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

Qualification => Subject Doubts => GCE AS & A2 Level => Math => Topic started by: cooldude on October 30, 2009, 07:01:13 am

Title: maths doubts
Post by: cooldude on October 30, 2009, 07:01:13 am: and also one sequence i gotta doubt in this sequence-
what will be the nth term in the following sequence-
(start with n=1)

13,14,18,27,43,68
Title: Re: maths doubts
Post by: astarmathsandphysics on October 30, 2009, 07:15:28 am: 13 14 18 27 43 68
1 4 9 16 25
u(n+1)=u(n)+n^2

For the others, do you want the solution to every one?
Title: Re: maths doubts
Post by: astarmathsandphysics on October 30, 2009, 07:17:33 am: Usuuallly if they want you to solve a quadratic equation they ive you want of the roots.
Title: Re: maths doubts
Post by: astarmathsandphysics on October 30, 2009, 02:25:52 pm: The only way you can do them systematically is using iteration/trial and improvement (really long method)/ bisection (also really long) or the Newton Raphson Method. There are exact methods but these are not part of IGCSE or even A level maths. Which method have you been taught to use?
Title: Re: maths doubts
Post by: astarmathsandphysics on October 30, 2009, 04:03:38 pm: I will have to do it tomorrow. Something urget came up and I will be occupied for the rest of the day. There will be an announcemt tomorrow.
Title: Re: maths doubts
Post by: astarmathsandphysics on October 31, 2009, 08:09:12 am: I have been thinking seriously about this since yesterday. I don't seriously think they can expect you to find all three roots of a cubic polynomial using the Newton Raphson method. You dont even know how many roots there are. The very first thing you would have to do would be to sketch the curve and see if you can find interval in which each root lies. Can you scan in the page with the question? I think there is something missing.
Title: Re: maths doubts
Post by: Ghost Of Highbury on October 31, 2009, 09:42:15 am: if u use Fx-991Ms

do this,..

On-->3 times "mode"--> "1" (Eqn) --> press the "right arrow" --> "3" --> type th co-efficient of x³ nd press "=" -->

type th co-efficient of x² nd press "=" --> type the co-efficient of x nd press "=" --> type the value of "d" i.e co-efficient of x⁰ and press "=".

U'll get an answer..press "=" 2 more times to find the other values

e.g -> a cubic equation --> ax³ + bx² + cx + d
Title: Re: maths doubts
Post by: slvri on October 31, 2009, 09:43:35 am: coooooool.....i didnt know that........
so wassup adi? hw r ur papers going?
Title: Re: maths doubts
Post by: Ghost Of Highbury on October 31, 2009, 09:44:33 am: Quote from: slvri on October 31, 2009, 09:43:35 am
coooooool.....i didnt know that........
so wassup adi? hw r ur papers going?

hey..ssup..actually u can solve matrices and simultaneous equations too in Fx-991 MS.

and yea..my papers are going good..2morrow again a holiday followed by english paper 3!
Title: Re: maths doubts
Post by: @d!_†oX!© on October 31, 2009, 09:45:10 am: Quote from: A@di on October 31, 2009, 09:42:15 am
if u use Fx-991Ms

do this,..

On-->3 times "mode"--> "1" (Eqn) --> press the "right arrow" --> "3" --> type th co-efficient of x³ nd press "=" -->

type th co-efficient of x² nd press "=" --> type the co-efficient of x nd press "=" --> type the value of "d" i.e co-efficient of x⁰ and press "=".

U'll get an answer..press "=" 2 more times to find the other values

e.g -> a cubic equation --> ax³ + bx² + cx + d
dude!!!
fx-991 MS isn't allowed!!!!
Title: Re: maths doubts
Post by: Ghost Of Highbury on October 31, 2009, 09:45:56 am: Quote from: @d!_†oX!© on October 31, 2009, 09:45:10 am
dude!!!
fx-991 MS isn't allowed!!!!
ofcourse it is allowed..all of us used it in paper 2 maths..which calculator do u use?
Title: Re: maths doubts
Post by: Ghost Of Highbury on October 31, 2009, 09:47:52 am: Quote from: A@di on October 31, 2009, 09:45:56 am
ofcourse it is allowed..all of us used it in paper 2 maths..which calculator do u use?

one of my friends used Fx-991 ES..which is better..

u can directly get the table by simply typing an expression..
Title: Re: maths doubts
Post by: @d!_†oX!© on October 31, 2009, 09:48:59 am: damn man!!!!
I know about ES too....i used that inititally
but acc. to our school it's not allowed....
we've gottause that s*cky 82 MS
THIS IS BAD!!!!!!!!!!!!
Title: Re: maths doubts
Post by: astarmathsandphysics on October 31, 2009, 09:49:19 am: yes that 991ms is allowed. Brilliant calc. I have one and always recommend it.
Title: Re: maths doubts
Post by: Ghost Of Highbury on October 31, 2009, 09:50:51 am: Quote from: @d!_†oX!© on October 31, 2009, 09:48:59 am
damn man!!!!
I know about ES too....i used that inititally
but acc. to our school it's not allowed....
we've gottause that s*cky 82 MS
THIS IS BAD!!!!!!!!!!!!

hahaha..amazing!!!...wow!!..i mean that fx-81 MS..is the best calci i have ever seen.lol!!..

go buy a new one rite noww!!
Title: Re: maths doubts
Post by: slvri on October 31, 2009, 09:52:15 am: Quote from: @d!_†oX!© on October 31, 2009, 09:45:10 am
dude!!!
fx-991 MS isn't allowed!!!!
really? i uesd 991ms in all my june 2009 papers :P :P :P
and thats good to hear adi.......so which papers have u already given?
Title: Re: maths doubts
Post by: Ghost Of Highbury on October 31, 2009, 09:55:25 am: Quote from: slvri on October 31, 2009, 09:52:15 am
really? i uesd 991ms in all my june 2009 papers :P :P :P
and thats good to hear adi.......so which papers have u already given?

only computer studies finished...as a subject..many more to go, :P
Title: Re: maths doubts
Post by: @d!_†oX!© on October 31, 2009, 10:00:00 am: dude for this question.....don't u just have to find the points of intersection of the both functions!!!!
cuz it says the equation is a simplified form of f(x)=g(x)
so the points where these both grphs meet is the answer.....it says "USE YOU GRAPH"
Title: Re: maths doubts
Post by: Ghost Of Highbury on October 31, 2009, 10:01:47 am: Quote from: cooldude on October 31, 2009, 09:57:06 am

okay i got the soft copy. it was on fep all the time. they usually give us a range, in this q 2.3-2.7 but i got 2.2. i usually find the exact ans by trial and improvement but that method is too time-consuming. so please temme another method to do it. this questions equation simplifies to (x^3)+3(x^2)-3x-27=0, i checked the ans by 991-ms, we get two complex roots and one real root, so if u hve a method to find the real root to about 3-4 sf i would appreciate it.

http://www.freeexampapers.us/IGCSE/Maths/CIE/2004%20Jun/0580_s04_qp_4.pdf (q2 (c) (ii))

there is another method..but its not dere for maths..v have it in add. math..

for this, first - u did some error in ur calci. u get correct values. no complex roots.

and yea..for the answer..u have to draw the curve very accurately..thats the only way ..wat i do is..

find the answer from my calculator..show the intersection in my graph..and write an answer which is close to the calci's answer and the graph answer..

@adi - i guess he already knows that!...he just said that he doesnt get an answer in the range provided in the ms ... hets it close to it!..CHILL MAN!..
Title: Re: maths doubts
Post by: slvri on October 31, 2009, 10:03:21 am: Quote from: A@di on October 31, 2009, 09:55:25 am
only computer studies finished...as a subject..many more to go, :P
was it easy or hard because the june 2009 one was &^&%^@ :P :P :P
Title: Re: maths doubts
Post by: Ghost Of Highbury on October 31, 2009, 10:05:29 am: Quote from: slvri on October 31, 2009, 10:03:21 am
was it easy or hard because the june 2009 one was &^&%^@ :P :P :P

lol..the june 2009 wasnt $#$%@ ... :P.. it was easy..but confronted lots of new questions,, :D
Title: Re: maths doubts
Post by: @d!_†oX!© on October 31, 2009, 10:06:43 am: ya cooldude!!!!!!
fuys pls get us a proof!!!!!!
we have to shut that tiny teacher of ours man!!!!!!!!!
Title: Re: maths doubts
Post by: Ghost Of Highbury on October 31, 2009, 10:13:42 am: Quote from: cooldude on October 31, 2009, 10:06:59 am

yeh dude but since we're not allowed those calcis so we cant get the exact roots. if u silvri or astar have any proof we are gonna stuff it into our maths teachers face on mon when we give fle.
any calcultors shud not be able to have these/or be capable of doing any of these

•   graphic display (tick)
•   data banks (tick)
•   dictionaries (tick)
•   language translators (tick)
•   retrieval or manipulation of text or formulae (tick)
•   QWERT keyboards (tick)
•   built-in symbolic algebra manipulations (tick)
•   symbolic differentiation or integration (not sure abt this, because i can do differentiation in this calci, wat is symbolic differentiation?)
•   capability of remote communication with other machines (tick) (ofcourse not lol :P)
Title: Re: maths doubts
Post by: astarmathsandphysics on October 31, 2009, 10:15:26 am: Quote from: cooldude on October 31, 2009, 09:57:06 am

okay i got the soft copy. it was on fep all the time. they usually give us a range, in this q 2.3-2.7 but i got 2.2. i usually find the exact ans by trial and improvement but that method is too time-consuming. so please temme another method to do it. this questions equation simplifies to (x^3)+3(x^2)-3x-27=0, i checked the ans by 991-ms, we get two complex roots and one real root, so if u hve a method to find the real root to about 3-4 sf i would appreciate it.

http://www.freeexampapers.us/IGCSE/Maths/CIE/2004%20Jun/0580_s04_qp_4.pdf (q2 (c) (ii))

use the Newton raphson method like this:
$\fract {dy}{dx} =f'(x)=3x^2+6x-3$
take $x_0 =2.2$

use $x_{n+1} =x_n- \frac {f(x_n)}{f'(x_n)}$

$x_{1} =x_0- \frac {f(x_0)}{f'(x_0)} =2.2- \frac {2.2^3+3*2.2^2 -3*2.2 -27}{6*2.2^2+6*2.2-3)} =2.2 -\frac{-8.432}{24.72 =2.541$
now put $x_1 =2.541$
$x_2 =2.518$
$x_3 =2.5095$
$x_4 =2.5061$
$x_5 =2.5048$
$x_6 =2.5044$
etc
Title: Re: maths doubts
Post by: @d!_†oX!© on October 31, 2009, 10:15:42 am: Quote from: A@di on October 31, 2009, 10:13:42 am
any calcultors shud not be able to have these/or be capable of doing any of these

•   graphic display (tick)
•   data banks (tick)
•   dictionaries (tick)
•   language translators (tick)
•   retrieval or manipulation of text or formulae (tick)
•   QWERT keyboards (tick)
•   built-in symbolic algebra manipulations (tick)
•   symbolic differentiation or integration (not sure abt this, because i can do differentiation in this calci, wat is symbolic differentiation?)
•   capability of remote communication with other machines (tick) (ofcourse not lol :P)

built-in symbolic algebra manipulations (tick)
that is not a tick dude!!!!!!!!!
Title: Re: maths doubts
Post by: Ghost Of Highbury on October 31, 2009, 10:21:19 am: Quote from: @d!_†oX!© on October 31, 2009, 10:15:42 am
built-in symbolic algebra manipulations (tick)
that is not a tick dude!!!!!!!!!

ofcourse it is a tick

if i define Y = X + 2

and define X as 4

i wont get the value of Y as 6!!
Title: Re: maths doubts
Post by: @d!_†oX!© on October 31, 2009, 10:27:14 am: yeah cooldude...lets give it a shot!!!
nd ya this is from a file that sweetish posted rite???
i got that file too but didnt really pay attention on this.....
By the way aadi...wont the equations that we can solve on it count under this point????
Title: Re: maths doubts
Post by: Ghost Of Highbury on October 31, 2009, 10:29:01 am: Quote from: @d!_†oX!© on October 31, 2009, 10:27:14 am
yeah cooldude...lets give it a shot!!!
nd ya this is from a file that sweetish posted rite???
i got that file too but didnt really pay attention on this.....
By the way aadi...wont the equations that we can solve on it count under this point????

i dont think so ,,, By the way...dont argue now..just show it to her..its good for u...
Title: Re: maths doubts
Post by: @d!_†oX!© on October 31, 2009, 10:31:15 am: give me a link for this file plss aadi
Title: Re: maths doubts
Post by: Ghost Of Highbury on October 31, 2009, 11:12:55 am: Quote from: cooldude on October 31, 2009, 11:08:46 am
and also shudnt the value of f'(x0) while finding x1 be (3*(2.2^2)+(6*2.2)-3) since f'(x)=3(x^2)+6x-3 and not 6(x^2)+6x-3??

wen u differentiate 3x² u get 6x
Title: Re: maths doubts
Post by: Ghost Of Highbury on October 31, 2009, 11:17:58 am: Quote from: cooldude on October 31, 2009, 11:15:42 am

no dude i know that im talking about when finding x1 the derivate of x^3 = 3x^2, read my post carefully again ull see what i mean and can u please post the link for the calculators also, i think theres been a substitution error been made just clarifying though it cud just be a mistake

https://studentforums.biz/index.php/topic,4171.0.html
Title: Re: maths doubts
Post by: @d!_†oX!© on October 31, 2009, 11:20:20 am: cool dude...can u get it printed by monday???
Title: Re: maths doubts
Post by: astarmathsandphysics on October 31, 2009, 11:20:39 am: The number of sf is said in the question. Carry out the calulation until two answers agree to that number of sf.. In the question above you would stop at x_4 (though this gives the wrong answer)