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# STEP Prep Thread 2016 (Mark. II)

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Why bother with a post grad course - waste of time? 17-10-2016
1. (Original post by drandy76)
*sees textbooks worth 40 quid*
*whistles*
*immediately finds a pdf*

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Are you talking about the infamous Spivak's Calculus? It is pretty expensive. However, I feel like it is best for you to buy "First Course in Mathematical Analysis" by J.C Burkill since that one is specifically for this course. Also, I feel like Spivak's Calculus is more borderline Calculus and Analysis than just pure Real Analysis. Differences like these is why I need to ask someone experienced for textbook choice.
2. Guys (FP2 help) how do you turn a locus given by something in terms of complex numbers, into a cartesian equation?!

For example, say you have z1 = 3 + 4j and z2 = -3 + 2j
and you have to find the cartesian equation of the locus given by |z - z1| = 2|z - z2|

... Makes absolutely no sense to me, even the next part that asks me to sketch is confusing me?!
3. (Original post by ComputerMaths97)
Guys (FP2 help) how do you turn a locus given by something in terms of complex numbers, into a cartesian equation?!

For example, say you have z1 = 3 + 4j and z2 = -3 + 2j
and you have to find the cartesian equation of the locus given by |z - z1| = 2|z - z2|

... Makes absolutely no sense to me, even the next part that asks me to sketch is confusing me?!
Let , substitute and then take modulus (square both sides).
4. (Original post by ComputerMaths97)
Guys (FP2 help) how do you turn a locus given by something in terms of complex numbers, into a cartesian equation?!

For example, say you have z1 = 3 + 4j and z2 = -3 + 2j
and you have to find the cartesian equation of the locus given by |z - z1| = 2|z - z2|

... Makes absolutely no sense to me, even the next part that asks me to sketch is confusing me?!
Note that the definition of |x + iy| is root(x^2 + y^2)
5. (Original post by Insight314)
Are you talking about the infamous Spivak's Calculus? It is pretty expensive. However, I feel like it is best for you to buy "First Course in Mathematical Analysis" by J.C Burkill since that one is specifically for this course. Also, I feel like Spivak's Calculus is more borderline Calculus and Analysis than just pure Real Analysis. Differences like these is why I need to ask someone experienced for textbook choice.
Lol yeah, I've got that one too but I had to drop it because I had to revise for exams, completely forgot about it actually :/

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6. (Original post by drandy76)
Lol yeah, I've got that one too but I had to drop it because I had to revise for exams, completely forgot about it actually :/

Posted from TSR Mobile
Go to the Contents page, and compare it to the the parts of Analysis I on https://www.maths.cam.ac.uk/system/files/schedules.pdf. I see why there is a dagger next to it.
7. (Original post by Insight314)
Let , substitute and then take modulus (square both sides).
(Original post by 13 1 20 8 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
8. (Original post by ComputerMaths97)
Nope sorry guys you're going to have to dumb it down for me I apologise
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)
9. (Original post by 13 1 20 8 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

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 Thanks again
10. Mathemagicien,

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

I am watching it right now.
11. 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?
12. (Original post by ComputerMaths97)
Nope sorry guys you're going to have to dumb it down for me I apologise
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...
EDIT: I see you got it already, hope this helps anyway!
13. (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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14. (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:

Attachment 556605556607
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.
Attached Images

15. (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.
16. (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.
17. (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.
18. (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.
19. (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
20. (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:
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