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STEP Prep Thread 2016 (Mark. II)

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Original post by Geraer100
...


year?
Original post by Vesniep
year?


Sorry forget to add that:tongue:
Original post by Geraer100
Sorry forget to add that:tongue:


Sorry mate haven't done the paper yet .
Original post by Vesniep
Sorry mate haven't done the paper yet .


Yeah no problem, thanks any way!:smile:
Original post by Geraer100
STEP II, 2013 Q3 part ii, to deduce b>0, I used the fact that the smaller root of the turning points >0 so -a-sqroot(a^2-b)>0, so
-sqroot(a^2-b)>a, then squaring and cancelling gives b>0, I don't know if this is right.

and to deduce a<0, I used the same argument as above, as -sqroot(a^2-b)>a, a must be negative.

and c<0, I just said that this can be deduced from the graph (in order to have 3 positive roots).

I don't know if all this is correct or not (The answer from TSR forum is done in a different way).:smile:


Would you mind spoilering this? Haven't done this paper yet


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Step iii, 2014

Spoiler




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Original post by drandy76
Would you mind spoilering this? Haven't done this paper yet


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Done! And sorry about that, didn't notice that before:biggrin:
Original post by Zacken
Ah, alright. You'll have a bank of solutions up on TSR by the end of the second day for further checking/worrying. :tongue:


Cool.

On a side note, I am practicing STEP complex numbers/vectors questions right now, and I am kind of stuck on understanding one thing. I am currently doing III 2014 Question 5 and for ABCD being a square, none of the solutions I've looked at (TSR, mark scheme, official hints and solutions, examiner's report) explain why the iff condition is the one that needs to be shown. The only hint I got was from the mark scheme which says that arg⁡(b−a)+π2=c−b\arg(b-a) +\frac{\pi}{2} = c-b but do not explain further that. What am I missing? It is possible that it is something simple and basic so don't judge me, I almost never did any complex number questions before this week. :biggrin:


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Reply 528
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Zacken
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Original post by Insight314
Cool.

On a side note, I am practicing STEP complex numbers/vectors questions right now, and I am kind of stuck on understanding one thing. I am currently doing III 2014 Question 5 and for ABCD being a square, none of the solutions I've looked at (TSR, mark scheme, official hints and solutions, examiner's report) explain why the iff condition is the one that needs to be shown. The only hint I got was from the mark scheme which says that arg⁡(b−a)+π2=c−b\arg(b-a) +\frac{\pi}{2} = c-b but do not explain further that. What am I missing? It is possible that it is something simple and basic so don't judge me, I almost never did any complex number questions before this week. :biggrin:


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Sorry, I haven't done III 2014 just yet! :frown:
(edited 7 years ago)
Original post by Insight314
Cool.

On a side note, I am practicing STEP complex numbers/vectors questions right now, and I am kind of stuck on understanding one thing. I am currently doing III 2014 Question 5 and for ABCD being a square, none of the solutions I've looked at (TSR, mark scheme, official hints and solutions, examiner's report) explain why the iff condition is the one that needs to be shown. The only hint I got was from the mark scheme which says that arg⁡(b−a)+π2=c−b\arg(b-a) +\frac{\pi}{2} = c-b but do not explain further that. What am I missing? It is possible that it is something simple and basic so don't judge me, I almost never did any complex number questions before this week. :biggrin:


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Do you know that multiplying by e^iθ represents a rotation of theta degrees anti-clockwise?


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Original post by Krollo
Do you know that multiplying by e^iθ represents a rotation of theta degrees anti-clockwise?


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Yeah. This is for last part of the question as far as I can recall.


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Original post by Zacken
Sorry, I haven't done III 2015 just yet! :frown:


It's 2014 though!


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Reply 532
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Zacken
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Original post by Insight314
It's 2014 though!


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Whoops, I meant 2014.
Reply 533
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fa991
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Can I quote the arctan addition formulae or do I have to prove them?

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For 1 2014 question 2(iii) why do they lose the modulus signs on the first line of working in the mark scheme?


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Original post by fa991
Can I quote the arctan addition formulae or do I have to prove them?

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quoting shud be ok tbh. it is one line prof anyway just say "let A=arctan n B= leads to A+B=...
Original post by Glavien
For 1 2014 question 2(iii) why do they lose the modulus signs on the first line of working in the mark scheme?


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think about |x|=x or -x dependng if x>=0 or x<0.
Reply 537
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Zacken
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Original post by fa991
Can I quote the arctan addition formulae or do I have to prove them?

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I'd add in the extra line of proof. It shouldn't take longer than 10 seconds extra than just quoting it.
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fa991
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Original post by physicsmaths
quoting shud be ok tbh. it is one line prof anyway just say "let A=arctan n B= leads to A+B=...





Original post by Zacken
I'd add in the extra line of proof. It shouldn't take longer than 10 seconds extra than just quoting it.


Okay thanks, I'll just prove it since it's not too big a deal
Reply 539
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Zacken
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Original post by fa991
Okay thanks, I'll just prove it since it's not too big a deal


This is the way I would do it:

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