Author Topic: C1 Edexcel Jan2010 Question! Please help!  (Read 4528 times)

Offline Blizz_rb93

  • SF Senior Citizen
  • *****
  • Posts: 815
  • Reputation: 1175
  • Gender: Male
C1 Edexcel Jan2010 Question! Please help!
« on: April 21, 2010, 04:47:44 pm »
Hi everyone, sorry for my inactivity lately. Been studying for my mocks and externals :(

So I have this C1 mock exam tomorrow and I've been solving pastpapers all day, on the January 2010 exam I came across this question that I didn't know how to solve, I checked the mark scheme but it was confusing, can anyone help me?
Here's the question

Question 10 :

f(x) = x2 + 4kx + (3 + 11k), where k is a constant

a) express f(x) in the form (x+p)2 + q, where p and q are constants to be found in terms of K.

Given that the equation f(x) = 0 has no real roots,

b) find the set of possible values of k.

Given that k=1,
c) Sketch the graph of y=f(x), showing the coordinates of any point at which the graph crosses a coordinate axis..

Please anyone help me, any replies will be VERY APPRECIATED!!

Thank you all in advance!!

Offline albiol18

  • Newbie
  • *
  • Posts: 4
  • Reputation: 14
Re: C1 Edexcel Jan2010 Question! Please help!
« Reply #1 on: April 21, 2010, 05:24:07 pm »
do u want the mark scheme?

Offline Angel.

  • Newbie
  • *
  • Posts: 39
  • Reputation: 224
  • Gender: Female
    • Twitter
Re: C1 Edexcel Jan2010 Question! Please help!
« Reply #2 on: April 21, 2010, 05:27:41 pm »
Okay, I'm going to try this :) :

a) x^2 + 4kx = (x + 2k)^2 - 4k^2   therefore     x^2 + 4kx + (3 + 11k) = (x + 2k)^2 - 4k^2 + 3 + 11k
therefore p = 2k and q = - 4k^2 + 3 + 11k

b) Since f(x) = 0 has no real roots, b^2 - 4ac < 0
a = 1, b = 4k and c = (3 + 11k)
therefore (4k)^2 - 4(1)(3 + 11k) < 0
therefore 16k^2 - 44k - 12 < 0
then divide by 4, so therefore 4k^2 - 11k - 3 < 0
therefore factorise so (4k + 1)(k - 3) < 0
therefore k = -1/4 or k = 3
therefore -1/4 < k < 3

c) k = 1 therefore using (x + 2k)^2 - 4k^2 + 3 + 11k, you know that y = (x + 2)^2 - 4 + 3 + 11 = (x + 2)^2 + 10
when x = 0, y = 14 therefore the curve cuts the y-axis at (0,14)
the curve will not cut the x-axis because f(x) = 0 has no real roots
the lowest point of the curve will be (-2,10)

I hope this helps :)
« Last Edit: April 21, 2010, 05:32:21 pm by Angel. »
"I don't suffer from insanity. I enjoy every minute of it."

Offline Blizz_rb93

  • SF Senior Citizen
  • *****
  • Posts: 815
  • Reputation: 1175
  • Gender: Male
Re: C1 Edexcel Jan2010 Question! Please help!
« Reply #3 on: April 21, 2010, 05:34:53 pm »
thank you for your reply man, but how did you get this part? i dont understand :/

a) x^2 + 4kx = (x + 2k)^2 - 4k^2  

Offline Angel.

  • Newbie
  • *
  • Posts: 39
  • Reputation: 224
  • Gender: Female
    • Twitter
Re: C1 Edexcel Jan2010 Question! Please help!
« Reply #4 on: April 21, 2010, 05:46:42 pm »
No problem :D

I got that by completing the square.
In the case above, you have x^2 + 4kx and you know that it will end up looking something like (x + ...)^2 + constant. When you complete the square, you have to halve the b value (which in this case is 4k) so that that can go in the bracket. Then you get (x + 2k)^2 although that will give you an extra 4k^2 when you expand the bracket. Therefore you need to minus 4k^2 from this and you end up getting (x + 2k)^2 - 4k^2.

I'm sorry if that's an awful explanation, but I can't really explain it through words properly. If my reasoning makes no sense, you can Google 'completing the square', although I'm sure that you probably know how to do it ;)
"I don't suffer from insanity. I enjoy every minute of it."

Offline Blizz_rb93

  • SF Senior Citizen
  • *****
  • Posts: 815
  • Reputation: 1175
  • Gender: Male
Re: C1 Edexcel Jan2010 Question! Please help!
« Reply #5 on: April 21, 2010, 06:44:57 pm »
No problem :D

I got that by completing the square.
In the case above, you have x^2 + 4kx and you know that it will end up looking something like (x + ...)^2 + constant. When you complete the square, you have to halve the b value (which in this case is 4k) so that that can go in the bracket. Then you get (x + 2k)^2 although that will give you an extra 4k^2 when you expand the bracket. Therefore you need to minus 4k^2 from this and you end up getting (x + 2k)^2 - 4k^2.

I'm sorry if that's an awful explanation, but I can't really explain it through words properly. If my reasoning makes no sense, you can Google 'completing the square', although I'm sure that you probably know how to do it ;)

sorry for late replies lol, i was eating a while ago and i was using the phone

anyways thank you for your explanation!! you helped me out alot on a)

I already know how to do (b) and right now im gonna read part (c) and see if it helps :)

thank you very much, ill give u rep

Offline Angel.

  • Newbie
  • *
  • Posts: 39
  • Reputation: 224
  • Gender: Female
    • Twitter
Re: C1 Edexcel Jan2010 Question! Please help!
« Reply #6 on: April 21, 2010, 07:20:14 pm »
No problem! I'm glad that I could help and thank you for the rep! I only joined these forums yesterday, so I really appreciate it! :)

Good luck with part (c)! :D
"I don't suffer from insanity. I enjoy every minute of it."

Offline Blizz_rb93

  • SF Senior Citizen
  • *****
  • Posts: 815
  • Reputation: 1175
  • Gender: Male
Re: C1 Edexcel Jan2010 Question! Please help!
« Reply #7 on: April 21, 2010, 09:21:27 pm »
Thank you very much in total :) you helped me out alot :D

Offline Angel.

  • Newbie
  • *
  • Posts: 39
  • Reputation: 224
  • Gender: Female
    • Twitter
Re: C1 Edexcel Jan2010 Question! Please help!
« Reply #8 on: April 21, 2010, 10:35:04 pm »
Aww, honestly it was no problem. :)
"I don't suffer from insanity. I enjoy every minute of it."

Amr Fouad

  • Guest
Re: C1 Edexcel Jan2010 Question! Please help!
« Reply #9 on: April 22, 2010, 12:32:02 pm »
Thanks Angel

+rep

nid404

  • Guest
Re: C1 Edexcel Jan2010 Question! Please help!
« Reply #10 on: April 22, 2010, 12:33:13 pm »
yup thanks :)

Offline Blizz_rb93

  • SF Senior Citizen
  • *****
  • Posts: 815
  • Reputation: 1175
  • Gender: Male
Re: C1 Edexcel Jan2010 Question! Please help!
« Reply #11 on: April 22, 2010, 06:18:01 pm »
Today I aced the C1 Mock :D :D

Offline Angel.

  • Newbie
  • *
  • Posts: 39
  • Reputation: 224
  • Gender: Female
    • Twitter
Re: C1 Edexcel Jan2010 Question! Please help!
« Reply #12 on: April 22, 2010, 06:22:35 pm »
Thanks for the rep :)

Quote
Today I aced the C1 Mock :D :D

Ooh, well done! :D
"I don't suffer from insanity. I enjoy every minute of it."

Offline halosh92

  • SF Senior Citizen
  • *****
  • Posts: 730
  • Reputation: 1113
  • Gender: Female
    • meticulous-me
Re: C1 Edexcel Jan2010 Question! Please help!
« Reply #13 on: April 26, 2010, 11:50:19 am »
c2 edexcel
how do we solve this question?
Giving your answers in terms of pie, solve the equation
3 tan2? ? 1 = 0

for ? in the interval ?pie ? ? ? pie
everyday we wake up is a miracle, then how do we say miracles dont happen?????

Offline astarmathsandphysics

  • SF Overlord
  • *********
  • Posts: 11271
  • Reputation: 65534
  • Gender: Male
  • Free the exam papers!
Re: C1 Edexcel Jan2010 Question! Please help!
« Reply #14 on: April 26, 2010, 11:51:42 am »
Home in 1 hour