The Student Room Group

OCR Core 3 - Wed 9th June 2010.

So the exam's just round the corner, I'm wondering how everyone is feeling about it? Prepared? Also if you're stuck on any questions, feel free to post them here. Let's try and keep the thread alive until the exam day so hopefully we can get some solutions up after the exam to compare our answers against.
Good luck! :biggrin:
Answers, thanks to Mr M.
Mr M
OCR (not OCR MEI) Core 3 Answers June 2010


1 (i) dydx=x2e2x(3+2x)\frac{dy}{dx} = x^2 e^{2x} (3 + 2x) (2 marks)

(ii) dydx=4x3+2x2\frac{dy}{dx} = \frac{4x}{3+2x^2} (2 marks)

(iii) dydx=1(2x+1)2\frac{dy}{dx} = \frac{1}{(2x+1)^2} (2 marks)


2 (i) y=βˆ’ln⁑(xβˆ’4)y = - \ln (x-4) (2 marks)

(ii) 2S followed by 9T or 1T followed by 2S (2 marks)


3 (i) 6sin⁑2ΞΈβˆ’11sinβ‘ΞΈβˆ’10=06 \sin^2 \theta - 11 \sin \theta - 10 = 0 (3 marks)

(ii) -41.8 degrees and -138 degrees (3 s.f.) (3 marks)


4 (i) Show k = 4 (3 marks)

(ii) Volume = 32Ο€3 \frac{32 \pi}{3} (4 marks)


5 (i) βˆ’4≀x≀23-4 \leq x \leq \frac{2}{3} (5 marks)

(ii) 83\frac{8}{3} (2 marks)


6 (i) Show root between 1.0 and 1.1 (3 marks)

(ii) 1.05083 (5 d.p.) (4 marks)

(iii) x = 0.525 (3 s.f.) (3 marks)


7 Exact area = 45\frac{4}{5} (10 marks)

8 (i) 32cos⁑(xβˆ’Ο€4)3 \sqrt{2} \cos (x - \frac{\pi}{4}) (3 marks)

(ii) (a) βˆ’Ο€4-\frac{\pi}{4} OR any answer which results in xβˆ’Ο€4x-\frac{\pi}{4} being an odd multiple of Ο€2\frac{\pi}{2} (2 marks)

(b) x=Ο€36x = \frac{\pi}{36} (4 marks)


9 (i) xβ‰₯βˆ’9x \geq -9 (3 marks)

(ii) Not one to one unless the domain is restricted (2 marks)

(iii) Show a = -1 (4 marks)

(iv) b<βˆ’4b < -4 (4 marks)

Scroll to see replies

Reply 1
It's not the exam I'm afraid of, it's the when I get on TSR afterwards and Mr M confirms that I have failed epically that strikes the most fear.
HotCoco.
It's not the exam I'm afraid of, it's the when I get on TSR afterwards and Mr M confirms that I have failed epically that strikes the most fear.

It saves us from all the nervousness that builds up until results day, which will definitely be much scarier. I need Mr M's answers for peace of mind. :p:
Reply 3
any chance you have done question 7 from the june 08 paper? il type it out if i have to in a min but if u have done it, any chance of any help? cheers
jkkk32
any chance you have done question 7 from the june 08 paper? il type it out if i have to in a min but if u have done it, any chance of any help? cheers

What part are you stuck on?
Reply 5
erm all of it :s-smilie: i dont know how to start it, should i type it out or do you have it?

also thanks very much for your help in one of my other threads :smile:
Reply 6
it says in the markscheme A = 42, i would have thought the N was 42 so would have gone wrong there :s-smilie: and then how to work out k??
jkkk32
erm all of it :s-smilie: i dont know how to start it, should i type it out or do you have it?

also thanks very much for your help in one of my other threads :smile:

Ok, well firstly it says that today, the population is 42. That means when t=0, N=42.
So sub these into either equation to find A.
Then replace A with this constant.
Now it also says that the number of species is doubling every 9 years. This means that when t=9, N=84. Sub this into the first equation and use logs to rearrange to find k. Then do the same for the second expression with m.
Reply 8
Farhan.Hanif93
Ok, well firstly it says that today, the population is 42. That means when t=0, N=42.
So sub these into either equation to find A.
Then replace A with this constant.
Now it also says that the number of species is doubling every 9 years. This means that when t=9, N=84. Sub this into the first equation and use logs to rearrange to find k. Then do the same for the second expression with m.


thanks for your help, have finished it :smile:
Reply 9
any chance of help,
on the same paper question 5, i cant seem to do it correctly:

changed tan2a to 2tana / 1-tan^2 a

so have 2tana / 1-tan^2 a tan a = 8

multiply through by (1-tan^2 a)

2tana tana(1-tan^2 a) = 8 (1 - tan^2 a)

2tan a tan a - tan^3 a = 8 - 8tan^2 a



I think ive gone wrong...sorry thats a bit hard to follow, if you can show me how to do it though would be really grateful. you can do it from scratch if what i have done doesnt make sense.


thank you
Reply 10
jkkk32
any chance of help,
on the same paper question 5, i cant seem to do it correctly:

changed tan2a to 2tana / 1-tan^2 a

so have 2tana / 1-tan^2 a tan a = 8

multiply through by (1-tan^2 a)

2tana tana(1-tan^2 a) = 8 (1 - tan^2 a)


2tan a tan a - tan^3 a = 8 - 8tan^2 a

I think ive gone wrong...sorry thats a bit hard to follow, if you can show me how to do it though would be really grateful. you can do it from scratch if what i have done doesnt make sense.

thank you


I think the step in bold is where you have gone wrong, when multiplying by (1 - tan^2 a), it cancels with the denominator on the left hand side, giving:
2 tan a tan a = 8(1-tan^2 a)
jkkk32
any chance of help,
on the same paper question 5, i cant seem to do it correctly:

changed tan2a to 2tana / 1-tan^2 a

so have 2tana / 1-tan^2 a tan a = 8

multiply through by (1-tan^2 a)

2tana tana(1-tan^2 a) = 8 (1 - tan^2 a)

2tan a tan a - tan^3 a = 8 - 8tan^2 a



I think ive gone wrong...sorry thats a bit hard to follow, if you can show me how to do it though would be really grateful. you can do it from scratch if what i have done doesnt make sense.


thank you

You haven't multiplied through correctly.
(2tan⁑a1βˆ’tan⁑2a)tan⁑a=8\left(\frac{2\tan a}{1-\tan ^2a}\right)\tan a = 8
Then multiply through by 1βˆ’tan⁑2a1-\tan ^2a:
β€…β€ŠβŸΉβ€…β€Š((2tan⁑a)(1βˆ’tan⁑2a)1βˆ’tan⁑2a)tan⁑a=8(1βˆ’tan⁑2a)\implies \left(\frac{(2\tan a)(1-\tan ^2a)}{1-\tan ^2a}\right)\tan a = 8(1-\tan ^2a)
Then the 1βˆ’tan⁑2a1-\tan ^2a's cancel on the LHS because there's one in the numerator and denominator.
This gives you:
β€…β€ŠβŸΉβ€…β€Š2tan⁑2a=8βˆ’8tan⁑2a\implies 2\tan ^2a = 8-8\tan ^2a
Rearrange and solve.
Reply 12
sorry im not following how you multiplying through ...oh dear :s-smilie:
jkkk32
sorry im not following how you multiplying through ...oh dear :s-smilie:

Well it's simple fraction work.
ab=c\frac{a}{b}=c and you multiply through by b, you get a=bca=bc.
You do realise that 2tan⁑atan⁑a=2tan⁑2a2\tan a \tan a = 2\tan ^2a?
Reply 15
yeah get that, just confused like a/b = c, multiply by b get a =bc

why have you still got the b on the bottom then? the 1-tan^2 a??

i realise its not the same as your simple fraction work because its not = c, its just a/b c = 8

so i thought it would be like 'a cb = 8b' but obviously not?? im sorry im making such a mess of probably a very easy piece of work!!
jkkk32
yeah get that, just confused like a/b = c, multiply by b get a =bc

why have you still got the b on the bottom then? the 1-tan^2 a??

i realise its not the same as your simple fraction work because its not = c, its just a/b c = 8

so i thought it would be like 'a cb = 8b' but obviously not?? im sorry im making such a mess of probably a very easy piece of work!!

Oh, I did that to make sure you followed. That was the long and unnecessary way.
Look at it like this then, multiply the tan on the outside into the fraction to be neater:
2tan⁑2a1βˆ’tan⁑2a=8\frac{2\tan ^2a}{1-\tan ^2a} = 8

tan⁑2a1βˆ’tan⁑2a=4\frac{\tan ^2a}{1-\tan ^2a} = 4 (Divided through by 2 as it was a common factor)

tan⁑2a=4(1βˆ’tan⁑2a)\tan ^2a = 4(1-\tan ^2a)

Then expand and rearrange, it's just GCSE level fraction manipulation.
Reply 17
ok yep all understood! i realise it is only gcse level, i just hadn't understood how you had first written it!

all ok now though!
so how u feeling for these exams coming up? i presume you are doing c4 aswell?
Reply 18
All the more worried for knowing you're on the same exam board as me.

I pretty much want to get an A, because I know I'll do badly in D2. I've yet to do any past papers though, might do one tonight and another couple tommorow.

Good luck everone, though not really as I hope you all do badly for my own wellbeing :biggrin:
jkkk32
ok yep all understood! i realise it is only gcse level, i just hadn't understood how you had first written it!

all ok now though!
so how u feeling for these exams coming up? i presume you are doing c4 aswell?

Yeah, I'm feeling pretty confident (need an A* though to help make my other AS subjects look better :teehee:). Yeah, I've got C4 on the friday and then M1, then S1, then STEP I. I've also got physics unit 2 on the same days as C3 so things are fairly packed over here.

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