Further Mathematics: Post your doubts here!

[OakMoon!]

m too scared abt mechanics i really dont understand much of a things..any advice how can i get prepared till may-june well...
bt P1 and further stats isnt much a problm!!!
can u plz tell me how possibely can i be prepared!!!

I've a similar problem. It's the question number 5 and 11Either that are the real deal. Just do as much past papers as you can. The more you practice, the better you'll get. Post your problems here, and discuss them with your teacher and peers. You need to know the basics of each topic and even if you apply them to each questions you get a few marks. You don't even need to achieve the right answer. Make sure you do 10 years of papers before you go for the finals.

 

[Utsav.]

thnks mate!

 

[abcde]

How can the deduction required for the second part of Q8 be made?
http://www.xtremepapers.com/CIE/Int...el/9231 - Further Mathematics/9231_w05_er.pdf
It's a two mark question and is supposed to be very easy. Yet, at the moment, I cannot come up with the answer. Any F.M student reading this should at least check out the question.

 

[OakMoon!]

How can the deduction required for the second part of Q8 be made?
http://www.xtremepapers.com/CIE/International A And AS Level/9231 - Further Mathematics/9231_w05_er.pdf
It's a two mark question and is supposed to be very easy. Yet, at the moment, I cannot come up with the answer. Any F.M student reading this should at least check out the question.

First of all, you just posted the er. Secondly, this question is all about observation. What is the difference b/w the first and second expression? The x has been replaced by 1-x and vice versa. And so the same will happen with the x co-ordinate of centroid. 3/5 replaced with 1-3/5=2/5.

 

[abcde]

First of all, you just posted the er. Secondly, this question is all about observation. What is the difference b/w the first and second expression? The x has been replaced by 1-x and vice versa. And so the same will happen with the x co-ordinate of centroid. 3/5 replaced with 1-3/5=2/5.

My bad! Here's the qp: http://www.xtremepapers.com/CIE/Int.../9231 - Further Mathematics/9231_w05_qp_1.pdf
I get your point but why will the same happen with the x-coordinate of the centroid and why will the y-coordinate not change? I'm missing a line of argument. :/

 

[OakMoon!]

It's much like scaling or substitution you can say. The only thing that has changed is x with 1-x.
To make it more logical you can say that the co-ordinates of the centroid of second curve are (z,y) where z=1-x. If you use this substitution the second equation becomes y=(1-z)(z)² which is the same as the first equation and that is the reason y remains the same.

 

[steel]

Fur math (mechanic ) HELP !

 

[fhdaly]

Where can I study SUMMATION OF SERIES and MATHEMATICAL INDUCTION from? thanks.

 

[abcde]

Where can I study SUMMATION OF SERIES and MATHEMATICAL INDUCTION from? thanks.

1. Further Pure Mathematics, Bostock & Chandler.
2. Further Pure Mathematics, Gaulter & Gaulter.
3. http://patrickjmt.com/

 

[mrpaudel]

I have just started learning it from the internet as i m interested in maths...

Now, i got a prblm in Polar Coordinates. I don't have any teacher so thot it would be better if i posted my question here.

I can plot the graph and all..But, got confused in basic things..may be my concept is wrong or whatever, i hope u ppl will correct me.

r= radius or say length..So, how can the length be negative?
Like, if we need to convert from cartesian to polar...suppose (-1, -√3) into polar, then r=√(-1)^2 + (-√3)^2 to give 2....then, we don't get any negative values of r while converting..so where the hell from r turned negative as well?

 

[abcde]

I have just started learning it from the internet as i m interested in maths...

Now, i got a prblm in Polar Coordinates. I don't have any teacher so thot it would be better if i posted my question here.

I can plot the graph and all..But, got confused in basic things..may be my concept is wrong or whatever, i hope u ppl will correct me.

r= radius or say length..So, how can the length be negative?
Like, if we need to convert from cartesian to polar...suppose (-1, -√3) into polar, then r=√(-1)^2 + (-√3)^2 to give 2....then, we don't get any negative values of r while converting..so where the hell from r turned negative as well?

r isn't negative. Where did r 'turn negative', sir?

 

[OakMoon!]

R is more like a vector than only a magnitude. When r is negative it just becomes symmetrical about the pole(origin) i.e. it changes its direction to the opposite side.
For e.g:


Remember that (-2,45) is the same thing as (2, 225) or (2, -135). This is the difference b/w cartesian and polar co-ordinates that one point in polar curves can have many co-ordinates.

 

[OakMoon!]

Here, I found some notes that support my explanation:
http://tutorial.math.lamar.edu/Classes/CalcII/PolarCoordinates.aspx

 

[abcde]

AoA!
http://www.xtremepapers.com/CIE/International A And AS Level/9231 - Further Mathematics/9231_w06_qp_1.pdf
I need help with the very last part of 12 OR where it is asked to prove that the limit of S/hs as lambda approaches infinity is 4 pi.

Also: http://www.xtremepapers.com/CIE/International A And AS Level/9231 - Further Mathematics/9231_s08_qp_1.pdf
Q1. I'm only familiar with finding the centroids of 2D shapes. Is there a different formula for finding the centroid of a cone/3D shape? (The er mentions xy^2 in place of the usual xy while finding the centroid. Why that?) :S

 

[OakMoon!]

If you don't know what I did for the infinity limits pick up bostock and chandler's Mathematics (not FM) book and look at the Series (something) chapter.

Yes, there is separate formula for the 3D shape. That is the centroid of volume or mass. They are given above at the end of the picture. Only difference is the extra y in each term. And yes, don't mind my awesome writing and neatness of the scan.

 

[steel]

where can i get Fur Maths Making scheme ? from 2002 to 2007 ??

 

[abcde]

where can i get Fur Maths Making scheme ? from 2002 to 2007 ??

You can't. CIE did not publish the ms for these years.

 

[mrpaudel]

r isn't negative. Where did r 'turn negative', sir?

I don't know..may be i got wrong while explaining.....hamidali391 made me clear i guess..!! well, learning on yourself has this kind of disadvantages

 

[MW24595]

Hmm, I have a doubt.

Determine the value of m such that the equations

x^3+ mx- 1 = 0 and x^3- 3x + m= 0

have a common root. I eliminate x^3 and x from the equations to try and get an equation for m. I somehow end up with a quartic equation in m, which I can't really solve. Any ideas, guys?

 

[abcde]

Hmm, I have a doubt.

Determine the value of m such that the equations

x^3+ mx- 1 = 0 and x^3- 3x + m= 0

have a common root. I eliminate x^3 and x from the equations to try and get an equation for m. I somehow end up with a quartic equation in m, which I can't really solve. Any ideas, guys?

AoA!
Is the answer m = -2 ?
After elimination, you probably end up with x = (m+1)/(m+3). Insert this value into any one of the equations. (You'll end up with a cubic equation in case of the 1st equation and a quartic one in case of the second.) I was about to proceed with synthetic division of the resulting equation when a trial-and-error method showed that m= -2 satisfied both equations in m. When m = -2, x = -1 is a common root. This did not even require solving the complete cubic/quartic equation in 'm'.