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STEP Prep Thread 2016 (Mark. II)

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Original post by Insight314
Let z=x+iyz = x + iy , substitute and then take modulus (square both sides).


Original post by 1 8 13 20 42
Note that the definition of |x + iy| is root(x^2 + y^2)


Nope sorry guys you're going to have to dumb it down for me I apologise :biggrin:
Original post by ComputerMaths97
Nope sorry guys you're going to have to dumb it down for me I apologise :biggrin:


For instance with your example you have |x + jy - 3 - 4j| = 2|x + jy + 3 - 2j|
giving |(x-3) + j(y-4)| = 2|(x + 3) + j(y - 2)|
By the definition of modulus, and squaring both sides, this means (x - 3)^2 + (y - 4)^2 = 4((x + 3)^2 + (y - 2)^2)
Original post by 1 8 13 20 42
For instance with your example you have |x + jy - 3 - 4j| = 2|x + jy + 3 - 2j|
giving |(x-3) + j(y-4)| = 2|(x + 3) + j(y - 2)|
By the definition of modulus, and squaring both sides, this means (x - 3)^2 + (y - 4)^2 = 4((x + 3)^2 + (y - 2)^2)


Ohhh right I get it now, thank you :biggrin:

Guess if I think about it I should've been able to figure that out by myself, but im going to blame the time of day :biggrin: Thanks again
@Mathemagicien,

Have you seen this - https://www.youtube.com/watch?v=eYqzcqDtL3k ?

I am watching it right now.
For you guys wanting to learn so IA over the summer, just be clear that there is no need to do this. I have never met a single person who did this. Just what are you expecting to get from Cambridge if youre learning the content yourself without the lectures and supervisions?

Ive heard of people who read ahead on 1 or 2 courses, but even that was rare. If you do do this please dont spend money on any textbooks. Lecture notes are available for free online and are perfect for the course. They strip away everything thats not needed and teach what you do need in a concise way. You wont be wasting any time trying to cross reference between the syllabus and your textbook.

Finally, I recommend Groups over any course to read ahead on. Generally found to be one of the more difficult courses, but its a very interesting subject and you wont have seen anything like it before in A-level.

You've just finished STEP, concentrate on your upcoming exams then take at least a month off (preferrably do nothing til September). Youll be doing plenty of maths next year so why start early?
Original post by ComputerMaths97
Nope sorry guys you're going to have to dumb it down for me I apologise :biggrin:

Let z = x+jy.

Then |(x+jy) - (3 + 4j)| = 2*|(x+jy) - (-3 + 2j)|
|(x-3) + (y+4)j| = 2*|(x+3) + (y-2)j|
|(x-3) + (y+4)j|^2 = 4*|(x+3) + (y-2)j|^2
(x-3)^2 + (y+4)^2 = 4*[(x+3)^2 + (y-2)^2]
x^2 - 6x + 9 + y^2 + 8y + 16 = 4(x^2 + 6x + 9) + 4(y^2 - 4y + 4)
x^2 - 6x + 9 + y^2 + 8y + 16 = 4x^2 + 24x + 36 + 4y^2 - 16y + 16
0 = 3x^2 + 30x + 3y^2 - 24y + 27
0 = x^2 + 10x + y^2 - 8y + 9
25 + 16 = x^2 + 10x + 25 + y^2 - 8y + 16 + 9
32 = x^2 + 10x + 25 + y^2 - 8y + 16
(x+5)^2 + (y-4)^2 = 32

God I hope I didn't make any stupid arithmetic mistakes... :smile:
EDIT: I see you got it already, hope this helps anyway!
Original post by raff97
For you guys wanting to learn so IA over the summer, just be clear that there is no need to do this. I have never met a single person who did this. Just what are you expecting to get from Cambridge if youre learning the content yourself without the lectures and supervisions?

Ive heard of people who read ahead on 1 or 2 courses, but even that was rare. If you do do this please dont spend money on any textbooks. Lecture notes are available for free online and are perfect for the course. They strip away everything thats not needed and teach what you do need in a concise way. You wont be wasting any time trying to cross reference between the syllabus and your textbook.

Finally, I recommend Groups over any course to read ahead on. Generally found to be one of the more difficult courses, but its a very interesting subject and you wont have seen anything like it before in A-level.

You've just finished STEP, concentrate on your upcoming exams then take at least a month off (preferrably do nothing til September). Youll be doing plenty of maths next year so why start early?


Well you know more then me, but i spoke to 2-3 people in your year who told me to learn a few courses at tons of people who get firsts wud have learnt a few courses before hand and have familiarity with them


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Original post by raff97
For you guys wanting to learn so IA over the summer, just be clear that there is no need to do this. I have never met a single person who did this. Just what are you expecting to get from Cambridge if youre learning the content yourself without the lectures and supervisions?

Ive heard of people who read ahead on 1 or 2 courses, but even that was rare. If you do do this please dont spend money on any textbooks. Lecture notes are available for free online and are perfect for the course. They strip away everything thats not needed and teach what you do need in a concise way. You wont be wasting any time trying to cross reference between the syllabus and your textbook.

Finally, I recommend Groups over any course to read ahead on. Generally found to be one of the more difficult courses, but its a very interesting subject and you wont have seen anything like it before in A-level.

You've just finished STEP, concentrate on your upcoming exams then take at least a month off (preferrably do nothing til September). Youll be doing plenty of maths next year so why start early?


1) I am probably not going to buy any textbooks (school might be able to buy it for me) but even then, why do you care?
2) I don't think you could waste any time 'cross-referencing' between syllabus and textbook, when most textbooks (especially those with 'daggers' in the recommended section of https://www.maths.cam.ac.uk/system/files/schedules.pdf) contain the topics in chronological order of how the lectures would be scheduled. For example, look at the Analysis I section and tell me it is not almost identical as this one from "First Course in Mathematical Analysis" by J.C. Burkill:

IMG_0493.jpg
Attachment not found

3) If you are afraid of us getting burnt out from maths or anything, can we not relax during the summer and still manage 5 or so hours of uni maths? I don't see the problem in that.

Thanks for recommending group theory though, definitely gonna go through that in the summer. :smile:
Reply 2468
Original post by raff97
You've just finished STEP, concentrate on your upcoming exams then take at least a month off (preferrably do nothing til September). Youll be doing plenty of maths next year so why start early?


This, this, this - so much this. That's precisely what my mindset is like at the moment. I've got no clue how some people can go on and learn IA as soon as they finish their exams (like seriously??), plus it'll make next year a bore anyway.
(edited 7 years ago)
Reply 2469
Original post by Insight314

3) If you are afraid of us getting burnt out from maths or anything, can we not relax during the summer and still manage 5 or so hours of uni maths? I don't see the problem in that.


??? I manage 5 hours of work on an extremely good day in mid-exam season, I think your definition of "relax" is very different from that of a normal person.
Original post by Zacken
??? I manage 5 hours of work on an extremely good day in mid-exam season, I think your definition of "relax" is very different from that of a normal person.


5 hours: 9am to 2pm doing maths and then 2pm to 12am watching movies, TV series, playing games, going out. I can't see the problem in that.
Reply 2471
Original post by Insight314
5 hours: 9am to 2pm doing maths and then 2pm to 12am watching movies, TV series, playing games, going out. I can't see the problem in that.


I'm sure you can't see the problem in that, which is precisely my point.
Original post by Zacken
I'm sure you can't see the problem in that, which is precisely my point.


ye he can leave him alone
Original post by Zacken
I'm sure you can't see the problem in that, which is precisely my point.


OOOOOOOH SNAP THAT WAS A BIT DEEP UNO

Spoiler

Original post by Insight314
5 hours: 9am to 2pm doing maths and then 2pm to 12am watching movies, TV series, playing games, going out. I can't see the problem in that.


Lolllllll hahahahaha. You plan ur fun.


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Original post by physicsmaths
Lolllllll hahahahaha. You plan ur fun.


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:colonhash:
Original post by Zacken
I'm sure you can't see the problem in that, which is precisely my point.


Zacken. Wtf is wrong with u. Dnt be sad coz ur gna get pooled to my college then kings are gna pik my ass up cause they like me from summerpool. Leave insight alone u prick. Just cause u can't do something productive doesn't mean you turn on this ambitious yung boy. Hes gna go far going to cambridge at 16. All the way to CMS.


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Original post by physicsmaths
Well you know more then me, but i spoke to 2-3 people in your year who told me to learn a few courses at tons of people who get firsts wud have learnt a few courses before hand and have familiarity with them


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By all means get familiar with 2-3 courses, but thats not the same as learning all of IA in the summer.

Original post by Insight314
1) I am probably not going to buy any textbooks (school might be able to buy it for me) but even then, why do you care?
2) I don't think you could waste any time 'cross-referencing' between syllabus and textbook, when most textbooks (especially those with 'daggers' in the recommended section of https://www.maths.cam.ac.uk/system/files/schedules.pdf) contain the topics in chronological order of how the lectures would be scheduled. For example, look at the Analysis I section and tell me it is not almost identical as this one from "First Course in Mathematical Analysis" by J.C. Burkill:

IMG_0493.jpg
Attachment not found

3) If you are afraid of us getting burnt out from maths or anything, can we not relax during the summer and still manage 5 or so hours of uni maths? I don't see the problem in that.

Thanks for recommending group theory though, definitely gonna go through that in the summer. :smile:


I've just never heard any complaints about the lecture notes from anyone, so thought Id dissuade anyone reading this thinking they are necessary.

Perhaps you wont get burnt out, but 5 hours is a lot during a holiday is a lot. Some people were doing about that amount during exam term. I know I was...

Also, if you do all 4 example sheets at once without someone checking over them, thers a very good chance your going wrong somewhere. The good thing about doing that at Cambridge is you learn 1/4 of a course then do the example sheet which is checked by your supervisor. He will make sure you're not horribly missing the point somewhere, that you understand the course and just make sure your general question structure is good. You can then take his advice to the next 1/4 of the course and so on.

Also doing example sheets 4 months in advance of supervisions is very counter productive. You will have forgotten what you were doing in some question so will be slightly lost as to what your supervisor is explaining. Heck, Ive done sheets 4-5 days in advance and still forgotten some of my arguments.


You're gonna be at Churchill right? We want as many firsts as we can get! I wouldnt saying this if I didnt want you to do well.
(edited 7 years ago)
Original post by ホク水ね
Anyone got any ideas for II please?

Massive disclaimer: I haven't done paper II yet, but this sounds like you are headed for a low 1/ high 2 as my guess.
Original post by raff97
By all means get familiar with 2-3 courses, but thats not the same as learning all of IA in the summer.



I've just never heard any complaints about the lecture notes from anyone, so thought Id dissuade anyone reading this thinking they are necessary.

Perhaps you wont get burnt out, but 5 hours is a lot during a holiday is a lot. Some people were doing about that amount during exam term. I know I was...

Also, if you do all 4 example sheets at once without someone checking over them, thers a very good chance your going wrong somewhere. The good thing about doing that at Cambridge is you learn 1/4 of a course then do the example sheet which is checked by your supervisor. He will make sure you're not going horribly missing the point somewhere, that you understand the course and just make sure your general question structure is good. You can then take his advice to the next 1/4 of the course and so on.

Also doing example sheets 4 months in advance of supervisions is very counter productive. You will have forgotten what you were doing in some question so will be slightly lost as to what your supervisor is explaining. Heck, Ive done sheets 4-5 days in advance and still forgotten some of my arguments.


You're gonna be at Churchill right? We want as many firsts as we can get! I wouldnt saying this if I didnt want you to do well.


Ah then I fully agree with you :smile:


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