STEP Prep Thread 2016 (Mark. II)

@Insight314 @ Anyone doing fp3 tomorrow

Good luck and lets make the most of our last maths exam this year! https://dec41.user.srcf.net/ await!

Reply 2543

Original post by EnglishMuon

@Insight314 @ Anyone doing fp3 tomorrow

Good luck and lets make the most of our last maths exam this year! https://dec41.user.srcf.net/ await!

Yes! That link is the biggest motivational tool.

Good luck to you too, not that you need it, haha.

Reply 2544

Original post by Insight314

Yes! That link is the biggest motivational tool.

Good luck to you too, not that you need it, haha.

haha thanks, same to u too :tongue:

But actually just to check we are allowed to use the fact a diagonalised matrix consists of the eigenvalues down the leading diagonal without the long winded derivation everytime, yea?

Reply 2545

EricPiphany

17

Original post by EnglishMuon

@Insight314 @ Anyone doing fp3 tomorrow

Good luck and lets make the most of our last maths exam this year! https://dec41.user.srcf.net/ await!

Yeeeeeeaaaaah

Reply 2546

Original post by EnglishMuon

haha thanks, same to u too :tongue:

But actually just to check we are allowed to use the fact a diagonalised matrix consists of the eigenvalues down the leading diagonal without the long winded derivation everytime, yea?

Do you mean deriving the diagonalised matrix using

\textbf{D} = \textbf{P}^T\textbf{A}\textbf{P}

? If you are given eigenvalues, then you write them along the leading diagonal to get the diagonalised matrix, but if you are given eigenvectors then you form

\textbf{P}

which is the matrix with columns consisting of normalised eigenvectors. It depends on what the question is giving you. You can go either way since you can find eigenvalues using eigenvectors and vice versa using the characteristic equation for the matrix, but that would just waste unnecessary time.

Reply 2547

Original post by Insight314

Do you mean deriving the diagonalised matrix using

\textbf{D} = \textbf{P}^T\textbf{A}\textbf{P}

? If you are given eigenvalues, then you write them along the leading diagonal to get the diagonalised matrix, but if you are given eigenvectors then you form

\textbf{P}

which is the matrix with columns consisting of normalised eigenvectors. It depends on what the question is giving you. You can go either way since you can find eigenvalues using eigenvectors and vice versa using the characteristic equation for the matrix, but that would just waste unnecessary time.

yea I just mean when have the eigenvalues can you just straight up write out D or is there some dumb rule where the examiners secretly want the derivation everytime without actually asking for it. But yeah Ill just write it down right away then. I think its one of those stupid things my teacher used to do everytime so I wasnt sure if it was necessary :tongue:

But thanks.

Reply 2548

Original post by EnglishMuon

yea I just mean when have the eigenvalues can you just straight up write out D or is there some dumb rule where the examiners secretly want the derivation everytime without actually asking for it. But yeah Ill just write it down right away then. I think its one of those stupid things my teacher used to do everytime so I wasnt sure if it was necessary :tongue:

But thanks.

Sorry, I am confused. What derivation are you talking about? :biggrin:

If eigenvectors are given, you use

\textbf{D} = \textbf{P}^T\textbf{A}\textbf{P}

and if eigenvalues are given then you just write them down as you are telling me about. You can do it the other way (turning eigenvalues into eigenvectors and then using the alternative method) but there is no point and it would take you way too long.

Reply 2549

Original post by Insight314

Sorry, I am confused. What derivation are you talking about? :biggrin:

If eigenvectors are given, you use

\textbf{D} = \textbf{P}^T\textbf{A}\textbf{P}

and if eigenvalues are given then you just write them down as you are telling me about. You can do it the other way (turning eigenvalues into eigenvectors and then using the alternative method) but there is no point and it would take you way too long.

Yea thats what I mean, when you pointlessly find the eigenvalues then find eigenvectors and do P^TAP. Cus everyone I know doing the exam does that everytime but it seems like a massive time waste XD

Reply 2550

Original post by EnglishMuon

Yea thats what I mean, when you pointlessly find the eigenvalues then find eigenvectors and do P^TAP. Cus everyone I know doing the exam does that everytime but it seems like a massive time waste XD

Yeah, that's not needed. You can literally just place them on the leading diagonal, like you were talking about. :smile:

Reply 2551

Original post by Insight314

Yeah, that's not needed. You can literally just place them on the leading diagonal, like you were talking about. :smile:

Thanks, thats good! Also i looked a little into the "...with physics" course last year but cant remember what the major differences are aside from not doing the numbers and sets part. Is the extra stuff just more mechanics/relativity stuff?

Reply 2552

Original post by EnglishMuon

Thanks, thats good! Also i looked a little into the "...with physics" course last year but cant remember what the major differences are aside from not doing the numbers and sets part. Is the extra stuff just more mechanics/relativity stuff?

Have you taken a look at this - https://www.maths.cam.ac.uk/system/files/text_1.pdf ?

You replace D&R and N&S for first year Physics NatSci courses. Here is more detail on which are replaced, and which ones you are doing from the Physics part:

"The Mathematics with Physics option consists of courses given by the Faculty of Mathematics,which provide about three-quarters of the total workload, and courses given by the Physics department, including practical work, which provide the remaining quarter of the workload. The physics lectures provide a series of short courses on Dynamics,Rotational Mechanics and Special Relativity, Oscillating Systems, Waves and Quantum Waves, and Gravitational and Electromagnetic Fields. (These are the same as those in the first-year Physics component of the Natural Science Tripos.) The mathematical lectures are on Vectors and Matrices, Groups, Differential Equations, Vector Calculus,Analysis and Probability. There is no clash in the timetabling of the options, so that you can attend the lectures for both the Mathematics with Physics option and the Pure and Applied Mathematics option."

Reply 2553

Original post by EnglishMuon

Thanks, thats good! Also i looked a little into the "...with physics" course last year but cant remember what the major differences are aside from not doing the numbers and sets part. Is the extra stuff just more mechanics/relativity stuff?

How did you find it?

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Reply 2554

drandy76

13

FRREEEEEEWDDOOOOOOMMMM

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Reply 2555

Original post by drandy76

FRREEEEEEWDDOOOOOOMMMM

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No Physics tomorrow?

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Reply 2556

ComputerMaths97

17

Anyone else here do the FP2 (MEI) exam this morning? It was horrendous honestly never had a harder A level exam

Reply 2557

Original post by Insight314

How did you find it?

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Ah it was good thanks. I know I made one small error on the sin5x/sinx integration as I got an extra root 3/2 from somewhere but quite confident with the rest. How about u?

Reply 2558

Original post by EnglishMuon

Ah it was good thanks. I know I made one small error on the sin5x/sinx integration as I got an extra root 3/2 from somewhere but quite confident with the rest. How about u?

I found the whole paper pretty easy, finished it fast up to 8 c) and then spent about 30-40 minutes thinking how to tackle 8 c). At the end I got it, although I am not 100% sure I got all the marks, I still think it is 100UMS.

Physics next! :biggrin:

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Reply 2559