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VCE Specialist 3/4 Question Thread!

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TrueTears:
VCE SPECIALIST MATHS Q&A THREAD
To go straight to posts from 2020, click here.
What is this thread for?
If you have general questions about the VCE Specialist Maths course or how to improve in certain areas, this is the place to ask!


Who can/will answer questions?
Everyone is welcome to contribute; even if you're unsure of yourself, providing different perspectives is incredibly valuable.

Please don't be dissuaded by the fact that you haven't finished Year 12, or didn't score as highly as others, or your advice contradicts something else you've seen on this thread, or whatever; none of this disqualifies you from helping others. And if you're worried you do have some sort of misconception, put it out there and someone else can clarify and modify your understanding! 

There'll be a whole bunch of other high-scoring students with their own wealths of wisdom to share with you, including TuteSmart tutors! So you may even get multiple answers from different people offering their insights - very cool.


To ask a question or make a post, you will first need an ATAR Notes account. You probably already have one, but if you don't, it takes about four seconds to sign up - and completely free!

OTHER SPESH RESOURCESCLICK ME!* How I Got a 50 Raw in Specialist Maths
* Specialist 1/2 Question Thread
* Guide to Using the TI-Nspire for SPECIALIST
* All you need to know about inequalities!
* General solutions to circular functions
* Trinon's Guide to Sketching Trig Graphs
* Trinon's Guide to Anti-derivatives through derivatives
* Techniques for Sketching Nice-Looking Graphs
* Vector Proofs
* Volumes of Solids of Revolutions: How-To
Original post.similar to the methods one Methods [3/4] Summer Holidays Question Thread! post away your questions from your summer holidays self-studying, everyone can discuss and benefit! I'll try answer as much questions as possible too ^^

Special At Specialist:
Let w = 2cis(θ) and z = w + 1/w
Show that z lies on the ellipse with equation (x^2)/25 + (y^2)/9 = 1/4

brightsky:
z = w + 1/w = 2cist + 1/(2cist) = 2cist + 1/(2(cost + isint)) = 2cist + (cost - i sint)/(2) = 5/2 cost + 3/2 i sint
parameters:
x = 5/2cost
y =3/2 sint
convert into cartesian form and you get the equation of the ellipse.

brightsky:
what do you mean by complicated derivatives? the method of 'antideriving through derivatives' is called integration by recognition, which is just a more abstract form of integration by parts. not sure if this answers your question, but try wikipedia-ing integration by parts.

Special At Specialist:

--- Quote from: abd123 on November 27, 2011, 08:29:28 pm ---sorry for hijacking this thread.

heys you know the spesh derivatives that are complicated, it can done be through 'anitderiving through derivatives right'?
is it true that it is possible to antiderive through complicated derivatives? is it way of vce level?

if its possible can any of you guys show me an example of it?

--- End quote ---

I'm not sure what you mean by anti-deriving through derivatives...
Perhaps you mean is it possible to find an anti-derivative when given a similar derivative? If that's your question, then the answer is yes. Here is an example:

Given that dy/dx = cos(2x), d/dx (sin(2x)) = 2cos(2x) and that x = pi/4 when y = 5, solve for y.
So first you convert the integral of cos(2x) into 1/2 * Integral of 2cos(2x)
Then you use the information they gave you to say:
1/2 * Integral of 2cos(2x) = 1/2 * sin(2x) + C
Now you use the initial conditions to solve for C:
y = 1/2 * sin(2x) + C
5 = 1/2 * sin(pi/2) + C
5 = 1/2 * 1 + C
C = 5 - 1/2
C = 9/2
y = 1/2 * sin(2x) + 9/2

That is called a "differential equation" if you're interested.
I hope this answers your question.


--- Quote from: brightsky on November 27, 2011, 08:47:43 pm ---what do you mean by complicated derivatives? the method of 'antideriving through derivatives' is called integration by recognition, which is just a more abstract form of integration by parts. not sure if this answers your question, but try wikipedia-ing integration by parts.

--- End quote ---

Ye know too much for a year 10 student!

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