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# P5 OCR 21st June watch

1. how was it, i found it quite nice really. very similar in difficulty to previous years. should get an A hopefully.
2. yup very nice, that reduction formula for sin^n(x) was in the text book and i read it yesterday!

i didn't have enough time to finish the last question, I got lambda = 0 and mew = -1/6

surface area = 2pi(1 - e^-1)

can't think of much else, oh and i got one the the roots of the equation wrong, the alpha^4 + beta ^4 .... one. Oh well.
3. (Original post by jonas123)
yup very nice, that reduction formula for sin^n(x) was in the text book and i read it yesterday!

i didn't have enough time to finish the last question, I got lambda = 0 and mew = -1/6

surface area = 2pi(1 - e^-1)

can't think of much else, oh and i got one the the roots of the equation wrong, the alpha^4 + beta ^4 .... one. Oh well.
ditto, it was an easy paper just really long
4. sigma alpha^2 = 10

sigma alpha^3 = -3

sigma alpha^4 = 50

the very last question y=(pi/18)sin2x -(1/6)xsin3x

the length of the arc was 0.5e-0.5e^-1

the first question x=1.2 y=2.62

most of the other questions were show that.

And i think INT sin^5x between (pi/3)and 0 was 53/480
5. for the reduction formula one, i kinda got screwed on the second part, as i couldn't put my numbers into fractions lol!!!
6. (Original post by PhilC)
sigma alpha^2 = 10

sigma alpha^3 = -3

sigma alpha^4 = 50

the very last question y=(pi/18)sin2x -(1/6)xsin3x

the length of the arc was 0.5e-0.5e^-1

the first question x=1.2 y=2.62

most of the other questions were show that.

And i think INT sin^5x between (pi/3)and 0 was 53/480

i thought the complementary function for the last question was ACos3X + BSin3X???

A=(pi/6), B=1/18
7. Actually im not sure about the very last bit where you had to solve the defferential eqation.

did it say dy/dx=0 when x=pi/3

or did it say dy/dx=0 at some point (pi/3, y)
8. all those answers agree with mine from memory. i didn't get sigma^2 of the polynomila root question but i've since checked my answer and its definitely -3. fairly straight forward overall, took the 1:20 time almost exactly.
9. yes the complemantary function was Acos3x + bcin3x

Then you had to solve for the condtions
i think i may have misread the conditions though and made an error
10. (Original post by PhilC)
Actually im not sure about the very last bit where you had to solve the defferential eqation.

did it say dy/dx=0 when x=pi/3

or did it say dy/dx=0 at some point (pi/3, y)

i thought it said st. point at ((pi/6),0) (i.e dy/dx=0 when x=0 y=0)
11. Well

y=Acos3x+Bsin3x-(1/6)xcos3x

dy/dx=3Bcos3x-3Asin3x-(1/6)cos3x+(1/2)xsinx

x=pi/3
y=0
dy/dx=0

so
0=0-3A-0+(pi/6)
so A=(pi/18)

and from y equtaion
y=0+b-o
B=0

So
y=(pi/18)cos3x-(1/6)xcos3x

i think
12. x=pi/6
not
pi/3

sorry
13. another typo,

-(1/2)xsin3x

not

-(1/2)xsinx
14. "So
y=(pi/18)cos3x-(1/6)xcos3x"

agree completely there
15. Is that what you got then?

i actually got -(pi/180.....
so a minus sign in the wrong place, but should lose only one mark for that.

I think everything else was pretty much alright for me, but will the examiner be able to read my handwritting is the more important question.
16. actually, i cant remember now. i'll rework the question in after lunch and double check but it looked very similar to y=(pi/18)cos3x-(1/6)xcos3x.
i think i took a factor of 1/18 out tho. but thats makes no difference
17. all the prove it questions were relatively simple, i thought i wouldn't get them but they just popped out in the end.
18. Yea, they were ok, chain rule for the d/dx sinh^-1 questions,

Cosh^-1x=ln(x=root(xx-1)) or something, done that before.

that was about it for them wasnt it?
The newton-rapshon eon just set f(x)=1+2/x -lnx
and show f(4) is bigger than 0 and f(5) is less than 0.

4.32 was the root for that iteration i think.

I think that was about it really not too much, when i opened the question paper it looked a lot harder than it was i think, quite a lot of volume, but nothing too testing i don't think.

BTW Where and what are you doing at univeristy.
BTW.2 Ainsworth, you have the same birthday as me, and you doing the same A Levels, just thought that was a little bit of a coincidence.
19. really? 15th march 86.
currently i have an offer to study engineering at cambridge, girton college starting in october. where u going to uni?
20. Sidney Sussex, for Maths, but im not sure ill make it.
Ive done pretty poor in these exams, but if i put in a good performance in S2 i should get an A in further maths.

If of course i can have
P1,P2,P3,P4,D1 and S1 in maths
and P5,P6,M1,M2,M3 and S2 in Further maths but im not sure if thats allowed.

Then of course there is STEP, but ive done a lot of prctice for that so hopefully i should be ok.

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Updated: June 21, 2004
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