Bazza's 3/4 Question Thread

[BubbleWrapMan]

I don't know how, but I don't think you need to know how either. They'll give you ones you can do by hand.

Also, I used sin^-1 during the year but I use arcsin these days. VCAA would accept both of those.

[WhoTookMyUsername]

ahk thanks,
yeah solving parametric by CAS is not necessary,
but especially for MC it can help a little bit.
I think in previous OS it was a little "glitch" that solving for "t" actually eliminated t from the equation
but that was a helpful glitch!
and there seems to be no way of solving for parametric ATM

[WhoTookMyUsername]

Should wind force be labelled as a "pushing force" or a "pulling force :S" ?
thanks (also anyone know how to find parametric equation with CAS xD)

[meemz]

Should wind force be labelled as a "pushing force" or a "pulling force :S" ?
thanks (also anyone know how to find parametric equation with CAS xD)

depends
lets say a plane is travelling east, and the wind is travelling in the east direction, then it'll be a pushing force
and if the plane is travelling west and the wind in the east, then it'll a pulling force

[WhoTookMyUsername]

http://www.vcaa.vic.edu.au/Documents/exams/mathematics/2006specmath1-w.pdf

For this exam
Q 4a)
i labelled wind as a "pushing force" (on the other side) but not sure if it's correct :S or whether they'd accept both, vcaa had it as a pulling force

[BubbleWrapMan]

Just call it wind force, you can't go wrong with that, as long as you get the direction of it right as well.

[WhoTookMyUsername]

nah it's not about the name, it's about the placement of the arrow
i drew the arrow pointing "towards" the center from the left hand side
whereas the solutions drew it going from the centre to the "right."

I think my placement may be wrong because i think force arrows are supposed to be drawn with their tail on the object being acted on?
not 100% sure someone please help
(http://www.vcaa.vic.edu.au/Documents/exams/mathematics/2006specmath1-w.pdf

For this exam
Q 4a)
i labelled wind as a "pushing force" (on the other side) but not sure if it's correct :S or whether they'd accept both, vcaa had it as a pulling force)
(i.e.should a "pushing force" be labelled in the same way as a "pulling force" with the tail at the center of the object? is it technically incorrect to have the tail of the arrow not touching the object but only the head of the arrow touching :S?)


2)http://www.vcaa.vic.edu.au/Documents/exams/mathematics/2006specmaths2-w.pdf
Q 4cii)
For verifying a stationary point of inflection; how would you go about doing that when you have the double derivative in terms of Y only?
Can you still just go above and below and show it changes sign? Or do you have to make some kind of qualitative statement linking y to x or to dy/dx as well D:
Not sure what's going on here lol

Thanks!

[BubbleWrapMan]

Oh I see what you mean now, sorry. Putting the force in front of the plane is fine IMO, but now that you know that they do it like that, just put it behind the plane, if you get what I'm saying.

For the calculus question, you only need to show that the second derivative changes sign at that point.

[WhoTookMyUsername]

Thanks

Are we allowed to resolve force on a diagram for the purposes of working out for a following question?
My 1/2 teacher said they don't like resolution of forces drawn on a force diagram but im not sure
Thanks!

[BubbleWrapMan]

Would be fine if you draw the components as dotted lines, because if you draw the components and the vector itself as solid you're kind of doubling up on vectors. And only drawing the components is not such a good idea, because it doesn't make it 100% clear where you got them from.

[WhoTookMyUsername]

ahk thanks

Last question spurt most likely... ever !
1) Do we need to label POI for inverse cos etc. on graphs?
2) Anyway to convert an equation to hyperbolic form on CAS?
3) If the answer doesn't specify to give a numerical / approximate answer do we always leave the answer in terms of g?
4) For something like a=t^2 + t - 10 where a can only be positive or negative, should we indicate a as a vector (with tilde) or without tilde?
5) for a point on an argand plane should we put a "dotted line" to the origin?
6) where should friction be drawn from? the point of contact or the "centre" of the object?
7) Can you have a conjugate pair when the coefficients ARE NOT all real by coincidence?
Or does a conjugate pair for complex numbers imply that coefficients are definitely all real?
Anyway to graph complex numbers on cas? (not cartesian)
9) For volume of revolution do we have to account for intercepts? (my gut instinct was yes, but after playing around with x^2 - 4
S(0,2) + S(2,4) = S(0,4) (terminals for piSy^2 dx where S is integral symbol) so i'm not sure

thanks very much! Sorry for some questions which i know are slightly tedious :\

[BubbleWrapMan]

1) No.
2) What's hyperbolic form?
3) They usually say to take g to be 9.8 m/s^2 in the exam instructions.
4) If quantities like that are in one dimension you don't need the tilde.
5) No need.
6) Doesn't matter.
7) Only if there are other complex roots. If they are all in pairs then you always get real coefficients.



8 ) Not that I know of.
9) I don't think so? Are you saying that the sum of the integrals is not equal to the integral over the whole interval? Because it should be.

[Jenny_2108]

2) What's hyperbolic form?

Hyperbolic forms like sinh, cosh, tanh
Sometimes the CAS gives ans like that and we need to know how to convert it

2) Anyway to convert an equation to hyperbolic form on CAS?

I don't think so. CAS just gives this form
Maybe you can derive from CAS as

[WhoTookMyUsername]

thanks !
nah lol by hyperbolic i meant the "form of a hyperbola," although hyperbolic is technically quite incorrect xD
(not sure if cas can get into into form of a hyperbola form)

With 3) Would we lose a mark if it's in terms of g?
(e.g. obviously for tech free if we leave in terms of g less chance of making a mistake)
With 5) Would we lose a mark if we put the tilde?
With 9) As in, when you're doing area under the graph (or between graph and x axis) over a given interval, you have to split it up when you have intercepts over that region, do you have to do the same for volumes of revolution?

additionally (another tedious question)
10) how would you refer to a "region" of the x axis? Like, over the ... period (2,10) there are no x intercepts?
Over the ... region (2,10) there are no x intercepts? (if the domain is greater than (2,10)

Thanks a lot !

[BubbleWrapMan]

3) No
5) Maybe, just don't do it
9) No you don't, volumes don't come out as negative when you use that formula.
10) I'd call it an interval. "There are no x-intercepts in the interval (2,10)." 'Region' usually refers to an area, and 'period' refers to the period of a function like circular functions.