STEP I 2012 discussion thread Watch

snow leopard
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#81
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#81
Q11(i), I'll add (ii) later.

Q11
(i)




let \theta=\arctan \frac{7}{24}



\Rightarrow \cos \theta = \frac{24}{25} & \sin \theta = \frac{7}{25}





let \alpha=\arctan \frac{4}{3}



\Rightarrow \cos \alpha = \frac{3}{5} & \sin \alpha = \frac{4}{5}



R(A) (\mu R + 5mg\sin\theta)=T

R(B) (\mu S + 3mg\sin\alpha)=T



\mu R + 5mg\sin\theta=\mu S + 3mg\sin\alpha



\mu \frac{24}{5}mg + \frac{7}{5}mg = \mu \frac{9}{5}mg + \frac{12}{5}mg



\Rightarrow \mu = \frac{1}{3}



\Rightarrow T=3mg



Mg=2T=6mg \Rightarrow M=6m

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Xtrapolation
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#82
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Also to those who speak of using exact differential equations in the solution of the DE question, I am fairly sure that the equation we had was of the form (since it did cross my mind to try and use this technique to cut out some work):

dy/dx + P(x)/y = Q(x)

However, exact differential equations must be of the general form,

dy/dx + P(x)y = Q(x)

Hence it was not possible.
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TheJ0ker
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#83
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#83
(Original post by fruktas)
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
Do you mean (y+3x)^3 = k(y+2x)^2 because I used y=x/v as the sub and that's what I got, I'm pretty sure my algebra is right too. Sorry is that x a variable x or a times sign? :ninja:
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Lois:)
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#84
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#84
(Original post by TheJ0ker)
Do you mean (y+3x)^3 = k(y+2x)^2 because I used y=x/v as the sub and that's what I got, I'm pretty sure my algebra is right too.
I got this then stupidly forgot to write the ^2 and ^3 bit on my final answer. Grr. How much do you reckon I'll lose?
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LucasJ94
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#85
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I got out 3 full solutions, and 3 partial solutions (with the partials I got to the end of the question).

1 - Got to last part, couldn't get m out of the quartic.

2 - I finished this one, but I'm not sure about my answer to the last part, I think i got the graph right, but I have a feeling I didn't show enough information.

4 - Aced this one, some tricky algebra in places, but the end of the question confirmed I have it right (I hope).

5 - Got down to the last part, I tried to use the substitution x = x-pi/4, but i must have made a mistake because that didn't work out.

7 - Down to the equation on the third part, I managed to show a few of the conditions by playing around with simultaneous equations, but really annoyed about this. I found the rest of the question nice and easy.

8 - Got to the end, had a decent looking solution for the last question, but i'm not sure about it. (checking above solutions, mine match those, so I guess this one was ok too)

Not very confident about STEP II now, the whole way through that was a huge struggle and my solutions to every question but 4 felt lucky .
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fruktas
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#86
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#86
(Original post by TheJ0ker)
Do you mean (y+3x)^3 = k(y+2x)^2 because I used y=x/v as the sub and that's what I got, I'm pretty sure my algebra is right too. Sorry is that x a variable x or a times sign? :ninja:
yeah I meant (y+3x)^3 = k(y+2x)^2
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Farhan.Hanif93
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#87
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(Original post by Xtrapolation)
Also to those who speak of using exact differential equations in the solution of the DE question, I am fairly sure that the equation we had was of the form (since it did cross my mind to try and use this technique to cut out some work):

dy/dx + P(x)/y = Q(x)

However, exact differential equations must be of the general form,

dy/dx + P(x)y = Q(x)

Hence it was not possible.
It's not always that obvious. For example, if they didn't force you to do the first part by substitution, you could have divided by \dfrac{x}{2} to get:
2y\dfrac{dy}{dx} + \dfrac{2}{x}y^2 = 4x

And then note that \dfrac{d}{dx}[y^2] = 2y\dfrac{dy}{dx} to have an linear DE in y^2 that can be solved with an integrating factor.
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TheJ0ker
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#88
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(Original post by Lois:))
I got this then stupidly forgot to write the ^2 and ^3 bit on my final answer. Grr. How much do you reckon I'll lose?
1 mark, I left my answer as x=\frac{Ax(2x+y)^2}{(3x+y)^3} So I may also lose a mark as technically it's not in its simplest form but I think it would be harsh to knock a mark off for that...
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Xtrapolation
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#89
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(Original post by Farhan.Hanif93)
It's not always that obvious. For example, if they didn't force you to do the first part by substitution, you could have divided by \dfrac{x}{2} to get:
2y\dfrac{dy}{dx} + \dfrac{2}{x}y^2 = 4x

And then note that \dfrac{d}{dx}[y^2] = 2y\dfrac{dy}{dx} to have an linear DE in y^2 that can be solved with an integrating factor.
Ah fair enough - I obviously didn't take this route through the problem
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TheJ0ker
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#90
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(Original post by fruktas)
yeah I meant (y+3x)^3 = k(y+2x)^2
How many solutions did you get?
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Stray
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#91
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(Original post by In One Ear)
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!
Good point!

(Original post by In One Ear)
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.
Ditto. Hence I studied engineering (20 years ago). I now make engineering software. Currently modelling inverse-square field / attraction stuff
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anyone_can_fly
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#92
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(Original post by Plastonick)
Anyone attempt Q13? I had about 20 minutes at the end so I thought I'd sink my teeth in, managed to find out there were 3125 separate integers but got stuck up afterwards. Any one got an answer?
Q13 was probably the one I did best in - I finished it, and then realised that my answer was 2097/625 whereas the answer they told you to get was 2101/625. So close! I spent ages trying to work out where I'd gone wrong. Apart from that I attempted Q1,2 and 7, but didn't finish any of them. (And spent the last five minutes on Q5i, in the hope I could thereby get 1/20 on it or something.)
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8inchestall
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#93
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(Original post by fruktas)
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
think i got this same result using y=v/x (think) unless its mathematically imposs for me to do so in which case i definitely fudged something
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TheJ0ker
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#94
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(Original post by 8inchestall)
think i got this same result using y=v/x (think) unless its mathematically imposs for me to do so in which case i definitely fudged something
I used y=x/v so you probably did it right
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fruktas
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#95
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(Original post by TheJ0ker)
How many solutions did you get?
I didn't sit the paper, I am just working through the questions Done 8,5,2 now, maybe do 4

STEP II tomorrow wooo!
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In One Ear
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#96
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So now everyones had a while to look at the paper/discuss the paper what do people think the boundaries will be for an S/1/2/3?
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Wahrheit
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#97
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(Original post by In One Ear)
So now everyones had a while to look at the paper/discuss the paper what do people think the boundaries will be for an S/1/2/3?

80/61/47/34 I'm going to go for .
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slim0811
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#98
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Does anyone have any idea for this year's boundaries?

I need 'S' for my conditional offer and I'm so nervous...
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safmaster
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#99
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(Original post by In One Ear)
So now everyones had a while to look at the paper/discuss the paper what do people think the boundaries will be for an S/1/2/3?
Well, I think the general consensus is that it's certainly harder than your average STEP I paper. Working through the paper, I've managed to do 5 solutions (pure) in about 2 hours. I haven't tried any applied but they don't look too bad. Last year's paper was easier and the boundaries were quite low; with that in mind, if I had to guess I'd say 81/60/42/25.
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Wahrheit
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#100
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#100
(Original post by slim0811)
Does anyone have any idea for this year's boundaries?

I need 'S' for my conditional offer and I'm so nervous...
Which uni?!
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