How did everyone go? (1 Viewer)

[simonwang12]

Thoughts? Opinions? Questions?

 

[Seal7]

Thoughts? Opinions? Questions?

Very well in the first 15 questions, but gee that question 16 was nasty


If anyone could go through a proof of 16(c) I'd be extremely thankful.


For those who haven't sat the test, and just want to help out, the question was (I'm not familiar with Latex, sorry):

The Circle x^2+(y-c)^2=r^2 where c>0 and r>0, lies inside the parabola y=x^2. The circle touches the parabola at exactly two points symmetrically on opposite sides of the y axis.

i) Show that 4c=1+4r^2

ii) Deduce that c>1/2

 

[nmdsntfi]

Yeah, I sat on question 16 for literally an hour and 10 minutes.

 

[LoveHateSchool]

Well lucky I took in two calcs because usual one started stuffing up 10 mins in.

Did Q11-15, first, nothing was too bad in them except I realised I made an idiotic mistake in one Q at the end haha. Did MC=easy.

Q16...
...
...
o.0

I wrote stuff down for all the parts but ahahaha oh god it was so wrong.

 

[gr_111]

theres a solution in the Q16 thread.

 

[simonwang12]

Where's that?

 

[Seal7]

I did some work on Question 16 c

i) x^2 + (y-c)^2 = r^2

And y=x^2

Substitute 2 into 1

y + (y-c)^2= r^2


Rearrange (expand) to make a quadratic, y as the variable

y+y^2 -2yc + c^2 -r^2 = 0

Grouping terms

y^2 + y(1-2c) + (c^2-r^2) = 0

We know that there are two equal (in terms of y) solutions to this, because the circle and the parabola touch symmetrically around the y axis at the same value of y (given in the question). Therefore the discriminant of this quadratic = 0

discriminant = b^2-4ac

substituting in

(1-2c)^2 - 4(c^2-r^2) = 0
Expand and cancel (easy enough) to get 4c = 1 + 4r^2

In part ii) I got c>1/4, which is incorrect (we were meant to get c>1/2). Until I can figure this out I won't go any further.

Any further discussion of this question should go in the question 16 discussion thread, which I just discovered here: http://community.boredofstudies.org/showthread.php?t=293638&page=4

 

[Fakeuser]

Finishing question 16 took forever...but I did get it out in the end.

 

[blaisems]

Shit, I had no idea there was a question 16.c). I am SCREWED if it was worth more that around 4 or 5

 

[The Sped]

sounds like it was a hard exam ...

 

[Timske]

Shit, I had no idea there was a question 16.c). I am SCREWED if it was worth more that around 4 or 5

3 marks

 

[crazy_paki123]

Q16 a and b were easy just took time :L c was tough though, overall i rekn i got 95% raw