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June 07 - OCR C3 Paper

Hello

I'm really struggling on the last two questions of this paper (question 8 and 9):

http://www.ocr.org.uk/Data/publications/past_papers_2007_June/A_GCE_Mathematics_4723_01_June_2007_Question_Paper.pdf

I have done 8i, but cannot do the other two parts or any of question 9. I don't know where to start.

Any help would be greatly appreciated!!

Thank you!!
Reply 1
Avatar for SimonM
SimonM
18
8ii At what point does it cross the x-axis?
8iii π∫y2 dx\displaystyle \pi \int y^2 \, dx. Hint: ddxln⁡x=1x\dfrac{d}{dx} \ln x = \frac{1}{x}


9i Expand tan⁡(θ±60∘)\tan (\theta \pm 60^{\circ} ) as you usually would. Can you manipulate this to get the other side?
9ii Can you use the first identity and 1+tan⁡2x=sec⁡2x1+ \tan^2 x = \sec^2 x to get a polynomial (which you can solve) in terms of tan⁡x\tan x?
9iii Using the first identity again, and the method of 9ii, can you find a quadratic which would be useful? How can you prove that a quadratic has solutions? Hint: b2−4acb^2-4ac
Question 8 (ii)

You have to find the x coordinate where the curve cuts the x-axis ... we know that, that happens when y=0 // do that and solve for x and than you just subb the value into your gradient function

Question 8 (iii)

Can you relate the function you have to integrate with something from part 8(i) ?

Hint:

Spoiler

If you are stuck with Q9(iii)

this might help ====> QUESTION9(iii)
Reply 4
Avatar for campbellian
campbellian
OP
massive thanks for your help folks.
However, I'm still stuck on part iii for both questions. :smile:
Reply 5
Avatar for campbellian
campbellian
OP
bump. :smile:
Reply 6
Avatar for SimonM
SimonM
18
Please post the working you've done on those questions so far
Reply 7
Avatar for campbellian
campbellian
OP
8iii. i got the wrong answer.

what does y^2 integrate to? That's the bit i am stuck on, i can do the rest I think.

for 9iii:

tan^2A-3 OVER 1-3tan^2A =k^2

tan^2A-3 = k^2(1-3tan^2A)

tan^2A-3 = k^2 - 3k^2tan^2A

tan^2A = k^2 - 3k^2tan^2A + 3

And I don't know where to go from there...
Reply 8
Avatar for ttoby
ttoby
15
campbellian
8iii. i got the wrong answer.

what does y^2 integrate to? That's the bit i am stuck on, i can do the rest I think.

for 9iii:

tan^2A-3 OVER 1-3tan^2A =k^2

tan^2A-3 = k^2(1-3tan^2A)

tan^2A-3 = k^2 - 3k^2tan^2A

tan^2A = k^2 - 3k^2tan^2A + 3

And I don't know where to go from there...


For 8 (iii), have a look at http://www.thestudentroom.co.uk/showthread.php?p=19159933

For 9 (iii), rearrange your equation to make tan^2 A the subject and see http://www.thestudentroom.co.uk/showpost.php?p=19161188&postcount=8 for where to go from there.
Reply 9
Avatar for campbellian
campbellian
OP
Thank You!!

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