VCE Methods Question Thread!

[kinslayer]

Thanks Monsieur Kebab and b^3

The horizontal translation was: E=

I substituted in the other 2 sets of points and I got the following:

But why can't we use ?

If you think about it, you can shift the graph left or right by any multiple of its period (3pi) and you will get the same graph. So apart from pi, -2pi and 4pi also work (for example).

The -pi/2 and 5pi/2 etc. are equivalent to shifting half periods, which means that the zeroes of y + 4 will coincide but otherwise it just goes in the other direction.

Check out 's link again and play around with the parameter a and it should be clearer:

https://www.desmos.com/calculator/ax0x0gvtrd

[Outclass]

How do i solve this? :|

log(base e)(x+2) = x

Cheers

[Zealous]

How do i solve this? :|

log(base e)(x+2) = x

Cheers

I believe that's a transcendental equation. We can't actually solve this algebraically but rather only find approximations for a solution

[Jason12]

I don't understand chapter 7D about functional equations could someone give a few tips how to approach them.

For f (x) = 2x + 3, show that f (x + y) can be written in the form f (x) + f (y) + a and
give the value of a.

For the function with rule f (x) = 1/x^2 , show that f (x) + f (y) = (x^2 + y^2) f(xy)

[Phy124]

f(x) = 2x + 3
f(y) = 2y + 3
f(x+y) = 2(x+y) + 3 = 2x + 2y + 3 = (2x + 3) + (2y + 3) - 3 = f(x) + f(y) - 3
=> a = -3

f(x) = 1/x^2
f(y) = 1/y^2
f(xy) = 1/(xy)^2 = 1/(x^2y^2)
f(x) + f(y) = 1/x^2 + 1/y^2 = (y^2 + x^2)/(x^2y^2) = (x^2 + y^2)*1/(x^2y^2) = (x^2 + y^2)f(xy)

[paper-back]

If you think about it, you can shift the graph left or right by any multiple of its period (3pi) and you will get the same graph. So apart from pi, -2pi and 4pi also work (for example).

The -pi/2 and 5pi/2 etc. are equivalent to shifting half periods, which means that the zeroes of y + 4 will coincide but otherwise it just goes in the other direction.

Check out 's link again and play around with the parameter a and it should be clearer:

https://www.desmos.com/calculator/ax0x0gvtrd

Thanks kinslayer

[soNasty]

could someone tell me if i'm right please lol,

for the graph, instead of the right-hand end point shown, i had 2pi, -5/2

can someone please confirm? if not, tell me where i went wrong

[paper-back]

could someone tell me if i'm right please lol,

for the graph, instead of the right-hand end point shown, i had 2pi, -5/2

can someone please confirm? if not, tell me where i went wrong

1) Expand brackets
2) Substitute in 2 and solve



Hope this helps

[soNasty]

thanks paperback, i mixed up the values lol.

also this question is annoying me..

find the x intercepts of f(x)=-2cos(2x-pi/3)+1 over [-2pi,2pi]

the domain i had was [-13pi/3,11pi/3].. im getting too many answers

[keltingmeith]

It looks like you do have the right domain for , so how about we predict how many answers you should have, to see if that puts your mind at rest?

For the equation , there should be four answers across . If we multiply this angle by 2, this means that we have twice as many periods. Therefore, our number of answers should be doubled, so we are expecting eight answers.

Since our original domain is across 2 periods exactly, changing the horizontal translation shouldn't affect the number of answers we expect to see. So if you have eight answers, even though it seems like a lot, this is what we would expect to see.

[alchemy]

thanks paperback, i mixed up the values lol.

also this question is annoying me..

find the x intercepts of f(x)=-2cos(2x-pi/3)+1 over [-2pi,2pi]

the domain i had was [-13pi/3,11pi/3].. im getting too many answers

When cos(x) = y:
x = ± cos^-1(y)+ (2k*pi) .
2x - pi/3= ± pi/3+(2k*pi)
2x=2pi/3+(2k*pi) or 2x=2k*pi
x=pi/3+(k*pi) or x=kpi
Now sub in values for k in the equation (x=pi/3+(k*pi)) and check if they fit in your given domain [-2pi,2pi]
k=-3:-8pi/3 which is smaller than -2pi so don't consider this
k=-2:-5pi/3
k=-1:x=-2pi/3
k=0: x=pi/3
k=1:x=4pi/3
k=2:x=7pi/3 which is greater than 2pi so don't consider this.
Now sub in values for k in the equation (x=k*pi) and check if they fit in your given domain [-2pi,2pi]
k=-2:x=-2pi
k=-1;x=-pi
k=0: x=0
k=1: x=pi
k=2: x=2pi
So the solutions are: x=-2pi,-5pi/3,-pi,-2pi/3,0,pi/3,pi,4pi/3,2pi.

See here: https://www.desmos.com/calculator/nckxfxyelg

[juzza12]

Hey Guys! Really quick not exactly a methods specific question but does anyone know that for questions such as : "For f(x) Prove at x=3 there is a local maximum point/stationary point of inflection?" you would be allowed to use the second derivative to prove that this or would you only gain marks for a sign table? My own specialist and methods teacher says you can use anything you learn in specialist in methods, but I'm not sure she's correct, just wondering for the exam if examiners of methods would accept this!? Any help would be greatly appreciated

[Alwin]

Hey Guys! Really quick not exactly a methods specific question but does anyone know that for questions such as : "For f(x) Prove at x=3 there is a local maximum point/stationary point of inflection?" you would be allowed to use the second derivative to prove that this or would you only gain marks for a sign table? My own specialist and methods teacher says it is allowed but just wondering for the exam if examiners of methods would accept this!? Any help would be greatly appreciated

Hey

This seems comes up every year and the general reply (from a variety of schools and sources) is that yes, you are allowed to use second derivatives because it demonstrates your understanding BUT if the question stipulates that you must use sign table to prove a max/min/poi then you must use a sign table

edit: Oh, and remember that you need to specify values of f'(x) rather than just saying f(1) > 0, its something that my teachers always stipulated we must do. And someone correct me if I'm wrong, but in one Methods vcaa agesss ago they said second derivative was an accepted method

[juzza12]

Hey

This seems comes up every year and the general reply (from a variety of schools and sources) is that yes, you are allowed to use second derivatives because it demonstrates your understanding BUT if the question stipulates that you must use sign table to prove a max/min/poi then you must use a sign table

Thanks for the quick reply Alwin really appreciate it!  xoxoxoxox

[M_BONG]

Ok here's a question I need help with.....


Can anyone help pls!!!!!! I won't get any sleep tonight if I don't get this tbh -.-

"A massive conical vat, 10 metres in height, is filled to its capacity of 120pi cubic metres of pure glacier water

A massive crane raises the conical vat above an empty swimming pool at an exclusive resort. (diagram of swimming pool provided) in attachment

The glacier water is siphoned into the swimming pool.

If the water level in the conical vat decreases at a constant rate of 1 meter per second, at what level does the water in the swimming pool rise at the point in time when the water level in the vat is 6 metres deep?"

Final answer: 0.39m/s

Srs spent 2 hours on this and still can't figure it out... Our teacher is really, really sadistic...


EDIT: Photo cut off; it's 2m (the cut-off part)

Thanks!

Also, this is the only diagram the question provided, if you were wondering..