STEP I 2012 discussion thread Watch

MW94
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#61
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#61
How many bloody quartics you want in that exam, i got to about 3 out of the 5 questions i attempted...

EDIT: As in 3 quartics, not 3 solutions, pressure gets to you in exam....
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Farhan.Hanif93
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#62
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#62
(Original post by MHRed)
The question on integrating the cos2x ln (cos x) or whatever it was...

I did the first two parts easily, but how do you do the last bit?!
Sub u=x-\dfrac{\pi}{4}. The limits give it away.
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deejayy
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#63
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#63
(Original post by Xero Xenith)
IBP integrating cos2x (which gives 0.5*sin2x) and differentiating ln(cosx) (which gives -tanx). Then 0.5*sin2x*tanx simplifies to sin²x (which can be expressed in terms of cos2x).

That's all IIRC

Big regret on this paper for me was not reading all the questions properly before starting ones that looked nice (but weren't). Lesson learned.
What do you mean by reading them properly?

Do you suggest going through the later phases (as well as the early) and thinking of plans of attack whilst reading through the questions?
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shanban
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#64
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#64
Anyone for question 2?! Thats probably the only one I made 'good' progress on...
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In One Ear
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#65
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#65
(Original post by fruktas)
I got Q8 here in anyone is interested?
yes!
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David_Skiller
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#66
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#66
well I didnt find this paper easy but I managed to still patch out 6 full solutions...did question 1,4,5,8,10,12
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f1mad
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#67
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#67
(Original post by fruktas)
I got Q8 here in anyone is interested?
Me too, took me about 5mins :lol:.
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MHRed
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#68
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(Original post by Farhan.Hanif93)
Sub u=x-\dfrac{\pi}{4}. The limits give it away.
Of course. I got carried away with IBP and didn't stop to consider anything else. Poo.
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mathslive101
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#69
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#69
Did anyone do question 11 about tensions and stuff. That was the only question I managed to complete. The rest were partly done and most of it were fragments. I don't think it went well at all. Warwick dream is almost dead.

Anyone got an answer for (mu) in question 11


This was posted from The Student Room's iPhone/iPad App
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Stray
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#70
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#70
*sympathy face* to those who sat this on Monday.

What a lot of curves.

And no pure-trig question (only one that was mixed in with geometry), no diophantine equations, no permutations or numerical analysis - I guess the series question was numerical, but still...

No modulus stuff, no inequalities, no vectors... No interesting proofs or straight up "think about this!" questions.

I have to say it looks a hard paper, partly just because on first reading it feels very narrow - lots of function analysis and a bit of integration / diff equations, and not a lot of choice if you're not a fan of those.

Instinctively it also looks a kind of boring paper. There wasn't a pure question that jumped out at me and made me want to solve it. Is that just me? If I'd been sitting it, excited at what goodies the STEP folk have in store this year, I'd have been deflated.

Actually - for me, the most fun question on the paper is 13, which is a shame as I bet a lot of people don't bother reading the stats questions and would actually have liked that one, which has more in common with past pure questions than typical stats questions. No doubt the examiners report will comment on what a shame it is that more people didn't choose their questions more wisely *sigh*.

I wonder whether things have shifted this year because of all the extra offers at other universities hinging on STEP I? The pure section just felt a bit 'straight'. Lots of hard work and less opportunity for creativity / insight than usual IMO.

Fingers crossed the grade boundaries are low - it sounds like you've all had a similar experience. Given that they advise you just to do past questions as prep, it seems unlikely that there's a whole bunch of people for whom that was just the paper they were expecting / hoping for.
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RooT_Fifteen
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#71
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#71
Anyone with solution to Q2? I semi-guessed what the question was asking...:P
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MW94
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#72
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#72
Only question i completed was 9. (quartic solved! woop!)

Couldn't finish 1, stupid m^4....

2, some more graphs, reasonably ok, ran out of time

Question 5, dont know how they henced from the first 2 parts, impossible.

And 4, oh boy, more quartics.
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RooT_Fifteen
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#73
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#73
(Original post by Stray)
*sympathy face* to those who sat this on Monday.

What a lot of curves.

And no pure-trig question (only one that was mixed in with geometry), no diophantine equations, no permutations or numerical analysis - I guess the series question was numerical, but still...

No modulus stuff, no inequalities, no vectors... No interesting proofs or straight up "think about this!" questions.

I have to say it looks a hard paper, partly just because on first reading it feels very narrow - lots of function analysis and a bit of integration / diff equations, and not a lot of choice if you're not a fan of those.

Instinctively it also looks a kind of boring paper. There wasn't a pure question that jumped out at me and made me want to solve it. Is that just me? If I'd been sitting it, excited at what goodies the STEP folk have in store this year, I'd have been deflated.

Actually - for me, the most fun question on the paper is 13, which is a shame as I bet a lot of people don't bother reading the stats questions and would actually have liked that one, which has more in common with past pure questions than typical stats questions. No doubt the examiners report will comment on what a shame it is that more people didn't choose their questions more wisely *sigh*.

I wonder whether things have shifted this year because of all the extra offers at other universities hinging on STEP I? The pure section just felt a bit 'straight'. Lots of hard work and less opportunity for creativity / insight than usual IMO.

Fingers crossed the grade boundaries are low - it sounds like you've all had a similar experience. Given that they advise you just to do past questions as prep, it seems unlikely that there's a whole bunch of people for whom that was just the paper they were expecting / hoping for.
I thought question 13 was nice, as I normally enjoy/do well in stats questions, but I just couldnt see a simple way of doing it, without using combinatorics for every type of possibility...... so instead I went for Q4 and only got it half done...:'(
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fruktas
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#74
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#74
My scanner is being funny, scanned files are too big.

Q8, for part ii) use the same substitution, and I got

(y+3x)^3 = k x (y+2x)^2
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Llewellyn
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#75
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I thought it was okay. When I first skipped through, apart from seeing the noun "curve" an oddly large number of times, my initial reaction was that it looked quite tough (the pure questions). Some of the questions were really interesting though, and as always, some questions were a lot easier than others.

I decided on 2, 5, 7, 8, 9, 11, 12 as the questions that looked most approachable for me. Iirc, I did them in the order: 5 -> 9 -> 7 -> 8 -> 2 -> 11 -> 12 After doing those, I had a bit under an hour left, and I spent that doing 3, 4, 10 and 13. I didn't complete 13, but that was because I was writing a load of paragraphs to explain my reasons for my omissions and why I had to add on certain values because I subtracted them twice as I went along. If I'd actually just done the maths first and then explained it that would have been more wise.

Question 6 wasn't as bad as it looked (it was actually one of the less algebra-heavy pure questions), so obviously my judgement of difficulty there wasn't very good. I haven't had a good think about question 1 but the 2nd part of it put me off immediately and I don't regret leaving it out.

In retrospect, my judgement of the questions wasn't very good (e.g. 6 was easier than 2). Also, I probably should have spent the last hour going over the questions I'd done to pick up on any slips/ bad reasoning. I'm also quite upset there weren't more Statistics questions as I normally do quite well in those.

It went quite well, but I agree with everyone saying it was harder. I think they really turned up the difficulty in some of the pure questions. The standard deviation for STEP is around 5 iirc and from that I'd guess we're probably looking at the average -5 for each boundary. Now I'm off to S2 revision >_>
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alvina9894
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#76
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#76
(Original post by Stray)
*sympathy face* to those who sat this on Monday.

What a lot of curves.

And no pure-trig question (only one that was mixed in with geometry), no diophantine equations, no permutations or numerical analysis - I guess the series question was numerical, but still...

No modulus stuff, no inequalities, no vectors... No interesting proofs or straight up "think about this!" questions.

I have to say it looks a hard paper, partly just because on first reading it feels very narrow - lots of function analysis and a bit of integration / diff equations, and not a lot of choice if you're not a fan of those.

Instinctively it also looks a kind of boring paper. There wasn't a pure question that jumped out at me and made me want to solve it. Is that just me? If I'd been sitting it, excited at what goodies the STEP folk have in store this year, I'd have been deflated.

Actually - for me, the most fun question on the paper is 13, which is a shame as I bet a lot of people don't bother reading the stats questions and would actually have liked that one, which has more in common with past pure questions than typical stats questions. No doubt the examiners report will comment on what a shame it is that more people didn't choose their questions more wisely *sigh*.

I wonder whether things have shifted this year because of all the extra offers at other universities hinging on STEP I? The pure section just felt a bit 'straight'. Lots of hard work and less opportunity for creativity / insight than usual IMO.

Fingers crossed the grade boundaries are low - it sounds like you've all had a similar experience. Given that they advise you just to do past questions as prep, it seems unlikely that there's a whole bunch of people for whom that was just the paper they were expecting / hoping for.
I feel bad for those who haven't done C4 and sat for this paper on monday. It must have been a tough one. Not too many choices. Probably just Q1, Q2, Q4, Q9-11, Q12-13. But mechanics and probabilities weren't exactly helpful...
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In One Ear
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#77
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#77
(Original post by Stray)
*sympathy face* to those who sat this on Monday.

What a lot of curves.

And no pure-trig question (only one that was mixed in with geometry), no diophantine equations, no permutations or numerical analysis - I guess the series question was numerical, but still...

No modulus stuff, no inequalities, no vectors... No interesting proofs or straight up "think about this!" questions.

I have to say it looks a hard paper, partly just because on first reading it feels very narrow - lots of function analysis and a bit of integration / diff equations, and not a lot of choice if you're not a fan of those.

Instinctively it also looks a kind of boring paper. There wasn't a pure question that jumped out at me and made me want to solve it. Is that just me? If I'd been sitting it, excited at what goodies the STEP folk have in store this year, I'd have been deflated.

Actually - for me, the most fun question on the paper is 13, which is a shame as I bet a lot of people don't bother reading the stats questions and would actually have liked that one, which has more in common with past pure questions than typical stats questions. No doubt the examiners report will comment on what a shame it is that more people didn't choose their questions more wisely *sigh*.

I wonder whether things have shifted this year because of all the extra offers at other universities hinging on STEP I? The pure section just felt a bit 'straight'. Lots of hard work and less opportunity for creativity / insight than usual IMO.

Fingers crossed the grade boundaries are low - it sounds like you've all had a similar experience. Given that they advise you just to do past questions as prep, it seems unlikely that there's a whole bunch of people for whom that was just the paper they were expecting / hoping for.
Ahah, tbh i think when sitting the paper (especially if your offer hinges on it) people probably arn't so bothered about how interesting or thought provoking the questions are- they just bloody well hope they can start answering them, and fast!

Personally i enjoyed the question about the well and dropping the stone. It wasn't really thought provoking or difficult, but its just cool to see how you can (relatively) easily work things like the depth of a well with just a little knowledge of physics and some maths. Tbh i'm in general quite a fan of mechanicsy questions and am much more open to non-pure than most people. Its just a shame i didn't have the courage to attempt the stats questions as as someone pointed out earlier, one of them looked quite interesting. Its just been so long since i've done any stats i didn't want to risk wasting my time in such an important exam!
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TheJ0ker
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#78
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#78
(Original post by alvina9894)
Is the last part of Q1 (a^2/3 + b^2/3)^3/2 ? Anyone got the same thing?
Yes that is right.
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Xtrapolation
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#79
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#79
Yeah I got complete solutions to the differential equations q and the integration q. I can't remember for sure but I think my final answer to the integration q was,

1/8 (pi - ln(16))

Everything cancelled pretty nicely after some transformations and jiggery-pokery. But I'm kicking myself for making a REALLY bad tactical decision error - went for more pure (qs 1 and 2 which really weren't too great) instead of looking at the mechanics section. 20 minutes left and I almost completed the projectiles question and the pulley question looks very doable as well. That error may have cost me

But now I'm going for STEP II WITH A VENGEANCE!! :jitsu:
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Farhan.Hanif93
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#80
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#80
(Original post by RooT_Fifteen)
Anyone with solution to Q2? I semi-guessed what the question was asking...:P
Since a few people are asking.
Q2
(i)
Note y=(x^2-3)^2 so it's non-negative and finding points of interest are easy.

(a) b>9
(b) Not possible
(c) b=9 or b <0
(d) b=0
(e) 0<b<9


(ii)
\dfrac{dy}{dx} =0 and \dfrac{d^2y}{dx^2} =0:

\begin{Bmatrix} 4x^3 -12x + a =0 & (1) \\ 12x^2 -12 =0 & (2)

(2) tells us that we need to find a s.t. (1) is satisfied by x=\pm 1

This yields \boxed{a=\pm 8}
In the case a=8: Stat. point of inflection at (1,b+3) and minimum at (-2,b-24) so f(x) = x^4 -6x^2 +8x + b =0 has:
No roots if b > 24
Exactly one root if b=24
Exactly two roots if b<24

In the case a=-8, we have f(-x) so the curve has just been reflected in the y-axis. It follows that the same conditions on b apply as above.


(iii)
The curve passes through the origin, has only one minimum for x<0 and has a non-stationary point of inflection for x>0. It has one root for x<0.
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