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STEP Prep Thread 2015

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Original post by Karoel
Maybe rearrange so that 5−219<245 - \dfrac{2}{19} < \sqrt{24}, simplify LHS and then go from there?

EDIT:
Here's my working:

Spoiler



Like this. Saves the annoying calculations.

Original post by raff97
I did it without rationalising the denominator.

They want you to show 1/ (5+root(24)) < 2/19 = 1/9.5 = 1/(5+4.5)

You can easily compute 4.5^2 and show its smaller than 24


Thanks - much simpler than my method.
Anyone knows any easy STEP III questions so I can get back in the flow with it? The past few questions I haven't been able to answer :biggrin:
Original post by Karoel
Anyone knows any easy STEP III questions so I can get back in the flow with it? The past few questions I haven't been able to answer :biggrin:


STEP III 2001 Q1 is nice imo.


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Original post by Karoel
Anyone knows any easy STEP III questions so I can get back in the flow with it? The past few questions I haven't been able to answer :biggrin:

Almost anything in 2003 III - did it as a mock today and was a lovely paper.
Just done STEP III 2012, as a mock in timed conditions, which went relatively well.
I got full solutions to 1,2,7,8,10 in that order, then I did the first part of 4. How many marks do people think part (i) of 4 is worth? I obviously haven't done the second half (previously I wasted time on another question, 20 minutes!) so I don't know how much work it involves, but I can imagine The first being less than 10 marks, as the last part is usually harder.

So yeah, what do people think? 7 marks, maybe?
(edited 9 years ago)
Would tuition help with STEP? Anyone taking it? Sorry for firing away with the questions :biggrin:
Original post by Karoel
Would tuition help with STEP? Anyone taking it? Sorry for firing away with the questions :biggrin:


This thread is tuition lol.


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Original post by Karoel
Would tuition help with STEP? Anyone taking it? Sorry for firing away with the questions :biggrin:


I can't see tuition helping tbh. You really need to develop the intuition to tackle questions yourself, and if you get stuck there is always this thread, with plenty of undergraduates and graduates willing to help for free.
Original post by ThatPerson
I can't see tuition helping tbh. You really need to develop the intuition to tackle questions yourself, and if you get stuck there is always this thread, with plenty of undergraduates and graduates willing to help for free.


...who will most likely be better at maths than your tutor.
Original post by DomStaff
...who will most likely be better at maths than your tutor.


Especially Dfrank, hes a don


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Original post by physicsmaths
Especially Dfrank, hes a don


Posted from TSR Mobile


DFranklin is god like.

But on the the topic of tuition how the heck do you do 2012 III Q1 part(i)?

I understand we take n as 1 but after that I get dz/dy = root(y)

I can solve that for z but the result is different to the initial condition and I just get confused :/ Does anyone have any resources for learning second order differentials such as these?
Original post by Brubeckian
DFranklin is god like.

But on the the topic of tuition how the heck do you do 2012 III Q1 part(i)?

I understand we take n as 1 but after that I get dz/dy = root(y)

I can solve that for z but the result is different to the initial condition and I just get confused :/ Does anyone have any resources for learning second order differentials such as these?


Sorry havent touched that paper. I belive dom staff completed it.


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Original post by Brubeckian
DFranklin is god like.But on the the topic of tuition how the heck do you do 2012 III Q1 part(i)?I understand we take n as 1 but after that I get dz/dy = root(y)I can solve that for z but the result is different to the initial condition and I just get confused :/ Does anyone have any resources for learning second order differentials such as these?


You're slightly off with that.

Should be dz/dx =dy/dx rooty.


Actually you are correct (I read it wrongly) but you need to rearrange.

(into the form I just gave you. What you need to d after that should be relatively clear.)
(edited 9 years ago)
Original post by DomStaff
You're slightly off with that.

Should be dy/dx rooty.


That's what I meant :P

It's ok I got it now, you get z = blah blah, you then equate it to what they gave you at the start and then solve to get y in terms of x.

I need to practice more of these things...
If this year's STEP III is geometry/complex-number heavy I have come to the conclusion that I am utterly screwed :lol:
Original post by ThatPerson
If this year's STEP III is geometry/complex-number heavy I have come to the conclusion that I am utterly screwed :lol:


Try STEP III 2000 Q3 good intro to complex numbers for step. I love complex numbers haha. The geometric complex numbers is just equilateral tringles most of the time 😂 then its just mutiplying by e^ipi/3.


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Can someone check this for me as it's different to the TSR solutions.
STEP II Q5 2002 first part
let. 0<1/2<=x<1 <=> 0<X<=1/2
Therefore. 0< X(1-x)<=1/4
0<k<4 so
0<Kx(1-x)<1 true if 0<x<=1/2<1 by symmetry of the multiplication.
I did this with x_0 and then induction etc etc.
is the above


Posted from TSR Mobile
Original post by physicsmaths
Can someone check this for me as it's different to the TSR solutions.
STEP II Q5 2002 first part
let. 0<1/2<=x<1 <=> 0<X<=1/2
Therefore. 0< X(1-x)<=1/4
0<k<4 so
0<Kx(1-x)<1 true if 0<x<=1/2<1 by symmetry of the multiplication.
I did this with x_0 and then induction etc etc.
is the above


Posted from TSR Mobile


Correct*


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With STEP III 2007 Q9 I have:
θ=α+(β−α)cos(kt) \displaystyle \theta = \alpha + \left (\beta - \alpha \right ) cos(kt)

But I am not entirely sure how changing the starting position would affect the oscillations, and how to show these changes mathematically. Also, while alpha is a constant, I would have thought that the value of alpha is more important for determining oscillations as the 'origin' of the motion is at alpha.
i.e.
θ¨=−k2(θ−α) \ddot{\theta} =-k^2(\theta - \alpha)

Also, based on that expression for acceleration, would there always be SHM unless theta is less than or equal to alpha?
does anyone know any "nice" STEP III mechanics questions ???:eek2::eek3::dots::france::jitsu::juggle::judge:

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