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STEP Maths II, III 2009 Solutions

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Reply 20
STEP III, Question 12:

(i)



(ii)

Reply 21
STEP III, Question 3:

(i)



(ii)



(iii)



sketch

(edited 7 years ago)
Doing III Q8 right now :smile:.
STEP III, Question 8

(i)



(ii)



(iii)

(edited 7 years ago)
Reply 24
Done Q7 I can try and type it up now.
II
Reply 25
STEP II Question 7
(i)

Spoiler

(ii)

Spoiler

(iii)

Spoiler

(edited 7 years ago)
Original post by B_9710
STEP III Question 7
(i)

Spoiler

(ii)

Spoiler

(iii)

Spoiler



Probably better to use the fact that (fgh)=fgh+fgh+fgh(fgh)'=f'gh+fg'h+fgh' for the differentiation at the start.
Reply 27
Original post by B_9710
STEP II Question 7
(i)

Spoiler




As an alternative to the above, you can also take logs to get:

logy=nlog(xa)+bx+12log(1+x2)\log y = n \log (x-a) + bx + \frac{1}{2} \log (1+x^2) then differentiate implicitly to get yy=nxa+b+x1+x2\frac{y'}{y} = \frac{n}{x-a} + b + \frac{x}{1 + x^2}
Reply 28
Original post by Zacken
As an alternative to the above, you can also take logs to get:

logy=nlog(xa)+bx+12log(1+x2)\log y = n \log (x-a) + bx + \frac{1}{2} \log (1+x^2) then differentiate implicitly to get yy=nxa+b+x1+x2\frac{y'}{y} = \frac{n}{x-a} + b + \frac{x}{1 + x^2}


I tried that to begin with but it didn't seem to make it any less painless.
Reply 29
Original post by IrrationalRoot
Probably better to use the fact that (fgh)=fgh+fgh+fgh(fgh)'=f'gh+fg'h+fgh' for the differentiation at the start.


You're probably right. :wink:
Reply 30
Original post by B_9710
I tried that to begin with but it didn't seem to make it any less painless.


It worked out okay if you pulled out the denominator and 1xa\frac{1}{x-a} right away. Either way is fine, anyways. :-)
Is there a thread for STEP I 2009 solutions already? I can't seem to find one.
Reply 32
Original post by IrrationalRoot
Is there a thread for STEP I 2009 solutions already? I can't seem to find one.


Nopes, it's just that the official examiner solutions are already beautifully laid out and intricately detailed. If there'd demand, we can always just add in a STEP I section after we've completed II and III.
Original post by Zacken
Nopes, it's just that the official examiner solutions are already beautifully laid out and intricately detailed. If there'd demand, we can always just add in a STEP I section after we've completed II and III.


Oh yeah the I solutions are lovely. I don't get why they don't do that for II and III, would be so nice.
Reply 34
Original post by IrrationalRoot
Oh yeah the I solutions are lovely. I don't get why they don't do that for II and III, would be so nice.


Different examiners - the examiner for STEP I is a nice dude, or so I've heard. :lol:
Original post by Zacken
Different examiners - the examiner for STEP I is a nice dude, or so I've heard. :lol:


Oh wow, so the II and III examiners are just lazy lol.
Reply 36
Original post by IrrationalRoot
Oh wow, so the II and III examiners are just lazy lol.


I think that tends to be the norm with maths examiners, unfortunately xD
STEP III Q10

Solution

STEP III Q6

Solution

STEP III Q7

Solution

(edited 7 years ago)

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