 2 Maths questions!

Still, thanks for participating in the forums so actively! Hope to see you around here soon :)
ATAR: 99.80

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Happy Physics Land

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Re: 93 in 4U Maths: Ask me Anything!
« Reply #27 on: February 14, 2016, 12:52:26 am »
+1
Hey HPL.

Typical you giving me incredibly difficult 4U maths questions at Midnight. Couldn't resist though, so this is the solution I came up with! An extremely, extremely difficult graphing question, and I definitely may have missed some components, so if anyone in the community wants to correct me please do.

(Image removed from quote.)
(Image removed from quote.)
(Image removed from quote.)
(Image removed from quote.)
(Image removed from quote.)

Like I said, if anyone has any corrections, suggestions, or anything like that, please feel free to post below. Extension 2 is an incredibly difficult course, one that even University professors often struggle with.

Still, this is a lot of fun (to me, I know I'm a bit of a nerd) so keep posting, and keep answering questions! We're starting to build a real community, and I love watching it grow.

Yours,

Jake :)


I swear you enlighten me Jake, this is actually more than what my teacher will ever explain for me. Omg thank you sooo much Jake this must have taken you an extensive amount of time and I reallly reallly reallly reallly reallllllyyyy appreciate this. So elaborative and it just helped me to understand so much better (the difficulty of this question essentially dropped from a 10/10 to a 5.5/10, which I reckon is a huge achievement). I am just extremely grateful, thank you so much for everything you have done Jake!!!!!!!!  :D :D
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keltingmeith

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Re: 93 in 4U Maths: Ask me Anything!
« Reply #28 on: February 14, 2016, 12:52:36 am »
+5
Like I said, if anyone has any corrections, suggestions, or anything like that, please feel free to post below. Extension 2 is an incredibly difficult course, one that even University professors often struggle with.

Holy crap that was beautiful to watch. o.o I feel I have a name change coming on...

The only thing I have to add is this:
Just as Jake did, if you're ever in doubt - sub in some points, and draw lines between them. From there, it's a really good idea to pick out the "nice" points to pick out.

For example, in the case of the f(1/x) question, x=1 is easy - both functions share that point! Other easy cases include x=+/- infinity (as they go to zero) and x=0 (because that'll go to infinity). In fact, it's worth going through all the functions you know, and thinking about what the easy points are - for example, f(x)=sin(x) and f(x)=e^x. Not just for answering these types of questions, but any type of graphing question - if you ever get stuck on a graphing question, and you know some "easy" points, then you can very quickly take a guess at the graph's shape by picking some points and drawing lines between them!

(a bunch of that was really just repeating - but I felt it needed a stronger emphasis, soz Jake :P)
(also, hi from Victoria, where our maths subjects don't try to kill us~)

katherine123

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Re: 93 in 4U Maths: Ask me Anything!
« Reply #29 on: February 17, 2016, 11:28:12 pm »
0

For the poly ques how do u find the leading coefficient? I only know that there are 2 known roots
and for the trig ques  i dont know how to simplify it after implicitly differentiating

please help thank you