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STEP Prep Thread 2016 (Mark. II)

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For question 8(i) 1,2013, why is the domain of da infinity to infinity? Thanks!
Original post by Glavien
For question 8(i) 1,2013, why is the domain of da infinity to infinity? Thanks!


da(x)=x2=∣x∣da(x)=\sqrt{x^2}=|x|. This clearly has domain (−∞,+∞)(-\infty,+\infty), since domain of aa is this and the range of aa is a subset of the domain of dd. (In fact the range of aa is the domain of dd.)
(edited 7 years ago)
Original post by IrrationalRoot
da(x)=x2=∣x∣da(x)=\sqrt{x^2}=|x|. This clearly has domain (−∞,+∞)(-\infty,+\infty), since domain of aa is this and the range of aa is a subset of the domain of dd. (In fact the range of aa is the domain of dd.)


Thanks!
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Original post by Glavien
For question 8(i) 1,2013, why is the domain of da infinity to infinity? Thanks!


You could also just argue that in general fg(x) has the domain of g(x). So da has domain of a.
Original post by Zacken
You could also just argue that in general fg(x) has the domain of g(x). So da has domain of a.


So in general fg(x) has the domain of g(x), but what is the domain of f(x) is restricted? Shouldn't the domain of fg(x) be the domain of f(x) as it is a tighter interval? Sorry that may be a bit confusing.


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Original post by Glavien
So in general fg(x) has the domain of g(x), but what is the domain of f(x) is restricted? Shouldn't the domain of fg(x) be the domain of f(x) as it is a tighter interval? Sorry that may be a bit confusing.


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No, in a composite function. You feed things (x's) into g(x), not f(x) so your domain is g(x)'s domain in general.

However, you need to ensure that g(x)'s image fits into f(x)'s domain because you put g(x) into f(x).

In your case, can you see how a's range fits into d's domain?
Original post by Zacken
No, in a composite function. You feed things (x's) into g(x), not f(x) so your domain is g(x)'s domain in general.

However, you need to ensure that g(x)'s image fits into f(x)'s domain because you put g(x) into f(x).

In your case, can you see how a's range fits into d's domain?


a's range is a(x) =>0 which is the same as d's domian so it fits, right?
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Original post by Glavien
a's range is a(x) =>0 which is the same as d's domian so it fits, right?


Yes.
Original post by Zacken
You could also just argue that in general fg(x) has the domain of g(x). So da has domain of a.


No in general the domain of fg(x) is the largest subset S of of the domain of g such that the image of S under g is a subset of the domain of f; that's why my explanation wasn't so simple.
(edited 7 years ago)
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Original post by Zacken
No, in a composite function. You feed things (x's) into g(x), not f(x) so your domain is g(x)'s domain in general.

However, you need to ensure that g(x)'s image fits into f(x)'s domain because you put g(x) into f(x).

In your case, can you see how a's range fits into d's domain?


Original post by IrrationalRoot
No in general the domain fg(x) is the largest subset S of of the domain of g such that the image of S under g is a subset of the domain of f; that's why my explanation wasn't so simple.


..
Original post by Zacken
..


"You could also just argue that in general fg(x) has the domain of g(x). So da has domain of a."
"so your domain is g(x)'s domain in general."

were not correct so had to correct them. Anyway, what I said is (somewhat subtly) different to the statement
'it's the domain of g(x) as long as you make sure the image is part of the domain of f',
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Original post by IrrationalRoot
"You could also just argue that in general fg(x) has the domain of g(x). So da has domain of a."
"so your domain is g(x)'s domain in general."

were not correct so had to correct them. Anyway, what I said is (somewhat subtly) different to the statement
'it's the domain of g(x) as long as you make sure the image is part of the domain of f',


Yeah, I agree with all that. I was just trying to go for brevity and informalness. :lol:
Original post by Zacken
Yeah, I agree with all that. I was just trying to go for brevity and informalness. :lol:


No worries, you can probs tell by now that I'm super pedantic with technical stuff :smile:.
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Original post by IrrationalRoot
No worries, you can probs tell by now that I'm super pedantic with technical stuff :smile:.


It's good for keeping me on my toes! :smile:
STEP II 2014 Q 13:

Spoiler


While I'm at it, STEP II 2004 Q 13: (back in the good old days when there were three stats questions):

For the last part -- "Given that the cook stirs 6 sixpences..." -- a simple counting argument (all ways of distributing coins are equally likely, 9 ways in total, one is a success) suggests the answer is 1/9, but that isn't correct. What am I doing wrong?
(edited 7 years ago)
Original post by sweeneyrod
STEP II 2014 Q 13:

Spoiler


While I'm at it, STEP II 2004 Q 13: (back in the good old days when there were three stats questions):

For the last part -- "Given that the cook stirs 6 sixpences..." -- a simple counting argument (all ways of distributing coins are equally likely, 9 ways in total, one is a success) suggests the answer is 1/9, but that isn't correct. What am I doing wrong?


For the 2014 question,


The question's ambiguous, but I'm fairly sure they're just summing from 1 to n.


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@physicsmaths,

How much easier are older papers compared to newer ones? I did 1998 III, and I got 96/120 but not sure if this is S or Grade 1. What do you think might be the grade boundaries for it? You should consider that Q1, 2 and 9 are literally a 10 minute job for current STEP III candidates (not sure about then though, since I don't know if standard M.I techniques were in M5 back in the old days).

Also, has anyone tried 1998 III (@IrrationalRoot since I know you do 90s papers)? We can discuss if you want, I found 3 very difficult and Question 7 I couldn't spot the binomial expansion and how to pretty much integrate b(x)b(x) at the end. I did 1, 2, 3, 4, 7, 9, 10.
(edited 7 years ago)
Original post by Krollo
For the 2014 question,

Spoiler


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Spoiler

Original post by Insight314
@physicsmaths,

How much easier are older papers compared to newer ones? I did 1998 III, and I got 96/120 but not sure if this is S or Grade 1. What do you think might be the grade boundaries for it? You should consider that Q1, 2 and 9 are literally a 10 minute job for current STEP III candidates (not sure about then though, since I don't know if standard M.I techniques were in M5 back in the old days).

Also, has anyone tried 1998 III (@IrrationalRoot since I know you do 90s papers)? We can discuss if you want, I found 3 very difficult and Question 7 I couldn't spot the binomial expansion and how to pretty much integrate b(x)b(x) at the end. I did 1, 2, 3, 4, 7, 9, 10.


Pretty easy tbh Although the boundaries were normal back then still due to lack of resources etc. It would have been an S i think back then. But that would translate to a 1 imo nowadays.


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Original post by physicsmaths
Pretty easy tbh Although the boundaries were normal back then still due to lack of resources etc. It would have been an S i think back then. But that would translate to a 1 imo nowadays.


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All right thanks. :smile:

No S grades yet then. :frown:


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