Now after you do that to the quadratics, use substitution to turn u=x+b , so you end up with a fraction that looks like one of the integrals given in the booklet. Get it?

Reply 544

username1162972

18

Original post by Gome44

Do you mean Flemings left/right hand rule? Grip rule is to do with direction of the field or something

Na I mean grip rule.
The thumb is direction of normal vector. With direction vectors being the turn from a to b ie axb.

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Reply 545

math42

20

Original post by nayilgervinho

How do you integrate coth2x

Try using a natural log

Reply 546

nayilgervinho

7

I can't do this question it looks straightforward, but..

https://3a14597dd5c7aa2363f0675717665774b02557b0.googledrive.com/host/0B1ZiqBksUHNYQWE5bVRTVE9BLW8/June%202014%20%28R%29%20QP%20-%20FP3%20Edexcel.pdf

q4a

Reply 547

math42

20

Original post by nayilgervinho

I can't do this question it looks straightforward, but..

https://3a14597dd5c7aa2363f0675717665774b02557b0.googledrive.com/host/0B1ZiqBksUHNYQWE5bVRTVE9BLW8/June%202014%20%28R%29%20QP%20-%20FP3%20Edexcel.pdf

q4a

It isn't really, one of the hardest reductions yet (basically the same idea as the regular 2014 paper). Maybe this will help
x^2(x^2 - a)^(k) = x^2(x^2 - a)^(k) - a(x^2 - a)^(k) + a(x^2 - a)^(k)

Reply 548

nayilgervinho

7

Original post by 1 8 13 20 42

It isn't really, one of the hardest reductions yet (basically the same idea as the regular 2014 paper). Maybe this will help
x^2(x^2 - a)^(k) = x^2(x^2 - a)^(k) - a(x^2 - a)^(k) + a(x^2 - a)^(k)

I tried looking at the mark scheme but I don't understand one of their steps can you just do it, it's the only thing in the paper I can't do.

Reply 549

ninjasinpjs

2

Original post by gagafacea1

I checked myself multiple times. And yeah I'm pretty sure he never said anything about normalizing the vectors. Also see..
Capture dâ€™Ã©cran 2015-06-21 Ã 13.09.01.png

Capture dâ€™Ã©cran 2015-06-21 Ã 13.09.01.png

What was the whole question , ill try it now

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Reply 550

math42

20

Original post by nayilgervinho

I tried looking at the mark scheme but I don't understand one of their steps can you just do it, it's the only thing in the paper I can't do.

I assume you got to having an integral that contains an expression of the form (x^2(3 - x^2)^(n - 1))

x^2(3 - x^2)^(n - 1) = x^2(3 - x^2)^(n - 1) - 3(3 - x^2)^(n - 1) + 3(3 - x^2)^(n - 1)
= (x^2)(3-x^2)^(n - 1) - 3(3 - x^2)^(n - 1) + 3(3 - x^2)^(n - 1)
= (x^2 - 3)(3 - x^2)^(n - 1) + 3(3 - x^2)^(n - 1)
= -(3-x^2)^(n) + 3(3 - x^2)^(n - 1)

And these will give you your In and In-1
(I wasn't looking at the question/was using memory while doing this so if the numbers are in fact not quite the same I apologize)

Reply 551

nayilgervinho

7

Original post by 1 8 13 20 42

I assume you got to having an integral that contains an expression of the form (x^2(3 - x^2)^(n - 1))

x^2(3 - x^2)^(n - 1) = x^2(3 - x^2)^(n - 1) - 3(3 - x^2)^(n - 1) + 3(3 - x^2)^(n - 1)
= (x^2)(3-x^2)^(n - 1) - 3(3 - x^2)^(n - 1) + 3(3 - x^2)^(n - 1)
= (x^2 - 3)(3 - x^2)^(n - 1) + 3(3 - x^2)^(n - 1)
= -(3-x^2)^(n) + 3(3 - x^2)^(n - 1)

And these will give you your In and In-1
(I wasn't looking at the question/was using memory while doing this so if the numbers are in fact not quite the same I apologize)

This paper was harder than june 14 but the grade boundaries were at 65 for an a

Reply 552

username1599987

12

Original post by ninjasinpjs

What was the whole question , ill try it now

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Try ANY question lol, it'll always work. The one I used in the picture was just symmetrical matrix I remember seeing somewhere. The thing is, I don't think you need to normalize the eigenvectors at all!

Reply 553

rachu

8

Original post by gagafacea1

Guys do you know why we have to normalize the eigenvectors when making the orthogonal matrix (in the process of diagonalization)? Because I've tried numerous times, and I saw on one of the MIT OCW videos the professor NOT doing that, and it still works out the same. Btw I looked at the mark scheme and apparently you HAVE to do that (it says unit eigenvectors), I just don't get why?

if you don't normalise then the final diagonal matrix is multiplied by scalars. So to eliminate that, it is normalised so that value of scalar = 1

Reply 554

username1599987

12

Original post by rachu

if you don't normalise then the final diagonal matrix is multiplied by scalars. So to eliminate that, it is normalised so that value of scalar = 1

Okay but look at this:

Original post by gagafacea1

I checked myself multiple times. And yeah I'm pretty sure he never said anything about normalizing the vectors. Also see.. Capture dâ€™Ã©cran 2015-06-21 Ã 13.09.01.png

Reply 555

username1599987

12

Original post by rachu

if you don't normalise then the final diagonal matrix is multiplied by scalars. So to eliminate that, it is normalised so that value of scalar = 1

also this: http://algebra.math.ust.hk/eigen/01_definition/lecture3.shtml

Reply 556

username1259045

17

does anyone have anytips for the reduction questions? i always get stuck of them and i really don't want it to mess up my whole paper. any steps that you usually have to follow? or any methods that you commonly use?? really need help on this :s

Reply 557

Teddysmith123

19

Can some help me with June 10 question 8b

https://2d31ca6ec4f6115572728c3a9168ad5dfc897f33.googledrive.com/host/0B1ZiqBksUHNYSjAyWFYyQmU5Tjg/Edexcel-Set-2/Ch.2%20Further%20Coordinate%20Systems.pdf

I have found X and Y and I subbed them in but I don't get how to simplify for (x^2+y^2)^2

Reply 558

smem_96

1

June 2013, qu 6 a), I've got this so far, but I don't understand what to do next :confused:

someone please help :smile:

june 13 qu 6.pdf198.1KB

Reply 559

username1259045

17

June 2014 ial question 5a
markscheme https://3a14597dd5c7aa2363f0675717665774b02557b0.googledrive.com/host/0B1ZiqBksUHNYQWE5bVRTVE9BLW8/June%202014%20(IAL)%20MS%20%20-%20F3%20Edexcel.pdf

qustion paper https://3a14597dd5c7aa2363f0675717665774b02557b0.googledrive.com/host/0B1ZiqBksUHNYQWE5bVRTVE9BLW8/June%202014%20(IAL)%20QP%20-%20F3%20Edexcel.pdf

i don'tt understand where they got the sin^2(theta) in the first line of the markscheme?? split up cos^n(x) to cos(x)cos^n-1(x) and got v=sinx so where did they get sin^2(x) ???

(by x i mean theta, x is just faster to type)

also questions 7a, how to you simplify 720^3/2 x2/9 ???? calc doesn't give exact ans???

and question8d, i don't understand why they have used 2i+j+3k as the point a i thought A in the vector equation of a line is a point on the line, but they have used the direction vector of it???

(edited 8 years ago)

Edexcel FP3 June 2015 - Official Thread

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