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# STEP Prep Thread 2016 (Mark. II)

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1. (Original post by Geraer100)
June 2000, step ii, q3,

When a, b and c are small, why (1+(13a-2b+24c)/49)^1/2 is more or less equal to (1+(13a-2b+24c)/98)), with just the denominator doubled?
sqrt(1+a) approx 1 + a/2 by the binomial expansion
2. I also did STEP II 2015 today

Spoiler:
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Q1) I liked this question.
Q4) Lovely, though I spent too long on it really.
Q5) Nice question, but it took longer than I would have liked.
Q6) Alright. The first two parts were straightforward. Made a silly algebra mistake in the final part.
Q7) I am annoyed at this. I had an expression for y, but thought it was too ugly to be correct so crossed it out and tried to start again. Turns out I was actually right in the first place.

Overall: I got a solid 1 so I am happy, though I would have preferred to atleast start a 6th question.

3. STEP II 2015:
Spoiler:
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Seems like I missed out on not attempting 4 or 5. I'm a bit surprised no-one else tried 3, it turned out to be pretty easy IMO.

Edit: Definitely missed out on with 4, would've been an easy 15 marks certainly.
4. (Original post by Zacken)
sqrt(1+a) approx 1 + a/2 by the binomial expansion
Okay, many thanks!
5. (Original post by Vesniep)
I've done the paper today.
Well done!

Q 13:
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Did you do the first part in the same way as the mark scheme? I tried doing it by saying C = ky + 0P(X<=y) + a(X-y)P(X > y) = ky + a(X-y)(1 - (1 - e^(-lambday))) and then doing E(C) as E(ky - aye^(-lambday)) + ae^-(lambday)E(X), but that didn't get me the right answer as I had an extra aye^(-lambday) term.
6. (Original post by EnglishMuon)
Just a quick check: when showing arcoshx= ln{1+(x^2-1)^1/2} I am able to look at cosh { ln{1+(x^2-1)^1/2}}= x and deduce the result from this?
And mention ln(x + root(x^2 - 1)) is positive so that it is arcosh x and not -arcosh x?
7. (Original post by 16Characters....)
And mention ln(x + root(x^2 - 1)) is positive so that it is arcosh x and not -arcosh x?
and yep, did put that in my workings
8. (Original post by sweeneyrod)
Well done!

Q 13:
Spoiler:
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Did you do the first part in the same way as the mark scheme? I tried doing it by saying C = ky + 0P(X<=y) + a(X-y)P(X > y) = ky + a(X-y)(1 - (1 - e^(-lambday))) and then doing E(C) as E(ky - aye^(-lambday)) + ae^-(lambday)E(X), but that didn't get me the right answer as I had an extra aye^(-lambday) term.
E(C) = P(X<y) * E(ky) + P(X>y) * E(ky+a(X-y) I Y>y ) =ky+ a e^(-λy) (E(X I X>y) - y)
E( X I X>y)= [ integral of (λe^(-λχ)) from y to infinity ] / P(X>y) = y + 1/λ
Comment : I know it was quiet difficult and it got me into trouble .
part ii was too much , very messy integrals I don't see the point
9. just did 2013 ii - 105
10. (Original post by Vesniep)
E(C) = P(X<y) * E(ky) + P(X>y) * E(ky+a(X-y) I Y>y ) =ky+ a e^(-λy) (E(X I X>y) - y)
E( X I X>y)= [ integral of (λe^(-λχ)) from y to infinity ] / P(X>y) = y + 1/λ
Comment : I know it was quiet difficult and it got me into trouble .
part ii was too much , very messy integrals I don't see the point
I see, I forgot the given part. Thanks
11. When explaining a simple idea such as the first part of q5 III 2001, is it usually acceptable to use a diagram instead of words? i.e. in this case is it enough to differentiate and show f(x) is an increasing function and then give a rough sketch of a strictly increasing cubic (instead of saying as x tends to +- infinity....)? (followed by stating the conclusion)
12. (Original post by 16Characters....)
I also did STEP II 2015 today
Spoiler:
Show

Q1) I liked this question.
Q4) Lovely, though I spent too long on it really.
Q5) Nice question, but it took longer than I would have liked.
Q6) Alright. The first two parts were straightforward. Made a silly algebra mistake in the final part.
Q7) I am annoyed at this. I had an expression for y, but thought it was too ugly to be correct so crossed it out and tried to start again. Turns out I was actually right in the first place.

Overall: I got a solid 1 so I am happy, though I would have preferred to atleast start a 6th question.

Spoiler:
Show
Q3 was very easy btw .
13. (Original post by Number Nine)
just did 2013 ii - 105
which q's
14. (Original post by Vesniep)
Spoiler:
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Q3 was very easy btw .
Spoiler:
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Not as easy as q2, one of the easiest questions for m ever,
15. (Original post by EnglishMuon)
When explaining a simple idea such as the first part of q5 III 2001, is it usually acceptable to use a diagram instead of words? i.e. in this case is it enough to differentiate and show f(x) is an increasing function and then give a rough sketch of a strictly increasing cubic (instead of saying as x tends to +- infinity....)? (followed by stating the conclusion)
It would be more rigorous especially if you mention Bolzano's theorem for continuous functions (at least one root) and that it's a 1-1 function (at most 1 root) but perhaps they'd accept it
16. (Original post by physicsmaths)
Spoiler:
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Not as easy as q2, one of the easiest questions for m ever,
Didn't try it yet . I thought geometry => let's move on
17. (Original post by gasfxekl)
which q's
1,2,3,5,7,8
18. (Original post by Vesniep)
It would be more rigorous especially if you mention Bolzano's theorem for continuous functions (at least one root) and that it's a 1-1 function (at most 1 root) but perhaps they'd accept it
I mean i cant imagine mentioning bolzanos theorem would get u any more credit especially as you are not required to know it and it is just the same as saying there is only 1 root if u dont give proof.
19. (Original post by EnglishMuon)
Just a quick check: when showing arcoshx= ln{1+(x^2-1)^1/2} I am able to look at cosh { ln{1+(x^2-1)^1/2}}= x and deduce the result from this?
Well yes.

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20. (Original post by EnglishMuon)
When explaining a simple idea such as the first part of q5 III 2001, is it usually acceptable to use a diagram instead of words? i.e. in this case is it enough to differentiate and show f(x) is an increasing function and then give a rough sketch of a strictly increasing cubic (instead of saying as x tends to +- infinity....)? (followed by stating the conclusion)
Yep that is perfectly fine. Infact much better.

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