VCE Methods Question Thread!

[paper-back]

I find drawing Mini Venn-diagrams on the side of the page useful when doing these sorts of questions
E.g.
Lets say we were given

And we needed to find

I'd draw a Venn diagram, shade in Pr(A), then on another shade in Pr(A∩B')
From this we can deduce that Pr(A∩B) can be found by Pr(A)-Pr(A∩B')
Therefore,
0.7-0.5
And Pr(A∩B)=0.2

EDIT:
For your question we have

If we draw a small Venn diagram, We can see that Pr(A'∩B) encompasses the right-side circle of the Venn diagram excluding the Pr(A∩B)
Hence we can say that Pr(A'∩B)+(A∩B)=Pr(B)


Edit: Thanks

[TrebleClef]

I find drawing Mini Venn-diagrams on the side of the page useful when doing these sorts of questions
E.g.
Lets say we we're given

And we needed to find

I'd draw a Venn diagram, shade in Pr(A), then on another shade in Pr(A∩B')
From this we can deduce that Pr(A∩B) can be found by Pr(A)-Pr(A∩B')
Therefore,
0.7-0.5
And Pr(A∩B)=0.2

(Image removed from quote.)

EDIT:
For your question we have

If we draw a small Venn diagram, We can see that Pr(A'∩B) encompasses the right-side circle of the Venn diagram excluding the Pr(A∩B)
Hence we can say that Pr(A'∩B)+(A∩B)=Pr(B)


By the way, how do you make images smaller?

Thank you so much!
I added them as attachments using the "+" under the text box.

[myanacondadont]

Alright I got a questions. 1: How do you find the period of
 

[psyxwar]

Alright I got a questions. 1: How do you find the period of
 

Graph it and see when it repeats itself. You can do this pretty easily just by solving it for 0 and comparing the solutions you get to the graph

[Sayf44]

|x| = sqrt(x^2)

=> d/dx (|x|) = 1/2(x^2)^-1/2 * (2x) = x/sqrt(x^2) = x/|x| = sign (x) = |x|/x

All this means is that if x<0 then dy/dx=-1 and if x>0 then dy/dx=1 (i.e. the derivative takes on the sign of x (+ or -)) and this is something the hybrid function tells you anyway. I'd personally just do a hybrid function.

Ohhh thanks. I prefer this approach though. I really dislike the hybrid functions.

[knightrider]

When referring to transformations

When they say

Translation of 2 parallel to x axis and
Translation of 2 parallel to y axis

Which one is referring to vertical translation and which one refers to horizontal translation  and why?

Thanks

[speedy]

When referring to transformations

When they say

Translation of 2 parallel to x axis and
Translation of 2 parallel to y axis

Which one is referring to vertical translation and which one refers to horizontal translation  and why?

Thanks

From = 'away from'
Parallel to = 'along'

Therefore parallel to the x-axis is along the x-axis is thus horizontal.
Parallel to y-axis is along the y-axis is thus vertical.

'From' is simply the opposite

[knightrider]

From = 'away from'
Parallel to = 'along'

Therefore parallel to the x-axis is along the x-axis is thus horizontal.
Parallel to y-axis is along the y-axis is thus vertical.

'From' is simply the opposite

Thanks speedy

Does that mean when they say from x-axis it is along y axis so vertical translation
Also when they say from y-axis it is along the x-axis so horizontal translation

Are these statements right?

[myanacondadont]

Thanks speedy

Does that mean when they say from x-axis it is along y axis so vertical translation
Also when they say from y-axis it is along the x-axis so horizontal translation

Are these statements right?

Yes that's correct. Everytime they give me "from x" I instantly recognize it means "parallel to y" and vice versa - it helps a lot for me personally, to articulate it anyway.

[knightrider]

Yes that's correct. Everytime they give me "from x" I instantly recognize it means "parallel to y" and vice versa - it helps a lot for me personally, to articulate it anyway.

Thanks myanacondadont

Just wondering where in the methods textbook do they actually teach you this

[keltingmeith]

Thanks myanacondadont

Just wondering where in the methods textbook do they actually teach you this

There are a few different methods textbooks, you should clarify which one you use.

[knightrider]

There are a few different methods textbooks, you should clarify which one you use.

I use essentials and maths quest

[GeniDoi]

VCAA 2009 Exam 2 question 1e ii)

Why does the left part of h(x) (x < 0) exist, since f(x) isn't defined for x < 0?

[faredcarsking123]

VCAA 2009 Exam 2 question 1e ii)

Why does the left part of h(x) (x < 0) exist, since f(x) isn't defined for x < 0?

(Image removed from quote.)

It is defined for x < 0, just not for x=0 as x is the denominator.

[lzxnl]

It is defined for x < 0, just not for x=0 as x is the denominator.

Be careful of using that logic. The function f(x) = e^(-1/(x^2)) when x isn't 0 and f(x) = 0 when x = 0 is continuous everywhere on the real numbers. Furthermore, it is infinitely differentiable, despite there being a zero in the denominator of the argument of the exponential.

Similarly, y = sin x/x when x isn't 0 and 1 when x = 0 is also infinitely differentiable across the real numbers, even though if you sub in x = 0, you get 0/0. Your reasoning may work for VCE, but not in higher level maths.

A more appropriate way to say why it doesn't exist is because there is no unique tangent at x = 0. It's pointy there so you can't define a tangent.