BEC'S methods questions

[/0]

has the same roots as .
So if you transform to and you want a cubic polynomial which has the same roots as , simply transform using the same transformations. Since there aren't any transformations in the y-direction, the max and min values will remain the same as with g.

[bec]

Oh! Thanks - that's so much simpler than I thought. I was wondering why it was only a 2-mark question, I have a page of working in front of my for this...

[bec]

What am I doing wrong?
4

0

          4                        4

          0                        0
 
                       4        4

                       0        0




...but it's meant to be 12, isn't it?

[danieltennis]

(Image removed from quote.)

How?? I don't understand how you could do it "hence" and my efforts at "otherwise" finding the solution weren't very successful...
(I'm fine with (d), the transformations are translation 1 left, reflection in y-axis)

Which exam is this from again?

[Collin Li]

What am I doing wrong?
4

0

          4                        4

          0                        0
 
                       4        4

                       0        0




...but it's meant to be 12, isn't it?

The left integral is equal to zero.

[bec]

ahhh
thank you

you know when you re-do the same mistake, 400 times over, and you can't see what you're doing wrong? yep.

[/0]

Which exam is this from again?

VCAA 2007 CAS Exam 2

[bec]

Is Q13 in Kilbaha 2008 exam 2, wrong?

I keep getting C.....they say D, and their working appears to have the terminals of the integral upside down. Anyone else come across this?

[trinon]

If then is equal to:







C is correct.

Edit:
After further investigation, I realised that Kibhala made a mistake. They gave the wrong terminals to begin with. For the question that they provided, C is correct. They have either made a mistake with the question, or with the answers.

[bec]

Thanks trinon!

[bec]

I have a few more questions from the same kilbaha exam...

1. Consider the function
Find the coordinates on the graph of where the gradient is a maximum.
The solutions are and
But, considering the domain, I thought that the graph wasn't differentiable at x=0 or x=4pi, and therefore couldn't have maximum gradient here?

2. When you give a general solution, shouldn't "n" be an element of Z, not J?

3. A question with a few parts initially asked to sketch , then its inverse, giving:



Then: "One of the coordinates of the points of intersection between the graphs of and is given by (p,p), where p>0. Find the value of p to 3dp." (p=2.88)

Then, "Show and explain why the area of the region enclosed by the graph of f, the x-axis and the line x=p is given by "

I thought this would just be the integral of f(x) between 0 and p.....but this is their working:



Can anyone explain this to me? I'm very lost...


Thanks

[Mao]

1. you are totally correct.

2. N is the set of natural numbers (0 onwards), and J is the set of integers. In that sense, since general solutions to circular functions (i believe that's what you mean) extends left AND right, J is in fact the more appropriate set. [though for MM, you are not required to know this. the only set you need to know is R, real numbers]

3. that question was explained in another thread [dekoyl's thread I believe], it is a very strange question, and there are multiple ways of tackling it. that is one of the way, which wouldn't make sense to many [I did not accept it at the start]
take a look at that, and see what people came up with. =]

[bec]

Thanks mao. I'll have a look now at that other thread.

With the J/Z thing (and yes, I did mean circular functions sorry!), would it also work if you used Z but not , as opposed to just + and using J?

And, sorry for the overload, but one more question...

4. Consider the graphs of y=kx and y=x^2 +bx +c^2 where b, c and k are all real numbers. Which of the following statements is false?

A. If k=b+2c, the graph of y=kx is a tangent to the graph of y=x^2 + bx + c^2.
B. If k=b-2c, the graph of y=kx touches the graph of y=x^2 + bx + c^2.
C. If b+2c<k<b-2c, the graph of y=kx does not intersect the graph of y = x^2 +bx +c^2.
D. If k>b+2c the graph of y=kx intersects the graph of y = x^2 +bx +c^2.
 at two distinct points.
E. If k<b-2c the graph of y=kx intersects the graph of y = x^2 +bx +c^2.
 at two distinct points.

[nerd]

I was under the impression that J and Z are the same thing, ie. the set of whole numbers = {...-3, -2, -1, 0, 1, 2, 3...}

[Mao]

oooH, ooops, sorry, J and Z are the same thing, I misread the "Z" as "N".

J and Z are interchangeable, it just depends on what you feel like. [though wikipedia uses Z. but I have definitely seen J used in the same sense before]