Author Topic: maths p1 help  (Read 1811 times)

Offline I'm a mistake - legalize abortion!

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maths p1 help
« on: May 11, 2010, 09:07:15 pm »
ok can anybody help me?q.no.10 of M/J 2009


The function f is defined by f : x  ? 2x2 ? 12x + 13 for 0 ? x ? A, where A is a constant.
(i) Express f(x) in the form a(x + b)2 + c, where a, b and c are constants.
(ii) State the value of A for which the graph of y = f(x) has a line of symmetry.
(iii) When A has this value, find the range of f.
The function g is defined by g : x  ? 2x2 ? 12x + 13 for x ? 4.
(iv) Explain why g has an inverse.
(v) Obtain an expression, in terms of x, for g?1(x).

thanks in advance
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Freaked12

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Re: maths p1 help
« Reply #1 on: May 11, 2010, 09:22:33 pm »
Sorry internet is slow right now..Paper is being downloaded.

Offline I'm a mistake - legalize abortion!

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Re: maths p1 help
« Reply #2 on: May 11, 2010, 10:53:34 pm »
hello anybody there who can help?? i would be thankful :D
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nid404

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Re: maths p1 help
« Reply #3 on: May 12, 2010, 04:37:41 am »
ok can anybody help me?q.no.10 of M/J 2009


The function f is defined by f : x  ? 2x2 ? 12x + 13 for 0 ? x ? A, where A is a constant.
(i) Express f(x) in the form a(x + b)2 + c, where a, b and c are constants.
(ii) State the value of A for which the graph of y = f(x) has a line of symmetry.
(iii) When A has this value, find the range of f.
The function g is defined by g : x  ? 2x2 ? 12x + 13 for x ? 4.
(iv) Explain why g has an inverse.
(v) Obtain an expression, in terms of x, for g?1(x).

thanks in advance


Nid to your rescue  :)
I hope im not late

i) completing the square method 2(x-3)2-5
ii) the line of symmetry is given by -b/2a   or you can simply derivate and equate to 0
using the first method
-(-12)/ 2X2= 3
x=3 (line of symmetry passes through x=3)

second method
dy/dx= 4x-12
line of symmetry will pass through the maxima or minima as it's a quadratic
4x-12=0
x=3

u can use any method

iii) Just substitute 3 in the eqn
u get y= -5
now to decide whether this is max or min
sub 3 in d2y/dx2 = 4x
4X3=12 >0  hence minima
that mean all values of y will be greater than -5
y>=-5 is the range

iv) g has an inverse because it is a 1-1 function. It has a given set of domain.

v) y=2x2-12x-13
  We wrote this is the form (a-b)2+c
    2(x-3)2-5
y=2(x-3)2-5

make x the subject

y+5=2(x-3)2
y+5
----= (x-3)2
 2
\sqrt{(y+5)/2} = (x-3)
x=\sqrt{(y+5)/2} +3
in terms of x, so u swap the y with x

g-1(x)= \sqrt{(x+5)/2}+ 3
« Last Edit: May 12, 2010, 04:44:53 am by nid404 »

Offline I'm a mistake - legalize abortion!

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Re: maths p1 help
« Reply #4 on: May 12, 2010, 04:43:23 am »
"nid to the rescue." lol(superman)
thank u so much miss "nidman"
I hope u r not mad at me anymore
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nid404

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Re: maths p1 help
« Reply #5 on: May 12, 2010, 04:46:01 am »
superwoman  :P

Nooo...I'm not  :D

Offline I'm a mistake - legalize abortion!

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Re: maths p1 help
« Reply #6 on: May 12, 2010, 04:51:59 am »
@nid why dont u change ur name to "nicole nidman"? ;D Sounds like a nice name to me.... :P :P
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nid404

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Re: maths p1 help
« Reply #7 on: May 12, 2010, 04:52:51 am »
no, I like to be original  :P

Offline ifraha18

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Re: maths p1 help
« Reply #8 on: May 12, 2010, 05:24:41 am »
(ii) Only a few candidates realised that because y = f(x) has a line of symmetry at x = 3, then A = 6.

y is it so in the june 2009 q10?

Offline cashem'up

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Re: maths p1 help
« Reply #9 on: May 12, 2010, 05:44:59 am »
didnt get ur questio n :P u sayin why is the ER say so......... or wat 

nid404

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Re: maths p1 help
« Reply #10 on: May 12, 2010, 05:46:03 am »
the domain is

0<=x<=A

you found x=3 is line of symmetry

to the left of this line x is only uptil 0 difference of 3 units. To the right as well it should be at the same difference to have a reflection along x=3. Hence maximum value x can is 6

Hope ur getting me

Offline cashem'up

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Re: maths p1 help
« Reply #11 on: May 12, 2010, 05:54:07 am »
hmm i actualy got that......  :P

but i didnt understand why  ifraha18 was quoting from the Examiner Report and asking why many pppl didnt get it correct  lolz...
 ;D ;D ;D

Offline princess12

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Re: maths p1 help
« Reply #12 on: May 12, 2010, 06:18:58 am »
WHICH PAPER U HAVE
 ??? ???
ANSWER ME
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Offline princess12

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Re: maths p1 help
« Reply #13 on: May 12, 2010, 06:20:44 am »
??? ??? ??? ???
We should be kind to after teachers

Offline XaM!!

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Re: maths p1 help
« Reply #14 on: May 12, 2010, 07:43:07 am »
but line of smmetry comes 6... acc to mark scheme..
Dnt walk As iF u RulE da WorLd..... Walk As if U dOnT CarE wHO RuLzz It.......