Edexcel FP2 Official 2016 Exam Thread - 8th June 2016

Could someone help me on how to solve part b, the markscheme doesnt make sense to me. Where does the -pi/9*2^2 part come from?

It's the area "underneath" the equation r=2... When you find the area of r=1.5+sin3(theta), you get an excess area you don't want. In the marks scheme, they subtracted this area bounded by r=2 using the formula 1/2(r)^2(theta) You only want R, not the entire area underneath it.

So here

you want the area where only the blue lines are visible (region S), so you subtract region r=2 (which covers all the area in black) from the "upper" point at where they intersect to the "lower" point they intersect. These points are 5pi/18 and pi/18. Integrate r^2 = 2^2 = 4 between these two points and you should get 4pi/9. This is the area bounded by the line r=2 and the initial line, in other words, the area shaded by BOTH the blue and black lines. Sorry for my bad explanation. Hope it helps.

...

I understand how areas work with polar coordinates for the most part, but how does integrating r=2 find between the coordinates find the excess area? Does it not form a sector with the origin as opposed to the second shape? I feel like I'm missing something.

Not sure I fully understand, are you referring to the yellow lines in the diagram and how these don't cover "the whole region" in a sense?

(image)

Edit: I think I know what you mean and although I'm not 100% sure so don't take my word for it (I'm an FP2 student myself :P), logically, you apply the same process when integrating the other curve, so yes, the original curve also forming a sector - "sector" of area found by integrating r=2 gives you area S.

Could a question come up where we have to set up the differential q? After last year I'm shook they could give anything.
Also I remember in I think review ex 2 a q where you had to set up it was about embryos or something.
Please any assistance.

does anyone have resources (other than the FP2 past papers) for questions?

Would you ever be asked to prove ?

I do not think so, but it is very easy to do so with the series expansions of $sin \theta$, $cos \theta$ and $e^{x}$, where $x = i\theta$.

You only really need to use it.

ah okay, thank you

Is that a Maclaurin and Taylor series expansion? I am working my way through FP2 and haven't reached that chapter yet

can anyone help with part b? (the area). Can't see how to get the region because of the slim bits that the area of the sector misses out

can anyone help with part b? (the area). Can't see how to get the region because of the slim bits that the area of the sector misses out

Draw a line to where they meet, see that integrating the polar cureve between 0 and the angle at where they meet gives that little patch outside the sector.


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