STEP I 2012 discussion thread

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.

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?

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.

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?

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.

yeah I meant (y+3x)^3 = k(y+2x)^2

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.

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?

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

How many solutions did you get?

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?

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?

Does anyone have any idea for this year's boundaries?

I need 'S' for my conditional offer and I'm so nervous...