Login

Welcome, Guest. Please login or register.

March 29, 2024, 12:45:07 am

Author Topic: VCE Methods Question Thread!  (Read 4802400 times)  Share 

0 Members and 15 Guests are viewing this topic.

Geoo

  • MOTM: DEC 19
  • Victorian Moderator
  • Forum Leader
  • *****
  • Posts: 596
  • Class of 2020
  • Respect: +685
Re: VCE Methods Question Thread!
« Reply #18540 on: May 23, 2020, 10:19:49 pm »
0
I use a CASIO class pad and I need to find more solutions, except my calculator will only offer me three. (its says warning there are more solutions)

Is there anyway I can access more solutions?

Thanks
2020: VCE 93.2
2022: BSci/Arts (Chemistry/Pharmacology and French)@Monash

Geoo

  • MOTM: DEC 19
  • Victorian Moderator
  • Forum Leader
  • *****
  • Posts: 596
  • Class of 2020
  • Respect: +685
Re: VCE Methods Question Thread!
« Reply #18541 on: May 25, 2020, 10:12:06 pm »
0
So I have been asked to describe the differentiability of a function, how would I say this without saying "you get a derivative?"
2020: VCE 93.2
2022: BSci/Arts (Chemistry/Pharmacology and French)@Monash

eloisegrace

  • MOTM: April 20
  • Forum Obsessive
  • ***
  • Posts: 288
  • she/her ~ class of 2021
  • Respect: +264
Re: VCE Methods Question Thread!
« Reply #18542 on: May 25, 2020, 10:46:06 pm »
+1
So I have been asked to describe the differentiability of a function, how would I say this without saying "you get a derivative?"

I would say where the function is and isn't differentiable, which is usually spots of discontinuity and end points.
2020 - mathematical methods [42] | further mathematics [45]
2021 - english language [45] | chemistry [36] | french [33] | physical education [44]
ATAR - 98.75
my vce journey !
2022 - bachelor of commerce and bachelor of politics, philosophy and economics @ the australian national university

ArtyDreams

  • MOTM: Jan 20
  • Victorian Moderator
  • Forum Leader
  • *****
  • Posts: 518
  • Fly against the wind. Not with it.
  • Respect: +599
Re: VCE Methods Question Thread!
« Reply #18543 on: May 26, 2020, 05:57:40 pm »
+2
Hi! I'll start you off on this question as I dont have time to type out a full answer, but please call out if you need more help!

For the first question, essentially it has given you an equation in terms of cosh(x)
It is also telling you the equivalent of cosh(x), which is given to you in the exponential form.
As this question is asking you to write cosh(x) in terms of the exponential form, you essentially need to sub in (e^x + e^-2)/2 wherever you see cosh(x) in the original equation. (similar to the way you'd figure out a composite function....)

So this is your first equation: 4(3-cosh(x/5))
But you know that cosh(x) also equals (e^x + e^-2)/2.

So if you sub the second equation into the first, you essentially write 4(3-(e^x/5+x^-x/5)/2)
(sorry if this doesnt make sense, I don't yet know how to write maths eqs into this!

Then if this is a TA question you can use CAS to draw the graph and find the derivative, but you could find the derivative by hand by using the quotient rule or something similar.

I really hope this made sense! I'm not very good at explaining things  :D
Let me know if anything needs clarification, and I'll try draw up a better solution.

colline

  • MOTM: NOV 19
  • Forum Obsessive
  • ***
  • Posts: 341
  • ♡ 2 Timothy 1:7 ♡
  • Respect: +512
Re: VCE Methods Question Thread!
« Reply #18544 on: May 26, 2020, 06:03:29 pm »
+4
Hi guys,

So ive been given this application question as revision for our upcoming SAC, and i'm complelely clueless. Could someone please show me worked solutions for these questions. The file seems to be too big so ive attached the question over two posts.

Thanks so much in advance

What parts are you confused by?

I'll give you a clue for the first question. Cosh(x) isn't on the methods study design, but since you're given the exponential form, you can sub x/5 into where x is for Q1.

edit - beaten by Arty ^-^

VCE: Literature [50] Methods [50] Further [48] Chemistry [40] Biology [33]
2022: Bachelor of Science (Mathematical Economics) @ ANU

Geoo

  • MOTM: DEC 19
  • Victorian Moderator
  • Forum Leader
  • *****
  • Posts: 596
  • Class of 2020
  • Respect: +685
Re: VCE Methods Question Thread!
« Reply #18545 on: May 26, 2020, 06:23:24 pm »
0
Wait a minute, this is the exact question I have for on of my application assignment.

I ended up with h(x)= 4[3-cos(e^x-e^-x/10)]+5/2.

Why does Cos end up getting removed?
Edit, mine has the slight difference of have a vertical translation of 5/2
« Last Edit: May 26, 2020, 06:28:49 pm by Geoo »
2020: VCE 93.2
2022: BSci/Arts (Chemistry/Pharmacology and French)@Monash

ArtyDreams

  • MOTM: Jan 20
  • Victorian Moderator
  • Forum Leader
  • *****
  • Posts: 518
  • Fly against the wind. Not with it.
  • Respect: +599
Re: VCE Methods Question Thread!
« Reply #18546 on: May 26, 2020, 06:34:46 pm »
+2
Wait a minute, this is the exact question I have for on of my application assignment.

I ended up with h(x)= 4[3-cos(e^x-e^-x/10)]+5/2.

Why does Cos end up getting removed?
Edit, mine has the slight difference of have a vertical translation of 5/2

So if cosh(x) = (e^x+e^-x)/2
Then say for example, the question asks you to replace cosh(x/2) with the exponential form, you get:
cosh(x/2) = (e^x/2+e^-x/2)/2

The cosh completely gets removed, because that equation in exponential form is the exact same as cosh(x) (play around with it on desmos or a similar graphing software, it'll help visualise it more clearly!), you can directly substitute the exponential equation in replacement of cosh(x), thus cancelling it out completely.

Hope this made sense!

ArtyDreams

  • MOTM: Jan 20
  • Victorian Moderator
  • Forum Leader
  • *****
  • Posts: 518
  • Fly against the wind. Not with it.
  • Respect: +599
Re: VCE Methods Question Thread!
« Reply #18547 on: May 26, 2020, 07:01:41 pm »
+1
What is the derivative in part b attached? Would it be h(x) = -4sinh(x/5)/5? However, since it says in terms of exponential functions in factorized form do i need to change sinh(x/5) to something else and if so what?

Thanks so much!

Yes the expansion is correct. You need to find the derivative with the new function, the one with e^x. That is the derivative in exponential form, and make sure it is fully simplified in factorised form.

colline

  • MOTM: NOV 19
  • Forum Obsessive
  • ***
  • Posts: 341
  • ♡ 2 Timothy 1:7 ♡
  • Respect: +512
Re: VCE Methods Question Thread!
« Reply #18548 on: May 26, 2020, 07:06:39 pm »
+4
What is the derivative in part b attached? Would it be h(x) = -4sinh(x/5)/5? However, since it says in terms of exponential functions in factorized form do i need to change sinh(x/5) to something else and if so what?

Thanks so much!

Your working out is correct. But I'm not sure if you'd be allowed to leave your answer as h(x)=-4sinh(x/5)/5 since it's not on the study design. Instead, use the rule for deriving e --> for example, the derivative of e^(x/2) is (1/2)*e^(x/2).

Wait a minute, this is the exact question I have for on of my application assignment.

I ended up with h(x)= 4[3-cos(e^x-e^-x/10)]+5/2.

Why does Cos end up getting removed?

Arty explained it perfectly already, but another way to think about it is, for example, if you have an equation that says g(x)=2*f(x) and you know f(x)=3x, you can write g(x) as 2*(3x), you wouldn't write 2*f(3x). Hope that makes sense. ^-^

VCE: Literature [50] Methods [50] Further [48] Chemistry [40] Biology [33]
2022: Bachelor of Science (Mathematical Economics) @ ANU

colline

  • MOTM: NOV 19
  • Forum Obsessive
  • ***
  • Posts: 341
  • ♡ 2 Timothy 1:7 ♡
  • Respect: +512
Re: VCE Methods Question Thread!
« Reply #18549 on: May 26, 2020, 07:13:47 pm »
+1
Thank you! Would the derivative be the first or second one out of the ones attached?
I reckon the second one (but factorised), since sinh(x) is not on the study design. :)

VCE: Literature [50] Methods [50] Further [48] Chemistry [40] Biology [33]
2022: Bachelor of Science (Mathematical Economics) @ ANU

Geoo

  • MOTM: DEC 19
  • Victorian Moderator
  • Forum Leader
  • *****
  • Posts: 596
  • Class of 2020
  • Respect: +685
Re: VCE Methods Question Thread!
« Reply #18550 on: May 26, 2020, 07:16:33 pm »
+1
So if cosh(x) = (e^x+e^-x)/2
Then say for example, the question asks you to replace cosh(x/2) with the exponential form, you get:
cosh(x/2) = (e^x/2+e^-x/2)/2

The cosh completely gets removed, because that equation in exponential form is the exact same as cosh(x) (play around with it on desmos or a similar graphing software, it'll help visualise it more clearly!), you can directly substitute the exponential equation in replacement of cosh(x), thus cancelling it out completely.
Hope this made sense!
Yes that makes sense thank you so much!
Arty explained it perfectly already, but another way to think about it is, for example, if you have an equation that says g(x)=2*f(x) and you know f(x)=3x, you can write g(x) as 2*(3x), you wouldn't write 2*f(3x). Hope that makes sense. ^-^
That's a great way to think about it. You guys not only saved me 9 marks, but I have know learnt something, so thank you!
2020: VCE 93.2
2022: BSci/Arts (Chemistry/Pharmacology and French)@Monash

colline

  • MOTM: NOV 19
  • Forum Obsessive
  • ***
  • Posts: 341
  • ♡ 2 Timothy 1:7 ♡
  • Respect: +512
Re: VCE Methods Question Thread!
« Reply #18551 on: May 26, 2020, 07:50:07 pm »
+1
Thanks so much! Sorry last thing, to factor that all i had to do is take out the 2/5 and put the rest in brackets?
Yeah, I don't think you can factorise anything else.

VCE: Literature [50] Methods [50] Further [48] Chemistry [40] Biology [33]
2022: Bachelor of Science (Mathematical Economics) @ ANU

Azila2004

  • Trailblazer
  • *
  • Posts: 32
  • Respect: 0
Re: VCE Methods Question Thread!
« Reply #18552 on: May 26, 2020, 10:13:11 pm »
0
Hellooo!

Hope you guys are well. I have a question on circular functions: A circle passes through the origin and has the equation x^2+y^2+bx+cy=0. It also passes through (4,4). For what value of b does the circle touch the y-axis?

I seriously need to work on circular functions lol.
Just someone who likes to learn a lot of questions.

Aspiring medical practitioner! ʕ•́ᴥ•̀ʔっ


2021: Biology, Psychology
2022: Mathematical Methods, Specialist Maths, English Language and Chemistry (We'll see!)

whys

  • VIC MVP - 2020
  • Forum Leader
  • ****
  • Posts: 722
  • Respect: +916
Re: VCE Methods Question Thread!
« Reply #18553 on: May 26, 2020, 10:35:24 pm »
+3
Hellooo!

Hope you guys are well. I have a question on circular functions: A circle passes through the origin and has the equation x^2+y^2+bx+cy=0. It also passes through (4,4). For what value of b does the circle touch the y-axis?

I seriously need to work on circular functions lol.
A successive list of hints: (try to do it yourself with as few hints as possible)
Spoiler
sub in (4,4) into the equation and see what you get.
Spoiler
rearrange the equation you got for c in terms of b.
Spoiler
sub this into the original equation.
Spoiler
to find where it touches the y-axis, let x = 0
Spoiler
your answer should be -2 (the equation has two y-ints: (0,0) and (0,-2)
psych [50] bio [50]
2021-2025: BMedSci/MD @ Monash

Trent2002

  • Fresh Poster
  • *
  • Posts: 1
  • Respect: 0
Re: VCE Methods Question Thread!
« Reply #18554 on: May 27, 2020, 03:02:43 pm »
0
Hello All,

Could someone please show how you work out the attached questions (I'll be sooo grateful). If it helps to find the answers, the area of the window is 44/3 m^2 and the perimeter is 4.59+3+3+4 = 14.59m (im pretty sure this is correct). I'm mostly unsure about the first question and i believe the second question is found be just doing 44/3 x 855.60 (is this still correct?).

Thank-you!
« Last Edit: May 27, 2020, 03:05:35 pm by Trent2002 »