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# OCR (MEI) Mathematics C3 20/01/2010 watch

• View Poll Results: How did you find the paper?
Easy
13
19.12%
OK-ish
28
41.18%
Hard
25
36.76%
I'm not sure/ i didnt take the exam/ ?
2
2.94%

1. Very hard paper. Think I got it all right, but that "here's the second derivative, find the maximum value of the derivative" was new and conceptually hard.
2. way harder than any of the previous year's exams i thought. (past papers i've revised from)

definite re-sit.
3. (Original post by icegemsf)
Oh ok lets hope so, thanks for that I don't know what made me do that really, usually im always in radians but i think i spent so long on the whole xcos3x=0 thing tht i just got bored! haha

Technically, finding P and Q in (i) you could do using degrees or radians.

however, the integration and differentiation bits involing gradients and P and Q would have to have degrees because the derivitive of cos(3x) isn't -1/3sin(3x) in degress. You'd only lose like 1 mark though I'd have thought.

Thought it went okay. FP1 which I did afterwards was probably easier actually.
4. (Original post by Tallon)
Technically, finding P and Q in (i) you could do using degrees or radians.

however, the integration and differentiation bits involing gradients and P and Q would have to have degrees because the derivitive of cos(3x) isn't -1/3sin(3x) in degress. You'd only lose like 1 mark though I'd have thought.

Thought it went okay. FP1 which I did afterwards was probably easier actually.
Oh rite. Yh I think I worked out the differentiation and integration in radians. I got the gradient as - pi/2 and the integration as pi/18 -1/9. What did u get?
5. anyone got the paper to post up?

6. (Original post by icegemsf)
Oh rite. Yh I think I worked out the differentiation and integration in radians. I got the gradient as - pi/2 and the integration as pi/18 -1/9. What did u get?

memory is a bit fuzzy having done fp1 as well, but those figures look familiar to me.
7. (Original post by Tallon)
memory is a bit fuzzy having done fp1 as well, but those figures look familiar to me.
oh ok cool! Yeah Im guessing after 3 hours of exams it would be! haha
8. (Original post by Snake91)
anyone got the paper to post up?

I can remember all the questions, so can put that up, not the actual paper.
9. Go for it
10. (Original post by Game_boy)
Very hard paper. Think I got it all right, but that "here's the second derivative, find the maximum value of the derivative" was new and conceptually hard.
I really liked that question, but when the I spoke to my school's head of maths later he was really surprised that it was in there... I guess it's good to have something that's a slight extension of the syllabus to really test people though.

Probably one of the hardest C3 papers I've come across, but the most interesting

Realised five minutes from the end that I'd messed up a part of one of the section B questions, but I think (hope ) I fixed it in time!
11. I've done all the past papers and I can tell you now that it was marginally harder than most years. I didn't find it too bad though. Not being arrogant because I bet anybody who does 2 hours of lessons of maths a day would say the same thing. If it's any consolation to you people though, Further pure 1 was a lot easier in my opinion, and the grade boundaries will probably be lower. Plus it only counts for 80%
tbh I'm not too bothered, I can live with a few marks lost. It's my exams next week that are kinda make or break.

btw what modules are you doing for FM?
Erm, I'm not sure which modules will be allocated to which, but so far (applied) i've done M1 M2 S1 S2 and in June doing D1 D2 DE M3 M4 and possibly S3 S4. (and C1-4 FP1-3)
13. Relatively hard, one of the hardest I've seen for C3 but not too bad
I actually enjoyed it
14. I thought this paper was easy in comparison to past papers actually! I was expecting some harder proof questions, and the calculus wasn't anything unexpected I didn't think.

Head of maths saying that f''(x) question shouldn't be on the paper? I think your wrong, since you do second derivatives in C2, you're supposed to know everything from C1 and C2 in C3! (Plus, in the MEI C3 textbook, they have examples with second derivatives)

Don't think I dropped any marks. I had S3 afterword, which I thought was hard paper
15. that test was kinda hard.. the question wiv p and q did me.. tbh i think im gna have to retake.. but i did answer most qz preeti confidenrli.. im probz gna get c or d.. and that definetli means retake..
16. (Original post by theycallmesarah)
can anyone tell me how they answered the f(x) g(x) question where you had to prove gf(x) was even?
thankyou

p.s don't worry about it too much marks2, i mean it wasn't like u were the only one who found it hard. there were loads of people who didnt like it
i dont know if im right but i said that for any value of "n" 2n+1 would be even and for any value of "n", 2n would be odd. so if f(x)=2n+1 and g(x)=2n

then gf(x)
=g[2n+1]
so sun n=2n+1 into 2n
=2(2n+1)
=4n+2 which is always even and is the same as (4n+1)/2
=2n+1

i dont usually revise much for mei maths, i got As in c1 and c2 with little to non revision, i remebered almost everything from class, but this took me by supirse, i mean question 8, i differentiated right but i couldnt find the value the P and q, so for the rest of 8, i used ltteres to show ho i would have found the gradient and area etc, so i should get method marks. the last question was ok, i think i lost marks becuase i got different parts confused, the last part was really easy, just change the position of x and y and rearrange to find g(x) but i still think i lost a crap load of marks.

i would like a B at least so it doesnt look to bad, but im surprised, ive looked at the grades boundaries for the last couple of years, and to get the required grades A for example) you need regular amount of percentage (80% e.g for an A) in raw marks or sometimes even higher (83%) to get the score in ums and thats scary, for other subjects the percentage needed can drop as low as much as 15% (last year for unit 2 of the new chem or physics ocurse i cant remeber which you needed 69% in raw marks for an A, 69% people!!!
17. (Original post by Recluse)
Head of maths saying that f''(x) question shouldn't be on the paper? I think your wrong, since you do second derivatives in C2, you're supposed to know everything from C1 and C2 in C3! (Plus, in the MEI C3 textbook, they have examples with second derivatives)
Oh, I mean he was suprised at the context of the question - not the fact that it was a second derivative, but applying the concept in that way... if that makes sense? I found that question fine, but I know a lot of people who didn't
18. Right I'll do it anyway:

1. e^(2x) - 5e^x = 0

Solve for x

2. T = 20 + b.e^(kt)

T=100 when t=0, T=60 when t=5

i) find b and k

ii) Find the time when T=50

3) y=[(3x^2)+1]^(1/3)

i) differentiate a la the chain rule

ii) y^3 = (3x^2) + 1

Use implicit differentiation to differentiate above equation and show that this is the same result as part i)

4)
i) Integrate [2x/(x^2)+1] with respect to x (limits: x=1 and x=0). Give answer in exact terms

ii) Integrate [2x/(x+1)] with respect to x (limits: x=1 and x=0). Give answer in exact terms

5 Sine graphs of the form a + bsin(cx)

i) cba using autograph. Basically graph has a range -3< y <3 (should be greater/less than and equals to signs), with a period of pi. Find values of a,b and c (this is better understood with the graph.

ii. Graph has range 0 < y < 2, period 2pi. Has also been reflected in either the x-axis or y-axis (whichever way you interpret it.) Find values of a,b and c.

6. State conditions for f(x) to be an odd function and g(x) to be an even function. Hence, prove that gf(x) is always an even function

7. Prove that since arccosy=arcsinx, x^2+y^2=1 [Hint-use arcsinx = theta]

I'll do Section B in a bit. If any of these questions are wrong then just let me know.
19. (Original post by kat_s)
Oh, I mean he was suprised at the context of the question - not the fact that it was a second derivative, but applying the concept in that way... if that makes sense? I found that question fine, but I know a lot of people who didn't
Isn't it the idea that the point on the graph where the gradient is largest is at a point of inflexion, hence when f''(x)=0. I get what you mean though, I haven't seen it in previous papers or any of our worked examples.
20. Ryt wat i did (not saying this is the best or only way) was to first let h(x)=gf(x), this just makes this neater.
Then it follows that h(-x)=gf(-x) but as f(x) is odd f(-x)=-f(x)
Therefore h(-x)=g(-f(x)) and as g(x) is even g(watevers in here)=g(-wateva that is) i.e g(-f(x))=gf(x)
Thus as required we have shown h(-x)=h(x) i.e. given that f(x) is odd and g(x) is even, the composite function gf(x) will be even.

If someone doesn't agree plz let me know but yeah out of all the q's i felt this was the one most people will drop marks.

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