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# STEP Prep Thread 2016 (Mark. II)

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1. Can an S in STEP 1 make up for a high 2 in STEP 2? That is, supposing that STEP 3 goes to plan...
2. (Original post by Gunawardana)
Did I get a 1 with this?
Certainly.
3. (Original post by Zacken)
Certainly.
k thnx
4. (Original post by Zacken)
I cut myself 11 marks in Q1 for doing the cubic wrong, not showing the graphs intersect and not showing the locus. i.e: only 9 marks for writing down the tangents to the curves, equating them and solving for x and y, and writing down a cubic and getting the shapes of the graph right.

Then cut myself 2 marks in Q3 for a dubious justification of the even n case.

Gave myself 9 marks in Q4 for what I've listed, given that I did the y^2 + 1 > 4(y-1)^2 bit wrong and didn't try finding x or tan theta.

12 marks in Q6 for doing the first three parts and not the last (iv) part.

17 marks in Q7 for doing pretty much all of it but slipped at the end of the last integral.

9 marks in Q8 for the measly attempt I have.
I did a similar thing in Q1, and I'm inclined to be a bit more generous, maybe 10-14 marks. I feel like the first three parts of Q6 will be worth more than 12 marks, though I'm not sure exactly what. And I think you'd lose at most 1 mark in Q3 for dubious justification (not that that will make much of a difference).
5. (Original post by IrrationalRoot)
Wow it seems like we both have a problem with exam conditions, I also underperformed, got only 1 full solution (integration in less than 20 mins lol) and then did as much of 5 others as I could. Luckily I got an almost full in Q3 (or whatever the one with the almost e^x series was) at the end.
Pretty sure I got a 1 but not an S.
Seems unfair that you're not getting S's in these though with how good you are .
Hopefully STEP III goes well.
Ah, a 1 is really good though. I had the same problem with not getting complete solutions, that last part of the DE question was pure death. Only got fulls to Q7 and 3 and then measly pathetic partials to 4 other questions.
6. (Original post by sweeneyrod)
I did a similar thing in Q1, and I'm inclined to be a bit more generous, maybe 10-14 marks. I feel like the first three parts of Q6 will be worth more than 12 marks, though I'm not sure exactly what. And I think you'd lose at most 1 mark in Q3 for dubious justification (not that that will make much of a difference).
Ah, cheers. Hoping Q1 will be a bit generous, but I can't see the parts that I've done being worth very much. If only I'd solved that cubic properly, arghhhhh.

(at this point, 1 mark is going to make a lot of a difference )

Thanks!
7. (Original post by Zacken)
x
For question 3, you don't need to investigate the possibility of repeated roots. f_n(x) and f'_n(x) can't both be 0 unless x = 0, and there is obviously no root there.
8. (Original post by Remyxomatosis)
Can an S in STEP 1 make up for a high 2 in STEP 2? That is, supposing that STEP 3 goes to plan...
Yes, I think you would be likely to get in with S, 2, 1. Around 75% of people with 2, 1 in II and III get in (according to the stats people posted earlier) and most of those people won't have an S in STEP I, so your chances are even higher.
9. (Original post by Zacken)
Ah, cheers. Hoping Q1 will be a bit generous, but I can't see the parts that I've done being worth very much. If only I'd solved that cubic properly, arghhhhh.

(at this point, 1 mark is going to make a lot of a difference )

Thanks!
I've got an awful feeling that I didn't even state the cubic properly, I don't think I squared y. My thinking is that going from x and y to 4y^2 = 3x - 1 is just a bit of algebra, and even if you didn't have correct x and y you shouldn't lose too much for that.
10. (Original post by StrangeBanana)
For question 3, you don't need to investigate the possibility of repeated roots. f_n(x) and f'_n(x) can't both be 0 unless x = 0, and there is obviously no root there.
Yeah, I reckon I needed to mention that.

Basically my justification went as such, as x tends to +- infinity, f_n(x) tends to +infinity since the x^n term dominates, so since there is at most one repeated root, f_n(x) can't possible have a root. But then I didn't mention that f_n(x) and its derivative can't possibly be 0 which might have been needed?
11. (Original post by Zacken)
Yeah, I reckon I needed to mention that.

Basically my justification went as such, as x tends to +- infinity, f_n(x) tends to +infinity since the x^n term dominates, so since there is at most one repeated root, f_n(x) can't possible have a root. But then I didn't mention that f_n(x) and its derivative can't possibly be 0 which might have been needed?
): damnit I'd wish I'd written it down; perhaps its implied by my sketch o:

I just said complex roots come in pairs, because the coefficients of the polynomial are real. so if there's at most 1 real root then for even n there's 0 and for odd n there's 1.
12. Could anyone tell me roughly what I got? I was thinking maybe low 60's?

Q1 Full
Q3 showed up to f'(a)f'(b) < 0
Q5 did parts i, ii couldn't do iii
Q6 couldn't do last part but verified it for a few simple cases
Q7 made a few mistakes probably 14 in total
Q8 did sketch, showed first two approximations, made arithmetic slip showing 3rd, found the error in approximation but didn't get started on the last bit

Thanks, bit annoyed I didn't get enough time to finish Q3, ahh well, exam conditions
13. (Original post by StrangeBanana)
): damnit I'd wish I'd written it down; perhaps its implied by my sketch o:

I just said complex roots come in pairs, because the coefficients of the polynomial are real. so if there's at most 1 real root then for even n there's 0 and for odd n there's 1.
That's elegant, does it nicely - reckon you don't need any additional justification for that.
14. Ok so just to make sure this is definitely a 1 or more:
Spoiler:
Show
Binomial/n choose r question- Full, but a little messy in places so maybe 19 ish?
Integration Q- All but didnt finish last integral. got to 1/cosx(cosx+sinx) and attempted some rearranging with secs but not the correct one. 15?
Differential equation- Got upto completing the sub to get the equation in z and didnt get much further. ~8/9?
Q3- Full, but didnt 100% verify the even case fully although correct answers. 19/20.
Q8 Approximation- Full, apart from I may have not used the best approx. for E for the last bit so my answer was a tiny bit out of the desired one, but definitely correct method. 18 ish?
Factor Theorem- Factorised the first expression, but incorrect multiple of it and moved on cus it looked fiddly.
y=f(sin, cos, x) q- Didnt find values for x, tan theta for the last bit. 13/14?

So Im thinking mark, M, satisfies ish? Does this sound reasonable?
15. (Original post by mpaterson)
Could anyone tell me roughly what I got? I was thinking maybe low 60's?

Q1 Full
Q3 showed up to f'(a)f'(b) < 0
Q5 did parts i, ii couldn't do iii
Q6 couldn't do last part but verified it for a few simple cases
Q7 made a few mistakes probably 14 in total
Q8 did sketch, showed first two approximations, made arithmetic slip showing 3rd, found the error in approximation but didn't get started on the last bit

Thanks, bit annoyed I didn't get enough time to finish Q3, ahh well, exam conditions
20 + 14 + 15(?) + 13 + 14 + 10 = 85+
16. (Original post by Zacken)
Ah, a 1 is really good though. I had the same problem with not getting complete solutions, that last part of the DE question was pure death. Only got fulls to Q7 and 3 and then measly pathetic partials to 4 other questions.
I had a really pathetic partial to Q2 which is annoying. Probably like 6/7 marks idk, it was the whole first part but it seemed like there was a lot more left in that Q.

Later I'll post a brief overview of the Qs I attempted and hopefully someone can tell me approx what mark I got. But yeah my performance was pretty pathetic, I say 1 but idk how the marks work out exactly.

(I've got C4 now lol.)
17. (Original post by EnglishMuon)
Ok so just to make sure this is definitely a 1 or more:
Spoiler:
Show
Binomial/n choose r question- Full, but a little messy in places so maybe 19 ish?
Integration Q- All but didnt finish last integral. got to 1/cosx(cosx+sinx) and attempted some rearranging with secs but not the correct one. 15?
Differential equation- Got upto completing the sub to get the equation in z and didnt get much further. ~8/9?
Q3- Full, but didnt 100% verify the even case fully although correct answers. 19/20.
Q8 Approximation- Full, apart from I may have not used the best approx. for E for the last bit so my answer was a tiny bit out of the desired one, but definitely correct method. 18 ish?
Factor Theorem- Factorised the first expression, but incorrect multiple of it and moved on cus it looked fiddly.
y=f(sin, cos, x) q- Didnt find values for x, tan theta for the last bit. 13/14?

So Im thinking mark, M, satisfies ish? Does this sound reasonable?
19 + 17 + 11 + 19 + 18 + 14 = 98
18. (Original post by Zacken)
That's elegant, does it nicely - reckon you don't need any additional justification for that.
I smiled when I saw it ^^

But I think I still needed to talk about there being no repeated roots; I did say f'(x) > 0 or f'(x) < 0 for roots at one point, hopefully that's enough
19. In question 8 how many marks would finding the approximations (2,5/3,33/20) be worth? I managed to get it to the diophantine equation stage but due to exam mind blanking i couldnt find m and n for the required values of E. Also I dont understand how but I got 1.42 for the last bit instead of 1.08...
Is it wrong to say that E=integral from 1/2 to infinity - sum from 1 to infinity (1/4r^2)?
20. (Original post by computerkid)
Could anyone possibly tell me how close is this above/below a 1?
Spoiler:
Show
Question 1 - full other than messed up the y coordinate for the points where they touched by being careless
Question 2 - showed that b+a-c is a factor
Question 3 - differentiated fn to give fn-1
Question 4 - did everything but finding values of x and tan theta
Question 6 - full
Question 7 - full
@Zacken sorry to bother you marking all these people's, but could you look at what I might have gotten for this?

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