VCE Specialist 3/4 Question Thread!

[LiquidPaperz]

bit of a stupid question, i know. But my mate says he could answer any spesh/methods question, so could someone tell me some of the hardest questions they have come across?

Cheers

[keltingmeith]

Check any MAV or Kilbaha paper. Good examples from VCAA exams (off the top of my head) is the phone question from last year, exam 2 and the space station question from 2012, exam 2.

Any particular reason you're out to prove your mate wrong? (or am I reading that wrong? Hahah)

[LiquidPaperz]

Alright thanks. Nah were just talking n stuff, nothing serious, he brang it up so just wanna see him in "action" haha

[Valyria]

Can we use spesh techniques in methods or is that condemned by examiners?

[keltingmeith]

Can we use spesh techniques in methods or is that condemned by examiners?

I have been told that if something is mathematically correct, the examiners will still give you the marks. Having said that, it's probably best to try and stick to methods techniques wherever possible. Is there a specific situation you were referring to, for reference?

[Valyria]

I have been told that if something is mathematically correct, the examiners will still give you the marks. Having said that, it's probably best to try and stick to methods techniques wherever possible. Is there a specific situation you were referring to, for reference?

Thanks for the insight and the thought propped up when I was doing an integration problem in methods which (for me) could have been done more efficiently through integration by substitution. Plus, I'm sure there will be some situations where spesh techniques would be more efficient than their methods counter part

[nhmn0301]

Ok this question is really pissing me off because I can't get it... seems easy though.


Prove:


Can someone please work from the RHS and reach the LHS please?

The answers start from the LHS and work to the RHS, which is fine, but you should always clean up the messier side don't you? (I know you don't have to, but can someone show me how to anyway?)

I have tried to get RHS to LHS for like half an hour and still can't get it. Someone help please?

Let me know if there is any errors !

[keltingmeith]

So, remember the definition of a derivative is . Since this limit is not positive/negative specific, this means it's referring to the limit being on BOTH sides.

Now, consider the function (for a very easy example). If you tried to take the limit as x approaches zero, you can do this from the positive side, but not the negative - because there's nothing on the negative side for you to actually approach from. Because you can't take the limit from both sides, the original definition of the limit cannot be applied, and so that point is not differentiable.

Ergo, you cannot take the derivative of an endpoint.

[keltingmeith]

No, because for that specific function, there's no negative side for you to approach from, so there is no limit on both sides. For the actual relationship, yes, you could - but we're not talking about differentiating the relationship, we're talking about the function. For example:



f and g have the same relationship, but they're two completely different functions, as they're defined over different domains.

NEAP made a screw up, sorry to say. It happens, I noticed a few errors in my methods book last year with them.

[brightsky]

dA/dt = (dA/dy)*(dy/dt). we already know dy/dt from previous part. to find dA/dy, use the formula for the area of a circle A = pi(y)^2. dA/dy = 2pi*y. we need our answer in terms of x so sub in y = 6x/sqrt(1+x^3) into dA/dy = 2pi*y to obtain dA/dy in terms of x. you should be good to go now.

[tiff_tiff]

dT/dt = -k(T-8) +H, where k and H are constants T temp. t time
solve the DE to give the sol. T = B e^-kt +8+3/k, if H = 3.

I guessing B was an introduced constant, rather than the usual A? im not sure how to do this question

[rhinwarr]

A ball, just before it hits the ground, has position vector r(t)=2ti-tj+3tk. At what angle does the ball hit the ground?

The solution is:
v(t) = 2i-j+3k
|v|=sqrt(14)
cos(a)=3/(sqrt(14))
a=37
Angle = 90-37=53 degrees

Can some please explain?

[Equilibriaas]

To calculate angle of projection,  you always use the velocity vector. Hence you have differentiate first. Then since it is known that speed= |velocity|, you find the magnitude. Then we come to calculate the angle of projection, we always calculate the angle that the k component makes.(only for 3D vectors)

 Hence why it is cos a= 3/sqrt(14). This is derived from the rule
Cos theta= a.b/|a| |b|
 
Not sure if this makes sense or is correct.

[keltingmeith]

dT/dt = -k(T-8) +H, where k and H are constants T temp. t time
solve the DE to give the sol. T = B e^-kt +8+3/k, if H = 3.

I guessing B was an introduced constant, rather than the usual A? im not sure how to do this question

You're right that it's an introduced constant - so, what we're going to do, is start by flipping the equation, and from there solving as per usual:

[hyunah]

i have a probability question....
in a game,
one coin of each (5c, 10c, 20c, 50c, $1 and $2), participants are asked to guess either heads or tails for each coin tossed and if guessed correctly they win that coin. If they managae to guess correctly for all throws, they also win back the entrance fee.
WHat amount in dollars needs to be charged by organisers to break even?

options are in atachment

thank you