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# OCR MEI C3 Maths June 2015 watch

1. (Original post by SH0405)
1. (1.107, 4.094) [6]
2. (3(2x-1)(4/3))/8 + c [4]
3. u = 2x-1, (1/16)(64ln2 - 15) [5]
4. r=h, 1/20pi = 0.0159 [5]
6. i) x = ½ [2]
ii) x = sqrt(2)/2 [2]
7. i) f(f(x)) = x via substituting in. f-1(x) = f(x) = (1-x)/(1+x) [3]
ii) g(x) is even since g(-x) = g(x). Symmetrical about the y-axis. [3]
8. i) f'(x) = 1 - 4/x2, f''(x) = 8/x3which is less than zero when x=-1 and so Q is a maximum point. [7]
ii) Area was 3 take away integral which gave ½(15-8ln4) [6]
iii) f(x-1)-1=g(x) so g(x) = (x2-3x)/(x+1) [3]
iv) This is the negative of the previous answer, and yes it's negative, because it asked for the value. [2]
9. i) x = ln3 [2]
ii) x = ln2, y = -1 [4]
iii) The integral came out as negative, but this question asked for the area, so the given answer must be positive; 4 - 3ln3 [5]
iv) f-1(x) = ln(sqrt(x+1)+2), with the domain as x >= -1 and range as y >= ln2. The sketch of the graph was a reflection in the line y = x, but subject to the 'new' domain and range (i.e. not below ln2). [7]

8.ii) I'm pretty sure answer was 1/2(15-8ln2) not ln4 😊
2. (Original post by chizz1889)
8.ii) I'm pretty sure answer was 1/2(15-8ln2) not ln4 😊
I got 15/2 - 8ln2... I think?

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3. (Original post by _Caz_)
I got 15/2 - 8ln2... I think?

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I'm fairly certain it was 15/2 - 4ln2

EDIT: Infact no it was 3ln3!!! I think, I will work it out again in a sec 😊
4. Mark scheme done

http://www.thestudentroom.co.uk/show...5#post56931025
5. Infact yes I concur! I was getting mixed up between questions ☺️
6. (Original post by _Caz_)
I got 15/2 - 8ln2... I think?

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Yeah that's right 😀
7. (Original post by _Caz_)
I got 15/2 - 8ln2... I think?

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The answer was 15/2 - 4ln4

which is the same as what you got
8. I forgot about the rectangle in q.8 completely worked out the area perfectly for the integral of f(x) just forgot to to minus it from the area of the rectangle. I didn't do any calculations for the rectangle either, or write out how to obtain the area. I also could work out what it was on about for g(x), so put it into my graphical calculator and go -1.95... the decimal answer. And I also messed up my graph but I did a some sort of sketch (but then wrote reflected in the line y=x. I think these were my only mistakes, that I know of.

How many marks would I lose for this?
9. isnt there a asymptote at x=3 therefore the domain for f(x) should be ln2<=x<3
10. Does anybody have a list of 90UMS boundaries for past papers?
11. arcsinx=arccosx --> tanx=1 -->x=pie/4
12. (Original post by Duskstar)
The answer was 15/2 - 4ln4

which is the same as what you got
(Original post by chizz1889)
Yeah that's right 😀
(Original post by chizz1889)
I'm fairly certain it was 15/2 - 4ln2

EDIT: Infact no it was 3ln3!!! I think, I will work it out again in a sec 😊

to be fair there was so much natural log in that paper it's all blurred into one! Hope the exam was okay for everyone. Strange paper this year - the whole thing seemed to be on functions?! No proof really, no exponential equations, no modulus. Was quite surprised.
13. (Original post by 123BOBBY)
arcsinx=arccosx --> tanx=1 -->x=pie/4
I think it might be sqrt2/2 although I put pi/4 as well. :/
14. (Original post by OwenEllicott1996)
I forgot about the rectangle in q.8 completely worked out the area perfectly for the integral of f(x) just forgot to to minus it from the area of the rectangle. I didn't do any calculations for the rectangle either, or write out how to obtain the area. I also could work out what it was on about for g(x), so put it into my graphical calculator and go -1.95... the decimal answer. And I also messed up my graph but I did a some sort of sketch (but then wrote reflected in the line y=x. I think these were my only mistakes, that I know of.

How many marks would I lose for this?
You probably lost 2 marks for not doing the rectangle, and then 2 marks for the g(x) question, because the intention was to literally write down you answer before * -1. On the sketch question you probably lost 1 or 2 marks on the actual sketch (out of 2) depending what qualities it had of what it was supposed to be.
15. (Original post by 123BOBBY)
arcsinx=arccosx --> tanx=1 -->x=pie/4
(Original post by _Caz_)
I think it might be sqrt2/2 although I put pi/4 as well. :/
Yep, refer to this:

16. (Original post by Duskstar)
Yep, refer to this:

do you reckon ill get a mark for getting up to the pi/4? I mean it was a two mark question so maybe not...
17. wasnt there an asymptote at x=3
18. (Original post by Duskstar)
I'm going to try and do a mark scheme here. Bare in mind that I'm in Year 12 too >.>

Firstly, thanks to Barrel who actually posted the paper (page 15). here are the pages in order:
http://www.thestudentroom.co.uk/atta...9&d=1434104177
http://www.thestudentroom.co.uk/atta...1&d=1434104202
http://www.thestudentroom.co.uk/atta...3&d=1434104269
http://www.thestudentroom.co.uk/atta...5&d=1434104300

- I wasn't completely sure of the method for the second part, this is what a friend told me the method was (I think I do it correctly). Because of the nature of these two questions, however, I'm not 100% sure you need a method if you get the answer correct. It's only 1 mark each either way ~

Anything I missed or got wrong just ask. If you think it would be marked differently then say so too.
e^x - 2 = \pm 1
e^x = 0, 2 \,\, \mathrm{(0 \ is \ impossible)}

I'm sorry if this has already been corrected, but in the solution of 9) you state that 2+1=2 and 2-1=0.
19. Grade boundries for a c anyone ?
20. (Original post by AccountName)
e^x - 2 = \pm 1
e^x = 0, 2 \,\, \mathrm{(0 \ is \ impossible)}

I'm sorry if this has already been corrected, but in the solution of 9) you state that 2+1=2 and 2-1=0.
That hasn't, thank you. I keep getting ln2 and ln3 mixed up lol - I thought I was doing the second part

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