IGCSE/GCSE/O & A Level/IB/University Student Forum

Qualification => Subject Doubts => GCE AS & A2 Level => Math => Topic started by: Twinkle Charms on May 22, 2010, 08:51:44 am

Title: MAth DOubts
Post by: Twinkle Charms on May 22, 2010, 08:51:44 am
Find the derivatives of
(a) ln(1-2x)
(b) ln(a+bx)
(c) ln(x^2(x-1))
(d) ln(2x)

please post the answers asap i did it buh want to check , a bit confused, Thank You.
Title: Re: MAth DOubts
Post by: Twinkle Charms on May 22, 2010, 10:40:20 am
wow 10 views ns till no reply?? =(
i got math exam ppl, need help...
Title: Re: MAth DOubts
Post by: Kim on May 22, 2010, 10:43:16 am
wait ill ask a friend she might know she takes maths
Title: Re: MAth DOubts
Post by: CHEMMASTER6000 on May 22, 2010, 10:50:18 am
its probably cause of the implication of derivative. what do you mean dirivative of the ln functions. i dont think we need that for p3
Title: Re: MAth DOubts
Post by: Kim on May 22, 2010, 10:58:12 am
my friend says the questions dont make sense lol
Title: Re: MAth DOubts
Post by: Alpha on May 22, 2010, 11:13:02 am
d/dx [ln f(x)] = f '(x)/ f(x), where f ' (x) is the derivative of f(x).


Derivatives:

(a) ln(1-2x) > -2/ (1-2x)

(b) ln(a+bx) > b/ (a+bx)

(c) ln(x^2(x-1)) >>> clear this one, power is only 2 or 2(x-1)?

  I think you forgot to add the brackets, must have been  ln((x^2)(x-1)).
For this one, use the properties of logarithms. ln ((x^2)(x-1)) = ln (x^2) + ln (x-1)
                                                                       
Differentiate by step to get the derivative.

ln (x^2) > 2x/ (x^2)
ln (x-1) > 1/(x-1)

Therefore,  ln (x^2) + ln (x-1) = 2x/ (x^2) + 1/(x-1)

Simplify further if you want.

(d) ln(2x) > 2/2x
Title: Re: MAth DOubts
Post by: Twinkle Charms on May 22, 2010, 11:35:20 am
d/dx [ln f(x)] = f '(x)/ f(x), where f ' (x) is the derivative of f(x).


Derivatives:

(a) ln(1-2x) > -2/ (1-2x)

(b) ln(a+bx) > b/ (a+bx)

(c) ln(x^2(x-1)) >>> clear this one, power is only 2 or 2(x-1)?

  I think you forgot to add the brackets, must have been  ln((x^2)(x-1)).
For this one, use the properties of logarithms. ln ((x^2)(x-1)) = ln (x^2) + ln (x-1)
                                                                       
Differentiate by step to get the derivative.

ln (x^2) > 2x/ (x^2)
ln (x-1) > 1/(x-1)

Therefore,  ln (x^2) + ln (x-1) = 2x/ (x^2) + 1/(x-1)

Simplify further if you want.

(d) ln(2x) > 2/2x
thankyou alpha, n
its x square multiplied by x-1, so for it we open the brackets n then differientiate? N how to do the diff. part?
Title: Re: MAth DOubts
Post by: Twinkle Charms on May 22, 2010, 11:38:00 am
its probably cause of the implication of derivative. what do you mean dirivative of the ln functions. i dont think we need that for p3
yes ofc its there in p3, the main thing dude :p
Title: Re: MAth DOubts
Post by: CHEMMASTER6000 on May 22, 2010, 01:16:18 pm
oh woops haha , my mistake  i didnt take derivative as differentiate. makes a load of sense now, i can explain here if the you dont understand the guy above
Title: Re: MAth DOubts
Post by: Twinkle Charms on May 22, 2010, 01:18:38 pm
oh woops haha , my mistake  i didnt take derivative as differentiate. makes a load of sense now, i can explain here if the you dont understand the guy above
nop i got her, actually i did it just wanted to confirm, cz sum1 was confusing me :|

Title: Re: MAth DOubts
Post by: Twinkle Charms on May 22, 2010, 01:19:45 pm
oh and also i find vectors difficult, if someone can gimme good notes or site from which to refer, Vectors in 2D n 3D? the vector equation n all tht crap :|
Title: Re: MAth DOubts
Post by: Alpha on May 22, 2010, 01:40:41 pm
thankyou alpha, n
its x square multiplied by x-1, so for it we open the brackets n then differientiate? N how to do the diff. part?


ln [x^2(x-1)] = ln [x^(2x-2)]

Using laws of indices,

                  = ln (x^2x/ x^2)

Using laws of logarithms,

                 = ln (x^2x) - ln (x^2)

Derivative > 2x. x^(2x-1) {which can be simplified to 2x^(2x-1+1)= 2x^2x}/ x^(2x) - 2x/ x^2

              = 2x^2x/ x^2x - 2x/ x^2

This one's more complex.
Welcome~
Title: Re: MAth DOubts
Post by: Twinkle Charms on May 22, 2010, 01:42:19 pm

ln [x^2(x-1)] = ln [x^(2x-2)]

Using laws of indices,

                  = ln (x^2x/ x^2)

Using laws of logarithms,

                 = ln (x^2x) - ln (x^2)

Derivative > 2x. x^(2x-1) {which can be simplified to 2x^(2x-1+1)= 2x^2x}/ x^(2x) - 2x/ x^2

              = 2x^2x/ x^2x - 2x/ x^2

This one's more complex.
Welcome~
uh-oh seems u neva got wht actually im asking :|

its x(square) this multiplied to (x-1) now get it??
Title: Re: MAth DOubts
Post by: Alpha on May 22, 2010, 01:45:55 pm
uh-oh seems u neva got wht actually im asking :|

its x(square) this multiplied to (x-1) now get it??

Yeah, but isn't that what I did earlier? My first post?
Title: Re: MAth DOubts
Post by: Twinkle Charms on May 22, 2010, 01:47:33 pm
Yeah, but isn't that what I did earlier? My first post?
ooopps my bad, i was reading it rong ur first post...sooorrryyy :-[ and thank youu so mucchh  :)
Title: Re: MAth DOubts
Post by: CHEMMASTER6000 on May 22, 2010, 01:49:53 pm
i can help you with vectors. do you have a specific part of vectors or is it vectors as a whole . so there eqn of a line, using 2 points, 1 directioin vector and a point. point of intersetion . foot of a line . angle between two lines. and for plane there is equn plane . finding eqn using 3 points , using another plane. then there intersection between 2 planes, angle between two planes. and plane and line which consist of angle between line and plane  and point of intersection . im sure theres abit more but i cant think of it from the top of my head. pm if you want me to go through a specific one
Title: Re: MAth DOubts
Post by: Twinkle Charms on May 22, 2010, 01:51:55 pm
i can help you with vectors. do you have a specific part of vectors or is it vectors as a whole . so there eqn of a line, using 2 points, 1 directioin vector and a point. point of intersetion . foot of a line . angle between two lines. and for plane there is equn plane . finding eqn using 3 points , using another plane. then there intersection between 2 planes, angle between two planes. and plane and line which consist of angle between line and plane  and point of intersection . im sure theres abit more but i cant think of it from the top of my head. pm if you want me to go through a specific one
*coughs* aheemm ill get back to you, lemme hit my books n see if sumthing gets inside.
Title: Re: MAth DOubts
Post by: Alpha on May 22, 2010, 01:52:09 pm
ooopps my bad, i was reading it rong ur first post...sooorrryyy :-[ and thank youu so mucchh  :)


No worries. And you're welcome. Lucky, today I have some time to help you.

I see you are a good fan of 'Another Cinderella story'.  :)
Title: Re: MAth DOubts
Post by: CHEMMASTER6000 on May 22, 2010, 01:55:22 pm
sure ;D
Title: Re: MAth DOubts
Post by: Twinkle Charms on May 22, 2010, 03:49:54 pm
Q2) Find the integral of

root of (4-x^2) ; use substitution x=2sintheta

im stuck half way :\  hellpp please =)
Title: Re: MAth DOubts
Post by: Alpha on May 22, 2010, 04:09:26 pm
Q2) Find the integral of

root of (4-x^2) ; use substitution x=2sintheta

im stuck half way :\  hellpp please =)

I'll use @ for theta.

x = 2 sin 2
x^2 = 4 sin^2 @

/ for root.

/ (4 - x^2) = / [4(1-sin^2@)]

Using identity sin^2@ + cos^2@ = 1,

/ [4(1-sin^2@)] = / 4 cos^2@
                        = 2 cos @

Now integrate.

Differentiation of sin@ > cos@,

Integration of cos@ > sin@.

Integrate 2 cos@ > 2 sin@.
Title: Re: MAth DOubts
Post by: Twinkle Charms on May 22, 2010, 04:23:59 pm
oh ohkay i got it, was skippin one step, Thank You..
Title: Re: MAth DOubts
Post by: Twinkle Charms on May 23, 2010, 11:24:39 am
Q3)Integral of (50-m)^-2??

 the answer given is (50-m)^-1 buh im gettin -(50-m)^-1, where am i rong?:S
Title: Re: MAth DOubts
Post by: astarmathsandphysics on May 23, 2010, 11:27:19 am
You are ignoring the - in -m
Title: Re: MAth DOubts
Post by: Twinkle Charms on May 23, 2010, 11:34:59 am
You are ignoring the - in -m
ohh so we mutiply -1 in the denominator with -1 to get +1? ohkk...Thank You astar=)
Title: Re: MAth DOubts
Post by: astarmathsandphysics on May 23, 2010, 06:02:58 pm
is ok.
Title: Re: MAth DOubts
Post by: Twinkle Charms on May 23, 2010, 06:49:40 pm
Q4)Two planes have equation x+2y-2z=2 and 2x-3y+6z=3. The planes intersect in the straight line L. Find a vector equtaion for line L. 

ok so i just know to get the vector equation of a line we use this>> r=a+$p, where a is the position vector, $ is a scaler and p is direction vector, after that how to get all that i dunno....please help...=\
Title: Re: MAth DOubts
Post by: CHEMMASTER6000 on May 23, 2010, 07:25:10 pm
so to find the direction vector you cross multiply the normals using matrices rules. and to find the point on the line you do simultaneous equation using the two plane quations but thats where it gets tricky. the trick is to sub in a value for x y or z which will give zero thus only one unknown is left. i rather not type the answer here cause its difficult to type and i dont know how to scan in the work sheet into forum ???hope it my methods helps
Title: Re: MAth DOubts
Post by: Twinkle Charms on May 23, 2010, 07:27:55 pm
so to find the direction vector you cross multiply the normals using matrices rules. and to find the point on the line you do simultaneous equation using the two plane quations but thats where it gets tricky. the trick is to sub in a value for x y or z which will give zero thus only one unknown is left. i rather not type the answer here cause its difficult to type and i dont know how to scan in the work sheet into forum ???hope it my methods helps
u scan ur worksheet and attach to your post cz i aint gettin what u said to do for the point on the line =\ to attach click on the additional options...
Title: Re: MAth DOubts
Post by: CHEMMASTER6000 on May 23, 2010, 07:35:23 pm
hahaa ok i think i failed at the scanning thing but il try it here .

(a)x+2y-2z=2 and (b)2x-3y+6z=3

so point on line would be . so simultaneously solve both of them . (trick) sube 0 into one of them . i choose z

when z=0

(a)x+2y=2 (b) 2x-3y=3
 
now its easy so you can solve for x and y. sub back into eqn and walla you get the point ahh haha sound so nerdy

Title: Re: MAth DOubts
Post by: Twinkle Charms on May 23, 2010, 07:47:44 pm
hey thnxxx i got it =)
Title: Re: MAth DOubts
Post by: CHEMMASTER6000 on May 23, 2010, 07:48:10 pm
awesome ;D
Title: Re: MAth DOubts
Post by: Twinkle Charms on May 23, 2010, 08:15:48 pm
Q5)How to sketch the graph of y=secx, for 0<=x<=2pi
Title: Re: MAth DOubts
Post by: T.Q on May 23, 2010, 09:35:33 pm
Q5)How to sketch the graph of y=secx, for 0<=x<=2pi

check this  Trig graph  (http://www.intmath.com/Trigonometric-graphs/4_Graphs-tangent-cotangent-secant-cosecant.php)
Title: Re: MAth DOubts
Post by: Twinkle Charms on May 23, 2010, 09:36:59 pm
check this  Trig graph  (http://www.intmath.com/Trigonometric-graphs/4_Graphs-tangent-cotangent-secant-cosecant.php)
this stuff is just soo cool n helpful!!  im really thankful to you!! ;D
Title: Re: MAth DOubts
Post by: Twinkle Charms on May 25, 2010, 07:58:25 pm
Q1 part 1 how to do it? :S

http://www.srepapmaxeeeerf.org/A%20Level/Maths/CIE/2009%20Jun/9709_s09_qp_6.pdf
Title: Re: MAth DOubts
Post by: chaosking on May 25, 2010, 08:11:11 pm
i did it on pakistanis hea...
Title: Re: MAth DOubts
Post by: immortal on May 25, 2010, 08:40:31 pm
Q1 part 1 how to do it? :S

http://www.srepapmaxeeeerf.org/A%20Level/Maths/CIE/2009%20Jun/9709_s09_qp_6.pdf

225/900=0.25(contains mor dan 1002)
1-0.25=0.75
Q(x)=0.75
x=0.6745

(1002-mu)/8=0.6745
mu=996.6
Title: Re: MAth DOubts
Post by: Twinkle Charms on May 25, 2010, 08:59:06 pm
i did it on pakistanis hea...
Thanks got it=)
Title: Re: MAth DOubts
Post by: Twinkle Charms on May 25, 2010, 09:00:09 pm
225/900=0.25(contains mor dan 1002)
1-0.25=0.75
Q(x)=0.75
x=0.6745

(1002-mu)/8=0.6745
mu=996.6
Thanks buddy, Q3 (i), in ms why have they taken 0.84?? please explain
Title: Re: MAth DOubts
Post by: Twinkle Charms on May 25, 2010, 09:00:35 pm
http://www.srepapmaxeeeerf.org/A%20Level/Maths/CIE/2009%20Jun/9709_s09_ms_6.pdf


here this is the mark scheme
Title: Re: MAth DOubts
Post by: immortal on May 25, 2010, 09:07:30 pm
Thanks buddy, Q3 (i), in ms why have they taken 0.84?? please explain
dey hve asked 4 probability of busses which is 16%, so da other vehicles r 100-16=84% which is 0.84
Title: Re: MAth DOubts
Post by: Twinkle Charms on May 25, 2010, 09:08:51 pm
dey hve asked 4 probability of busses which is 16%, so da other vehicles r 100-16=84% which is 0.84
k...Q4 (iii) ???
Title: Re: MAth DOubts
Post by: immortal on May 25, 2010, 09:14:35 pm
BBBB"T(odd 1 out)"TTT
so 4P4*3P3*2
*2 because it cud b TTTTBBBB as well..
Title: Re: MAth DOubts
Post by: immortal on May 25, 2010, 09:16:15 pm
By the way how come u hve doubts in S1, because u helped me in P3 questions which r tough :o
Title: Re: MAth DOubts
Post by: Twinkle Charms on May 25, 2010, 09:30:02 pm
By the way how come u hve doubts in S1, because u helped me in P3 questions which r tough :o
because this is the only component of math i suck at  :'( im so freaked out for tom's exam...=\

and By the way thaaank yoouuu soo much.....
Title: Re: MAth DOubts
Post by: immortal on May 25, 2010, 09:34:48 pm
No need 2 worry,u'll do gud, after all this component comes 2 only 20% . :)
Title: Re: MAth DOubts
Post by: Twinkle Charms on May 25, 2010, 10:10:25 pm
Q7 part (i) and (ii) how to do??

http://www.srepapmaxeeeerf.org/A%20Level/Maths/CIE/2007%20Nov/9709_w07_qp_6.pdf
Title: Re: MAth DOubts
Post by: Twinkle Charms on May 25, 2010, 10:15:31 pm
Q7 part (i) and (ii) how to do??

http://www.srepapmaxeeeerf.org/A%20Level/Maths/CIE/2007%20Nov/9709_w07_qp_6.pdf
ooopps i got it...was not reading the question properly =\
Title: Re: MAth DOubts
Post by: insane.kid on May 26, 2010, 10:19:27 am
could some 1 plz explain me question 7iii) in WO3 pure 3 maths plz thank u :)
Title: Re: MAth DOubts
Post by: ferrari2win on May 26, 2010, 12:12:03 pm
Can anyone help me with these math questions (past years CIE P3)

M/J 08 (5 ii)
M/J 09 (6 ii and iii)
O/N 09 3/1 7(iv)

please show all the working of algebra working clearly 
thank  ;D
Title: Re: MAth DOubts
Post by: sm on May 26, 2010, 01:47:22 pm
HORRIBLE STATISTICS PAPER!!! :'(
GD LUCK 4 PURE !!!
Title: Re: MAth DOubts
Post by: astarmathsandphysics on May 26, 2010, 03:10:05 pm
w03 7iii
Title: Re: MAth DOubts
Post by: immortal on May 26, 2010, 03:32:42 pm
HORRIBLE STATISTICS PAPER!!! :'(
GD LUCK 4 PURE !!!
How waz ur P1
Title: Re: MAth DOubts
Post by: astarmathsandphysics on May 26, 2010, 03:32:53 pm
M/J 08 (5 ii)
M/J 09 (6 ii and iii)
O/N 09 3/1 7(iv)
Title: Re: MAth DOubts
Post by: ferrari2win on May 26, 2010, 04:24:35 pm
thanks for the help  ;D
Title: Re: MAth DOubts
Post by: Twinkle Charms on May 26, 2010, 05:09:34 pm
HORRIBLE STATISTICS PAPER!!! :'(
GD LUCK 4 PURE !!!
soo trueee =( anyways GOoOOod NewS!!!
my sir said dont worry about this paper, however you do, if u get around 65 in pure math 3 ull end up with an overall A , i cant be any more happier ;D
Title: Re: MAth DOubts
Post by: immortal on May 26, 2010, 05:31:13 pm
soo trueee =( anyways GOoOOod NewS!!!
my sir said dont worry about this paper, however you do, if u get around 65 in pure math 3 ull end up with an overall A , i cant be any more happier ;D
Easier said, dan done :(
Title: Re: MAth DOubts
Post by: Freaked12 on May 26, 2010, 05:33:15 pm
soo trueee =( anyways GOoOOod NewS!!!
my sir said dont worry about this paper, however you do, if u get around 65 in pure math 3 ull end up with an overall A , i cant be any more happier ;D

and what do you need to get in P1 to get a good chance of a A overall
Title: Re: MAth DOubts
Post by: insane.kid on May 26, 2010, 05:33:42 pm
Thank u astarmathsandphysics but can u plz explain why cant we do 180 - tan^-1 (2/1) like y does this give the wrong answer it gives me 116 but y ? i hope u understand wht i meant  :-\
Title: Re: MAth DOubts
Post by: Freaked12 on May 26, 2010, 05:35:11 pm
and what do you need to get in P1 to get a good chance of a A overall

If you did today's S1  >:(
Title: Re: MAth DOubts
Post by: insane.kid on May 26, 2010, 05:38:55 pm
oh cool i got it thank u astar :D
Title: Re: MAth DOubts
Post by: Twinkle Charms on May 26, 2010, 05:47:26 pm
Easier said, dan done :(
nope, p3 is manageable =)
anything but stats -__-
Title: Re: MAth DOubts
Post by: Twinkle Charms on May 26, 2010, 05:50:42 pm
and what do you need to get in P1 to get a good chance of a A overall
65 plus too...im hopin for 75 By the way in p1 it was good...May Allah make tht happen...
Title: Re: MAth DOubts
Post by: Twinkle Charms on May 26, 2010, 05:51:32 pm
If you did today's S1  >:(
yea i swear todays S1 was just sooo horrible  >:(
Title: Re: MAth DOubts
Post by: Freaked12 on May 26, 2010, 06:02:48 pm
yea i swear todays S1 was just sooo horrible  >:(

i have business tomorrow and my hand , legs hurt so much.
JESUS!

i feel like crying
(not for S1 that went well Alhamdullilah but for tomorrow's exam)
Not able to find strength
Title: Re: MAth DOubts
Post by: immortal on May 26, 2010, 06:03:13 pm
Is it dat mostly girls find stats difficult.. :P
Title: Re: MAth DOubts
Post by: Twinkle Charms on May 26, 2010, 06:10:26 pm
Is it dat mostly girls find stats difficult.. :P
apparently
Title: Re: MAth DOubts
Post by: lhl_anecar on May 27, 2010, 03:21:39 pm
ermm anyone has the workings for CIE Pure Maths 3

may/june09 paper
oct/nov varient 31 and 32 2009 papers.
pleaseeeeeeeeee. i don't seem uncerstand them.
thanks!!!
am doing last min crammings....thank u very very much in advance. my p3 will be in 10hrs time..
Title: Re: MAth DOubts
Post by: falafail on May 27, 2010, 03:25:00 pm
ermm anyone has the workings for CIE Pure Maths 3

may/june09 paper
oct/nov varient 31 and 32 2009 papers.
pleaseeeeeeeeee. i don't seem uncerstand them.
thanks!!!
am doing last min crammings....thank u very very much in advance. my p3 will be in 10hrs time..

ummm if you tell me what specific questions you don't get i'll try to help? i'm not gonna do three whole papers for you though -_-
Title: Re: MAth DOubts
Post by: lhl_anecar on May 27, 2010, 03:37:42 pm
ummm if you tell me what specific questions you don't get i'll try to help? i'm not gonna do three whole papers for you though -_-

ahh. thanks for the offer!! u're so kind.

mayjune 2009
Q8(ii) Q10

oct/nov2009 variant 31
Q1 Q5(ii) Q7(iv) Q9 Q10

oct/nov2009 variant 32
Q2(i) Q4 Q6 Q9(iii) and Q10

thank u!!!
Title: Re: MAth DOubts
Post by: falafail on May 27, 2010, 04:04:10 pm
ahh. thanks for the offer!! u're so kind.

mayjune 2009
Q8(ii) Q10

oct/nov2009 variant 31
Q1 Q5(ii) Q7(iv) Q9 Q10

oct/nov2009 variant 32
Q2(i) Q4 Q6 Q9(iii) and Q10

thank u!!!

um here's the first one http://i45.tinypic.com/28lxfds.jpg


i have to go study physics now though so i don't have time to do them all atm  :-\
i'll try to do them later if no one else has.
Title: Re: MAth DOubts
Post by: lhl_anecar on May 27, 2010, 04:56:04 pm
um here's the first one http://i45.tinypic.com/28lxfds.jpg


i have to go study physics now though so i don't have time to do them all atm  :-\
i'll try to do them later if no one else has.

alrite! thank u once again... :D
Title: Re: MAth DOubts
Post by: insane.kid on May 27, 2010, 06:05:11 pm
cld some1 plz help me in W07 10i) only the first part with explanation plz thank u
Title: Re: MAth DOubts
Post by: khi2ruh on May 27, 2010, 06:13:20 pm
hey could some one please help me with

j09 Q6(ii)
Title: Re: MAth DOubts
Post by: Alpha on May 28, 2010, 02:21:55 am
Why don't you people post the link to the papers directly??

Whenever I have some free time, come here, and keep wondering which papers you are talking about.  :P

So, please, it's a request: state your papers clearly, along with your exams board.