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Further Mathematics: Post your doubts here!

U

usman123

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My paper is in a week time so if anybody can help me in any part of following questions, I will be very gratefull to him/her.
Question 4 June 03 Paper2 http://www.xtremepapers.com/papers/...athematics - Further (9231)/9231_s03_qp_2.pdf

Question 11 November 5 Paper2 http://www.xtremepapers.com/papers/...athematics - Further (9231)/9231_w05_qp_2.pdf

question 4 June 06 Paper 2 http://www.xtremepapers.com/papers/...athematics - Further (9231)/9231_s06_qp_2.pdf

question 1,2,3 November 6 Paper 2http://www.xtremepapers.com/papers/...athematics - Further (9231)/9231_w06_qp_2.pdf


Please help me!!!!!!!!!!!!!!!!
 
M

MW24595

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Shalan said:
when do we assume equal population variances for a t test ?
Click to expand...

When neither of the variances have been given, and the test involves both distributions, you calculate a Pooled- Variance. Otherwise, the variances will be stated to be different.
 
DragonCub

DragonCub

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Glaedr93 said:
How do we do questions like s09 p1 Q.9 last part?

http://www.xtremepapers.com/papers/CIE/Cambridge International A and AS Level/Mathematics - Further (9231)/9231_s09_qp_1.pdf
Click to expand...
This is how I think (I'm not sure if it is nonsense :p)
k^n × A^n = (k^n) P (D^n) (P^-1) = P × (k A)^n × P^-1
So I think just need to ensure that k A has all elements less than 1 and greater than -1. Then the whole thing tends to 0 as n gets larger.
Here the Diagonal matrix you came up with should be like this:
1 0 0
0 5 0
0 0 7
The non-zero numbers' orders may be different but it doesn't matter.
Here to make these three all > -1 and < 1, k should be < 1 and > -1.
So the set is -1 < k < 1.
Hope my reponse is helpful to you. :)
 
V

varadhjain

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How do you do Q6, p13 Summer 2011
How's the prep going for tomorrows exam?
Anyone expecting A*'s? (not me LOL)
 
grumpy

grumpy

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yara please aik baat batao
ye z^5 +1 ko kese factorise karte hai jaldi
 
G

Glaedr93

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DragonCub said:
This is how I think (I'm not sure if it is nonsense :p)
k^n × A^n = (k^n) P (D^n) (P^-1) = P × (k A)^n × P^-1
So I think just need to ensure that k A has all elements less than 1 and greater than -1. Then the whole thing tends to 0 as n gets larger.
Here the Diagonal matrix you came up with should be like this:
1 0 0
0 5 0
0 0 7
The non-zero numbers' orders may be different but it doesn't matter.
Here to make these three all > -1 and < 1, k should be < 1 and > -1.
So the set is -1 < k < 1.
Hope my reponse is helpful to you. :)
Click to expand...

But the MS says -1/7 < k < 1/7
 
DragonCub

DragonCub

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Glaedr93 said:
But the MS says -1/7 < k < 1/7
Click to expand...
Ouch I know where I got wrong...
In D, the numbers are 1, 5 and 7. Here 7 is the largest. So we need to ensure that -1 < 7 k < 1. The answer is then that stated on the MS.
Sorry about my mistake. :p
 
M

MW24595

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Exactly, essentially, for the diagonal to limit to 0, mod(7/k)<1. Solving that leads easily to the above answer.
 
M

MW24595

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varadhjain said:
How do you do Q6, p13 Summer 2011
How's the prep going for tomorrows exam?
Anyone expecting A*'s? (not me LOL)
Click to expand...

Haha, preps going good. I hope so, lol.
And your question's simple really. You just have to pay attention to the wording and your diagram.

Now, the diagram should be simple enough, just use your protractor, scale and calculator.
Label both curves and the intersection point. It helps.

Next, to find the intersection point's angle, simply equate the equations with each other and find theta.
So, you have a= 2a cos 2(theta) which gives you, (theta)= pi/6.

Now, to find the area, just use the area of a sector in polar co-ordinates formula, i.e (integral)0.5 r^2 d(theta). Gosh, math is a piss off on the keyboard. lol.
First find the area under curve 1 with limits 0 to (pi/6) and add that to the area of curve 2 with limits (pi/6) to (pi/4). The integrals are easy enough. You need the double angle cos formula though. 2cos^2(theta)-1 = cos 4(theta).

Proceed to evaluate. Easy as Pi. :p

Now I have a question which, may seem stupid, but I just need to be sure. In this question- Q6, P13 MJ11- the domain of theta hasn't been given for the first curve.
Do we assume that the domain given for C2 applies here too? Or do we draw the entire curve from 0 to 2pi?
Good luck everybody.
 
M

MW24595

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Gosh, and can somebody please post up all the vector distance formulas? :/ I'm still rather struggling with the concept of Vector projection and calculating distances. Are there any specific notes or tips for that?
 
DragonCub

DragonCub

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MW24595 said:
Gosh, and can somebody please post up all the vector distance formulas? :/ I'm still rather struggling with the concept of Vector projection and calculating distances. Are there any specific notes or tips for that?
Click to expand...
I don't remember them all, but these should be of use:

projection length a onto b = a dot b / |b|

distance between two skew lines l1 and l2:
find a point A on l1 and B on l2
distance = AB dot (l1 cross l2) / |l1 cross l2|

distance between two parallel planes:
similar to the lines
distance = AB dot n / |n|

area of triangle AOB:
|OA cross OB| / 2
 
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