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# STEP Prep Thread 2016 (Mark. II) watch

1. (Original post by gasfxekl)
x=+-1 and tan theta is -1/y i think.
YUS
2. Here's how I did (expecting very low marks) so would appreciate some help on the questions I got wrong + a mark approximation would be greatly appreciated although I'm not expecting anything

1) Didn't do much, couldn't prove that they met on the c2 curve. I didn't really see what the shape of the graph was supposed to be, I went with it being an exponential-shaped curve in the positive x-y quadrant, and that being reflected in the x axis so the points P and Q where at x1,y1 and x1,-y1 if symmetrical. But couldn't work out how their tangents met, I think I got them meeting at something like x = 2t^2 not sure though

2) Was able to get most of this question done, just didn't have enough time to finish the last last part. We had to solve an equation, and I got to the point with solutions x=2 and x=f(b) (I can't remember f(b) but it was something in terms of b). I really liked this question, sucks that I only decided to do it at the end of the paper, was pretty simple once you realise the first part.

3) Did this question really quickly, but got stuck when I was supposed to draw the graph of fn(x) to show the position of fn(c) or something like that. Hoping I still got some credit for what I did do here

12) Just proved that initial formulae using that P(AnB) general formulae. Hopefully a few marks for doing that.

I went into this exam hoping to get 3 fulls, then just get some marks from elsewhere wherever I could If I had spare time. This failed miserable, didn't even get 1 full!

How did you guys find it? I'm also really annoyed I forgot how to do the integral of f(x) = integral of f(a-x) - I've definitely done that before.
3. (Original post by shamika)
Estimate of grade boundaries: 99 / 70 / 60 (for S / 1 / 2).

Please note that I am in the minority who think the paper was generally OK, but some of that is me underestimating the difficulty of Q6 (I think this is OK as I overestimated the difficulty of Q3), and because Q12-13 were both on the easy side (but not many try the stats).
Hopefully I'll get a 1 haha (and yeah found out 6 was tough the hard way ; and didnt try 3 bc i thought 3 was tough...)
4. (Original post by username1987)
If others agree with you then I'm probably wrong; the way I was thinking of it was I imagined there were only n-1 cards, considered the probability that all were wrongly ordered and then put in the last card in one of n spaces including the ends... now that I think about it though, I don't think that would multiply the probability by n. Ah well, I'll just have to aim for an S in 3 by doing all the mechanics questions...
Yeah that seems logical as well (that's the problem with probability, you can come up with completely different but equally convincing answers where one is subtly wrong). I feel like my way is right, but I don't have a good argument why.
5. (Original post by computerkid)
Any idea how many marks that last bit was worth?
like 5 maybe idk
6. If somebody could put my mind to rest as to whether I got a 2 or a 1, I'd be eternally grateful:
Spoiler:
Show
Q1:
Spoiler:
Show
Wrote down the equations of the tangents at P and Q, equated them and solve for the x and y coordinates in terms of p and q. Then for whatever reason, I kept writing pq = -4/9 instead of pq = -1. I don't even know. So couldn't get the 4y^2 = 3x - 1 thing, although I did plug my x and y coordinates (in terms of p and q) into that equation, so maybe a mark for that.

Then, plugged in t^3 and t^2 into the curve to get a cubic in t^2, but then (for whatever reason, wrote down the wrong thing on the next line) so said that there were no roots.

Did the graph sketch, so correct shapes and stuff, but obviously drew them with no intersections.

Q3:
Spoiler:
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Should be a full, didn't investigate the possibility of there being a "double root" (i.e: tangent to the x-axis) for the even n case.

Q4:
Spoiler:
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Did the first (y cos - sin)^2 > 4(y-1)^2 bit. Expanded the (ycos - sin)^2 bit (so might get a mark for that?) but otherwise didn't do the y^2 + 1 > 4(y-1)^2 bit. (well I did, but it was incorrect...)

Then did the 4 - sqrt(7) / 3 < y < 4 + sqrt(7) / 3 bit all correctly.

Did the show that bit in part (ii), i.e: if y = 4 + sqrt(7) / 3 then sqrt(y^2 + 1) = 2(y-1) corretly, didn't even try finding x or tan theta.

Q6:
Spoiler:
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Did the first three bits flawlessly, differentiated v(x) in part (iv) and left it at that.

Q7:
Spoiler:
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Did it all, got up to 1/cos x (cos x + sin x) in the last integral, did a t-sub but wrote down the wrong thing on the next line (happens too often...) so got the wrong answer, probably only dock two marks though.

Q8:
Spoiler:
Show
Did the first integral, the graph sketch, the first approximation all correctly. Then wrote 1 + sum from r=2 to infinity for the next approximation but my arithmetic failed me, so left it at that. Wrote 5/4 + sum from r=3 to infinity for the next approximation but my arithmetic failed me, so left it at that.

Did the bit about 1/(4r^4) approximating the integral (although I didn't work through all the algebra, so dock a mark or two here) and then didn't even try the last part.
7. (Original post by Zacken)
If somebody could put my mind to rest as to whether I got a 2 or a 1, I'd be eternally grateful:
nah thats definitely a 1. Even without q1 I think you'd get high 70s.
8. (Original post by EnglishMuon)
nah thats definitely a 1. Even without q1 I think you'd get high 70s.
How come? I'm pegging myself at low 70's even with Q1.
9. (Original post by Zacken)
How come? I'm pegging myself at low 70's even with 70's.
well i mean, could you let me know how many marks u were thinking of for each question? Id be good to see if Ive been too generous/stingy etc. in places
10. 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
11. (Original post by Zacken)
How come? I'm pegging myself at low 70's even with Q1.
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.
12. (Original post by Zacken)
If somebody could put my mind to rest as to whether I got a 2 or a 1, I'd be eternally grateful:
I'm fairly sure that's a one. It looks like you'll certainly cross 70 and perhaps even 80
13. (Original post by ComputerMaths97)
Being honest if you found a paper tough - it was a tough paper. I'd bet anything that you've done much better that 2 fulls and 4 partials in STEP II papers plenty of times before, so you should be expecting lower grade boundaries no? Did you find it considerably harder that usual ones?
I found it tough ngl. In the sense that I simply failed to do complete Qs, it was a matter of getting as much as I could in 5 Qs (and only one full). In mocks I usually got 4 fulls and then a partial on average. Dk if this is just me but I would expect low grade boundaries?
Since when was it so hard to finish a DE question???
14. (Original post by Gunawardana)
That was one rough STEP 2 exam - here's what happened to me:

Q1- Decided to start here but couldnt see the point (i.e couldnt interpret the 90 degree thing and kept staring at the question for a while) and so just wrote down tangents using general points (p^2,p^3) and (q^2,q^3) and then realised that p=-1/q and finally got the equation. Then found the graphs touch at x=0.5 (is this correct?) and drew graphs (hopefully fine). But the time penalty caused in the beginning haunted me through the whole exam.

&amp;amp;amp;amp;amp;amp;amp;amp ;amp;lt;br&amp;amp;amp;amp;amp;a mp;amp;amp;amp;gt;Q7- Did the intro, (i) and (ii) but got stuck midway in (iii) when I got to a step where i had to integrate an expression very similar to (iv) but with x=u/2 (is this supposed to happen?) and so couldnt do (iv) either but wrote down a substitution for (iv). The time penalty from before was still in action so I had to leave the Q at this point.

Q6- This wasnt very nice towards the end. Did (i) and (ii) and found y2n thing in (iii) but couldnt do the show that in (iii) correctly after attempting to differentiate z(x). In (iv) I just differentiated v(x) and tried creating a differential equation but failed.

Q9- Did (i) correctly but got nowhere really in (ii). I dont know whether my methods were correct in (ii) or whether there were errors in that as well. I just tried to use momentum once and tried doing something for b and c after that (attempted to use a relative acceleration but idk whether thats correct) but I didnt get too far.

Q4 - Did the first part (hopefully correctly) and the show that in (ii) I think I tried to find x and tan(theta) after that but failed and left the Q.

Q11- With a bare 20 min left I took this up hoping to do at least (i) but I got lucky and managed to do both (i) and (ii) except for the final explanation which I didnt get (and at which point I had just 2 min or so left which wasnt helping my brain) so i guess this Q can be called an almost full maybe?

Anyways what do u guys think I'll get ?
Did I get a 1 with this?
15. (Original post by EnglishMuon)
well i mean, could you let me know how many marks u were thinking of for each question? Id be good to see if Ive been too generous/stingy etc. in places
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.
16. Can an S in STEP 1 make up for a high 2 in STEP 2? That is, supposing that STEP 3 goes to plan...
17. (Original post by Gunawardana)
Did I get a 1 with this?
Certainly.
18. (Original post by Zacken)
Certainly.
k thnx
19. (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).
20. (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.

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