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# STEP Prep Thread 2016 (Mark. II)

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1. (Original post by 13 1 20 8 42)
Merit in AEA is probably easier
(Warwick consider distinction in AEA equivalent to a 2 in any STEP, they probably know better than me)
Cool.

Bath have the "2 in any STEP or Merit in AEA requirement"...
2. (Original post by jneill)
Cool.

Bath have the "2 in any STEP or Merit in AEA requirement"...
Probably no harm in doing both, I didn't bother with AEA but the papers are pretty fun
3. (Original post by 13 1 20 8 42)
Probably no harm in doing both, I didn't bother with AEA but the papers are pretty fun
That might be a plan...
4. (Original post by jneill)
Folks, how does STEP I compare with AEA.

Specifically, a requirement to achieve 2 in STEP I vs Merit in AEA - which is "easier"...?
Merit in AEA.
5. (Original post by jneill)
That might be a plan...
Yeah A distinction in AEA is much easier than a 2 in STEP I. Id say AEA is more comparable to the MAT than STEP.
6. (Original post by EnglishMuon)
Yeah A distinction in AEA is much easier than a 2 in STEP I. Id say AEA is more comparable to the MAT than STEP.
Distinction, or Merit? My comparison was 2 in STEP vs Merit in AEA
7. (Original post by EnglishMuon)
Yeah A distinction in AEA is much easier than a 2 in STEP I. Id say AEA is more comparable to the MAT than STEP.
I would say MAT is certainly harder than AEA (at least in my opinion), I messed up my MAT so bad that I didn't ask for my mark but Imperial still accepted me lol.
8. (Original post by jneill)
Distinction, or Merit? My comparison was 2 in STEP vs Merit in AEA
yep I think distinction. I know a couple people who took AEA last year and so long as you are good with rearranging the problem solving part isnt that hard, so in that sense it depends what you prefer to be doing. Its that sort of accuracy but less detail vs more detail but less fiddly (step) kind of thing
9. (Original post by IrrationalRoot)
I would say MAT is certainly harder than AEA (at least in my opinion), I messed up my MAT so bad that I didn't ask for my mark but Imperial still accepted me lol.
lol same with me. I did AEA papers in prep for MAT but the MAT papers felt less obvious (although id hope theyd seem trivial now! )
10. STEP III 2015, Q5, part (ii):
Spoiler:
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Isn't proving that the cube root of 2 is irrational enough to do the second part of (ii)? Letting S = {n | n is natural and n*2^1/3 is an integer} and knowing that 2^1/3 < 2 gives the same contradiction. Now, if 2^2/3 is rational, then 2^1/3 is rational (first part of (ii)), which we just proved false, so 2^2/3 is also irrational.

I'm asking because the set proposed in the mark scheme is different from mine.
11. (Original post by EnglishMuon)
yep I think distinction. I know a couple people who took AEA last year and so long as you are good with rearranging the problem solving part isnt that hard, so in that sense it depends what you prefer to be doing. Its that sort of accuracy but less detail vs more detail but less fiddly (step) kind of thing
So if a Distinction is easier than a 2 then a Merit is even easier... Coolio.
12. (Original post by jneill)
Folks, how does STEP I compare with AEA.

Specifically, a requirement to achieve 2 in STEP I vs Merit in AEA - which is "easier"...?
Merit in AEA is a lot easier than a 2 in STEP 1.
Distinction in AEA is slightly easier than a 2 in STEP 1.
13. (Original post by to4ka)
STEP III 2015, Q5, part (ii):
Spoiler:
Show
Isn't proving that the cube root of 2 is irrational enough to do the second part of (ii)? Letting S = {n | n is natural and n*2^1/3 is an integer} and knowing that 2^1/3 < 2 gives the same contradiction. Now, if 2^2/3 is rational, then 2^1/3 is rational (first part of (ii)), which we just proved false, so 2^2/3 is also irrational.

I'm asking because the set proposed in the mark scheme is different from mine.
That was my method as well. Can't see why they wouldn't accept it, in fact imo it's a cleaner solution
14. Could I have some advice about (iv) of Q 2 III 2015?
Spoiler:
Show
So the ms does some induction, however I did another method (although it isnt 'cleaner' but I still believe it works (although maybe a little harder to justify):

Let . Then the difference between two consecutive terms (n and n-1) is for s,t respectively. and then the difference between these two consective differences is respectively. As increases, its clear 2^{n-2} > 2 for all n>3 hence the difference between 2 terms (rate of increase) is eventually greater for all n greater than some m so 2^n>n^2 for all n > than some n. Is this valid? How many marks would I likely get for this?
15. (Original post by EnglishMuon)
Could I have some advice about (iv) of Q 2 III 2015?
Spoiler:
Show
So the ms does some induction, however I did another method (although it isnt 'cleaner' but I still believe it works (although maybe a little harder to justify):

Let . Then the difference between two consecutive terms (n and n-1) is for s,t respectively. and then the difference between these two consective differences is respectively. As increases, its clear 2^{n-2} > 2 for all n>3 hence the difference between 2 terms (rate of increase) is eventually greater for all n greater than some m so 2^n>n^2 for all n > than some n. Is this valid? How many marks would I likely get for this?
Spoiler:
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"you should give a proof which includes an explicit determination of an appropriate m"

I think your method is fine, but you will lose a mark if you don't mention some value for m.
16. (Original post by to4ka)
Spoiler:
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"you should give a proof which includes an explicit determination of an appropriate m"

I think your method is fine, but you will lose a mark if you don't mention some value for m.
Spoiler:
Show
thankyou. I did write down the correct value of m at the end, but the only problem Im having is that my method doesnt explicitly show that m=4 is the correct value for which 2^n overtakes n^2 (i.e. n=1, 2^1>1^2, 2^3<3^2). All I do know is that it occurs for some value of m, whereas with the inductive method we can guess this is the value then prove it. Do u reckon docking 2/3 marks then is reasonable?
17. (Original post by EnglishMuon)
Spoiler:
Show
thankyou. I did write down the correct value of m at the end, but the only problem Im having is that my method doesnt explicitly show that m=4 is the correct value for which 2^n overtakes n^2 (i.e. n=1, 2^1>1^2, 2^3<3^2). All I do know is that it occurs for some value of m, whereas with the inductive method we can guess this is the value then prove it. Do u reckon docking 2/3 marks then is reasonable?
Spoiler:
Show
If sn < tn from some point on (call that m), then sn < tn is also true from, say, m + 10. What I'm saying is m=4 isn't the value; also check the hints and solutions file, they say "we can choose m=4", so no, I wouldn't take away any marks.

How did you find the paper as a whole? I struggled a lot with 2011-2014 but this one was, strangely, a very easy S for me.
18. (Original post by EnglishMuon)
Spoiler:
Show
thankyou. I did write down the correct value of m at the end, but the only problem Im having is that my method doesnt explicitly show that m=4 is the correct value for which 2^n overtakes n^2 (i.e. n=1, 2^1>1^2, 2^3<3^2). All I do know is that it occurs for some value of m, whereas with the inductive method we can guess this is the value then prove it. Do u reckon docking 2/3 marks then is reasonable?
I used a similar sort of idea but more rigorous
Spoiler:
Show
n^2<2^n is equivalent to n/ln(n)>2/ln(2) and differentiation shows that n/ln(n) is strictly increasing for all n>e. 5>e and 5^2<2^5 so we can choose m=5 and we're done.
19. (Original post by to4ka)
Spoiler:
Show
If sn < tn from some point on (call that m), then sn < tn is also true from, say, m + 10. What I'm saying is m=4 isn't the value; also check the hints and solutions file, they say "we can choose m=4", so no, I wouldn't take away any marks.

How did you find the paper as a whole? I struggled a lot with 2011-2014 but this one was, strangely, a very easy S for me.
ok, well Ill deduct 1 just incase anyway , but thanks! But yeah I have to admit this was a much easier paper than usual for III. Normally I can get a 'healthy' S by about 5 or so marks, but think I got ~105,110 in this one. I just hope Thursdays isnt too much worse.
20. If anyone has the time give me a quick mark approximation from I and II (I didn't do great so should be that many marks to 'count' xD)
STEP I
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Q1 - Full, correct.
Q2 - Did at last second, so only differentiated the terms but didn't get to full simplify - hopefully some credit? Might've got it wrong too, very rushed.
Q3 - Did the full question but it seems a got a few things wrong, however I explained everything I did in a lot of detail (every point, every change etc) so hopefully lots of method marks? I think I got parts ii, iii and iv not perfect, with a few errors in each. Just assume I got them wrong I guess.
Q7 - Got parts i and ii perfect, but was stuck on part iii. Did a good 10 minutes of work on iii but was unable to prove anything so there might be something to credit there? I specified quite a few things just couldn't put it all into a nice proof.
Q8 - Only did part i: Got the first one correct, did the 2nd one but couldn't find Un for some reason, really obvious now I see it. Then of course I messed up the next part as I was unable to use the "hence" so had to try find it another way, in which I fully worked through but got the wrong answer.
Q12 - Part i correct. Part ii I used the exact same method as part i but got the wrong answer so there must be a mistake in there. Part iii I worked through fully but didn't get any of it correct, used a multiple of p2 for the formula, but I couldn't find a way of getting p1 in there. So bascially got part iii completely wrong, just 30 minutes of work for nothing
As you can tell, a few little mistakes led to some wrong answers and some big mess ups, but hopefully some credit throughout it. Hoping for a 2 but I've accepted I will be quite lucky to get that.

STEP II
Spoiler:
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Q1 - Tried it but could not show they met on the curve c2. Spent way too long on Q1 because of my belief of them automatically being my best chance of a full solution About 3 pages of working and couldn't prove it xD
Q2 - Correct part i(although didn't do any of this f(a,b,c) stuff I see everyone else did, but I got all the solutions correct). Part ii I worked mostly through and got x=2 but didn't have time to get the other two solutions.
Q3 - Part i and ii perfect. Part iii I proved the f'n(a)f'n(b)<0 but could not figure out how to do the sketch part so stopped there.
Q12 - I proved the first part and then got part i right and nothing after that.
Really didn't want to completely fail this but it seems I have xD Really frustrating I forgot how to do the first part of Q7 so stupidly didn't bother doing it, looks an easy question now I look back. Also Q6 looked pretty nice. I screwed myself over by having so much faith in Q1, lost a full hour to that. Then saw Q2 and Q3 were doable so just automatically did them. Big mistake with time management and exam technique here.

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