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Edexcel FP2 Official 2016 Exam Thread - 8th June 2016

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Original post by SeanFM
:hmmmm2: do you have an example of what you mean?


x2x>x+3x \frac{x}{2-x} > \frac{x+3}{x}
Original post by kkboyk
x2x>x+3x \frac{x}{2-x} > \frac{x+3}{x}


You never know, so you have to multiply both sides by (2-x)^2 and x^2 unless the domain is restricted to 0<x<20<x<2.
Original post by SeanFM
You never know, so you have to multiply both sides by (2-x)^2 and x^2 unless the domain is restricted to 0<x<20<x<2.


Sometimes the marks scheme does it normally by multiplying the denominators to both sides, which reay confuses me :s
Original post by kkboyk
Sometimes the marks scheme does it normally by multiplying the denominators to both sides, which reay confuses me :s


:hmmmm2: have you got an example or mark scheme that does this? :tongue:
Original post by SeanFM
:hmmmm2: have you got an example or mark scheme that does this? :tongue:


June 2011

3x+3>x4x \frac{3}{x+3} > \frac{x-4}{x}
Original post by Zacken
Ah, your hint gave it away. :tongue:

It's not hard to prove that tanx2=sinx1+cosx\tan \frac{x}{2} = \frac{\sin x}{1+\cos x} from which you argue that cotx2=cscxcotx\cot \frac{x}{2} = \csc x - \cot x and hence cscx=cotx2cotx\csc x = \cot \frac{x}{2} - \cot x.

So your sum is: cot1cot2+cot2cot4++cot2n1cot2n\cot 1 - \cot 2 + \cot 2 - \cot 4 + \cdots + \cot 2^{n-1} - \cot 2^n which telescopes down to cot1cot2n\cot 1 - \cot 2^n.


III 2006 reminds me of those identities. Thank god.


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Please could anyone explain how to do question 17b? I don't know if I'm missing something ovbious but wouldn't multiplying by theta make it very difficult to integrate? Thanks :smile:image.jpg
Reply 807
Original post by economicss
Please could anyone explain how to do question 17b? I don't know if I'm missing something ovbious but wouldn't multiplying by theta make it very difficult to integrate? Thanks :smile:image.jpg

You use by parts from C4
Reply 808
Why does (cos theta)= cos(-theta )
and -sin(theta) = sin(-theta )

and how do I remember this and not get confused
Reply 809
image.jpg
Original post by Patrick2810
do we have to know how to do these? they seem a lot harder than any of the exam qs

can i ask how you would approach 9a?
Original post by Rkai01
image.jpg
How did you get it down to the second line please?


I've written it as if it were an actual FP2 question, if that gives any hints.

(a) Show that

lnsec2x=ln2+lnsin2xlnsin4x\ln |\sec 2x| = \ln 2 + \ln |\sin 2x| - \ln |\sin 4x|

(b) Use the method of differences to show that

n=1mlnsec2rθ=mln2+lnsin2θlnsin2m+1θ\displaystyle \sum_{n=1}^{m}\ln |\sec 2^{r}\theta| = m\ln 2 + \ln |\sin 2\theta| - \ln |\sin 2^{m+1}\theta|

(c) Hence, or otherwise, show that

n=1mtan(2rθ)=2cot2θ2m+1cot(2m+1θ)\displaystyle \sum_{n=1}^{m}\tan \left(2^{r}\theta\right) = 2 \cot 2\theta - 2^{m+1}\cot\left( 2^{m+1} \theta \right)
Original post by Cpj16
Why does (cos theta)= cos(-theta )
and -sin(theta) = sin(-theta )

and how do I remember this and not get confused


Draw the graphs. The cosx graph is reflected in the y axis so any negative value for x could be positive and give the same result. The sinx graph when x<0 is just the negative of the sinx graph when x>0.
Original post by Rkai01
You use by parts from C4


Thank you :smile:
Reply 813
Original post by Craig1998
Draw the graphs. The cosx graph is reflected in the y axis so any negative value for x could be positive and give the same result. The sinx graph when x<0 is just the negative of the sinx graph when x>0.


thank you. you are a genius
I just went on desmos to sketch them
Original post by kkboyk
June 2011

3x+3>x4x \frac{3}{x+3} > \frac{x-4}{x}


:hmmmm2: I do not know, sorry! :colondollar:

:bump: - why can they multiply both sides of this by the denominators of each side, rather than the square? There is nothing else to the question.
Please could anyone do me a massive favour and post a worked solution to question 16b as I always seem to just get stuck at the same stage in these types, thanks :smile:image.jpg
Original post by SeanFM
:hmmmm2: I do not know, sorry! :colondollar:

:bump: - why can they multiply both sides of this by the denominators of each side, rather than the square? There is nothing else to the question.


Thanks anyway :tongue:

I realised that squaring the denominator would work although its much longer.
Original post by kkboyk
Thanks anyway :tongue:

I realised that squaring the denominator would work although its much longer.


Stick to multiplying by squares, you cannot be sure of the sign of what your multiplying if you do not.
is anyone else finding the latest GCE and IAL papers (~2013 onwards) relatively more difficult than previous ones?
Original post by waqasabbasi
is anyone else finding the latest GCE and IAL papers (~2013 onwards) relatively more difficult than previous ones?


I think that's been a trend for most modules, but in my opinion FP2 has stayed relatively the same, (hence why we are seeing GBs of 71 for A*).

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