VCE Methods Question Thread!

[Valyria]

Can someone please explain question 1)f part i, on last years exam 2?
And for part ii) i dont understand why P is multiplied by m, since it's from the y-axis, shouldn't it be multiplied by 1/m

c= sqrt 3 + 2pi/3
X= (2pi/3,0)
P=(2pi/3,sqrt3/2)

You're intuitively thinking about a trig function where for example; y=sin(mx) the dilation factor from the y axis is actually 1/m so you'd multiply all the x coordinates by 1/m. However, as they have distinctly told you that the dilation factor is 'm' you don't need to use the reciprocal.

[Rishi97]

Could someone please help me with 2007 VCAA Exam 2 Q1 d?
I don't understand why you use the lower endpoint :/
Thank yeee

[BLACKCATT]

Sorry i don't quite get what you mean, for example
For: (x-1)^2, dilation factor of 2 units from the y-axis would be ((x/2) - 1)^2 right?

So whats the difference between this and part ii

[katiesaliba]

Can someone please help me with Q.8 from this exam: http://www.vcaa.vic.edu.au/Documents/exams/mathematics/2013/2013mmcas1-w.pdf

I understand that it involves integration by recognition, but I'm so confused by the extra X. 

[BLACKCATT]

Here you go

[paper-back]

When you are finding E(x) you add an extra x to the function
Hence, in this case we just need to rearrange the function to get

And solve as usual...

[soNasty]

what makes a cubic polynomial have no stationary points?
all i know is that if its like
y=x^3+x
then dy/dx= 3x^2+1
0=3x^2+1
but thats not possible, so no SP's for x^3+x

but is there like a general rule for cubics without SP's? (if that makes sense)

[keltingmeith]

what makes a cubic polynomial have no stationary points?
all i know is that if its like
y=x^3+x
then dy/dx= 3x^2+1
0=3x^2+1
but thats not possible, so no SP's for x^3+x

but is there like a general rule for cubics without SP's? (if that makes sense)

Consider the general cubic y=ax^3 + bx^2 + cx + d. Can you find a coordinate in terms of a, b and c such that its derivative function has zero solutions? (hint: when will a quadratic have zero solutions?)

[BLACKCATT]

Consider the general cubic y=ax^3 + bx^2 + cx + d. Can you find a coordinate in terms of a, b and c such that its derivative function has zero solutions? (hint: when will a quadratic have zero solutions?)

That was on last years MC

Can someone please explain question 1)f part i, on last years exam 2?
And for part ii) i dont understand why P is multiplied by m, since it's from the y-axis, shouldn't it be multiplied by 1/m

c= sqrt 3 + 2pi/3
X= (2pi/3,0)
P=(2pi/3,sqrt3/2)

Halp pls

[chocolatechipcookies]

Function g(x) is defined as
g(x)=abs(x-pi)+sin(x)-(pi/2)
The average value of g in the interval [2pi/3, 4pi/3] is closest to:

So did 1/((4pi-3)-(2pi/3) times the integral of g(x) between 2pi/3 and 4pi/3 and I got -pi/3 (I did this on calculator)

But when I looked at the answer, they did it as:
the integral of g(x) between 2pi/3 and 4pi/3
divided by
4pi/3-2pi/3

and the answer became -1.04

??

[soNasty]

Consider the general cubic y=ax^3 + bx^2 + cx + d. Can you find a coordinate in terms of a, b and c such that its derivative function has zero solutions? (hint: when will a quadratic have zero solutions?)

it will have no solutions when its discriminant is less than zero
so 4b^2-12ac<0?

[keltingmeith]

it will have no solutions when its discriminant is less than zero
so 4b^2-12c<0?

Very close - you've lost an a, and can divide by 4 (just cleaning purposes). Otherwise, you're right! So, if the inequality b^2<3ac holds true, the cubic will have no stationary points.

[soNasty]

oh cool! Alright - well that's going in my summary book

[Valyria]

Sorry i don't quite get what you mean, for example
For: (x-1)^2, dilation factor of 2 units from the y-axis would be ((x/2) - 1)^2 right?

So whats the difference between this and part ii

In short, a dilation from the y axis is where the x coordinates of the graph change. When we say, "dilation by a factor of 2 from the y axis" we would 'stretch' the graph by multiplying all the x coordinates by 2. So when we transform a function through a dilation from the y axis, we use f(1/k) where k is the dilation factor.

Your example is right and so you're multiplying the x coordinates by 2 not 1/2, it's only for the sake of the function that the dilation appears as 1/2. So for your question, a dilation from the y axis by 'm' will result in the x coordinates being multiplied by m not 1/m.

[keltingmeith]

That was on last years MC

Hahah, serious? Don't remember it at all... Granted, I also don't remember the exam 2 being difficult because exam 1 was the crap one, and everybody keeps telling me otherwise, so.