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OCR MEI FP1 20th January 2010 pm watch

1. (Original post by Donor)
I found it quite straight forward up to the method of differences which I worked out in the end. I definitely made some silly mistakes though. I was lucky actually as all the revision I'd done was a couple of exam papers yesterday (resitting) and everything that came up was similar to that.

For the last question did anyone just sub values of r = 50 and r=100 in and then take one from the other?
Do you mean n = 100? That is what I did. I accidently put 0.0105 instead of 0.0104. Would I lose a mark?
2. for the shaded region question you take 2 + j from 46 plus what eva j , then find the argument of that, and because the argument is higher than pi over 4, the point lies within the shaded region
3. (Original post by tsiyan13)
for the shaded region question you take 2 + j from 46 plus what eva j , then find the argument of that, and because the argument is higher than pi over 4, the point lies within the shaded region
That is what I did

Also did you draw dotted lines for both the lines?
4. nopee did you? lol but it was a good paper, all my mistakes will probably be silly mistakes like that lol
5. I did. The reason I did was because It didn't have any inclusive inequality (is that generally correct?) Yeah it was a good paper, except the last question.
6. lol same i didnt see it say 3 sig fig, but owel
7. Do you believe believe the grade boundaries will be low? If yes, how low (or how high even)?
8. Hey, IMO it was an ok paper (defo A on it)

some bits were a bit weird like that summation but there were definately a load of easy marks here and there. As for grade boundaries i think it will be something like :-
A:80%; B:70%; C:60%; D:50%; E:40%
this is because it seems people found it a fair paper
(not too hard not too easy or something along those lines)

---------------------------------------------------------------------

Here are a few notes on some of the questions people seem worried about:-

For the shaded region the question stated two inequalities were needed; here is what i put:
|z-(a+bj)|>1 for the small circle (A)
|z-(c+dj)|<4 for the bigger circle (B)
with a,b,c,d being the real and imaginary parts of circle A and circle B respectively.

--------------------------------------------------------------------
polynomial roots:
a = 1
d^2 = 0.25
so d was +/- 0.5 which still gave the same roots (i.e. a-d, a, a+d)
i think that'll be a mark for saying that the roots are the same regardless
k = 11
defo an easy few marks here

--------------------------------------------------------------------
for the complex number within the region i took:
arctan 47/43 = 0.8298

as this lies within the range: pi/4 < arg(..) < 3pi/4
i said that 43 + 47j was within the required range
(which seems ok for 3 marks tbh)

--------------------------------------------------------------------

for the method of differences between r = 100 and r = 50 i though it would be
(the summation between 100 and 0) - (the summation between 49 and 0)
as r = 50 is within the required range. which came out as 0.0104 or something

-------------------------------------------------------------------
anyhow, hope everyone gets a good grade and if you need any help with anything then please reply to my post

good luck for the rest of your exams

Craig
9. (Original post by Summerdays)
Also did you draw dotted lines for both the lines?
I didn't draw dotted lines, but I made sure that I included a statement that made it clear not to include the lines in the region, just as they did with the shaded region at the start of the question "...the shaded region between, but not including, circles A and B."
10. (Original post by craigp100)
Hey, IMO it was an ok paper (defo A on it)

some bits were a bit weird like that summation but there were definitely a load of easy marks here and there. As for grade boundaries i think it will be something like :-
A:80%; B:70%; C:60%; D:50%; E:40%
this is because it seems people found it a fair paper
(not too hard not too easy or something along those lines)

---------------------------------------------------------------------

Here are a few notes on some of the questions people seem worried about:-

For the shaded region the question stated two inequalities were needed; here is what i put:
|z-(a+bj)|>1 for the small circle (A)
|z-(c+dj)|<4 for the bigger circle (B)
with a,b,c,d being the real and imaginary parts of circle A and circle B respectively.

--------------------------------------------------------------------
polynomial roots:
a = 1
d^2 = 0.25
so d was +/- 0.5 which still gave the same roots (i.e. a-d, a, a+d)
i think that'll be a mark for saying that the roots are the same regardless
k = 11
defo an easy few marks here

--------------------------------------------------------------------
for the complex number within the region i took:
arctan 47/43 = 0.8298

as this lies within the range: pi/4 < arg(..) < 3pi/4
i said that 43 + 47j was within the required range
(which seems ok for 3 marks tbh)

--------------------------------------------------------------------

for the method of differences between r = 100 and r = 50 i though it would be
(the summation between 100 and 0) - (the summation between 49 and 0)

as r = 50 is within the required range. which came out as 0.0104 or something

-------------------------------------------------------------------
anyhow, hope everyone gets a good grade and if you need any help with anything then please reply to my post

good luck for the rest of your exams

Craig
Btw which formula did you use for the part in bold because i did that too but got the wrong answer
11. You really think it would be a mark for stating that the roots would be the same regardless (even though it was quite self-explanatory)? Also I disagree with your complex number answer (I believe you had to subtract it by 2 + j).

I don't understand the method you used for the last question. I substituted r = 50 into 4+r/r(r+1)(r+2) and then I then took that away (n=100) by 3/2 - 2/n+1 + 1/n+2 , and then added this answer to 3/2 . I got 0.0104 (but I accidently wrote 0.0105)
12. (Original post by DaGianni)
I didn't draw dotted lines, but I made sure that I included a statement that made it clear not to include the lines in the region, just as they did with the shaded region at the start of the question "...the shaded region between, but not including, circles A and B."
Ok So is it right to use dotted lines instead, as well?
13. (Original post by Summerdays)
Ok So is it right to use dotted lines instead, as well?
Strictly speaking yes (the only reason I drew solid lines was to make the region a bit more clear to see), you have done it the correct way.
14. (Original post by Summerdays)
You really think it would be a mark for stating that the roots would be the same regardless (even though it was quite self-explanatory)? Also I disagree with your complex number answer (I believe you had to subtract it by 2 + j).

I don't understand the method you used for the last question. I substituted r = 50 into 4+r/r(r+1)(r+2) and then I then took that away by 3/2 - 2/r+1 + 1/r+2 , and then added this answer to 3/2 . I got 0.0104 (but I accidently wrote 0.0105)
For the last question where (r+4)/(r)(r+1)(r+2) i just subbed in 50 and 100 and took one away from the other,

so 104/(100x101x102) - 54/(50x51x52)

but it gave me something like -3.06 x 10^-4, I think I should have taken this from 3/2 but that could be completely the wrong method.
15. Incase anyone wanted the matrix question, while i've still got it on my calculator, the matrix was:

The second part to solve the equations (from the bits i remember..) was and i got something like as 'x', 'y' and 'z'.
16. Thought it went okay.

for the method of differences.
the limit was 3/2. This is because as n tends to infinitely 2/(n=1) and 1/n or whatever it was tends to 0

for the last part, just sub n = 50 into that. It ends up 1.49 I think.

Was okay. I walked out and realised I got the last part of the second to last question wrong though because I forgot to take away 2-1j from 43+47j. Should be okay though.
17. That's what I got as well
18. just looking through the thread now.

for the polynominal I got k = 11, d = 0.5 and a = 1 I think.

and in the matrix one, k = 5.
19. i got the same x y and z values

I liked the induction question, I thought that was nice, And the one using standard formulae for r^2 and r
20. Yup, i messed up the polynomial one, but got deffo k=5 in the matrix.

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