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# STEP Prep Thread 2016 (Mark. II) watch

1. (Original post by Zacken)
No, of course not, why would they?
Wouldnt of thought so but my school were going on and on about how strict they were
2. For step ii 2015 question 5 i've just proved by induction S(n)=arctan(n/(n+1)) for the first bit but then i realised that I should have proved tanS(n)=n/(n+1) for the first bit and S(n)=arctan(n/(n+1)) for the second bit, are they not the same thing? surely if one is true then the other is true? also how would you prove anS(n)=n/(n+1) without using S(n)=arcgan(n/(n+1))? sorry the mark scheme was a bit cryptic so i just asked on here
3. (Original post by porridgepie)
For step ii 2015 question 5 i've just proved by induction S(n)=arctan(n/(n+1)) for the first bit but then i realised that I should have proved tanS(n)=n/(n+1) for the first bit and S(n)=arctan(n/(n+1)) for the second bit, are they not the same thing? surely if one is true then the other is true? also how would you prove anS(n)=n/(n+1) without using S(n)=arcgan(n/(n+1))? sorry the mark scheme was a bit cryptic so i just asked on here
Well, no - tan S_n = a and S_n = arctan a are two different things, remember that tangent is a pi-periodic function, so how do you know that it's know S_n = arctan a + pi, for example? You need to prove that S_n is bounded between 0 and pi for you to assert that S_n = arctan a.
4. (Original post by Zacken)
Well, no - tan S_n = a and S_n = arctan a are two different things, remember that tangent is a pi-periodic function, so how do you know that it's know S_n = arctan a + pi, for example? You need to prove that S_n is bounded between 0 and pi for you to assert that S_n = arctan a.
so do i just have to state that 0=<arctanx=<pi/2 ?
also how do i even prove tanS(n)=n/(n+1) without using the tan formula to show that S(k)= arctann/(n+1) + arctan1/2k^2 ?
5. (Original post by Zacken)
Well, no - tan S_n = a and S_n = arctan a are two different things, remember that tangent is a pi-periodic function, so how do you know that it's know S_n = arctan a + pi, for example? You need to prove that S_n is bounded between 0 and pi for you to assert that S_n = arctan a.
ya mean -pi/2,pi/2
6. (Original post by porridgepie)
so do i just have to state that 0=<arctanx=<pi/2 ?
also how do i even prove tanS(n)=n/(n+1) without using the tan formula to show that S(k)= arctann/(n+1) + arctan1/2k^2 ?
No, of course not. You have to prove it.

Well, you do it by induction.
7. (Original post by Zacken)
No, of course not. You have to prove it.

Well, you do it by induction.
sorry so do i start by showing tan(arctan.5 + arctan.125...+arctan1/2k^2) =n/(n+1) then do the k+1 induction
i realise i must sound like a moron but i'm just really pants at induction proof
8. (Original post by porridgepie)
sorry so do i start by showing tan(arctan.5 + arctan.125...+arctan1/2k^2) =n/(n+1) then do the k+1 induction
i realise i must sound like a moron but i'm just really pants at induction proof
yes
9. (Original post by porridgepie)
sorry so do i start by showing tan(arctan.5 + arctan.125...+arctan1/2k^2) =n/(n+1) then do the k+1 induction
i realise i must sound like a moron but i'm just really pants at induction proof
No, you assume that tan (arctan 0.5 + ...) = n/n+1 and then use that assumption to prove that the k+1 case is also true.

(Original post by porridgepie)
the question tells you that arctan is in interval (0, pi/2)
Exactly, hence why you need to prove that S_n is bounded above by pi/2 in order to apply the arctan function.
10. (Original post by Zacken)
No, you assume that tan (arctan 0.5 + ...) = n/n+1 and then use that assumption to prove that the k+1 case is also true.

Exactly, hence why you need to prove that S_n is bounded above by pi/2 in order to apply the arctan function.
get it now thx for your help
11. (Original post by porridgepie)
get it now thx for your help
No worries.
12. So here is how I did:

Started off with question 2 (because calculus is usually my best and it looked easy) and I completed it.

Then I took up question 4 (more calculus ) did the first bit; used the first result in the second bit to give another differential equation and after squaring tried to find f(x) cant remember what I got but it was something weird not sure whether its right. Didnt give a geometric interpretation (or whatever was asked)

Question 1 and 3 came next - 1 was good i proved all the results then got factors in (ii) which I think are correct. As for question three the graphs were fine i saw sin3<sin2 which was good and i showed open and coloured circles where needed and I hope I got it completely.

Then I went for Q10 cuz it looked good but I couldnt complete it - i got the first result and then attempted (ii) after a lot of horrible algebra i came up with a weird cubic for lambda which i couldnt solve.

The final question was the real mess - I had roughly 20-25 mins left and I just went for 11 but i couldnt get the first result - i did resolve and write down equations and stuff but the answer didnt come. I did write differentiate then equalise to zero to get maximum. I also did Q9 bc 11 wasnt going far but i think i made an error with reaction but i wrote down as many resolving equations and moments as was needed - that reaction error didnt give me the result i think.

So how much do u guys think I would get? not really feeling very confident after messing up the last Q - looking back i think i shoulda done 8 instead of scratching at bits of mechanics questions at the end...
13. (Original post by Gunawardana)
So here is how I did:

Started off with question 2 (because calculus is usually my best and it looked easy) and I completed it.

Then I took up question 4 (more calculus ) did the first bit; used the first result in the second bit to give another differential equation and after squaring tried to find f(x) cant remember what I got but it was something weird not sure whether its right. Didnt give a geometric interpretation (or whatever was asked)

Question 1 and 3 came next - 1 was good i proved all the results then got factors in (ii) which I think are correct. As for question three the graphs were fine i saw sin3<sin2 which was good and i showed open and coloured circles where needed and I hope I got it completely.

Then I went for Q10 cuz it looked good but I couldnt complete it - i got the first result and then attempted (ii) after a lot of horrible algebra i came up with a weird cubic for lambda which i couldnt solve.

The final question was the real mess - I had roughly 20-25 mins left and I just went for 11 but i couldnt get the first result - i did resolve and write down equations and stuff but the answer didnt come. I did write differentiate then equalise to zero to get maximum. I also did Q9 bc 11 wasnt going far but i think i made an error with reaction but i wrote down as many resolving equations and moments as was needed - that reaction error didnt give me the result i think.

So how much do u guys think I would get? not really feeling very confident after messing up the last Q - looking back i think i shoulda done 8 instead of scratching at bits of mechanics questions at the end...
20, 16, 20, 15, 4, 8 = 86
14. (Original post by Zacken)
20, 16, 20, 15, 4, 8 = 86
I did 7 Qs btw (1,2,3,4,9,10,11) so wouldnt 1,2,3,4,10 and one of 9 or 11 be my best six? so wouldnt it be more like Q1=20, Q2=20, Q3=20? Q4=16, Q10=15, Q11=4? Q10=8? giving like more than 90?

*Q9 = 8 not Q10 =8
15. (Original post by Gunawardana)
I did 7 Qs btw (1,2,3,4,9,10,11) so wouldnt 1,2,3,4,10 and one of 9 or 11 be my best six? so wouldnt it be more like Q1=20, Q2=20, Q3=20? Q4=16, Q10=15, Q11=4? Q10=8? giving like more than 90?
yeah, you put two questions in the same paragraph so I double counted.
16. (Original post by Zacken)
yeah, you put two questions in the same paragraph so I double counted.
yeah sry about that - and no worries. btw in my last post i meant Q10=15, Q11=4 and Q9(not 10) = 8 haha

so yeah depends on where the S boundary would go - any guesses?
17. (Original post by Gunawardana)
yeah sry about that - and no worries. btw in my last post i meant Q10=15, Q11=4 and Q9(not 10) = 8 haha

so yeah depends on where the S boundary would go - any guesses?
100+ i'd say
18. (Original post by Zacken)
100+ i'd say
thought so too - so yeah i guess ive gotten a good 1 (if all went as expected and i didnt make some ridiculously large error and didnt notice it )

Well, good luck in STEP 2
19. (Original post by Gunawardana)
thought so too - so yeah i guess ive gotten a good 1 (if all went as expected and i didnt make some ridiculously large error and didnt notice it )

Well, good luck in STEP 2
Yeah, reckon I got the same. Incredibly annoyed about that.

Thanks, you too(?).
20. (Original post by Zacken)
Yeah, reckon I got the same. Incredibly annoyed about that.

Thanks, you too(?).
np and thanks to u too - yeah im doing STEP 2 (and 3 as well)

yeah annoyed about STEP 1 too, but I guess we shouldnt let that hold us back in STEP 2 and 3 haha . I just wanna make sure I choose my questions (mainly the last 1/2) well next time (cuz if i had selected a better last Q rather than scraping around i might have been able to get a better total) .

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