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

Qualification => IGCSE/ GCSE => Reference Material => Topic started by: ismailb_1993 on May 18, 2010, 09:58:23 am

Title: Math Paper 4
Post by: ismailb_1993 on May 18, 2010, 09:58:23 am
As we all know, the last question will probably be on sequences....does anyone have any useful notes regarding them??
Title: Re: Math Paper 4
Post by: ismailb_1993 on May 18, 2010, 10:07:02 am
and maybe some tips on graphs would help?

also i had a question in regards to function graphs...
sometimes you have to plot the points of a function...and they sometimes ask to find the inverse of a point for intance f^-1(5)...in this case what should i do?
Title: Re: Math Paper 4
Post by: BusinessMaNiac! ( Shizzle) on May 18, 2010, 02:12:15 pm
First find the inverse..
then the answer u get, use it on the x-axis....

Sometimes they give gf(x)...
In this case, u wud start from the Left eh?
::)
Title: Re: Math Paper 4
Post by: ismailb_1993 on May 18, 2010, 02:20:27 pm
First find the inverse..
then the answer u get, use it on the x-axis....

Sometimes they give gf(x)...
In this case, u wud start from the Left eh?
::)

shazil? if ive mistaken you then sorry

but i see this questions are usually worth 1 mark...and the process you have outlined is worth atleast 3 marks.
Title: Re: Math Paper 4
Post by: pap19 on May 18, 2010, 02:25:06 pm
pls tell me fast hot to do entire question no3 of maths paper 4 oct/nov 2000
Title: Re: Math Paper 4
Post by: ismailb_1993 on May 18, 2010, 02:32:40 pm
pls tell me fast hot to do entire question no3 of maths paper 4 oct/nov 2000

you can use the cos rule for the first question...you know three of the lengths of the triangle that is 4,5,6. calc as follows:

to find abc
(4^2+5^2-6^2) / (2x4x5)

when you get the answer of that you use cos^-1 and you get the angle ABC

for B.) and C.) ill have to draw it which i obviously cant do here.
Title: Re: Math Paper 4
Post by: Saavya on May 18, 2010, 02:44:14 pm
'Common Difference' Sequences

The general term for term number 'n' , common diff. 'd' and first term 'a'is:

dn + (a-d)

Find the nth term in this sequence : 13, 20, 27, 34, 41, 48 ...

a=13, d= 7

nth term = dn + (a-d) = 7n + (13-7) = 7n +6

this is one way of finding the nth term but its long i knoww

i get confused with the other ones though
Title: Re: Math Paper 4
Post by: Aayesha on May 18, 2010, 03:02:10 pm
yeah ..but how to find it when there is no common difference between the terms ???? ???
Title: Re: Math Paper 4
Post by: ismailb_1993 on May 18, 2010, 03:08:39 pm
yeah ..but how to find it when there is no common difference between the terms ???? ???

those are the other ones she's talking about :(
Title: Re: Math Paper 4
Post by: ismailb_1993 on May 18, 2010, 03:09:11 pm
'Common Difference' Sequences

The general term for term number 'n' , common diff. 'd' and first term 'a'is:

dn + (a-d)

Find the nth term in this sequence : 13, 20, 27, 34, 41, 48 ...

a=13, d= 7

nth term = dn + (a-d) = 7n + (13-7) = 7n +6


this is one way of finding the nth term but its long i knoww

i get confused with the other ones though


thanks alot!!! thats really helpful!!
Title: Re: Math Paper 4
Post by: Aayesha on May 18, 2010, 03:13:09 pm
oh okay. Thanks  :)
Title: Re: Math Paper 4
Post by: diva_sparkles on May 18, 2010, 03:15:26 pm
thanks alot!!! thats really helpful!!


no actualy this is used whn there is a common difference!!
otherwise u hv to find someother way 2 do it
Title: Re: Math Paper 4
Post by: Saavya on May 18, 2010, 03:16:35 pm
'Changing Difference' Sequences

The general term for term number 'n' , common diff. 'd' , first term 'a' and difference change 'c'is:

a+d(n-1)+c/2(n-1)(n-2)

i cant remember this one its long and u have to solve so many steps in order to reach the nth term

eg. find the nth term of 5, 7, 10, 14, 19 ........

remembering that the nth term is given by:

        1st term, 'a' =5

        first difference 'd' = 2

        difference increase 'c' = 1

replace and see what u get

i will only rely on my brain for this one
Title: Re: Math Paper 4
Post by: Saavya on May 18, 2010, 03:18:07 pm
thanks alot!!! thats really helpful!!



ur welcome :)
Title: Re: Math Paper 4
Post by: Saavya on May 18, 2010, 03:19:24 pm
no actualy this is used whn there is a common difference!!
otherwise u hv to find someother way 2 do it


the other way is to use yer brain im goin 2 do that for the changing difference ones :(
Title: Re: Math Paper 4
Post by: luv3life on May 18, 2010, 03:25:19 pm
For number patterns, my teacher gave me a method to find the equations...


First, find the diffrence between all the 2 consecutive numbers.

(1) If the differences are the same in the very first try, the equation to find the nth term will be in the first degree, which is:
nth Term = an + b,
Now replace a & b with numbers. You gotta do this by trial and error, I think.

(2) If the differnces are different in the first try, find the differences of the preveious differences. If they are same here, in the second try, the equation to find the nth term will be in the second degree, which is:
nth Term = an2 + bn + c
Now replace a, b & c with numbers. You gotta do this by trial and error, I think.

(3) If the diffrences are still diffrenet in the second try, ind the differences of the preveious differences. If they are the same, in the third try, the equation to find the nth term will be in the third degree, which is:
nth Term = an3 + bn2 + cn + d
Now replace a, b, c, & d with numbers. You gotta do this by trial and error, I think.


It's kind of long when you do it the first time, but once you get used to, it's easy, yet long. But it'll always get you the correct numbers. Most often, you just guess some of the equations. Like try- n2, n3, (n+/-1)2, and such.

You need lots of practice to do these quickly in the exams. Hopefully, I've practiced enough. :P



Hope I helped. All the best, guys. :D
Title: Re: Math Paper 4
Post by: ismailb_1993 on May 18, 2010, 03:41:19 pm
no actualy this is used whn there is a common difference!!
otherwise u hv to find someother way 2 do it

that's exactly what was said. the heading of the post was 'common difference'
Title: Re: Math Paper 4
Post by: BusinessMaNiac! ( Shizzle) on May 18, 2010, 03:47:13 pm
For number patterns, my teacher gave me a method to find the equations...


First, find the diffrence between all the 2 consecutive numbers.

(1) If the differences are the same in the very first try, the equation to find the nth term will be in the first degree, which is:
nth Term = an + b,
Now replace a & b with numbers. You gotta do this by trial and error, I think.

(2) If the differnces are different in the first try, find the differences of the preveious differences. If they are same here, in the second try, the equation to find the nth term will be in the second degree, which is:
nth Term = an2 + bn + c
Now replace a, b & c with numbers. You gotta do this by trial and error, I think.

(3) If the diffrences are still diffrenet in the second try, ind the differences of the preveious differences. If they are the same, in the third try, the equation to find the nth term will be in the third degree, which is:
nth Term = an3 + bn2 + cn + d
Now replace a, b, c, & d with numbers. You gotta do this by trial and error, I think.


It's kind of long when you do it the first time, but once you get used to, it's easy, yet long. But it'll always get you the correct numbers. Most often, you just guess some of the equations. Like try- n2, n3, (n+/-1)2, and such.

You need lots of practice to do these quickly in the exams. Hopefully, I've practiced enough. :P



Hope I helped. All the best, guys. :D



Thanks alot..
This Kinda Helped:P..... =D xD
Title: Re: Math Paper 4
Post by: BusinessMaNiac! ( Shizzle) on May 18, 2010, 03:49:42 pm
shazil? if ive mistaken you then sorry

but i see this questions are usually worth 1 mark...and the process you have outlined is worth atleast 3 marks.

Back off jerk!... i know this trick.. its old school now.."hey i think i no u"...
-.-
 >:( >:( >:( >:( >:( >:( >:( >:( >:( >:(

"unwanted relationships nowadays, i tell ya!"
[/size][/color]
Title: Re: Math Paper 4
Post by: ismailb_1993 on May 18, 2010, 03:59:26 pm
Back off jerk!... i know this trick.. its old school now.."hey i think i no u"...
-.-
 >:( >:( >:( >:( >:( >:( >:( >:( >:( >:(

"unwanted relationships nowadays, i tell ya!"
[/size][/color]

I said "sorry if i have mistaken you for someone else"

If there's any jerk in this situation you'd be the Merriam Webster definition. In fact you may also be the merriam webster definition for a jerk-off aswell. Go hide in a hole..don't worry, no one will notice you're gone.
Title: Re: Math Paper 4
Post by: holtadit on May 18, 2010, 05:49:46 pm
No fighting will be tolerated on the public forum.

Please continue your discussion on the PM service provided.

Thank You !
Title: Re: Math Paper 4
Post by: luv3life on May 19, 2010, 11:20:39 am
EEE!!! I did my Maths paper 4 today... It was great! :D Hopibng for an A* in Math. :) 'because Paper 2 also went well. Well, atleast according to me, it did. :P

Anyone else did it yet? How was it for you guys? :D