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# FP2 (Not MEI) - Thursday June 14 2012, AM Tweet

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1. Re: FP2 (Not MEI) - Thursday June 14 2012, AM
When doing a reduction formula question, for example p208, q13.

I prefer to go about these by rewriting the top to which then allows me to integrate and so on until the required answer. This works for me but I have seen several examples where you are first asked to differentiate something and then use this result to "deduce" the reduction. In this question you are first asked to find the differential of . I don't see how this helps you come to the final answer.

I think it's probably something to do with how if you take the function to by 1 * f(x) and integrate by parts that way, you would eventually come to that.. I just don't see it dammit!
2. Re: FP2 (Not MEI) - Thursday June 14 2012, AM
(Original post by SecondHand)
When doing a reduction formula question, for example p208, q13.

I prefer to go about these by rewriting the top to which then allows me to integrate and so on until the required answer. This works for me but I have seen several examples where you are first asked to differentiate something and then use this result to "deduce" the reduction. In this question you are first asked to find the differential of . I don't see how this helps you come to the final answer.

I think it's probably something to do with how if you take the function to by 1 * f(x) and integrate by parts that way, you would eventually come to that.. I just don't see it dammit!
Notice that:

.

I think by 'deduce' they want you to do it by parts, now that you know what the derivative of is.
3. Re: FP2 (Not MEI) - Thursday June 14 2012, AM
(Original post by Anon 17)
^ Haven't looked at the paper, but try showing that a point to the left has a negative gradient and a point to the right has a positive gradient?
That gets a bit messy, because I'm dealing with here. I suppose I could assign a random value and work from there - although that wouldn't really be formal, and I'm not sure if it'd get me the marks.
4. Re: FP2 (Not MEI) - Thursday June 14 2012, AM
(Original post by Ree69)
Notice that:

.

I think by 'deduce' they want you to do it by parts, now that you know what the derivative of is.
I used to hate induction formulae but they're quite juicy, nothing more satisfying than solving one
5. Re: FP2 (Not MEI) - Thursday June 14 2012, AM
(Original post by Ree69)
That gets a bit messy, because I'm dealing with here. I suppose I could assign a random value and work from there - although that wouldn't really be formal, and I'm not sure if it'd get me the marks.
Try using and ?

I would check the paper and the question but I've got to shoot, if I get time tommorow and you still haven't got it I'll try it myself.
6. Re: FP2 (Not MEI) - Thursday June 14 2012, AM
(Original post by Ree69)
Notice that:

.

I think by 'deduce' they want you to do it by parts, now that you know what the derivative of is.
Cheers, I think induction formula are the hardest part of the course, Good to be able to see two ways to do it though.
7. Re: FP2 (Not MEI) - Thursday June 14 2012, AM
(Original post by SecondHand)
Cheers, I think induction formula are the hardest part of the course, Good to be able to see two ways to do it though.
They get better with practice
8. Re: FP2 (Not MEI) - Thursday June 14 2012, AM
(Original post by Ree69)
That gets a bit messy, because I'm dealing with here. I suppose I could assign a random value and work from there - although that wouldn't really be formal, and I'm not sure if it'd get me the marks.
Took me way too long for 1 mark but here's how you do it.

Assuming you know that

It's easier if you start by first rewriting the given equation.

Then substitute the given value of x into this equation.

Which equals

9. Re: FP2 (Not MEI) - Thursday June 14 2012, AM
[QUOTE=SecondHand;38001410]Took me way too long for 1 mark but here's how you do it.

(Original post by SecondHand)
Oh... I see. Cheers.

I got as far as here, and then for some reason I thought it'd be acceptable to multiply right through by giving me a final answer of .

I think I just worked out how to show it's a minimum too.

We know that which is strictly positive for any . So the stationary point is a minimum.
10. Re: FP2 (Not MEI) - Thursday June 14 2012, AM
January 2009:

Question 9 parts ii) and iii), for part two I have no idea what it's asking me... In the slightest.

Part 3 I can't seem to get started, any loose hints (don't want a full answer or anything).
11. Re: FP2 (Not MEI) - Thursday June 14 2012, AM
(Original post by Anon 17)
January 2009:

Question 9 parts ii) and iii), for part two I have no idea what it's asking me... In the slightest.

Part 3 I can't seem to get started, any loose hints (don't want a full answer or anything).
Hints:

ii) Use the discriminant
iii) Split the integral into two parts and integrate them separately.
12. Re: FP2 (Not MEI) - Thursday June 14 2012, AM
^ Damn, I tried a much harder method for part ii - Just realised I should have made the first quadratic from f(x) instead of finding f'(x)...

Still trying part iii), thanks for the help =)

EDIT - Got both from the hints, cheers. Now I just need to work on doing this in an exam, without hints. I'm kinda hoping the experience from all the past papers will cover this (ala FP3).
Last edited by Anon 17; 09-06-2012 at 18:57.
13. Re: FP2 (Not MEI) - Thursday June 14 2012, AM
(Original post by Anon 17)
^ Damn, I tried a much harder method for part ii - Just realised I should have made the first quadratic from f(x) instead of finding f'(x)...

Still trying part iii), thanks for the help =)

EDIT - Got both from the hints, cheers. Now I just need to work on doing this in an exam, without hints. I'm kinda hoping the experience from all the past papers will cover this (ala FP3).
The thing about FP2 is there's usually an interesting question in there somewhere, amongst all the 'repetitive' ones

14. Re: FP2 (Not MEI) - Thursday June 14 2012, AM
Juicy question from the text book. P214, practice examination 2, Q6(iii). Can anyone show me a solution?
15. Re: FP2 (Not MEI) - Thursday June 14 2012, AM
Spent almost an hour trying to remember the double angle bull**** for integrating sin^6 (x), then found out that the mark scheme allows doing it by imaginary numbers which I could have done in about 2 minutes...

Also missed the fact I could have done it with a reduction formula.

June 2009, whole paper except that last bit (9b) was sooo easy. I really hate FP2 now...

Does anyone know if this is consistant? I.E., can we use FP3 techniques of integrating cos or sin ^ n with imaginary numbers if the question says "or otherwise"?
16. Re: FP2 (Not MEI) - Thursday June 14 2012, AM
(Original post by Anon 17)
Spent almost an hour trying to remember the double angle bull**** for integrating sin^6 (x), then found out that the mark scheme allows doing it by imaginary numbers which I could have done in about 2 minutes...

Also missed the fact I could have done it with a reduction formula.

June 2009, whole paper except that last bit (9b) was sooo easy. I really hate FP2 now...

Does anyone know if this is consistant? I.E., can we use FP3 techniques of integrating cos or sin ^ n with imaginary numbers if the question says "or otherwise"?
Was this a 'hence' question after doing polar coordinates? I think I remember it

If it says hence or it seems a bit ridiculous, ALWAYS look back at your previous working there's usually a clue in there somewhere.
17. Re: FP2 (Not MEI) - Thursday June 14 2012, AM
Yeah, I geniunely can't believe I didn't look at the first part of the question as I can integrate it in 2/3 of the ways allowed... I chose to try the one I couldn't do xD

I'm gonna learn that method tommorow anyway, just in case.
18. Re: FP2 (Not MEI) - Thursday June 14 2012, AM
Question 7, practice examination 1, anyone?
19. Re: FP2 (Not MEI) - Thursday June 14 2012, AM
^ Which part(s)?

I'm going out now, but if no one's answered tommorow I'll give the two questions a crack.

Reminds me - Anyone know where I can find the grade boundaries? Want to find the mean mark for 90 ums (A*).
20. Re: FP2 (Not MEI) - Thursday June 14 2012, AM
(Original post by Anon 17)
^ Which part(s)?

I'm going out now, but if no one's answered tommorow I'll give the two questions a crack.

Reminds me - Anyone know where I can find the grade boundaries? Want to find the mean mark for 90 ums (A*).
OCR website - for older papers (pre Jun 10 I think) they're at the end of the examiner reports. For the new papers just google June 2010 / Jan 11 / Jun 11 / Jan 12 OCR grade boundaries

EDIT: It's usually the case that 100% UMS is AROUND 66 raw marks. In January it was 61/62 raw marks for 100% UMS.
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